All-Fiber Pulsed Lasers

Based on Carbon Nanotubes

by

M. C. Iván Hernández Romano

Thesis submitted in partial fulfillment of the requirement for the degree of

DOCTOR EN CIENCIAS EN LA ESPECIALIDAD DE ÓPTICA

in

Instituto Nacional de Astrofísica, Óptica y Electrónica

October 2011

Tonantzintla, Puebla.

Supervisors: Dr. Daniel A. May Arrioja

Dr. José J. Sánchez Mondragón

© INAOE 2011 Derechos Reservados.

El autor otorga al INAOE el permiso de reproducir y distribuir copias de esta tesis en su totalidad o en partes.

ii

Dedicatoria

Dedico este trabajo a mi familia por todo el apoyo y los consejos que

siempre me han dado.

iii

Agradecimientos

Agradezco a mis asesores: Dr. Daniel A. May Arrioja y al Dr. Jose Javier

Sánchez Mondragón quienes me apoyaron de manera incondicional durante

todos estos años para realizar este trabajo de investigación.

Agradezco a los miembros del jurado por sus valiosos comentarios para

el mejoramiento de esta tesis de doctorado.

Quisiera agradecer al personal administrativo y demás personal que

labora en este instituto, que de alguna manera u otra me ayudaron a la

realización de este trabajo. En particular agradezco a las secretarias de la

coordinación de óptica y de formación académica quienes siempre me

ayudaron y fueron muy amables conmigo.

Finalmente agradezco al Instituto Nacional de Astrofísica, Óptica y

Electrónica (I.N.A.O.E.) y al Consejo Nacional de Ciencia y Tecnología

(CONACyT) por el apoyo económico brindado a través de la beca No. 160529

para realizar esta Tesis de Doctorado.

iv

Abstract

Compact sources of short pulses with high-repetition-rates are highly desirable for

a wide range of applications such as optical coherent tomographic, metrology,

optical communication, two photon microscopy, and optical clocks. This thesis is

focus on the research and development of fiber lasers that emit short optical

pulses. Here we purpose to use Polydimethylsiloxane (PDMS) and SU8-2075

polymers to fabricate thin films doped with SWCNTs that work like a saturable

absorber. Moreover, the nonlinear behavior of these films was investigated by

using an all-fiber power dependent transmission setup. Using this setup a

PDMS/SWCNT film (thickness 200 μm) and SU8-2075 film (thickness 100 μm) were

tested. The saturation intensity and the modulation depth of the PDMS/SWCNT

and SU8-2075 films are 5.1 MW/cm2, 0.7MW/cm2, 12.3 % and 10 %, respectively.

Passively mode-locked Erbium fiber ring lasers have been implemented by

using PDMS/SWCNT and SU8-2075 films, the first one produces pulses at a

repetition rate of 22.73 MHz with a pulse duration of 1.26 ps assuming a sech2

pulse profile. The second one has a repetition rate of 21.27 MHz with a pulse

duration of 871 fs assuming a sech2 pulse profile. A hybrid mode-locked Erbium-

doped fiber laser that provides very short pulse-widths while achieving high

repetition rates is proposed and experimentally demonstrated. This hybrid

configuration is realized by using a PDMS/SWCNT thin film composite as saturable

absorber, which is inserted within an active mode-locked laser system using angled

connectors. Therefore, the effect of the PDMS/SWCNT composite is to effectively

narrow the width of the pulses generated by the active system without modifying

its repetition rate. A pulse-width of 730 fs was generated at a repetition rate of 4

GHz, while achieving an average output power of 4 mW. A reduction in the noise

of the photodetected RF spectrum was also observed in the hybrid system. Finally,

a passively-Q-switching laser has also been built up by using a SU8-2075/SWCNT

film. The maximum average power, peak power, and pulse energy were 160 μW,

7.3 mW, and 5.1 nJ, respectively.

v

Publications

1. I. Hernandez-Romano, Dimitrios Mandridis, Daniel A. May-Arrioja, Jose J.

Sanchez-Mondragon, and Peter J. Delfyett, “Mode-locked fiber laser using

an SU8/SWCNT saturable absorber,” Opt. Lett. 36, 2122-2124 (2011).

2. I. Hernandez-Romano, J. Davila-Rodriguez, Dimitrios Mandridis, Jose. J.

Sanchez-Mondragon, Daniel A. May-Arrioja, and Peter J. Delfyett, “Hybrid

Mode Locked Fiber Laser Using a PDMS/SWCNT Composite Operating at 4

GHz”, Journal of Lightwave Technology, (accepted), 2011.

3. A. S. Shcherbakov, I. Hernandez-Romano, “Theoretical study of

implementing an all-optical analogue-to-digital conversion based on the

Mach–Zehnder interferometric configurations,” Opt. Int. J. Light Electron.

Opt. 121, 1330-1336 (2009).

Conference papers

1. I. Hernandez-Romano, J. Davila-Rodriguez, D. A. May-Arrioja, J. J.

Sanchez-Mondragon and P. J. Delfyett, “Fabrication of PDMS/SWCNT thin

films as saturable absorber,” Journal of Physics: Conference Series 274

012118, 2011.

2. I. Hernandez-Romano, J. Davila-Rodriguez, D. Mandridis, J. J. Sanchez-

Mondragon, P. J. Delfyett, and D. A. May-Arrioja, “4 GHz Hybrid Mode-

Locked Fiber Laser Using PDMS/SWCNT Thin Film Composite,” inCLEO:2011

- Laser Applications to Photonic Applications, OSA Technical Digest (CD)

(Optical Society of America, 2011), paper CMK4.

3. I. Hernandez-Romano, D. A. May-Arrioja, J. J. Sanchez-Mondragon, Peter

J. Delfyett, “Fabrication of SU8-2075/SWCNT Films As Saturable Absorbers,”

in Photonics Society Summer, IEEE\LEOS Topical Meeting Series, Playa del

Carmen, Quintana Roo (2010).

vi

4. I. Hernandez-Romano, D. Mandridis, D. A. May-Arrioja, J. J. Sanchez-

Mondragon, P. J. Delfyett, “Mode-locked fiber laser using SU8 resist

incorporating carbon nanotubes,” Photonics Technologies for Defense,

Security, and Aerospace Applications VII, Proceedings of the SPIE, Volume

8054, pp. 80540R-80540R-6 (2011).

5. J. E. Antonio-Lopez, I Hernandez-Romano, D. A. May-Arrioja. J. J.

Sanchez-Mondragon and P. LiKamWa; “Optofluidically Tunable Multimode

Interference Erbium Doped Fiber Laser,” in Photonics Society Summer,

IEEE\LEOS Topical Meeting Series, Playa del Carmen, Quintana Roo (2010).

6. D. Lopez-Cortes, J. R. Guzman-Sepulveda, I. Hernandez-Romano, M.

Torres-Cisneros, J. J. Sanchez-Mondragon, and D. A. May-Arrioja, “Fiber

Optic Bending Sensor Based on Multimode Interference (MMI) Effects,”

in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of

America, 2009), paper JWC41.

7. J. E. Antonio-Lopez, I. Hernandez-Romano, D. A. May-Arrioja, J. J.

Sanchez-Mondragon, and D. A. May-Arrioja, “Optofluidic Tuning of MMI

Bandpass Filter,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical

Society of America, 2009), paper FTuD6.

8. D. Lopez-Cortes, I. Hernandez-Romano, J. J. Sanchez-Mondragon, and

D. A. May-Arrioja, “Development of Bending Sensors using Multimode

Interference Effects,” LII Congreso Nacional de Física, 2009.

9. A. S. Shcherbakov and I. Hernandez-Romano, “Applying the potential

well technique to characterization of optical solitary pulses,” Proceeding,

SOMI XXIII, Xalapa Veracruz 2008.

10. A. S. Shcherbakov and I. Hernandez-Romano, “Theoretical study of

implementing an all-optical analogue-to-digital conversion based on the

Mach-Zehnder interferometric configurations,” Proceeding, SOMI XXIII,

Xalapa Veracruz 2008.

vii

TABLE OF CONTENTS

Chapter 1

Introduction

1.1 Overview……………………………………………………………….……………………………1

1.2 Aim of this thesis…………………………………………………………….………………..…3

1.3 Outline of this dissertation……………………………………………………..…..…..…..4

1.4 References...…………..……………………………………………………..……………………6

Chapter 2

Short Optical pulse Generation

2.1 Introduction……………………………………………………….………………………..……10

2.2 Mode-Locking………………………………………………………………………………..…..10

2.2.1 General Description…………………………………………….…………………….10

2.2.2 Active Mode-locking………………………………………………….………………13

2.2.2.1 Synchronously pumped mode-locking……………………………........16

2.2.3 Passive mode-locking…………………………………………………………..……17

2.2.3.1 Saturable absorber……………………………………………………..18

2.2.3.2 Saturation model………………………………………..……………...19

2.2.3.3 Fast saturable absorber……………………………………………….21

2.2.3.4 Slow saturable absorber………………………………………………22

2.2.3.5 Characterization of saturable absorber………………………....24

2.2.3.6 Organic dye as a saturable absorber…………………………….26

2.2.3.7 Kerr-lens mode locking………………………………………………..26

2.2.3.8 Additive pulse mode-locking…………………………………………28

2.2.3.9 Semiconductor saturable absorber……………………………….31

2.2.4 Hybrid mode-locking…………………………………………………………………31

viii

2.3 Optical properties of SWCNTs………………………………………………………………32

2.4 State of the art of the SWCNT as SAs…………………………………………………..36

2.5 Q-switching………………………………………………………………..……………………..38

2.5.1 General description…………………………………………………………………..38

2.5.2 Active Q-switching…………………………………………………………………...39

2.5.3 Passive Q-switching………………………………………………………………….40

2.6 References…………………………………………………………………………………………48

Chapter 3

Fabrication process and nonlinear absorption measurements of PDMS/SWCNT and SU8-2075/SWCNT films as SA

3.1 Introduction……………………………………………………………………….................60

3.2 SWCNTs as a Saturable Absorber…………………………………………………………61

3.3 Fabrication process of thin films using SWCNTs…………………………………….62

3.3.1 Fabrication of PDMS/SWCNT thin films….……………………………………62

3.3.2 Fabrication of SU8-2075/SWCNT thin films……………………………......64

3.3.3 Implementation of a saturable absorbers by using a PDMS film and a SU8 film………………………………………………………………………………..…66

3.4 Characterization of Saturable Absorber…………………………………………………67

3.4.1 Methods to characterizer a Saturable Absorber……………………………67

3.4.2 Measurement of the nonlinear absorption of the saturable absorber……………………………………………………………………………….…67

3.5 Summary…………………………………………………………………………..………………72

3.6 References…………………………………………………………………………………………72

ix

Chapter 4

Passively mode-locked Erbium fiber laser using PDMS/SWCNT and

SU8/SWCNT films as SA

4.1 Introduction……………………………………………………………………………….……..75

4.2 Mode-locked fiber laser configuration…………………………………………….…….77

4.3 Mode-locked fiber laser results using PDMS/SWCNT as SA…………………....79

4.4 Mode-locked fiber laser results using SU8-2075/SWCNT as SA……………....83

4.5 Summary…………………………………………………………………………..................87

4.6 References………………………………………………………………………………………..88

Chapter 5

Hybrid mode-locked laser using a PDMS/SWCNT as SA

5.1 Introduction………………………..………………………………………….………………...91

5.2 Active mode-locked laser……………………………………….……………………………92

5.3 Hybrid mode-locked laser…………………………………………….……………………..94

5.4 Summary…………………………………………………………………………..................98

5.5 References…………………………………………………………………………………….….99

Chapter 6

Passively Q-switched Erbium fiber laser using SU8/SWCNT as SA

6.1 Introduction………………………………………………………………………...............101

6.2 Passively Q-switched laser…………………………………………………………………101

6.3 Passively Q-switched fiber laser results using a SU8-2075/SWCNT as a

SA…………………………………………………………………………………………..………103

6.4 Summary…………………………………………………………………………................105

6.5 References……………………………………………………………………………………...106

x

Chapter 7

Conclusions

7.1 Conclusions………………………………………………………………………...............107

7.2 Future work………………………………………………………………………...............108

7.3 References………………………………………………………………………………………109

xi

List of Figures

Fig. 2.1 (a) Schematic of optical cavity with two mirrors, (b) Ring fiber cavity,

WDM: Wave Division Multiplexing………………………………………………………………….11

Fig. 2.2 (a) Laser gain and longitudinal modes; (b) Superposition of three equally

spaced frequency components which are all in phase……………………………………..12

Fig. 2.3 (a) Active mode-locked laser, the modulator is driven at the cavity round-

trip period; (b) illustration of gain and longitudinal modes when the modulator is

driven at a frequency Ω; (c) Periodic modulation loss and resulting mode-locked

pulses………………………………………………………………………………………………………..14

Fig. 2.4 Illustration of the synchronous pumping method for mode-locking of a

laser………………………………………………………………………………………………………....16

Fig. 2.5 Schematic illustration of the pulse formation in a synchronously pumped

mode-locked laser……………………..…………………………………………………………………17

Fig. 2.6 Schematic setup of a passive mode-locked laser…………………….……….…17

Fig. 2.7 Model of a four-level saturable absorber……………..…………………………….19

Fig. 2.8 Pulse-shaping gain and loss dynamics for fast-saturable absorber mode-

locking……………………………………………………………………………………….……………...22

Fig. 2.9 Pulse-shaping gain and loss dynamics for fast-saturable absorber mode-

locking……………………………………………………………………………………………………...23

Fig. 2.10 Using the fast absorber model the nonlinear absorption data was

fitting…...…………………………………………………………………………………………………..25

Fig. 2.11 Pulse shortening by dynamic self-focussing, or KLM, L1 and L2 are

lenses….......................................................................................................27

Fig. 2.12 Schematic setup of additive pulse mode-locked laser, SPM: self-phase

modulation…...……………………………..……………………………………………………………..28

Fig. 2.13 Pulse shortening by a NALM with an asymmetrically placed gain

element…………………………………………………………………………………………………..….29

xii

Fig. 2.14 Layout for mode-locked fiber ring laser exploiting nonlinear polarization

rotation. In this implementation the required polarizer function is included in the

isolator, PC: polarization controller………………………………………………………………...30

Fig. 2.15 (a) Schematic of a two-dimensional graphene sheet illustrating lattice

vectors 2.59, (b) zigzag nanotube, (c) armchair nanotube, and (d) chiral nanotube

[2.60]………………………………………………………………………………………………………...33

Fig. 2.16 (a) Kataura Plot, black points are semiconductor nanotubes, red points

are metallic nanotubes [2.61], (b) Energy versus 1-D electronic density of states

for semiconductor nanotubes with different diameters and chiralities

[2.62]………………………………………………………………………………………………………..34

Fig. 2.17 Schematic illustration of the Q-switching process………………..……………40

Fig. 2.18 Evolution of power, gain and loss in a passively Q-switched laser

[2.99]………………………………………………………………………………………………………..43

Fig. 2.19 Schematic illustration of the temporal evolution of the cavity gain/loss

and the output power during Q-switched laser pulse formation (a) close to lasing

threshold, (b) far above the lasing threshold [2.101]……….…………….……………….45

Fig. 3.1 Schematic representation: (a) two acrylic layers and the spacer between

them. (b) Lateral view of the cell fill up with PDMS/SWCNT…………………………..…63

Fig. 3.2 Schematic of the cell fabrication process: (a) Deposition of a PDMS layer

on a glass substrate. (b) Thickness and position of the spacers on the cell…….….65

Fig. 3.3 Lateral view of the cell with SU8-2075/SWCNT…………………...…………….66

Fig. 3.4 Implementation of a SA using either a PDMS/SWCNT or a SU8-

2075/SWCNTfilm………………………………….……………………………………………...……..67

Fig. 3.5 All fiber power dependence transmission setup. PC.: Polarization

Controller; VOA: Variable Optical Attenuator…………………………………………………..68

Fig. 3.6 PDMS/SWCNT film (200μm). (a) Device loss as function of input power

(dB); (b) Transmission vs. input peak intensity; (c) Normalizaed absorption vs.

input peak intensity; (d) Normalized absorption vs. input intensity…………………...69

Fig. 3.7 SU8-2075/SWCNT film (100μm). (a) Device loss as function of input

power (dB); (b) Transmission vs. input peak intensity; (c) Normalizaed absorption

vs. input peak intensity; (d) Normalized absorption vs. input intensity……………….70

xiii

Fig. 4.1 Schematic of the passively mode-locked fiber laser developed by using a

PDMS/SWCNT film between two connectors.WDM: wavelength division multiplexer;

PC.: Polarization Controller………………………….………………………………………………..78

Fig. 4.2 Output power vs. pump current………………………………………………………..78

Fig. 4.3 Mode-locked laser output characteristics at a pump power of 85 mW(a)

Pulse train of mode-locked laser; (b) RF tones………………………………………………..79

Fig. 4.4 Mode-Locked laser at different pump powers: (a) Optical spectrum and

(b) Autocorrelation trace……………………………………………………………………………….81

Fig. 4.5 (a) Output pulse duration and time-bandwidth product at different pump

powers, (b) Output power vs. pump power; Laser output characteristics at pump

power of 85mW: (d) Optical spectrum, (c) Autocorrelation trace………..……………82

Fig. 4.6 Schematic of the passively mode-locked fiber laser developed using a

PDMS/SWCNT film between two connectors. WDM: wavelength division

multiplexer; PC.: Polarization Controller………………………..………………………………..84

Fig. 4.7 Mode-locked laser output characteristics at a pump power of 88 mW (a)

Pulse train of mode-locked laser, (b) RF tones, (c) Optical spectrum, and (d)

Autocorrelation trace…………………………………………………………………………………..85

Fig. 5.1 Schematic of the active mode-locked fiber laser. EOM: electro-optical

modulator; WDM: wavelength division multiplexer; Pol. Con.: Polarization

Controller………………………………………………………………………………………..………...92

Fig. 5.2 (a) Optical spectrum, and (b) Autocorrelation trace from the active mode-

locked fiber laser………………..……………………………………………………………………...94

Fig. 5.3 Schematic of the hybrid mode-locked fiber laser. EOM: electro-optical

modulator; WDM: wavelength division multiplexer; Pol. Con.: Polarization

Controller…………………………………………………………………………………………….……..94

Fig. 5.4 (a) Optical spectrum, and (b) Autocorrelation trace from the hybrid mode-

locked fiber laser………………………………………………………………………………………...96

Fig. 5.5 Photo-detected RF spectrum of (a) Active, (b) Hybrid mode-locked laser

configurations…………………………………………..…………………………………………………97

Fig. 6.1 Schematic of the passively Q-switched fiber laser using a SU8-

2075/SWCNT film between two connectors………….………………………………….……102

xiv

Fig. 6.2 Passively Q-switchedfiber laser output characteristics at a pump current of

75 mA (a) CWoptical spectrum, (b) Q-switching optical spectrum, (c) Pulse train,

and (d) Pulse……………………………………………………………………………………………..104

Fig. 6.3 Average output power and pulse repetition rate as function of pump

current………………………………………………………………………………………………………105

xv

List of tables

Table 1.1 Application of mode-locked fiber lasers……………………..………………….2

Table 4.1 A list of polymers used to fabricate thin film to implement a passively

mode-locked fiber ring laser………………………………..…………………….86

1

Chapter 1

Introduction

1.1 Overview

The implementation of the first pulsed laser was made six year after the invention

of the laser [1.1], since then; different configurations and materials have been

used to generate ultrashort pulses. The demand of pulsed fiber laser has been

increased due to the reliability, robustness, stable output, no cooling elements, and

compactness of these systems. In the ideal case, most of the elements used to

assembling these lasers are well-matched with fiber technology. Speaking about

gain medium for fiber lasers, the most studied and popular gain mediums are

Erbium (Er), Ytterbium (Yb), Bismuth (Bi), Thulium (Tm), and Holmium (Ho). Er-

doped fibers offer a wavelength range from 1.53 μm to 1.62 μm, while Yb-doped

fibers emit around to 1 μm. Bi-doped fibers, Tm-doped fibers, and Ho-doped fiber

have a broad gain around 1.3 μm, 1.9 μm, and 2 μm, respectively. These large

family of rare earth doped fibers offer different possibilities for the generation of

ultrashort pulses at several different wavelengths with very high optical

efficiencies.

The most common way to produce ultrashort pulses is by mode-locking and Q-

switching techniques. Mode-locked lasers are classified in two types: active and

passive. The former can be constructed by incorporated an optical modulator

inside a fiber cavity laser and it produces pulses with a pulse-width of a few

picoseconds at gigahertz of repetition rate. The latter is built up by inserting a

saturable absorber (SA) in a fiber laser cavity and it generates pulses with pulse-

duration of subpicoseconds with repetition rates on the order of megahertz. On the

2

other hand, Q-switched fiber lasers produce pulses with durations a few

nanoseconds and they can also be classified as active and passive.

Continuous wave and pulsed fiber lasers have several applications not only in

optical laboratories but also in the industry. Some fields of applications are material

processing, biomedicine, optical communication, spectroscopy, imaging and laser

ranging. In the case of mode-locked lasers, they are used in modern

ophthalmology [1.2], microscopy [1.3], micromachining [1.4], optical

communication [1.5], and metrology systems [1.6]. Table 1.1 summarizes several

applications of mode-locked fiber lasers at different wavelength regimes. For Q-

switched lasers, some applications of such lasers are dental surgeries [1.7],

ablation of tissue [1.8], and LIDAR (Light Detection and Ranging) [1.9].

Table 1.1 Application of mode-locked fiber lasers.

Gain

fiber

Wavelength

range (μm) Application References

Yb ~1 Multiphoton microscopy,

micomachining [1.10], [1.11]

Bi 1.3-1.5 Optical communication [1.12]

Er ~1.5

Optical coherent

tomographic, metrology,

Optical communication, two

photon microscopy

[1.13] - [1.16]

Tm ~1.9

Optical coherent

tomographic, surgery, laser

lithotripsy*

[1.13], [1.17],

[1.18]

Ho-

YAG ~2 Laser lithotripsy [1.19]

*Laser lithotripsy is a surgical procedure to remove stones from urinary tract.

3

All these gain mediums allow us to construct fiber lasers that operate at

wavelengths that have several potential applications, but this also generates the

need to developed SA in order to produce pulsed fiber laser. Semiconductor

Saturable Absorbers (SESAM) can work at a wide variety of wavelengths by

engineering the bandgap of the quantum wells. The recovery time of SESAMs

varies between a few nanosecond for Q switching applications and few picosecond

for mode-locked lasers [1.20]. Up to now, SESAMs have been widely deployed to

develop mode-locked solid state lasers in a broad spectral range between 800 and

1550 nm, and they are grown by molecular beam epitaxy (MBE) or metal organic

vapor phase epitaxy (MOVBE) on distributed Bragg reflectors [1.21]. Recently,

Single Wall Carbon Nanotubes (SWCNTs) have attracted a lot of attention due to

their astonishing optical properties such as ultrafast recovery time [1.22], high

third-order optical nonlinearities [1.23], and the tunability of their band-gap energy

when the diameter of the SWCNTs is modified [1.24]. By choosing the correct

nanotube diameter it is feasible to work at a specific wavelength. Owing to these

optical properties, many SA based on SWCNTs were demonstrated [1.25] - [1.27].

This is a new research field which involves material scientists and laser physicists

to improve the performance of the SAs. One promising method for fabricating SAs

is by embedding SWCNTs in a polymer matrix to form a composite. By designing a

SA this composite can interact with the light in many different forms such as thin

film [1.27], fiber tapers [1.28], and by injecting it in the core of an optical fiber

[1.29], etc.

1.2 Aim of this thesis

The main objective of this thesis is to develop fiber lasers that generate

optical pulses at a communication wavelength (L-band erbium fiber). Thus

the goals of this thesis are:

4

Fabricate thin films of Polydimethylsiloxane (PDMS) as well SU8-2075 doped

with SWCNTs that works as SA.

Construction of an all-fiber power dependent transmission setup which

characterizes the optical properties of the SA.

The implementation of passively mode-locked Erbium fiber lasers using thin

films of PDMS/SWCNT and SU8-2075/SWCNT, as well as describing and

characterizing the performance of these two lasers.

The implementation of a hybrid mode-locked laser using a thin film of

PDMS/SWCNT, as well as describing and characterizing its performance.

The implementation of a passively Q-switched laser using a thin film of

SU8-2075/SWCNT, and describing and characterizing its performance.

1.3 Outline of this dissertation

A brief description of the chapters that form this thesis will be presented next.

Chapter 2 gives the dynamics of pulse formation in mode-locking and Q-

switching techniques, and also describes the interplay between loss and gain inside

the optical laser cavity due to SA and gain medium. Additionally, optical properties

of SWCNTs that are important for mode-locking operation are listed and briefly

explained and a review of state of the art SAs based on SWCNTs is also given.

In Chapter 3, the fabrication process of SAs based on polymer doped with

SWCNT is described. The polymers used for that purpose are PDMS and SU8-2075.

Moreover, a characterization of the nonlinear optical properties of SWCMTs is

accomplished by an all-fiber power dependent transmission setup. This setup

basically determines how the transmission of the film is changing as the optical

power is increasing.

5

In Chapter 4, two passively mode-locked fiber lasers are implemented by using

a PDMS/SWCNT film and a SU8-2075/SWCNT film as a SA. The thickness of the

PDMS/SWCNT film and SU8-2075/SWCNT are 200 μm and 100 μm, respectively.

This chapter is devoted to study how these lasers work at different pump powers

and the output of the laser is also characterized by taking its optical spectrum,

radio frequency spectrum, pulse width, and the average power.

In Chapter 5, a hybrid mode-locked Erbium fiber laser that incorporates active

mode-locking combined with a PDMS/SWCNT thin film as SA is reported. The

active system is built using a standard ring cavity laser incorporating an electro-

optical modulator (amplitude modulator). The hybrid system is constructed by

inserting a SA (a PDMS/SWCNT thin film composite) in the active system between

two FC/APC connectors. A comparison between active and hybrid system is made

in order to observe the benefits of the hybrid mode-locked laser. It is also shown

that the active mode-locked laser undergoes a reduction in the signal-to-noise ratio

(SNR) of the photodetected radio frequency (RF) spectrum by using this film.

In Chapter 6, a passively Q-switched fiber laser was implemented and tested

by using a SU8-2075 thin film doped with SWCNTs as SA. A study of the output of

the laser is carried out.

Finally, in Chapter 7 some conclusions and future work are presented.

6

1.4 References

[1.1] A. J. D. Maria, D. A. Stetser, and H. Heynau, “Self mode-locking of

lasers with saturable absorbers,” Appl. Phys. Lett. 8, 174-176 (1966).

[1.2] R. M. Kurtz, M. A. Sarayba, and T. Juhasz, “Ultrafast lasers in

ophthalmology,” in Ultrafast Lasers: Technology and Applications, M.E.

Fermann, A. Galvanauskas, and G. Sucha, (CRC Press, FL, USA, 2003).

[1.3] J. Clowes, “Next generation light sources for biomedical applications,”

Opt. Photon. 1, 36-38 (2008)

[1.4] L. Shah and M. E. Fermann, “High power femtosecond fiber chirped

pulse amplification system for high speed micromachining,” J. Laser

Micro/Nanoeng. 1, 176-180 (2006).

[1.5] H. Ohta, S. Nogiwa, N. A. Oda, and H. Chiba, “Highly sensitive optical

sampling system using timing-jitter-reduced gain-switched optical

pulse,” Electron. Lett. 33, 2142-2143 (1997).

[1.6] T. R. Schibli, K. Minoshima, F. L. Hong, H. Inaba, A. Onae, H.

Matsumoto, I. Hartl, and M. E. Fermann, “Frequency metrology with a

turnkey all-fiber system,” Opt. Lett. 29, 2467-2469 (2004).

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“Micromachining with a 50 W, 50 μJ, subpicosecond fiber laser system,”

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Popov, J. R. Taylor, “Bismuth fiber integrated laser mode-locked by

carbon nanotubes,” Laser Physics Lett. 7, 790–794 (2010).

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8

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9

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10

Chapter 2

Short Optical pulse Generation

2.1 Introduction

This chapter mentions the fundamental principles of mode-locker laser and

describes the dynamics of various configurations paying more attention in fiber

configuration. A mathematical explanation of the behavior of saturable absorbers

(fast or slow according to their recovery time) is given and their optical properties

that are important for mode-locking are explained. Additionally, optical properties

of SWCNTs that are important for mode-locking operation are listed and briefly

explained and a review of the state of the art of saturable absorber based on

SWCNTs is also given. Finally, Q-switched laser dynamics is explained.

2.2 Mode-Locking

2.2.1 General Description

The simplest picture of a laser system consists of an optical cavity, or optical

resonator, with a gain medium inside it. However, to produce a pulse and to

produce shorther pulses has become a demonstration of ingenuity. Let’s analyze

our resonant cavity, it can be built by using two highly reflecting mirrors or by

using a ring resonator, as shown in Fig. 2.1 (a) and (b), respectively. When the

light is traveling inside the cavity, standing waves are generated by the

counterpropagating electromagnetic waves. Since the boundary conditions, few

frequencies can be supported by the cavity. This discrete set of frequencies is

known as longitudinal modes which all of them are multiple of the fundamental

cavity frequency which is given by [2.1]:

11

,2

c

nL (2.1)

where c is the velocity of light in vacuum, n is the refractive index of the medium

and L is the optical length of the resonator. Eq. (2.1) can also accurately model a

unidirectional ring fiber laser by considering 2l L .

Fig. 2.1 (a) Schematic of optical cavity with two mirrors, (b) Ring fiber cavity, WDM: Wave Division

Multiplexing.

Let’s now look at the amplifying medium. The longitudinal modes that oscillate

in the cavity are those where the gain exceeds the loss of the resonator and such

a gain is assumed to have a bandpass spectral response, see Fig. 2.2 (a). The way

that these modes add up to produce an output of our laser is essential to produce

the desired pulse output. In Fig. 2.2 (b), top to bottom, we show in phase the sum

of three modes, and the optical pulses generated by their sum. Moreover, there

are transversal modes inside the cavity but it is assumed that the laser is

oscillating in a single transversal mode (like in a single-mode optical fiber).

12

Fig. 2.2 (a) Laser gain and longitudinal modes; (b) Superposition of three equally spaced

frequency components which are all in phase.

The longitudinal modes that are oscillating inside the optical cavity have

different amplitudes and phases and summing all of them produces an average

intensity which varies in time. Therefore, by assuming that all modes have the

same amplitude and phase and then summing all of them, we get [2.1]

1 1

( ) 000 0

0 0

( )N N

ii t i tn n

n n

E t E e E e e , (2.2)

where 0E is the amplitude of the mode, n is the frequency of that mode and 0

is the phase of the mode. By defining n as 1n N n and rewriting Eq.

(2.2) we obtain a convenient expression,

1

( )100

0

( )N

i n ti N

n

E t E e e . (2.3)

Its intensity can be calculated using Eq. (2.3)

22

2 20 0 2

1 sin ( 2)( )

1 sin ( 2)

iN t

i t

e N tI t E E

e t. (2.4)

13

This equation tells us that the output of the laser will be a train of pulses whose

separation between them is given by [2.1]

2

,nd

Tc

(2.5)

and the pulse width is [2.1]

pulse

1 1,

gain bandwidtht

N (2.6)

where N is the number of mode in phase and is the separation between two

consecutives modes. When the output of laser has these features is referred as a

mode-locked laser. It was shown that by fixing the modes’ phase of an optical

cavity, we can produce a train of pulses whose width could be reduced by

increasing the number of modes that has the same phase, Eq. (2.6). The

techniques that have been used to implement mode-locked laser are active mode-

locking, synchronously mode-locking, and passively mode-locking. They will be

briefly described in the next section.

2.2.2 Active Mode-locking

An active mode-locked laser consists of a laser cavity that has an optical modulator

inside, Fig. 2.3 (a). This device will induce a modulation of the amplitude of each

longitudinal mode. It is said that this element modulates the losses in the cavity.

14

Fig. 2.3 (a) Active mode-locked laser, the modulator is driven at the cavity round-trip period; (b) illustration of gain and longitudinal modes when the modulator is driven at a frequency Ω; (c)

Periodic modulation loss and resulting mode-locked pulses.

When the modulator is driven by an electrical signal whose angular frequency

and modulation depth are m and m respectively; n is the phase of the mode

n and is the phase of the electrical signal, the time dependency of mode n of

frequency n can be written as [2.2]

( ) cos( ) 1 (1 cos( )) ,n n n n m me t E t t (2.7)

for convenience let’s rewrite it as

( ) (1 ) cos( )

cos ( )2

cos ( ) , 2

n n m n n

mn n m n

mn n m n

e t E t

E t

E t

(2.8)

where two side bands appear at either side of mode ( )ne t . In particular, if the

2m is equal to the fundamental frequency , then these sidebands

correspond to the two cavity modes adjacent to the original mode, see Fig. 2.3 (b).

In Fig. 2.3 (c) is illustrating a periodic modulation loss and the resulting optical

15

pulses, it should be notice that those pulses appear when the loss is minimum.

Since the sidebands are driven in-phase, the central mode and the adjacent modes

will be jointly phase-locked. Further operation of the modulator on the sidebands

produces phase-locking of the 2n and 2n modes, and so on, until all

modes in the gain bandwidth are locked. Locking the modes in this manner brings

about to generate an optical pulse traveling inside the cavity. When that happens it

is called active mode-locking. It is also possible modulate at m , where m is an

integer, and in this case the mode n can be couple to mode n m and n m .

When the frequency of the modulation is a multiple of the , this is called

harmonic mode-locking.

In practice, an acousto-optic or electro-optic modulator is place inside the

cavity to modulate the losses. For illustration propose, let’s show the FWHM pulse

width of an amplitude modulation mode-locked homogeneous laser [2.3]

1124 1

0.45 ,m m

m a

p

f (2.9)

where m mp is the round-trip gain coefficient and af is the atomic line width. It

should be notice that the pulse width is inverse to m , and af . Ones can easy

realize that the pulse width of the harmonic mode-locking is shorter than the active

mode-locking. Moreover, a mode-locked laser can be built up using a phase

modulator (FM) and in this case the pulse width should be given by the Eq. (2.9)

times the constant 1 42 . The performance of a homogeneous laser using a FM

modulator is essentially the same as with AM modulator; but the FM mode-locked

pulse gets a small frequency chirp equal in magnitude to the pulse width

modulation [2.3].

Harmonic mode-locking has to advantages: the train of pulses that generates

has a closer pulse spacing than the cavity round-trip time (higher repetition rate);

and the optical output can be synchronize to a radio frequency signal (RF). Hence,

harmonic mode-locking is really useful in optical fiber communication where the

16

repetition rate is low and a pulse train of gigahertz is desired. As it was shown,

high repletion rate can be obtained by using this technique but it cannot produce

shorter pulses (<1 ps) [2.4].

2.2.2.1 Synchronously pumped mode-locking

Synchronous pumping is obtained by pumping the gain medium of a laser with the

output beam of another mode-locked laser, Fig. 2.4. It is like switching on the gain

for only a very short period of time while the short pulse is passing through the

gain medium. Both lasers should have the same repetition rate in order to maintain

the necessary switch timing (this is one of the drawbacks of the technique because

the optical length of the two cavities needs to be equal with a typical accuracy of a

fraction of the laser wavelength).

Fig. 2.4 Illustration of the synchronous pumping method for mode-locking of a laser.

The formation of the pulse at the output of the laser is shown in Fig. 2.5,

where the resulting pulse is shorter than the pump pulse. This scheme is useful

when the upper-state lifetime of the gain medium is not much longer than the

17

cavity round-trip time [2.5]. Recently, it has been used Vertical-External-Cavity

Surface Emitting lasers to obtain synchronously mode-locked laser [2.6].

Fig. 2.5 Schematic illustration of the pulse formation in a synchronously pumped mode-locked

laser.

2.2.3 Passive mode-locking

Passive mode-locking is similar to active mode-locking, but the optical modulator is

replace by a saturable absorber (SA), Fig. 2.6, which is a nonlinear optical element

that has a constant optical absorption to low intensities, but it decreases as the

laser intensity rise.

Fig. 2.6 Schematic setup of a passive mode-locked laser.

18

Passive mode-locking stars from noise fluctuation in the laser. One strong noise

spike experiences less loss per round-trip that other weaker noise spikes; and

hence this particular noise spike will be more strongly during the following cavity

round trip. This process goes on until the noise spike reaches a steady state and a

stable pulse train has been formed. Besides, if the response time (recovery time)

of the nonlinearity is sufficiently fast, the optically driven modulation function gets

faster as the pulse becomes shorter. Thus, the pulse shortening action can remain

effective even for very short pulses. Since the recovery time of the SA is really fast,

shorter pulses can be obtained. In general, the fast loss modulation introduced by

the recovery time is faster than any electronically driven loss modulation used to

drive any optical modulator.

Several kinds of SAs exist, but they can be classified into two: slow SA and fast

SA. In the next two sections both of them will be described.

2.2.3.1 Saturable absorber

A saturable absorber is a material that has decreasing light absorption with

increasing light intensity. This phenomenon can occur in a medium with absorbing

dopant ions, when a strong optical intensity leads to depletion of the ground state

of these ions. Similar effects can occur in direct gap semiconductors, as the

intensity increases photo-excitation causes the states near the edge of the

conduction and valence bands to fill, blocking any further absorption. At high

enough intensity, the semiconductor becomes transparent to light at photon

energies just above the bandedge [2.7]. This phenomenon is related with the third

optical nonlinearity [2.8]. Different materials have been used as saturable absorber

such as organic dyes, colored filter glasses, dye-doped crystals, semiconductor,

and recently Single Wall Carbon Nanotubes (SWCNTs).

19

2.2.3.2 Saturation model

The most common saturable absorber (organic dye solution and semiconductor)

can be model by a four-level system, see Fig. 2.7. The transition is a resonant

absorption for the laser radiation (1→2), and the absorption strength is

proportional to the population densities 1 2N N (where jN is the density in units

of m-3 of absorbers in level j ). The total density of absorbers is AN . The 2→3 and

4→1 relaxations are taken to be very fast. The 3→4 recovery time is finite and is

denoted A . It is assumed that the laser radiation does not interact with 3→4

transition and the absorption spectrum is homogenously broadened which can be

considered constant within the mode-locked bandwidth.

Fig. 2.7 Model of a four-level saturable absorber.

The saturation of the absorber can be described with the following differential

equation [2.4]:

2

311 2

0

( )( ),A

A A

a tNNN N

t A (2.10)

with

1 3 2 4 and N 0. AN N N N (2.11)

20

In Eq. (2.10), the first term on right is the relaxation out of level 3 and the second

term represents stimulated absorption. The pulse is normalized so that 2

( )a t

gives the time-dependent power carried by the pulse. A is the 1→2 absorption

cross section, 0 is the photon energy, and AA is the beam cross-section area in

the absorber. The Eq. (2.10) can be rewrite as

2

11 1( )

,A

A A A

a t NN N N

t P (2.12)

where

,A

AA A

AP (2.13)

is the absorber saturation power. Assuming a small loss per pass, the time-

dependent loss term ( )l t is proportional to the ground-state absorber density 1N

[2.4]:

1( ) ( ) ,2A

al t N t l (2.14)

where al is the length of the absorber medium.

Solving 1( )N t form Eq. (2.12) produces two important limiting cases. These

cases are determined from the comparison between the magnitude of the recovery

time A and that of the mode-locked pulse width pt . The first occurs when

A pt , and it is known as a fast saturable absorber. The second one is when

A pt , and it is identified as a slow saturable absorber. In the following two

sections these cases will be discussed.

21

2.2.3.3 Fast saturable absorber

In the case of a fast saturable absorber, the absorber recovery time is much faster

than the pulse duration (A pt ). In this manner, it is assumed that the

absorption instantaneously follows the absorption of a certain power 2

( )a t . Then

Eq. (2.12) convers into

2

11( )

0 ,A

A A A

a t NN N

P (2.15)

and solving for 1N

1 2( ) .

( )1

A

A

NN t

a t

P

(2.16)

1( )N t and ( )l t vary instantaneously with the laser power 2

( )a t . An increment in

the laser power produces a reduction in the absorption; therefore the peak of the

mode-locked pulse will experience lower loss than will the wings of the pulse [2.4].

Haus’s master equation can describe this passive mode-locking technique very

well [2.4]

0

2

2 2

1 ( ) ( )( ) ( ) ( ) 0,

c

d a t da tg t l t l a t T

dtdt (2.17)

where ( )g t is the gain, 0l is the linear time-independent cavity loss, and T is a

time shift arising due to the nonlinear pulse shaping action of ( )l t and ( )g t ; and

it is usually small compared to the steady-state pulse width.

It is possible to solve Eq. (2.17) by assuming that 2

( )a t remains sufficiently

below the saturation power AP and using Eq. (2.14) and Eq. (2.16), A complete

explanation of the solution of this equation is in [2.4], [2.9], [2.10]. With this

solution and the Eq. (2.17), we can figure out the dynamic of the pulse formation.

22

Fig. 2.8 shows the time dependence saturable absorption as a function of the

normalized time together with the position of the saturated gain level and the

pulse power. It is observed that the net gain before and after the pulse must be

zero. This is, in fact, a stability condition since if the net gain were positive before

or after the pulse, perturbations before or after the pulse would grow in amplitude.

Fig. 2.8 Pulse-shaping gain and loss dynamics for fast-saturable absorber mode-locking.

2.2.3.4 Slow saturable absorber

In the case of a slow saturable absorber, the excitation pulse duration is much

shorter than the recovery time of the absorber (A pt ). Thus, in Eq. (2.12) the

first term on the right is neglected and Eq. (2.12) reduces to:

2

11

( ).

A A

a tNN

t P (2.18)

The solution of the equation is

2

( ) ( )1 1 1

( ) ( )( ) exp exp ,

A A A

ti ia t U t

N t N dt NP U

(2.19)

23

where

2

( ) ( ) and .A A A

t

U t a t dt U P (2.20)

Here ( )1

iN is the initial absorber population in level 1 just before the laser pulse,

( )U t is the pulse energy up to time t , and AU is the absorber saturation energy.

One can obtain an insight on the pulse formation process itself, a complete

treatment of the problem can be seen in [2.4], [2.9], [2.10], by solving Eq. (2.17)

together with Eq. (2.14) and Eq. (2.19). In this case, dynamic gain saturation

supports the pulse formation process, Fig. 2.9, and pulses much shorter than the

recovery time of the saturable absorber are obtained [2.11].

Fig. 2.9 Pulse-shaping gain and loss dynamics for fast-saturable absorber mode-locking.

Dynamic gain saturation means that the gain experiences a fast pulse-induced

saturation that will recover back between consecutive pulses. Therefore, an

effective ultrashort net-gain window can be formed by the combined saturation of

24

the absorber and the gain, if the absorber can saturate and recover faster than the

gain, while the saturable absorber recovery time is much longer than the pulse

duration. Therefore, the absorber would preferentially absorb the leading edge of

the pulse, whereas gain depletion would cause loss on the trailing edge.

2.2.3.5 Characterization of saturable absorber

The nonlinear optical properties of a saturable absorber can be determined by

knowing four macroscopic parameters. The macroscopic properties of a SA are the

recovery time A , the modulation depth 0 , the nonsaturable absorption ns ,

and the saturation intensity/fluence ( / )sat satI F . The pulse generation process is

based on them, as well as the determination of the saturable absorber

performance. The recovery time is the decay time of photon-generated carriers

after the absorber is excited by a high optical intensity. It is usually measured by a

standard pump-probe technique [2.12]. The modulation depth is defined as the

maximum possible change in optical absorption , and the nonsaturable

absorption is part of the absorber loss which cannot be saturated even at high

intensity. A low value of ns is wanted to increase the modulation depth. The

saturation intensity satI is defined as the optical intensity that it takes in a steady

state to reduce the modulation depth to half its initial value. The fluence is the

incident pulse energy per unit surface area ( Asat satF I ). The last three

properties can be determined by using a Z-scan technique or a power-dependent

transmission experiment (this setup will be shown in the next chapter); these two

techniques measure the transmission of a SA at different input pump powers

levels. Pulse lasers, whose pulse width is shorter than the recovery time of the

sample, are used to implement these setups.

25

One can model the SA as a two photon absorption process by assuming that

the SA responds instantaneously to the optical intensity (fast absorber model of a

SA). The intensity-dependence absorption ( )I can be written as:

( ) .1

ns

sat

II

I

(2.21)

Fig. 2.10 shows the absorption as a function of peak intensity. We can figure out

that nslin . By normalizing , we get :

0( ),

1 1

ns lin

linsat sat

I

I II I

(2.22)

where the modulation depth is 0 lin . In the following chapter this model

will be used to fit the SA’s data.

5 10 15 20 25 30 35 40

0.32

0.34

0.36

0.38

0.40

ns

Ab

so

rpti

on

Input intensity (MW/cm2)

lin

Fig. 2.10 Using the fast absorber model the nonlinear absorption data was fitting.

Different materials have been used for SAs and each of one has its advantages

and drawbacks. In order to get an insight of these SAs a brief review will be

presented in the following sections.

26

2.2.3.6 Organic dye as a saturable absorber

Mode locking was first demonstrated in the mid-1960s by using a ruby laser [2.13],

and an Nd:glass laser [2.14]; both of them are solid-state laser. Nevertheless, at

that time solid-state lasers could not generate continuous-wave mode-locked

output, but they produced mode-locked picosecond pulses that are modulated with

a much longer Q-switched pulse envelope, which has a much lower repetition rate.

This regimen is called Q-switched mode-locking. At that time, 1970s and 1980s,

the dye lasers became so popular because they did not show Q-switching

instabilities and they could generate really short pulses. The first sub-picosecond

passively mode-locked dye lasers were shown in 1974, [2.15], [2.16], and the first

sub-100 fs colliding pulse mode-locked (CPM) dye laser was demonstrated in 1981

[2.17]. Using CPM, it was possible to generate pulses as short as 27 fs with

average output power of about 20 mW [2.18]. Furthermore, pulses as short as 6 fs

were reached by additional amplification and external pulse compression but only

at much lower repetition rates [2.19]. Nonetheless, dye lasers suffer from

significant disadvantages such as rapid degradation during operation, limited

output power, and the need for pumping e.g. with green or blue light, making the

pump sources expensive. Since dyes are poisonous and often even carcinogenic,

dealing with them should be done with a lot of care. For these reasons, others

techniques were suitable and less health dangerous that took over the generation

of short pulse generation.

2.2.3.7 Kerr-lens mode locking

The nonlinear effect based on χ(3) is known as Kerr effect and in a Kerr medium

the refractive index is nonlinear and depends on light intensity [2.20]. Due to the

high intracavity intensities, the Kerr effect is relevant in most ultrafast lasers.

These nonlinear refractive index changes bring about a lens focusing effect which

can describe in the following way: if a beam with a Gaussian profile is passing

through a Kerr media, the beam is more intensity at the center than at the edges

27

and for that reason the refractive index of the medium will become higher at the

center than at the edges of the beam; this effect behaves like a lens. The focusing

of the light depends on the intensity of the beam and on the path length that the

beam travels inside the material [2.1]. This leads to a so-called Kerr lens with an

intensity-dependent focusing effect which can be exploited for a passive mode-

locking mechanism.

Kerr lens mode-locking (KLM) is the most important method for pulse

generation from broadband solid-state laser. The first KLM of Ti:sapphire laser was

implemented in 1991 and it produced a pulse width of 6 fs [2.21]. An improved

mode-locking was demonstrated by Spinelli when a hard aperture was

appropriately placed in the cavity [2.22]. Fig. 2.11 shows a schematic illustration of

the pulse shortening of the KLM; this scheme has a hard aperture, with small

diameter, placed at a suitable location inside the cavity in order to introduce high

loss to the CW mode. Moreover, if a pulse of light with higher intensity than the

CW mode is traveling inside the cavity, it can generate self-focusing at the hard

aperture. Hence this reduction of the laser mode area for high intensities at the

aperture gives rise an effective fast saturable absorber (artificial SA). The same

aperture effect was achieved by reducing the beam radius (by Kerr lens effect) in

the gain medium, thus the short pulses undergo higher effective gain because the

pulses have a better spatial overlap with the pumped region [2.23]. Regardless of

all these features, there are some drawbacks like KLM lasers are not self-starting,

their laser cavities requires stringent mirror alignment, a clean environmental to

minimize losses and they operated close to the stability limit.

Fig. 2.11 Pulse shortening by dynamic self-focusing, or KLM, L1 and L2 are lenses.

28

2.2.3.8 Additive pulse mode-locking

The first exploited method for producing a self-amplitude modulation, via the

optical Kerr effect, used the nonlinear phase shift to modify the interference

between two coupled laser cavities. It was Additive Pulse Mode-Locking (APM) and

an illustration setup is shown in Fig. 2.12.

Fig. 2.12 Schematic setup of additive pulse mode-locked laser, SPM: self-phase modulation.

The main cavity has the gain medium and it is coupled to an auxiliary cavity

trough a partially reflector mirror. The lengths of the cavities are almost the same.

When one pulse hits the partially reflector mirror in the main cavity, part of the

pulse is reflected to the main cavity and another is transmitted into the auxiliary

cavity. The transmitted and reflected pulses will meet at the partially reflecting

mirror at the same time and they will interfere because the lengths of the two

cavities are nearly equal. The overall reflectivity seen by the main cavity depends

on the phase between these two sets of pulses. The highest reflectivity occurs

when the round-trip phases of the two cavities are identical (modulo 2 ) [2.4]. A

nonlinear medium is placed in the auxiliary cavity to produce self-amplitude

modulation. If the pulses of each cavity are out of phase and the nonlinear phase

shift bring them closer to being in phase, the overall reflectivity of the main cavity

increases. Thus, the peak of the pulses has the highest reflectivity due to self-

amplitude modulation. On the other hand, if the nonlinear phase shift increases

the mismatch between the pulses of each cavity, the reflectivity of the main cavity

will decrease and mode-locking will be suppressed. For this reason the relative

29

cavity length in APM lasers should be interferometrically stabilized (this is a

disadvantage). Two techniques are the most used to implement APM lasers using

optical fiber; they are nonlinear amplifying loop mirror (NALM) and nonlinear

polarization rotation.

A typical NALM layout is shown in Fig. 2.13, it consists of a 3 dB coupler which

splits the incident light into two equal intensities that counter propagates. The

important issue for a NALM is to place the gain very close to the end of the loop,

this asymmetry causes that one wave is first amplified to high power and then

undergo SPM (self-phase modulation); the other wave undergoes SPM at low

power and at the output is amplified. Furthermore, if the phase shift is close to

for the central intense part, this part of the pulse is transmitted, whereas pulse

wings are reflected because of their lower power levels and smaller phase shift.

This brings about output pulses that are narrower compared with themselves at

the entrance. Due to this behavior, the NALM is considered like a fast SA (artificial

SA). The first time that the NALMs were used was in 1991 [2.24] - [2.27]. They

are also used in figure-eight laser configuration [2.25].

Fig. 2.13 Pulse shortening by a NALM with an asymmetrically placed gain element.

Intensity dependent nonlinear polarization rotation also provides a mechanism

for artificial SA as shown in Fig. 2.14. To enforce unidirectional operation in the

30

laser cavity there are a gain medium, an output coupler, and an isolator. Other

elements are incorporated to promote nonlinear polarization evolution; these

include the two polarization controllers, a birefringent fiber piece, and a polarizer.

Nonlinear polarization evolution can occur either in birefringent or nonbirefringent

fibers. In nonbirefringent fibers, the nonlinear polarization evolution takes the form

of ellipse rotation, which is a superposition of two different circular polarization

states with different intensities. If they undergo different nonlinear shift phase,

because of different self-phase modulation and cross-phase modulation, their

combination can result in an intensity dependent polarization rotation. If the

system is well adjusted, the maximum transmission at the output polarizer occurs

at the highest intensity. The technique of nonlinear polarization rotation was first

used for passive mode-locked laser in 1992, [2.28], [2.29], [2.30]. The shortest

pulse obtained by this technique was 42 fs with energy < 1 nJ, using an Nd-doped

fiber laser in a Fabry-Perot configuration [2.31]. In a Erbium ring cavity

configuration pulses < 100 fs with energies > 0.5 nJ were obtained [2.32]. One of

the main drawbacks of these lasers is that they are very sensitive to environmental

instability due to their interferometric nature [2.33].

Fig. 2.14 Layout for mode-locked fiber ring laser exploiting nonlinear polarization rotation. In this implementation the required polarizer function is included in the isolator, PC: polarization controller.

31

2.2.3.9 Semiconductor saturable absorber

Semiconductor Saturable Absorber (SESAM) consists of an antiresonant

semiconductor Fabry-Pérot etalon formed by a semiconductor layer grown on top

of a highly reflecting semiconductor Bragg mirror and covered by a dielectric

reflector. Usually, the semiconductor layer contains absorptive quantum-well

layers. This device can work at a wide variety of wavelengths by engineering the

bandgap of the quantum wells. The recovery time of SESAMs vary between a few

nanosecond for Q-switching applications and few picosecond for ultrafast lasers

[2.34].

SESAMs based on III­V group binary and ternary semiconductor in the form of

multi quantum well are the most popular SAs [2.35]. Up to now, SESAMs have

been widely deployed to mode locked solid state lasers in a broad spectral range,

between 800 and 1550 nm, and they are grown by molecular beam epitaxy (MBE)

or metal organic vapor phase epitaxy (MOVBE) on distributed Bragg reflectors

[2.36]. These stringent fabrication methods (which are the shortcomings of

SESAMs) also require an ion implantation to create defects in order to reduce the

recovery time [2.37], [2.38].

2.2.4 Hybrid mode-locking

The improvement of the mode-locked laser performance can be achieved by

combining more than one mode-locking technique and this is called hybrid mode

locking. One way to implement a hybrid mode locked laser is by placing an

amplitude or phase modulator inside a passively mode-locked fiber laser. Typically

in hybrid mode-locking, the active modulation assists in pulse formation and helps

to stabilize the mode-locking process, while the SA is responsible for significant

reduction of the final pulse duration [2.4]. Since the modulator can operate at

multiples of the fundamental frequency of the cavity, the laser’s repetition rate can

reach gigahertz.

32

The first hybrid mode-locked laser was reported in 1991 [2.39], since then,

other configuration were implemented to improve laser performance.

Subpicosecond pulses at a repetition rate of 0.5 GHz were generated in 1994 by

using sigma configuration. This laser was made by coupling a linear section (that

contained a fiber amplifier and a passive mode-locking element composed of

quarter wave plates and a Faraday rotator) with a loop of polarization-maintaining

fiber that has a LiNbO3 inside it [2.40]. Based on the same configuration, a diode-

pumped stretched pulse erbium doped fiber laser was implemented and it

produced pulses whose energy and duration were 1.3 nJ and 1.5 ps, respectively

[2.41].

It is feasible to build a hybrid mode locked laser by combining these two

passive mode-locking techniques. In 1996, a SA was added to a mode-locked laser

based on nonlinear polarization rotation and it produced pulses whose energy and

duration were 100 pJ and 200 fs, respectively [2.42].

2.3 Optical properties of SWCNTs

Since SWCNTs were discovered in 1993 [2.43], they have been extensively studied

due to their astonishing optical properties; such as ultrafast recovery time [2.44],

high third-order optical nonlinearities [2.45], and in particular by the tunability of

their band-gap energy when the diameter of the SWCNTs is modified [2.46]. Due

to these optical properties, SWCNTs are good to fabricated saturable absorbers. By

choosing the correct nanotube diameter it is feasible to work at a specific

wavelength. They also show absorption from the UV to the near IR.

SWCNTs have a wide variety of potential applications including optical limiters

[2.47], optical noise suppression [2.48], optical switches [2.49], modulators [2.50],

wavelength converters [2.51], and nonlinear saturable absorbers (SA) [2.52] -

[2.56]. The implementation of SA based on SWCNTs has attracted a lot of

attention because they have been used to build up passive mode-locked ultrafast

33

lasers which can generate stable short pulses. These kinds of lasers can be used in

many different optical areas such as optical communication, microscopy,

spectroscopy [2.57] and biomedical applications [2.58].

A SWCNT is a graphene sheet that has been wrapped around a chiral vector to

form seamless cylinder whose minimum diameter is limited by the curvature-

induced strain to ~0.4 nm [2.59]. The diameter and helicity of a SWCNT are

uniquely characterized by the vector 1 2 ,hC na ma n m (chiral vector) that

connects crystallographically equivalent sites on two-dimensional graphene sheet,

where 1a and 2a are the graphene lattice vectors and n and m are integers

[2.60], Fig. 2.15 (a).

(a) (b) (c) (d)

Fig. 2.15 (a) Schematic of a two-dimensional graphene sheet illustrating lattice vectors [2.60], (b) zigzag nanotube, (c) armchair nanotube, and (d) chiral nanotube [2.61].

According to the specific indices of chiral vector, zigzag, armchair and chiral

nanotubes are formed. Moreover, the ,n m indices determine the metallic or

semiconducting behavior of SWCNTs [2.60]. Most of the nanotubes should be

semiconductor when a saturable absorber will be fabricated. As it was mention

before, SESAM are based on semiconductor materials and they have shown

astonishing results. SWCNTs are zigzag when ,0n , and they are metals if 3n is

an integer, Fig. 2.15 (b). When ,n n , they are armchair and they are expected

34

to be metallic with band crossings at 2 3k the one-dimensional Brilluoin zone,

Fig. 2.15 (c). Other possible combination of n and m brings about chiral SWCNTs

and they are metallic if 2 / 3 n m , otherwise they are semiconductor [2.60],

Fig. 2.15 (d). It is important to mention the relation between the chiral vector and

the diameter d of the nanotube,

2 2/h

ad C n nm m , where a is the

lattice constant of the honeycomb (a ≈ 1.42 Å) [2.61].

Each combination of the ,n m indices has a specific electronic band structure

and Kataura was the first in plotting the Gap Energy as function of the tube

diameter [2.46], Fig. 2.16 (a). The density states of the SWCNTs have series of

van-Hove singularities as it is shown in Fig. 2.16 (b) [2.63]. Moreover, Kataura’s

work points out that three large absorption bands exist due to the optical

transitions between van-Hove singularities. The first and the second lowest

absorption bands are because of the optical transitions between van-Hove

singularities in semiconductor SWCNTs and the third one is due to that in metallic

tubes [2.46].

(a) (b)

Fig. 2.16 (a) Kataura Plot, black points are semiconductor nanotubes, red points are metallic

nanotubes [2.62], (b) Energy versus 1-D electronic density of states for semiconductor nanotubes with different diameters and chiralities [2.63].

35

Several method have been developed to produce SWCNT including arc

discharge, laser ablation, high pressure carbon monoxide (HiPCo), and chemical

vapor deposition (CVD). The main problem in all these methods is the control of

the diameter and the chiral of the tubes. Therefore, in a SWCNTs sample the tubes

diameters and chiralities are not uniform. In addition, metallic and semiconductor

nanotubes are present in a sample. It has been shown that 1 3 is metallic

nanotubes and 2 3 is semiconductor nanotubes [2.64].

The SWCNTs third-order nonlinear optical susceptibility (χ(3)) has been

measured by several groups around the world. Here, we will be discuss two works,

one of them measure χ(3) using a Z-scant technique and the SWCNTs were sprayed

to form a film. It was reported that χ(3) ~10-7 esu, in resonant conditions [2.12].

The other work is a more complete investigation that shows how χ(3) changes

when different concentrations of SWCNTs are disperse in a suspension

(dichlorobenzene DCB) or in a polymer (PMMA). Moreover, different thickness of

the polymer film was tested in order to know what happens with the value of χ(3).

The macroscopic optical nonlinearities of diluted SWCNTs in DCB increase as the

density of solution increase until it reaches a critical density, χ(3) ~10-14 esu. After

this point, the third-order nonlinear susceptibility decreases due to the stronger

bundling of SWCNTs. The value of χ(3) for the SWCNTs in the PMMA was 10-10 esu

and it was found that χ(3) decrease with an increase in nanotube densities. For an

optimum concentration of tubes; different thickness was tested and they got

χ(3)~10-9 esu. They concluded that the nonlinearity of the SWCNT/PMMA does not

depend on the thickness. These measures were done by using the time-resolved

optical Kerr gate technique [2.45]. The best value of χ(3) for SWCNTs is one order

of magnitude higher than that for a GaAs super lattices commonly used in

telecommunications [2.65].

36

2.4 State of the art of the SWCNT as SAs

As we have shown in the last section, SWCNTs have been extensively studied due

to their excellent electrical and optical properties. One optical application that has

attracted a great deal of attention is the implementation of a SA based on

SWCNTs, because they have high third-order nonlinear susceptibility which is

fundamental phenomenon for saturable absorption. Since the first implementation

of SA base on SWCNTs [2.63]; a great effort has been made to design SAs which

are more sturdy, compact and reliable.

One of the techniques, first developed, to implement a SA was by spraying the

SWCNTs on a substrate (quartz). It consists in dissolved SWCNTs in a solution and

then sprayed onto a substrate [2.63], [2.66] -[2.68]. At the same time, growing

SWCNTs on a subtracted was proposal and tested [2.69], [2.70]. The most

common problems on either one of these two techniques are the low optical

damage threshold and the high scattering loss. The incorporation of the SWCNTs

into polymers is another technique that has been used to implement fiber ring

lasers [2.71] - [2.74] by setting a film between connectors, or solid state lasers

[2.52], [2.75] - [2.77]. This approach has several advantages such as, suppressing

bundles of SWCNTs, protecting the tubes from mechanical damage, avoiding

degradation of the tubes by air, easily film thickness control, etc. In the case of

thin films between fiber connectors, these SAs are robustness against external

vibration because they do not need any special alignment. Different kinds of

polymers have been used to fabricate reliable and reproducible films that contains

SWCNTs such as polycarbonate (PC) [2.74], carboxymethyl cellulose (CMC)

[2.77], [2.78] polyvinylalcohol (PVA) [2.79], polymide [2.72], poly-methyl-

methacrylate (PMMA) [2.80], polystyrene (PS) [2.80], and poly-3-hexylthiophene

(P3HT) [2.74], [2.73]. Although the majority of those composite films operate

fairly well as saturable absorbers, they exhibit different drawbacks such as being

special polymers, requiring polishing of the surfaces, as well as low glass transition

temperatures. Since SWCNTs absorb light they increase their temperature and

37

damage or burn themselves. Consequently, heat resistance materials should be

used to support high temperatures in order to dissipate heat. One way to

determine the heat resistance of a polymer is by considering the glass transition

temperature (Tg); for example the glass transition temperature is 100 ºC for

PMMA and PS, and 150 ºC for PC [2.81]. An ideal host polymer matrix should have

good mechanical and thermal features, as well as good dispersion of SWCNT.

By embedding SWCNTs in a polymer, it has been possible generate the

shortest pulse; its pulse width was 68 fs. This could be accomplished by a solid

state laser (gain medium Er/Yb:Glasss) whose SA was fabricated by spin-coating a

polymer doped with SWCNTs onto commercial dielectric laser-mirrors [2.75]. The

main drawback of these SAs is their low optical damage threshold. An alternative

possibility of designing SA appeared when the devices interact with the

evanescence field. Using this approach, the interaction length between electrical

field and SWCNTs is larger and the optical output power of the laser is bigger. This

can be achieved by making tapers (covering with polymer or by spraying the

nanotubes) [2.56], [2.82], deposition of carbon nanotubes around microfiber

[2.55], D-shaped fibers [2.69], [2.83], hollow optical fibers [2.53], injecting

SWCNTs solution in the core of an optical fiber [2.54], and special deposition

[2.84]. The fabrication methods are stringent and special equipment is needed to

implement one of this SAs. The interaction of the evanescence field with the

SWCNTs has generated the highest peak power, up to now. The peak power of the

taper fiber laser configuration was 2.933 kW [2.56] and for the D-shape fiber laser

was 6.5 kW [2.83].

It has been shown that mode-locked laser based on SWCNTs can produce

short pulses with high peak power, but also the repetition rate is important for

fiber optical communication. Hence, short cavity laser were developed to generate

pulses at frequencies of giga-hertz [2.66] - [2.68]. So far, the highest repetition

rate that has been generated is 19.45 GHz by using a cavity length of 5 mm

[2.68]. The laser operation is based on a fiber Fabry-Pérot cavity which has a

38

partial reflecting mirror covered by SWCNTs as a SA. Up to my knowledge, this

configuration is one of first commercial lasers based on SWCNTs; this laser emits

at telecommunication frequencies (1550 nm) and it is so compact that can fit in

the hand palm.

2.5 Q-switching

2.5.1 General description

Q-switching is a technique used to generate energy short pulses whose width is

usually nanoseconds, by modulating intracavity losses. This produces that the Q

factor of the laser resonator also changes. For this reason this technique receives

the name Q-switching. The Q factor can be defined as 2 times the ratio of the

stored energy to the energy dissipated per oscillation cycle and it can be write as

2Q E E where E is the energy stored in the resonator and E is the

energy lost on each cycle. The basic principle of operation of a Q-switching laser

can be described as follow: a laser pumping process is used to build up a large

population inversion inside the laser cavity; whereas the cavity losses are high (this

prevents the laser oscillations). After a large inversion has been developed,

suddenly the resonator losses are minimized generating an energy short pulse.

After a strong pulse, the high initial inversion drop back to a low level until the

next pulse stars to grow again. Many applications require Q-switched lasers that

emit nanosecond pulses with high energies such as in medicine, light detection,

nonlinear frequency conversion, optical time domain reflectometry (OTDR), and

material processing. Two methods to achieve Q-switching will be discussed in the

next section, the active and the passive.

39

2.5.2 Active Q-switching

Active Q-switching is performed by modulating the quality factor Q of the laser

cavity using typically bulk components, as electro-optic [2.85], acusto-optic

modulator [2.86], and rotating mirror [2.1]. The last method suffer from a lot of

disadvantages such as uncertain timing, slow switching speed, lack of reliability,

and vibration and mechanical noise. Electro-optic and acousto-optic modulators are

fast and they can improve the laser performance but bulk components need a fine

alignment and a good mechanical stability which make them impractical laser

devises.

Recently, different modulation techniques using all fiber lasers have been used

to implement Q-switched lasers, as all fiber intensity modulator [2.87], all fiber

acousto-optic attenuators [2.88], [2.89], all fiber lasers by tuning two FBG’s using

piezoelectric [2.90], magnetostrictive transducers [2.91], and by utilizing a Bragg

grating-based acousto-optic modulator (BG-AOM) [2.92].

The fundamental dynamics of an active Q-switched laser are shown

schematically in Fig. 2.17. The cavity losses are set at high value (low Q), when

the modulator does not allow the laser oscillates, while the pumping laser store

energy (by the inversion of the population) which increases the gain, Fig. 2.17.

When the modulator allows laser oscillations, the cavity losses are low (high Q); an

energy short pulse grows from spontaneous emission and gathers the energy

stored in the cavity (the inversion of population is depleted by this). Then, the

cavity losses are high when the modulator does not allow laser oscillations again.

40

Fig. 2.17 Schematic illustration of the Q-switching process.

2.5.3 Passive Q-switching

Passive Q-switching can be generated by placing a SA inside the laser cavity.

Several kinds of SAs have been used as crystalline materials Co2+:ZnS [2.93],

Co2+:ZnSe [2.94], semiconductor compounds [2.95], and semiconductor saturable

absorber mirrors (SESAM) [2.96]. Lately, doped fiber has been used as SA to

generate Q-switching pulses in all fiber lasers [2.97], [2.98].

We are going to show a simple derivation of relevant parameters of passively

Q-switching lasers. Let’s consider a gain medium (inside a laser cavity) whose

length is gL to provide a time-dependent round trip intensity gain coefficient g t ,

a SA with a saturable loss coefficient q t (unbleached value 0q and bleached

value 0); and output coupler with transmission outT and output coupling

coefficient outl , defined by 1 exp( )out outT l ; and a nonsaturable loss pl . The

total nonsaturable loss coefficient per round trip is out pl l l . The saturation

41

energy of the absorber AE is assumed to be small compared with the saturation

energy of the gain medium LE [2.99].

The stored energy in the pumped gain material is proportional to the excitation

density 2N , the photon energy Lh at the lasing wavelength, and the pumped

volume gAL [2.99]:

2stored g LE AL N h . (2.23)

The intensity gain coefficient per round trip is 22 L gg N L , in a standing wave

cavity, where L is the emission cross section of the laser material. This can be

rewrite as [2.99]

2L

stored LL

hE Ag E g , (2.24)

with the saturation energy LE of the laser medium given by [2.99]

2L

LL

hE A . (2.25)

If a Q-switched pulse reduces the gain by [2.99]

i fg g g , (2.26)

where ,i fg are the intensity gain coefficient just before and after the pulse. It

releases the energy released LE E g . The output pulse energy can be obtained by

multiplying the released energy with the output coupling efficiency [2.99]:

outp L L i

out p

lE E g E g

l l. (2.27)

Since ig g , the quantity L iE g is an upper limit for the attainable pulse

energy. To determine g is necessary to solve the rate equation, but an easy

42

solution can be obtained by considering four different phases of a Q-switched

pulse cycle.

a) In the first phase the absorber is in its unbleached state. The pulse stars

to develop when the gain is equal to the unsaturated value of the losses

[2.99]:

0ig l q . (2.28)

The power in the cavity begins from spontaneous emission noise and it

keeps growing until it is big enough to bleach the absorber.

b) In the second phase, the SA is fully bleached and the power grows

quickly until the gain starts to be depleted (net gain 0ig l q q with

0q ). The pulse maximum is reached when the net gain is zero, i.e.,

g l [2.99].

c) In the third phase, the power inside the cavity decays due to depletion

of the gain but the pulse extracts energy in this phase.

d) In the fourth phase, the absorber recovers its unbleached state and the

gain increases its value by the pumping.

The first phase starts all over again when the gain is equal to the threshold level. A

schematically illustration of the gain, loss and power in a passively Q-switched

laser cavity is shown in Fig. 2.18. For large output coupling ratios 0l q the gain

difference can be expressed by [2.99]:

02g q . (2.29)

Inserting Eq. (2.29) into Eq. (2.27) we obtain an expression for the pulse energy:

0 02 , .

2outl

pl out p

lhE A q l q

l l (2.30)

Both the gain ( g ) and the pulse energy can be increased by increasing 0q and

l . Nonetheless, the available gain limits the value of 0ig l q [2.99]. Moreover,

43

the parasitic losses increase with the increase in the modulation depth. Optimized

pulse energy can be achieved for values of l close to 0l q , for a SA with

nonsaturable loss.

Fig. 2.18 Evolution of power, gain and loss in a passively Q-switched laser [2.99].

The repetition rate of the Q-switched laser can be derived by dividing the

average output power by the output pulse energy [2.99]. The average power can

be written as ,av s P P thP P P , where PP is the pump power, ,P thP is the

threshold pump power, and s is the slope efficiency. The repetition rate is given

by [2.99]:

,

1s P P th

repP

P Pf r

E, (2.31)

where r is defined as the ratio of the pump power to the threshold pump power.

The pump power and the threshold power can be written as [2.99]:

0 0, .

2 2

p pP th

l L p l L p

h A h AP g P l q (2.32)

44

Here ph is the pump photon energy, p is the pumping efficiency, and L is the

upper state life-time of the gain medium. Inserting Eq. (2.27) and Eq. (2.32) into

Eq. (2.31) and using Eq. (2.29), the repetition rate can be expressed as [2.99]:

0 0 0 0

02rep

L L

g l q g l qf

g q. (2.33)

The repetition rate can also be estimated (at pump power well above the

threshold) by relating it to the ratio of absorbance pump power and absorbed

threshold pump power [2.100]

,

,

p abs

abs thresh L

Pf

P, (2.34)

where ,p absP is the total amount of the pump power absorbed with the lasing

mode volume, and ,abs threshP is the pump power required for reaching the

threshold inversion density. The last expression shows that the repetition rate

depends linearly on pump power assuming traditional theory.

So far, all the analysis that has been presented here is based on the theory of

microchip laser [2.99], where it is assumed low duty cycle and constant inversion

in a short cavity. In contrast, fiber lasers have higher duty cycle and longer cavity

lengths with large gain; the description of these cavities should be done by taking

into account more consideration. In 2008, a paper that describes passively Q-

switched fiber laser was published [2.101].

The saturation of the gain g in a Q-switched laser can be described by the

rate equation [2.101]:

0

,

,g sat g

dg t g t g gP t

dt E (2.35)

and the saturable absorption q can be found from a similar equation [2.101]:

0

,

,a sat a

dq t q t q qP t

dt E (2.36)

45

where ,sat gE and ,sat aE are the saturation energies and g and a the recovery

times for the saturable gain and loss, respectively. The temporal evolution of the

intracavity power P is given by [2.101]:

,r

dP Pg l q

dt T (2.37)

where rT is the cavity round-trip time. If the gain recovery is shorter than the time

between pulses and is long enough to let the SA saturated by the Q-switched

pulse, the recovery time of the absorber does not play an important role [2.101].

In this analysis two cases are going to be considered, when the system operates

near the threshold ( 0 0g q l ) and when the system operates far above the

threshold ( 0 0g q l ). The former correspond to a similar case that has been

analyzed; see Fig. 2.18 and Fig. 2.19 (a). The latter occurs by a strong pumping

which causes that the gain reaches a gain value above 0q l and then it

decreases to a value lower than 0q l , compare Fig. 2.18 with Fig. 2.19 (b).

Fig. 2.19 Schematic illustration of the temporal evolution of the cavity gain/loss and the output power during Q-switched laser pulse formation (a) close to lasing threshold, (b) far above the

lasing threshold [2.101].

46

During the gain recovery stage, between consecutive pulses, the intracavity

power is too small to cause any gain saturation. From Eq. (2.35) the gain can be

evaluated with 0P t [2.101]:

0 0 0exp ,gg t l q g t g (2.38)

assuming an unbleached saturation absorber. Here the gain reaches 0l q at the

time 0t (dashed line in Fig. 2.19 (b)). At the time 0t the pulse power starts

to develop from noise level 00P t P . When the pumping is above threshold,

the gain increases to reaches the value 0 ,sat g gg E . When the gain 0g is close to

the threshold gain, the gain recovers to 0g l q [2.101]. On the other hand,

when the gain is much higher than the threshold gain, the gain recovers to a much

higher value [2.101]. The intracavity power during gain recovery is [2.101]:

2 0 00exp 0.5

g r

g l qP t P t

T. (2.39)

Using this equation it is possible to express the time needed for the gain to be

recovered from the threshold value to the onset of the gain saturation when

0 ,sat g gP t g E [2.101]:

0 ,

0 0 0

2log

g r sat g

g

T g Et

g l q P. (2.40)

At this time the gain has recovered to the value [2.101]

0 ,0 0 0

0

2 logsat gr

ig g

g ETg l q g l q

P. (2.41)

47

Using the expression log 1 0ig l g g [2.99], that gives the gain

reduction during the Q-switching process; it is possible to evaluate the total gain

variation [2.101]:

,0 0 0 0

0

2 2 2 log 2 1sat gr

thresholdg g

ET Pg q g l q q APP

, (2.42)

with [2.101]

, 00

0 0

2 log , .sat gr

g g threshold

E gT PA l q

P P l q (2.43)

Using Eq. (2.42) the pulse energy and the repetition rate expression can be rewrite

for a passively Q-switched fiber laser. Let’s remind ourselves that the pulse energy

is given by ,released sat gE E g and the repetition rate is given by Eq. (2.33). It is

easily to realize that the pulse energy (as well as the output power) depends on

the pump power in contrast to the nearly constant pulse energy obtained using the

near-threshold (low duty cycle) analysis [2.101]. Moreover, the repetition rate also

depends on the pump power. It is also possible to derive an equation that evaluate

the pulse duration and it is [2.101]:

7.04 rT

g. (2.44)

From Eq. (2.44) we can realize that the pulse duration is directly proportional

to the cavity-round trip, which means longer pulse duration for longer cavities and

shorter pulse duration for shorter cavities [2.101].

48

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60

Chapter 3 Fabrication process and nonlinear

absorption measurements of PDMS/SWCNT and SU8-2075/SWCNT

films as SA

3.1 Introduction

This chapter has two main objectives; the first is to describe the fabrication

process of SA films based on polymers doped with SWCNTs. The second is to

characterize the nonlinear optical properties of these films by implementing an all-

fiber power dependent transmission setup.

One way to assembly a SA is by placing a thin film doped with SWCNTs

between two fiber connectors. The first polymer used to implement this kind of

SAs was polyvinyl alcohol (PVA) [3.1], but this film suffers from OH absorption loss

because water must be used as a solvent to disperse them. This becomes

disadvantageous for a thick film or a waveguide with a large optical path length.

Other polymer that have shown good results are carboximethyl cellulose (CMC)

[3.2], dimethylformamide (DMF) [3.3], polymide [3.4], and poly-3-hexylthiophene

(P3HT) [3.4], [3.6]. On the other hand, by using two fiber collimators and by

putting a film doped with SWCNTs between them it is possible to obtain a SA. This

technique has been implemented by using polymers such as

polymethylmethacrylate (PMMA), polystyrene (PS) [3.7], and polycarbonate (PC)

[3.8]. Moreover, in order to have a smooth surface these three films need to be

polished. Since the thickness of the PMMA and PS films were 1 mm, it was not

possible to set the film between two fiber connectors. The use of fiber collimator

requires alignment and the system is no robust again mechanical vibration.

61

In this work, we purpose to fabricate thin films of PDMS and SU8-2075 doped

with SWCNTs and then these films are set between two fiber angle connectors in

order to assembly a SA. The fabrication process of the two films is simple and does

not require expensive material or special equipment. In the case of the PDMS

films, either the PDMS polymer or materials used to fabricate the film (such acrylic

layers) are cheap, and good results can be obtained. In the case of SU8-2075 film,

given the functionality of this polymer for integrated devices, we believe that this

material could be very useful for the development of integrated non-linear devices

for different photonic applications.

3.2 SWCNTs as a Saturable Absorber

Among the different properties that make SWCNTs highly attractive is that their

energy bang gap varies inversely with the nanotubes diameter [3.9]. Therefore, if

the diameter of the nanotubes is properly selected they will operate at a specific

wavelength. Using this property, SAs operating from 1035 nm to 1600 nm have

been developed [3.10]. Since we are interested in working at a wavelength around

1550 nm, we chose the diameter of the SWCNTs from 0.8 to 1.2 nm. The SWCNTs

were purchased from the company Unidym and they were synthesized by high-

pressure CO (HiPCO) method.

Since we are interested in fabricating a SA as a thin film using PDMS and SU8-

2075 doped with SWCNTs, the most important issue is the absorption of the films.

The absorption of the films is directly related with the concentration of the

SWCNTs and the thickness of the films. If the concentration of SWCNTs is too

high, the nanotubes tend to bundle and such effect degrades their nonlinear

response (losses by scattering). This also increases the absorption of the film and

the composite can be damaged very easily. If we let a fix concentration and we

modify the thickness of film we can control the absorption value, but there is a

limit on the maximum film thickness that can used without compromising higher

losses due to diffraction. Therefore, finding an optimum concentration of SWCNTs

62

and the adequate thickness is the first step in the process of the fabrication of our

thin films. Based in our experiments we found that a good concentration for the

SWCNTs is 0.125 wt% and the thickness can be from 100 μm to 200 μm. This

optimum concentration value is very similar to the reported in a recent publication

which provides optimum mode-locked operation [3.11].

3.3 Fabrication process of thin films using

SWCNTs

3.3.1 Fabrication of PDMS/SWCNT thin films

Polydimethylsiloxane (PDMS) belongs to a group of polymeric organosilicon

compounds that are commonly referred to as silicones. PDMS has been used in

several optical applications such as lens fabrication, micro-fluidic devices,

waveguides, as a polymer to fill specialty fibers, etc. This material has also been

used to implement a SA but in a tapper configuration [3.11]. The main drawback

of such configuration is the need to fabricate a taper and thus the need for special

equipment as well as the problem of reproducibility.

In order to fabricate a thin film of PDMS doped with SWCNTs, a new and

simple process was developed. A critical issue when mixing carbon nanotubes with

a polymer is to achieve a well dispersed solution. The formation of bundles of

SWCNTs in the polymer matrix is detrimental for the nonlinear optical absorption,

which is the fundamental phenomenon to create a SA device [3.13]. In order to

fully disperse the SWCNTs, rather than mixing the nanotubes directly in the

polymer, we first disperse them in the polymer solvent. Since the solvent for PDMS

is chloroform, the SWCNTs were dispersed in chloroform and the suspension was

sonicated during 30 minutes. The concentration of SWCNTs was selected at 0.125

wt% for optimum operation of the film. After the nanotubes are fully dispersed

PDMS was slowly added to the solvent, and the new mixture was placed in the

63

ultrasonic bath and on the stirring machine for 2 hours and 3 hours, respectively.

Twenty percent of the solution weight is chloroform and eighty percent of the

solution weight is PDMS. After that, we add ten percent of the total solution weight

of the curing agent for the PDMS. Curing of the PDMS is obtained by an

organometallic cross-linking reaction to give an optically transparent polymer.

The fabrication process of PDMS/SWCNT film is described in Fig. 3.1. Two

acrylic layers were used to fabricate a cell whose thickness depends on the spacers

between them.

Fig. 3.1 Schematic representation: (a) two acrylic layers and the spacer between them. (b) Lateral view of the cell fill up with PDMS/SWCNT.

Acrylic material is used instead of any other material because PDMS doped with

SWCNTs does not stick to it. The PDMS/SWCNT solution was poured into the cell

and it was cured by heating up the sample at 95 ºC for one hour and then we let it

rest for 24 hours. After this process the cell can be separated and the resulting film

is equal to the thickness of the spacer, with very smooth surfaces. Using this

method, the thickness of PDMS/SWCNT films can be controlled accurately by

simply changing the thickness of the spacers. The thickness of the film was 200

μm.

64

3.3.2 Fabrication of SU8-2075/SWCNT thin films

The SU8 material has the advantage that is a well-known and inexpensive material

employed for micro-fabrication. Additionally, since SU8 is a photosensitive material,

its potential application on integrated waveguide devices provides a nice ground

for their study. The fabrication process of the SU8/SWCNT films requires few and

very simple steps to achieve well dispersed SWCNTs, and also the film thickness

can be accurately controlled.

In order to avoid bundle formation, the SWCNTs were first dispersed in the

solvent of SU8-2075 (Cyclopentanone) and this suspension was sonicated for 30

minutes. After the nanotubes are fully dispersed, SU8-2075 was added slowly to

the solution and the new mixture was placed in the ultrasonication bath and in the

stirring machine for 2 hours and 3 hours, respectively. The mixture of SU8-2075

and cyclopentanone was made by using 4 ml and 1 ml, respectively. SWCNTs were

incorporated in order to maintain a concentration of 0.125 wt%. The simplest way

to implement a SA with this composite is by making a thin film that can be placed

between two angled fiber connectors. To accomplish this task a technique was

developed to fabricate thin films using the SU8-2075/SWCNT mixture. The

technique requires inexpensive materials that help us to make cells whose

thickness can be controlled by changing the spacer thickness. First we made a

solution of PDMS polymer (Polydimethylsiloxane) which is mixed with ten percent

of the curing agent from the total PDMS weight. At the same time we cut two

glasses (microscope slide) and on top of them we deposited a layer of PDMS by

spin coating, see Fig. 3.2(a). The spin coater was operated at 2000 rpm for 30

seconds. After that, the glasses were heated on a hot-plate at 95 ºC for one hour.

Two spacers were placed between the two PDMS layers as shown in Fig. 3.2(b).

The PDMS material on the glass helps to peel-off the cured composite material

very easily without any complex procedure, while maintaining polished surfaces.

65

Fig. 3.2 Schematic of the cell fabrication process: (a) Deposition of a PDMS layer on a glass

substrate. (b) Thickness and position of the spacers on the cell.

The SU8-2075/SWCNT solution was poured into the cell and the solution was

cured according to the specification of the SU8-2075 polymer taking into account

that the film thickness was 100 µm, see Fig. 3.3. In order to cure the SU8-

2075/SWCNT, first the cell requires a prebake step on a hot-plate at a temperature

of 65 ºC for 2 min. After the pre-bake we let the cell cool down for 5 min, and we

put the cell at 95 ºC for 5 min. The cell was exposed to UV light using a KarlSuss

mask aligner during 50 sec (exposure energy 240 mJ/cm2). After the UV exposure,

the cell was heated at 65 ºC for 2 min and immediately heated at 95 ºC for 6.5

min. After this process we let the cell rest for one day. The cell was separated to

obtain a film whose thickness was equal to the thickness of the spacer (100 μm in

this case). It should be worth mentioning that the cell thickness can be easily

controlled by changing the spacer thickness.

66

Fig. 3.3 Lateral view of the cell with SU8-2075/SWCNT.

3.3.3 Implementation of a saturable absorbers by

using a PDMS film and a SU8 film

Both PDMS and SU8-2075 films were cut and placed between two FC/APC

connectors in order to have an all-fiber SA device. For accomplishing this task, first

an angle connector was screwed in a sleeve; meanwhile, a small section of the film

(PDMS or SU8-2075) was cut and placed in the tip of another angle connector

which was screwed latter in the other end of the sleeve, see Fig. 3.4. Index

matching liquid was not used because the FC/APC connectors suppress reflections.

This configuration shows to be easily assembled and does not need a special

alignment which makes it a sturdy device. Moreover, this technique used to

assembly a SA is free of any complex procedure and any expensive special

equipment. However, one drawback is always present in this configuration and is

related to the coupling losses due to non-physical contact between the connectors.

When the light travels through the film, it diffracts causing a coupling loss between

connectors. As the sample became thicker the coupling loss is bigger. For the

PDMS film whose thickness is 200 μm, the coupling loss was estimated to be -1.5

dB and for the SU8-2075 films whose thickness is 100 μm, the coupling loss was

estimated to be -1.2 dB.

67

Fig. 3.4 Implementation of a SA using either a PDMS/SWCNT or a SU8-2075/SWCNT film.

3.4 Characterization of Saturable Absorber

3.4.1 Methods to characterizer a Saturable Absorber

Z-scan technique is a wide used method in nonlinear optics to measure the

nonlinear refractive index and non-linear absorption coefficient. The technique

consists in moving a sample along the waist of a Gaussian beam with the main

goal of varying the laser-power density on the sample, which reaches its maximum

at the focal point. An analysis of the transmitted beam through the sample as a

function of the sample position, Z, is carried out either in the open or in the close-

aperture scheme. Open-aperture Z-scan is used for the investigation of processes

associated with nonlinear absorption, while close-aperture Z-scan is used to

investigate nonlinear refraction [3.14].

3.4.2 Measurement of the nonlinear absorption of the

saturable absorber

The implementation of an all-fiber power dependent transmission setup is feasible

by means of a pulsed laser, an optical attenuator, a polarization controller, an

optical coupler and a power meter, see Fig. 3.5. A commercial mode-locked fiber

68

laser (MenloSystems, Optical Frequency Synthesizer FC1500-250) with a pulse-

width of 150 fs and a repetition rate of 250 MHz was used. The optical attenuator

plays an important function in this setup because it gives us the capability of

changing the average optical power that is hitting the sample (in this case we are

unable to change the spot size of the beam that hits the sample as in a Z-scan

technique). Furthermore, by playing with the polarization controller we can obtain

the maximum absorption from the film (the film exhibited a slight polarization

dependence). The light is split by an optical coupler and 10% of light is directly

detected with a photo-detector to obtain the input average power, while 90% is

sent through the film. Using these two power measurements; power dependent

transmission of the film can be calculated.

The nonlinear absorption can be determined accurately by using a laser pulse

whose pulse duration is narrower that the recovery time of the material. Since the

recovery time of the SWCNTs has been measured to be less than 1 ps [3.15],

pulses on the order of 150 fs are more than enough to charactize the composite

films. By using the setup shown in Fig. 3.5, we sent pulses of 150 fs at a repletion

rate of 250 MHz without any additional dispersion compensation. The maximum

output power of the laser is 10 dBm, but to characterize the PDMS and SU8-2075

films it was not necessary to apply so much power because the peak power

achieved by the laser at low power was enough to saturate the samples.

Fig. 3.5 All fiber power dependence transmission setup. PC: Polarization Controller; VOA: Variable Optical Attenuator.

69

In the nonlinear optics literature there are several different ways to report the

data from the power dependent transmission setup. The way of the data are

plotted gives specific information regarding the performance of the device that can

be useful for some experimental configuration [3.16]. Fig. 3.6 and Fig. 3.7 show

four different ways of plotting the data for illustration propose. Extracting the most

important parameters that characterize a SA is easily done by plotting the

normalized absorption as a function of the peak intensity; see Fig. 3.6 (c) and Fig.

3.7 (c).

-18 -16 -14 -12 -10 -8 -6 -4 -2 01.6

1.7

1.8

1.9

2.0

2.1

2.2

0.45dB

De

vic

e l

oss (

dB

)

Input average power (dBm)

0 5 10 15 20 25 30 35 4059

60

61

62

63

64

65

66

67

68

69

0 = 7%

Tra

nsm

issio

n (

%)

Input peak intensity (MW/cm2)

(a) (b)

0 5 10 15 20 25 30 35 40

0.81

0.84

0.87

0.90

0.93

0.96

0.99

1.02

Isat = 2.4 MW/cm2

No

rma

lize

d A

bso

rpti

on

Input peak intensity (MW/cm2)

0 = 16.5%

ns

= 83.5%

0 1 2 3 4 5 60.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

No

rma

lize

d A

bso

rpti

on

Fsat

= 0.27 m J/cm2

0

= 16.5%

Input Fluence (m J/cm2)

(c) (d)

Fig. 3.6 PDMS/SWCNT film (200 μm). (a) Device loss as function of input power (dB); (b) Transmission vs. input peak intensity; (c) Normalized absorption vs. input peak intensity; (d)

Normalized absorption vs. input intensity.

70

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -81.40

1.45

1.50

1.55

1.60

1.65

1.70

1.75

De

vic

e l

oss (

dB

)

Input average power (dBm)

0.22 dB

0 5 10 15 2067.0

67.5

68.0

68.5

69.0

69.5

70.0

70.5

71.0

71.5

72.0

Tra

nsm

issio

n (

%)

Input peak intensity (MW/cm2)

3.4%

(a) (b)

0 5 10 15 200.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

ns

= 90%

Isat = 0.7 MW/cm2

0 = 10 %

No

rma

lize

d A

bso

rpti

on

Input peak intensity (MW/cm2)

0.0 0.5 1.0 1.5 2.0 2.5 3.00.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

0 = 10 %

Fsat = 91.26 pJ/cm2

No

rma

lize

d A

bso

rpti

on

Input Fluence (m J/cm2)

(c) (d)

Fig. 3.7 SU8-2075/SWCNT film (100 μm). (a) Device loss as function of input power (dB); (b)

Transmission vs. input peak intensity; (c) Normalized absorption vs. input peak intensity; (d)

Normalized absorption vs. input intensity.

Combining equations (2.21) and (2.22) we obtain

0( ) ,1

ns

sat

II

I

(3.1)

71

where ( )I is the intensity-dependent absorption, 0

is the modulation depth, and

satI is the saturation intensity. It is easy to realize that the nonsaturable absorption

is a percentage of the linear absorption and the saturable absorption is equivalent

to the modulation depth.

The PDMS film was the first to be tested in the setup of Fig. 3.5. In Fig. 3.6 (a)

we plotted the device loss as a function of input average power. The linear loss for

the PDMS film is 2.15 dB. As shown in Fig. 3.6 (a), when the input power start

increasing the device loss starts to decrease. The device loss is reduced by an

approximate value of 0.45 dB. On the other hand, the transmission is incremented

by 7% and it is easily noticed in Fig. 3.6 (b). Additional information can be taken

out from Fig. 3.6 (c), where the saturation intensity is 2.4 MW/cm2, the modulation

depth is 16.5% and the nonsaturable absorption is 83.5%. Fig. 3.6 (d) shows how

the normalized absorption changes as the input fluence (pulse energy per unit

surface area) is increased. We obtain a saturation fluence of 0.27 μJ/cm2.

The SU8-2075 film was also tested in the setup of Fig. 3.5. In Fig. 3.7 (a) we

plotted the device loss as a function of input average power. The linear loss for the

SU8-2975 film is 1.67 dB. As shown in Fig. 3.7 (a) the device loss is reduced by

approximately 0.22 dB when the input average power is increased. Also shown in

Fig. 3.7 (b) is the transmission which is incremented by 3.4% as the peak intensity

is incremented. The saturation intensity is 0.7 MW/cm2, the modulation depth is

10% and the nonsaturable absorption is 90% can be extracted from Fig. 3.7 (c).

Finally, the normalized absorption changes as a function of the input fluence is

shown in Fig. 3.7 (d), which provides a saturation fluence of 91.26 pJ/cm2.

F. Wang et al. developed a film doped with SWCNTs using a (P3HT) and they

determined its optical properties by using an all-fiber power dependent

transmission setup [3.6]. They reported that the saturation intensity, the

modulation depth and nonsaturable absorption are 5.1 MW/cm2, 12.3% and

87.5%, respectively. Making a comparison between these optical properties and

the properties reported here, we can say that saturation intensity of the PDMS’s is

72

lower by 2.7 MW/cm2, the modulation depth of the PDMS is higher by 4.2% and

the nonsaturable absorption of the PDMS is lower by 4% than their film. In the

case of the SU8-2075 film, it has lower saturation intensity and modulation depth

and higher nonsaturable absorption. However, the optical properties of these two

films are as good as the ones reported by F. Wang. Moreover, as we mentioned at

the beginning, the fabrication process of these two films are inexpensive and does

not require especial equipment.

3.5 Summary

The main goal of this chapter was to show special features of the SWCNTs that

should be taken into account when choosing the nanotubes for a SA. A description

of the fabrication process and how to assembly a SA are shown. Furthermore, it is

shown how to measure the nonlinear absorption by using an all-fiber power

dependent transmission setup. The PDMS/SWCNT film has a big modulation depth

16.5%, which is good for stabilizing the cavity pulses [3.11]. On the other hand,

although the SU8-2075/SWCNT film has a lower modulation depth (10%), this

should be good enough for implementing a SA. Since we used the same

concentration of SWCNTs in both samples, this low modulation depth is due to the

film thickness.

3.6 References

[3.1] A. G. Rozhin, Y. Sakakibara, S. Namiki, M. Tokumoto, H. Kataura, and Y.

Achiba, “Sub-200-fs pulsed erbium-doped fiber laser using a carbon

nanotube-polyvinylalcohol mode locker,” Appl. Phys. Lett. 88, 051118

(2006).

[3.2] A. V. Tausenev, E. D. Obraztsova, A. S. Lobach, A. I. Chernov, V. I.

Konov, P. G. Kryukov, A. V. Konyashchenko, and E. M. Dianov, “177 fs

erbium-doped fiber laser mode locked with a cellulose polymer film

73

containing single-wall carbon nanotubes,” Appl. Phys. Lett. 92, 171113

(2008).

[3.3] K. Kashiwagi, S. Yamashita, and S. Y. Set, “Optically manipulated

deposition of carbon nanotubes onto optical fiber end,” Jpn. J. Appl.

Phys. 46, L988-L990 (2007).

[3.4] N. Nishizawa, Y. Seno, K. Sumimura, Y. Sakakibara, E. Itoga, H.

Kataura, and K. Itoh, “All-polarization-maintaining Er-doped ultrashort-

pulse fiber laser using carbon nanotube saturable absorber,” Opt.

Express 16, 9429-9435 (2008).

[3.5] F. Shohda, T. Shirato, M. Nakazawa, J. Mata, and J. Tsukamoto, “147

fs, 51 MHz soliton fiber laser at 1.56 μm with a fiber-connector-type

SWCNT/P3HT saturable absorber,” Opt. Express 16, 20943-20948

(2008).

[3.6] F. Wang, A. G. Rozhin, V. Scardaci, Z. Sun, F. Hennrich, I. H. White, W.

I. Milne, and A. C. Ferrari, “Wideband-tunable, nanotube mode-locked,

fiber laser,” Nat. Nanotechnol. 3, 738-742 (2008).

[3.7] M. Nakazawa, S. Nakahara, T. Hirooka, and M. Yoshida, “Polymer

saturable absorber materials in the 1.5 μm band using poly-methyl-

methacrylate and polystyrene with single -wall carbon nanotubes and

their application to a femtosecond laser,” Opt. Lett. 31, 915-917 (2006).

[3.8] F. Shohda T. Shirato, M. Nakazawa, K. Komatsu, and T. Kaino, “A

passively mode-locked femtosecond soliton fiber laser at 1.5 μm with a

CNT-doped polycarbonate saturable absorber,” Opt. Express 16, 21191-

21198 (2008).

[3.9] H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka,

and Y. Achiba, “Optical properties of single-wall carbon nanotubes,”

Synth. Met. 103, 2555-2558 (1999).

74

[3.10] T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and

A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,”

Adv. Mater. 21, 3874-3899 (2009).

[3.11] J. C. Chiu, Y. F. Lan, C. M. Chang, X. Z. Chen, C. Y. Yeh, C. K. Lee, G. R.

Lin, J. J. Lin, and W. H. Cheng, “Concentration effect of carbon

nanotube based saturable absorber on stabilizing and shortening mode-

locked pulse,” Opt. Express 18, 3592-3600 (2010).

[3.12] K. Kieu and M. Mansuripur, “Femtosecond laser pulse generation with a

fiber taper embedded in carbon nanotube/polymer composite,” Opt.

Lett. 32, 2242-2244 (2007).

[3.13] H.W. Lee, J. H. Yim, A. J. Kiran, I. H. Baek, S. Lee, D.-I. Yeom, Y. H.

Ahn, K. Kim, J. Lee, H. Lim and F. Rotermund, “Bundling influence on

ultrafast optical nonlinearities of single-walled carbon nanotubes in

suspension and composite film,” Appl. Phys. B 97, 157-162 (2009).

[3.14] E. W. Van Stryland, M. Sheik-Bahae, in Characteristics techniques and

tabulations for organic nonlinear optical materials (Eds: M. G. Kuzy, C.

W. Dirk, Marcel Dekker, New York, 1998).

[3.15] J-S. Lauret, C. Voisin, G. Cassabois, C. Delalande, P. Roussignol, O. Jost,

and L. Capes, “Ultrafast carrier dynamics in single-wall carbon

nanotubes,” Phys. Rev. Lett. 90, 057404 (2003).

[3.16] F. Wang, Single-wall carbon nanotubes – polymer composites as

saturable absorber for ultrafast mode-locked fibre lasers, Ph. D Thesis,

University of Cambridge, 2008.

75

Chapter 4

Passively mode-locked Erbium fiber laser using PDMS/SWCNT and

SU8/SWCNT films as SA

4.1 Introduction

Compact sources of short pulses with high-repetition-rates are highly desirable for

a wide range of applications such as optical communication, metrology systems,

and optical clocks. Passively mode-locked fiber lasers are preferred to generate

short pulses rather than active mode-locked lasers, since they do not need

expensive modulators as mode-locker devices and the pulse quality is better. A SA

is an essential optical device that a passive mode-locked laser should have in order

to produce short pulses. It is well known that a SA works like an optical

discriminator introducing large loss to low intensities but low loss to high

intensities. Different kinds of these devices exist, but the most common is the

semiconductor SA whose fabrication process requires sophisticate equipment and a

clean room environment. During the last ten years, SAs based on SWCNTs have

been implemented and they generate picosecond and femtosecond pulses. The

key issue has been how to incorporate the SWCNTs in the laser cavity. This has

been solved by mixing the nanotubes with a polymer, and the solution can then be

cured to achieve a solid material with SWCNTs incorporated into the polymer. The

SA can now be placed in a laser cavity using several fiber laser configurations. The

process of fabricating thin film doped with SWCNTs is the simplest way to

implement a SA that interacts directly with the electric field [4.1] - [4.3]. We can

also have the interaction of the evanescent electric field with the nanotubes by

making tapers (covering with polymer or by spraying the nanotubes) [4.4], [4.5],

76

deposition of carbon around microfiber [4.6], D-shaped fibers [4.7], hollow optical

fibers [4.8], and special deposition [4.9]. Even when evanescent field devices show

good results, a stringent fabrication process has to be developed to accomplish an

adequate nonlinear interaction length. Moreover, all the techniques mentioned

above require special equipment and materials to obtain stable optical pulses.

In this chapter two passively mode-locked fiber lasers are implemented by

using both PDMS/SWCNT and SU8-2075/SWCNT films as a SA. The advantages of

building these lasers are the simple steps to fabricate the films, the process of

fabrication does not need special equipment or material (low price of the material),

their robustness (no systems of lenses and no special alignment is required), and

the quality of the optical pulses. We should be mention that PDMS doped with

SWCNT has been used before in a tapered fiber configuration [4.4], but having to

produce a taper presents reproducibility issues, or the need of expensive

equipment to obtain consistent tapers. Additionally we have to pay a great deal of

attention in order to optimize the nonlinear interaction length, and to avoid high

nonlinearities and large group velocity dispersion values at the waist of the taper

[4.10]. Speaking about SU8-2075, this is the first time that this polymer has been

used to implement a SA doped with SWCNTs. This polymer is a well-known and

inexpensive material employed for micro-fabrication. Furthermore, since SU8 is a

photosensitive material it has a great potential for the development of nonlinear

integrated waveguide devices.

This chapter is devoted to study how these lasers work at different pump

powers and the output of the laser is also characterized by taking its optical

spectrum, radio frequency spectrum, pulse width, and the average power.

77

4.2 Mode-locked fiber laser configuration

A passively mode-locked fiber ring cavity laser was built using a PDMS/SWCNT film

as a SA. A 3 m long erbium doped fiber (EDF) was used as the laser gain medium

(the peak absorption of the EDF was 94.59 dB at 1530 nm) and a laser diode

operating at 980 nm was used as the pump source via a 980/1550 WDM fiber

coupler. This WDM has an integrated isolator to guarantee unidirectional operation

in the laser cavity. The PDMS/SWCNT SA device was introduced in the fiber ring

laser, as shown in Fig. 4.1. Since the PDMS/SWCNT film exhibits slight polarization

dependence due to the random arrangement of the SWCNTs within the PDMS

polymer matrix, a polarization controller (PC) was inserted in the laser cavity.

Using a 3-dB coupler we extract 50% of the intracavity light while the remaining

50% is launched back into the laser cavity as feedback. For studying laser

dynamics, a 3-dB coupler was used to split the output of the laser into two paths.

One of the 50% ports was connected to an Optical Spectrum Analyzer (OSA ANDO

AQ6317B), while the other 50% port was split by another 3-dB coupler, whose

output ports were connected to a second harmonic generation (SHG

Femtochrome) autocorrelator and a photo-detector with a bandwidth of 16 GHz

(Discovery DSC 40S). Before the light reaches the autocorrelator it was passed

through an Erbium doped fiber amplifier. The electrical signal generated by the

photo-detector was sent to an oscilloscope and to an electrical spectrum analyzer

(RF HP-8566A).

As part of the characterization of the system, Fig. 4.2 shows output power as

function of the current, L-I curve of the pump diode laser.

78

Fig. 4.1 Schematic of the passively mode-locked fiber laser developed by using a PDMS/SWCNT

film between two connectors. WDM: wavelength division multiplexer; PC: Polarization Controller; OSA: Optical Spectrum Analizer; EDFA: Erbium Doped Fiber Amplifier.

0 30 60 90 120 150 180 2100

30

60

90

120

150

180

210

Ou

tpu

t P

ow

er

(mW

)

Pump Current (mA)

Fig. 4.2 Output power vs. pump current.

Before attempting to observe pulsed operation due to the PDMS/SWCNT SA,

the ring laser was first operated using a PDMS film without SWCNTs. As expected

continuous wave (CW) operation was achieved for any pumping power. We also

modified the PC at different pumping levels, and there was no indication of

79

nonlinear polarization rotation mode-locking since there is no polarizing element in

the laser cavity.

4.3 Mode-locked fiber laser results using

PDMS/SWCNT as SA

After placing the PDMS/SWCNT SA in the laser, a pulse train is attained above a

threshold power of 36 mW, this can be observed by a regular train of pulses

detected by the oscilloscope, see Fig. 4.3 (a). This pulse-train has a repetition rate

of 22.73 MHz which corresponds to a cavity length of 8.8 m. The frequency tones

are shown in Fig. 4.3 (b) and the first tone corresponds to the fundamental cavity

frequency as it was expected. The data plotted in Fig. 4.3 was obtained when the

pump power was at 85 mW because at that pump power the shortest pulse was

obtained. This will be explained latter.

0 100 200 300 400

0.00

0.02

0.04

Inte

sit

y (

a.

u.)

Time (ns)

50 100 150 200-80

-70

-60

-50

-40

dB

Frequency (MHz)

(a) (b)

Fig. 4.3 Mode-locked laser output characteristics at a pump power of 85 mW

(a) Pulse train of mode-locked laser; (b) RF tones.

80

From 36 to 90mW of pump power, the laser generated stable pulses which can

be optimized by playing with the PC. This means that shorter pulse width and

more stable train of pulses can be obtained by doing this. Furthermore, it was

noticed that the central wavelength of the laser could be detuned when the PC

was set in different positions; this detuning is approximately 0.5 nm. We believed

that this detuning behavior could be related with the fact that the SWCNTs change

the erbium fluorescent shape.

In order to analyze the dynamics of the laser when different pump powers

were applied, an experiment was done. First, the output of the laser was optimized

by playing with the PC at the pump power of 36 mW, and then the pump power

was increased in steps of 6 mW until it reached 90 mW. This experiment

demonstrates that the central wavelength of the laser is moving to shorter

wavelengths as shown in Fig. 4.4 (a). It is easy to observe that the central

wavelength at a pump power of 36 mW is 1566.71 nm and the central wavelength

at 90 mW is 1565.01 nm. Hence the total shift of the central wavelength is 1.7 nm.

81

Pump Power

36mA 42mA

48mA 54mA

60mA 66mA

72mA 78mA

84ma 90mA

1560 1562 1564 1566 1568 1570 1572-70

-65

-60

-55

-50

-45

-40

-35

-30

dB

m

Wavelength (nm)

(a)

-6 -4 -2 0 2 4 60.0

0.5

1.0

36mA

42mA

48mA

54mA

60mA

66mA

72mA

78mA

84mA

90mA

No

rma

lize

d I

nte

nsit

y (

a.u

.)

Delay Time (ps)

(b)

Fig. 4.4 Mode-Locked laser at different pump powers: (a) Optical spectrum and (b) Autocorrelation

trace.

This shift of the central wavelength must be linked with the changes in the

gain profile due to the combination of power and tubes (SWCNTs have a

broadband absorption spectrum). Moreover, at these different pump powers the

82

pulse-width of the pulses were measured by using the autocorrelator. The pulse-

width of the pulses is obtained after autocorrelation deconvolution of the measured

pulses, as shown in Fig. 4.4 (b), and assuming a sech2 profile. By plotting the

pulse-width and the time-bandwidth product (TBP) as a function of the pump

power we can find the shortest pulse and the minimum TBP, as shown in Fig. 4.5

(a). Additionally, the output power as a function of the pump power was also

plotted in Fig. 5 (b); the saturation behavior observed in this plot is related with

the saturation of the gain medium.

30 45 60 75 900.0

0.5

1.0

1.5

2.0

Pump Power (mW)

Pu

lse

Wid

th (

ps)

0.2

0.3

0.4

0.5

0.6

TB

P

30 40 50 60 70 80 90 1000

2

4

6

Ou

tpu

t P

ow

er(

mW

)

Pump Power (mW)

(a) (b)

1560 1565 1570-70

-60

-50

-40

-30

Wavelength (nm)

dB

m

-6 -4 -2 0 2 4 60.0

0.5

1.0

No

rma

lize

d I

nte

nsit

y (

a.u

.)

Delay Time (ps)

(c) (d)

Fig. 4.5 (a) Output pulse duration and time-bandwidth product at different pump powers, (b) Output power vs. pump power; Laser output characteristics at pump power of 85mW: (d)

Optical spectrum, (c) Autocorrelation trace.

83

We can notice from Fig. 4.4 (b) and Fig. 4.5 (a) that the pulse-width and TBP

are reduced as the pump power increases, until they reach their minimum value at

a maximum power of 85 mW. The optical spectrum of the laser at this pump

power reveals a peak wavelength of 1565.3 nm, with a spectral width at FWHM of

2 nm, as shown in Fig. 4.5 (c). The temporal width of the autocorrelation trace

was 2.23 ps, as shown in Fig. 4.5 (d), which corresponds to a pulse width of 1.26

ps assuming a sech2 pulse profile. This corresponds to a TBP of 0.318, which is

close enough to transform-limited sech2 pulses [4.11].

Using the data that were obtained at a pump power of 85 mW, it is feasible to

calculate the corresponding peak power. The peak power that is inside and outside

the cavity is 161.31 W and the output power is 4.89 mW. Furthermore, the energy

per pulse is 203.26 pJ, the fluence is 404.36 μJ/cm2, and the peak intensity is

320.92 MW/cm2. This peak intensity corresponds to a 134 times the saturation

intensity (2.4 MW/cm2) showed in the last chapter. Although the SA is fully

saturated, it worked for five continuous hours. This PDMS/SWCNT film can deal

with high power which is an important feature in a SA.

4.4 Mode-locked fiber laser results using SU8-2075/SWCNT as SA

Another passively mode-locked fiber ring cavity laser was built using a SU8-

2075/SWCNT film as a SA. The cavity has almost the same elements that the

previous laser, but the cavity length is much longer (the length of the fiber

connectors is longer); see Fig. 4.6 and Fig. 4.1. This variation in length modified

the repetition rate of this laser providing a lower value than the one assembled

with the PDMS/SWCNT SA. The SU8-2075 polymer doped with SWCNTs should

support more power than the PDMS; thus a (90/10) output coupler is used to have

more power inside the cavity laser. Besides, the length of the EDF is 3 m.

84

Fig. 4.6 Schematic of the passively mode-locked fiber laser developed using a PDMS/SWCNT film

between two connectors. WDM: wavelength division multiplexer; PC: Polarization Controller.

Before attempting to observe pulsed operation due to the SU8-2075/SWCNT

SA, the ring laser was first operated using a SU8-2075 film without SWCNTs. As

expected continuous wave (CW) operation was achieved for any pumping power.

We also modified the PC at different pumping levels, and there was no indication

of nonlinear polarization rotation mode-locking since there is no polarizing element

in the laser cavity.

This laser configuration was tested as the previous one and similar results were

found. A stable pulse train was observed within a pump power ranging from 36 to

88 mW, and the minimum pulse with duration was achieved with a pump power of

88 mW; remembering that the pulses can be optimized by playing with PC. We

also did the same experiment to observe the behavior when different pump

powers were applied. First the PC was set to optimize the pulse-width at a pump

power of 36 mW. Afterwards, different powers were applied that gave rise to a

shift of the central wavelength of the spectrum to shorter wavelengths as shown

before. At the optimum pumping power (88 mW), a pulse-train with a repetition

rate of 21.27 MHz was observed with a maximum output power of 1 mW. The

repetition rate corresponds to the laser cavity length of 9.4 m. The measured

85

pulse-train is shown in Fig. 4.7 (a). The frequency tones are shown in Fig. 4.7 (b),

and the first tone corresponds to the fundamental cavity frequency as expected.

The optical spectrum of the laser reveals a peak wavelength of 1565.3 nm, with a

spectral width at FWHM of 3.26 nm, as shown in Fig. 4.7 (c). The FWHM temporal

duration of the autocorrelation trace was 1.536 ps, as shown in Fig. 4.7 (d),

corresponding to a deconvolved pulse duration of 871 fs, assuming sech2 pulse

profile. This corresponds to a time-bandwidth product (TBP) of 0.344, which is

close enough to transform-limited sech square pulses [4.11].

0 100 200 300 400 500

0.00

0.02

0.04

Inte

nsit

y (

a.

u.)

Time (ns)

50 100 150 200-80

-70

-60

-50

-40

dB

Frequency (MHz)

(a) (b)

1565 1570 1575-50

-45

-40

-35

-30

-25

d

Bm

Wavelength (nm)

-4 -3 -2 -1 0 1 2 3 40.0

0.5

1.0

No

rma

lize

d I

nte

nsit

y (

a.u

.)

Delay Time (ps)

(c) (d) Fig. 4.7 Mode-locked laser output characteristics at a pump power of 88 mW (a) Pulse train of

mode-locked laser, (b) RF tones, (c) Optical spectrum, and (d) Autocorrelation trace.

86

The peak power inside cavity, the peak power outside the cavity, the energy

per pulse, the fluence, and the peak intensity are 485.8 W, 53.9 W, 423.13 pJ,

841.8 μJ/cm2, and 966.5 MW/cm2, respectively, all these data were obtained at a

pump power of 88 mW. The saturation intensity of this film is 0.7 MW/cm2 and

now is hitting with a peak intensity that is 1381 times higher that it, hence the SA

is working in full saturation mode showing that it can deal with high power.

Moreover, it can work for several continuous hours.

So far, it was shown that a mode-locked laser can be constructed by using

these two films, but it is necessary compare these results with other passively

mode-locked lasers that have the same configuration (the only different is the

polymer used to fabricate the film). Comparing the peak intensities of these films

with the peak intensity of PDMS and SU8-2075 films, we are going to evaluate the

performance of the films. Table 4.1 shows the peak intensity that films support

without optical damage.

Table 4.1 A list of polymers used to fabricate thin film to implement a passively mode-locked fiber ring laser.

Material Thickness

(μm)

Pulse-width

(fs)

Repetition Rate

(MHz)

Average power (mW)

Peak power supported by the film (W) Reference

1 PVA 35 178 22.8 1.55 382 [4.1]

2 CMC 4-100 177 50 7 791 [4.12]

3 Polymide 17 314 41.3 4.8 370 [4.2]

4 P3HT 40 2390 15 0.36 10 [4.3]

5 PMMA 1000 171 7.63 0.05 38.3 [4.13]

6 PC 340 115 39 3.4 758 [4.14]

7 Polymide 50 840 15.3 0.33 231 [4.15]

8 PVA 100 1850 11.1 0.2 92.52 [4.16]

9 SU8-2075 100 871 21.27 1 485.73 [4.17]

10 PDMS 200 1260 22.73 4.62 161.31 [4.18] The peak power is evaluated inside the cavity.

87

SU8-2075/SWCNT film support more peak power than the other films except

for the CMC/SWCNT and PC/SWCNT. PDMS/SWCNT support more peak power

than P3HT/SWCNT, PMMA/SWCNT, and PVA/SWCNT. The peak power that a film

can support depends on the design of the film (thickness and concentration of the

SWCNT) but and the end it depends on the polymer itself; this parameter shows if

the performance of the film is good. According to Table 4.1, SU8-2075/SWCNT and

PDMS/SWCNT films have a good performance as we expected. Moreover, the

fabrication process of both films are easy and do not require surface polish like

other films [4.13], [4.14]. PDMS/SWCNT film does not support so much peak

power like other films but this film is an alternative of fabricating a taper and its

fabrication process is cheaper than the others.

4.5 Summary

A passively mode-locked fiber laser was built up by using a PDMS/SWCNT film as a

SA. It has been shown that central wavelength of the spectrum is shifting to

shorter wavelengths as the pump power increases. At a pump power of 85 mW the

best data was detected, a pulse-width of 1.26 ps, a spectral width at FWHM of 2

nm and a TBP of 0.318. The laser fundamental frequency was 22.73 MHz and the

maximum output power was 4.91 mW. The maximum peak intensity inside the

cavity that was obtained without damage the film was 320.92 MW/cm2 and the

corresponding maximum output peak power was 161.31 W.

Another mode-locked fiber laser was constructed by using a SU8-2075/SWCNT

film as a SA. The central wavelength is also moving to shorter wavelength as the

pump power increases. At a pump power of 88 mW the best data was detected, a

pulse width of 871 fs, a spectral width at FWHM of 3.26 nm and a TBP of 0.344.

The laser fundamental frequency was 21.27 MHz and the maximum output power

was 1 mW. The maximum peak intensity inside the cavity that was obtained

88

without damage the film was 966.5 MW/cm2 and the corresponding maximum

output peak power was 53.9 W.

The main objective of this chapter was to show that both films can be used as

a SA in a fiber ring laser. As seen from the results, these films are the fundamental

key to produce pulses. Since the two films are not made of the same material and

they even have different modulation depths (related with the thickness), a direct

comparison cannot be made. Nevertheless, SU8-2075/SWCNT film handled a

higher peak intensity than the PDMS/SWCNT film. As we know, the problem of

propagating high intensities through the film is that the polymer or the nanotubes

absorb too much light and the polymer or the SWCNTs experience higher

temperatures which could damage the film. At first glance, the SU8-2075/SWCNT

film can support higher temperatures or the polymer has the ability of dissipate

heat more easily.

4.6 References

[4.1] A. G. Rozhin, Y. Sakakibara, S. Namiki, M. Tokumoto, H. Kataura, and Y.

Achiba “Sub-200-fs pulsed erbium-doped fiber laser using a carbon

nanotube-polyvinylalcohol mode locker,” Appl. Phys. Lett. 88, 051118

(2006).

[4.2] N. Nishizawa, Y. Seno, K. Sumimura, Y. Sakakibara, E. Itoga, H.

Kataura, and K. Itoh, “All-polarization-maintaining Er-doped ultrashort-

pulse fiber laser using carbon nanotube saturable absorber,” Opt.

Express 16, 9429-9435 (2008).

[4.3] F. Wang, A. G. Rozhin, V. Scardaci, Z. Sun, F. Hennrich, I. H. White, W.

I. Milne, and A. C. Ferrari, “Wideband-tunable, nanotube mode-locked,

fibre laser,” Nat. Nanotechnol. 3, 738-742 (2008).

[4.4] K. Kieu and M. Mansuripur, “Femtosecond laser pulse generation with a

fiber taper embedded in carbon nanotube/polymer composite,” Opt.

Lett. 32, 2242-2244 (2007).

89

[4.5] Y.-W. Song, K. Morimune, S. Y. Set, S. Yamashita, “Polarization

insensitive all-fiber mode-lockers functioned by carbon nanotubes

deposited onto tapered fibers,” Appl. Phys. Lett. 90, 021101 (2007).

[4.6] K. Kashiwagi and S. Yamashita, “Deposition of carbon nanotubes around

microfiber via evanescent light,” Opt. Express 17, 18364-18370 (2009).

[4.7] Y. W. Song, S. Yamashita, E. Einarsson, and S. Maruyama, “All-fiber

pulsed lasers passively mode locked by transferable vertically aligned

carbon nanotube film,” Opt. Lett. 32, 1399-1401 (2007).

[4.8] S. Y. Choi, F. Rotermund, H. Jung, K. Oh, and D.I. Yeom, “Femtosecond

mode-locked fiber laser employing a hollow optical fiber filled with

carbon nanotube dispersion as saturable absorber,” Opt. Express 17,

21788-21793 (2009).

[4.9] S. Chu, W.-S. Han, I.-D. Kim, Y.-G. Han, K. Lee, K. Lee, S. B. Lee, and

Y.-W. Song, “Ultrafast saturable absorption devices incorporating

efficiently electrosprayed carbon nanotubes,” Appl. Phys. Lett. 96,

051111 (2010).

[4.10] R. Zhang, X. Zhang, D. Meiser, and H. Giessen, “Mode and group

velocity dispersion evolution in the tapered region of a single-mode

tapered fiber,” Opt. Express 12, 5840-5849 (2004).

[4.11] J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena,

(Academic Press, California, 2006).

[4.12] A. V. Tausenev, E. D. Obraztsova, A. S. Lobach, A. I. Chernov, V. I.

Konov, P. G. Kryukov, A. V. Konyashchenko, and E. M. Dianov, “177 fs

erbium-doped fiber laser mode locked with a cellulose polymer film

containing single-wall carbon nanotubes,” Appl. Phys. Lett. 92, 171113

(2008).

[4.13] M. Nakazawa, S. Nakahara, T. Hirooka, and M. Yoshida, “Polymer

saturable absorber materials in the 1.5 μm band using poly-methyl-

90

methacrylate and polystyrene with single -wall carbon nanotubes and

their application to a femtosecond laser,” Opt. Lett. 31, 915-917 (2006).

[4.14] F. Shohda T. Shirato, M. Nakazawa, K. Komatsu, and T. Kaino, “A

passively mode-locked femtosecond soliton fiber laser at 1.5 μm with a

CNT-doped polycarbonate saturable absorber,” Opt. Express 16, 21191-

21198 (2008).

[4.15] L. Gui, X. Yang, G. Zhao, X. Yang, X. Xiao, J. Zhu, and C. Yang,

“Suppression of continuous lasing in a carbon nanotube polyimide film

mode-locked erbium-doped fiber laser,” Appl. Opt. 50, 110-115 (2011).

[4.16] J. C. Chiu, Y. F. Lan, C. M. Chang, X. Z. Chen, C. Y. Yeh, C. K. Lee, G. R.

Lin, J. J. Lin, and W. H. Cheng, “Concentration effect of carbon

nanotube based saturable absorber on stabilizing and shortening mode-

locked pulse,” Opt. Express 18, 3592-3600 (2010).

[4.17] I. Hernandez-Romano, D. Mandridis, D. A. May-Arrioja, J. J. Sanchez-

Mondragon, and P. J. Delfyett, “Mode-locked fiber laser using an

SU8/SWCNT saturable absorber,” Opt. Lett. 36, 2122-2124 (2011).

[4.18] I. Hernandez-Romano, J. Davila-Rodriguez, D. A. May-Arrioja, J. J.

Sanchez-Mondragon, and P. J. Delfyett, “Fabrication of PDMS/SWCNT

thin films as saturable absorb,” Journal of Physics: Conference Series

274 012118, 2011.

91

Chapter 5

Hybrid mode-locked laser using a PDMS/SWCNT as SA

5.1 Introduction

In the last five years, different approaches have been used in order to incorporate

SWCNTs in an all-fiber laser cavity, and we have reached the point where their

integration in fiber laser systems is relative simple, as was mentioned in chapter 2.

However, the main drawback of all these lasers is the low repetition rate. An

obvious approach is of course to make the cavity as short as possible [5.1] - [5.3],

but a small cavity length presents challenges that increase the system complexity.

On the other hand active mode-locked lasers, and in particular harmonic mode-

locked laser systems, can generate very high repetition rates by simply

incorporating a high speed modulator within the cavity. The key issue in active

mode-locking is that they generate pulses whose duration is longer than those of

passively mode-locked lasers, especially when etalons are added to stabilize the

supermode order [5.4]. The question remains on how to implement a simple and

reliable all-fiber laser with a high repetition rate while generating very short pulses.

In this chapter an active and a hybrid mode-locked Erbium fiber laser are

reported. The active system is built using a standard ring cavity laser incorporating

an electro-optical modulator (amplitude modulator). The hybrid system is

constructed by inserting a SA (a PDMS/SWCNT thin film composite) in the active

system between two FC/APC connectors. A comparison between active and hybrid

system is made in order to observe the benefits of hybrid mode-locked laser. It is

also shown that the active mode-locked laser undergoes a reduction in the signal-

92

to-noise ratio (SNR) of the photo-detected radio frequency (RF) spectrum by using

this film.

5.2 Active mode-locked laser

The simplest way to implement an active mode-locked laser is by placing an

amplitude electro-optical modulator (EOM) inside a ring cavity resonator. The

modulator is driven at a modulation frequency that exactly matches a multiple of

the fundamental frequency of the laser cavity, which is the inverse of the cavity

round-trip time. When the modulator is driven at a multiple of this frequency it is

referred to as harmonic mode-locking and this technique is used either to shorten

the mode-locked pulses or to raise the pulse repetition frequency [5.5].

Fig. 5.1 Schematic of the active mode-locked fiber laser. EOM: electro-optical modulator; WDM: wavelength division multiplexer; PC: Polarization Controller.

The active mode-locked fiber laser was built by using 3 m of Erbium doped

fiber (EDF) which was pumped by a laser diode operating at 980 nm via a

980/1550 WDM fiber coupler, see Fig. 5.1. The peak absorption of the EDF (L-

band) was 94.59 dB at 1530 nm. This WDM also has an integrated isolator for

unidirectional operation. An AEOM was placed in the cavity which can be operated

93

at a maximum modulating frequency of 10 GHz. Since the EOM is polarization

dependent, a polarization controller (PC1) is placed in the cavity before the EOM.

This helps to achieve higher modulation and shorter pulses with wider spectra. The

second polarizer (PC2) does not play a role in this active configuration but it will

when PDMS/SWCNT SA is incorporated in the cavity (the goal is compare the

performance of both cavities under the same experimental conditions). Therefore,

we incorporate it in the active configuration such that the only difference between

both configurations will be the PDMS/SWCNT film. The laser output is obtained

from one port of a 3-dB fiber coupler. The cavity fundamental frequency is 19.23

MHz which corresponds to a laser cavity length of about 10.4 m. Using directional

couplers at the laser output simultaneous measurements of the optical spectrum

and second harmonic generation (SHG) autocorrelation are performed.

During active mode-locked laser operation, the RF frequency driving the EOM

is chosen to match the 209th harmonic of the fundamental frequency, i.e., 4.0205

GHz. A stable pulse train is achieved with a pump power of 100 mW. At this pump

power, optical spectrum and SHG autocorrelation trace of the laser output were

measured, as shown in Fig. 5.2 (a) and (b). The active mode-locked laser’s central

wavelength was 1559.45 nm with a FWHM of 2.46 nm; see Fig. 5.2 (a). The

FWHM of the autocorrelation trace was 2.47 ps, as shown in Fig. 5.2 (b),

corresponding to a deconvolved pulse-width of 1.39 ps, assuming sech2 time

intensity profile. The time-bandwidth product was 0.42 (compared to a transform

limited of 0.315). A maximum average output power of 8 mW was also measured.

The peak power that is inside the cavity is 1.43 W. Furthermore, the energy per

pulse, the fluence, and the peak intensity are 1.989 pJ, 3.96 μJ/cm2, and 2.85

MW/cm2, respectively.

94

1556 1560 1564-70

-65

-60

-55

-50

-45

-40

-35FWHM 2.46 nm

Wavelength (nm)

dB

m

-6 -4 -2 0 2 4 60.0

0.5

1.0

Delay Time (ps)

FWHM 2.47 ps

No

rma

lize

d I

nte

nsit

y (

a.u

.)

(a) (b)

Fig. 5.2 (a) Optical spectrum, and (b) Autocorrelation trace from the active mode-locked fiber laser.

5.3 Hybrid mode-locked laser

The hybrid mode-locked laser was built by combining the active mode-locked

system with the PDMS/SWCNT SA which was incorporated in the cavity, as shown

in Fig. 5.35.3. In principle, the active modulation should give rise to pulse

formation, and the addition of the SA should narrow the temporal width of the

pulses [5.6]. The film that was characterized in chapter 3 (PDMS film) is the same

that was used in this setup.

Fig. 5.3 Schematic of the hybrid mode-locked fiber laser. EOM: electro-optical modulator;

WDM: wavelength division multiplexer; PC: Polarization Controller.

95

The hybrid mode-locked laser is assembled by adding the PDMS/SWCNT film

after the second polarization controller in the experimental setup of the active

configuration, as shown in Fig. 5.3. Taking into account that the only difference

between the active mode-locking and the hybrid setup is the insertion of the SA,

i.e. all the experimental condition were the same as in the active mode-locked

laser, thus any reduction of the temporal pulse-width should be attributed to the

SA. The length of the cavity was not significantly altered due to the PDMS/SWCNT

thin film, and therefore the cavity fundamental frequency is the same. In order to

achieve mode-locking the modulator was driven using the same modulation

parameters as with active configuration, i.e. the amplitude modulation was

operated to match the 209th harmonic of the fundamental frequency with the same

modulation depth. A stable pulse train is achieved by applying a pump power of

231 mW, and also adjusting the PC2 (due to the small film polarization

dependence of the PDMS/SWCNT film), see Fig. 5.3. At this pump power, optical

spectrum and autocorrelation trace of the laser output were measured, as shown

Fig. 5.4 (a) and (b). The hybrid mode-locked laser’s central wavelength was

1562.18 nm with a FWHM of 3.79 nm; see Fig. 5.4 (a). The FWHM of the

autocorrelation trace was 1.29 ps, as shown in Fig. 5.4 (b), corresponding to a

deconvolved pulse-width of 730 fs, assuming sech2 time intensity profile. The time-

bandwidth product was also 0.344, which is close enough to transform-limited

sech2 pulses [16]. A maximum average output power of 4 mW was also measured.

The peak power that is inside the cavity is 1.36 W. Furthermore, the energy per

pulse, the fluence, and the peak intensity are 0.995 pJ, 1.98 μJ/cm2, and 2.7

MW/cm2, respectively. This peak intensity is a little higher than the saturation

intensity (2.4 MW/cm2) showed in the last chapter.

96

1552 1556 1560 1564 1568 1572

-70

-60

-50

-40

-30

Wavelength (nm)

dB

mFWHM 3.79 nm

-6 -4 -2 0 2 4 60.0

0.5

1.0

Delay Time (ps)

FWHM 1.29 ps

N

orm

ali

ze

d I

nte

nsit

y (

a.u

.)

(a) (b)

Fig. 5.4 (a) Optical spectrum, and (b) Autocorrelation trace from the hybrid mode-locked fiber

laser.

Even though the pump power for the active mode-locking is 100 mW and the

pump power for the hybrid mode-locking is 231 mW, the peak power that is

circulating in the active cavity laser is almost equal to the peak power that is in the

hybrid cavity laser, the same occurs with the peak intensity. This means that both

active and hybrid cavities were working at the same experimental condition. It is

obviously that in the case of the hybrid mode-locking laser we needed to apply

more pump power due to the SA losses.

When comparing the active and hybrid mode-locked results, we can easily

notice that the pulse-width duration is 48% narrower when going from the hybrid

configuration. Additionally, the optical spectrum generated by the hybrid

configuration is 54% wider than the spectrum generated by the active one.

We then measured the RF spectrum of both configurations around 4 GHz and,

as shown in Fig. 5.5, we can notice a remarkable difference. It is well known that

harmonic operation of mode-locked lasers gives rise to noisy laser performance

due to the limited correlation between the intra-cavity pulses, which is

97

demonstrated as supermode noise spurs (SNS) in the RF spectra of the photo-

detected pulse train [5.7].

3.0 3.5 4.0 4.5 5.0-50

-40

-30

-20

-10

0Active

dB

c

3.0 3.5 4.0 4.5 5.0-50

-40

-30

-20

-10

0

RBW: 3MHz

Hybrid

RBW: 3MHz

Frequency (GHz)Frequency (GHz)

(a) (b)

Fig. 5.5 Photo-detected RF spectrum of (a) Active, (b) Hybrid mode-locked laser configurations.

As shown in Fig. 5.5 (a), for the active configuration we have a signal noise

ratio (SNR) of less than 30 dB, and the SNS exhibits considerable fluctuation.

However, in the case of the hybrid configuration the SNR was improved by

approximately 5 dB (~ 35 dB), Fig. 5.5 (b), but more importantly is the fact that

the SNS fluctuations were considerable reduced. This result is very important

because such effects occur when some kind of frequency stabilization is

implemented in the cavity, for example by adding a Fabry-Pérot etalon in the

cavity [5.4]. In fact, there are a couple of references that mention such phase

stabilization for passive mode-locked lasers using SWCNTs [5.8], [5.9]. The key

factor here is that such phase stabilization is also transferred into the hybrid mode-

locked system.

98

Based on our experiments, the SNS could be further improved by increasing

the absorption of the film (currently 32%) by not increasing the nonsaturable

losses which means a bigger modulation depth. In order to fulfill both

requirements, we have to completely isolate the SWCNTs in the polymer matrix,

and this is a limitation for thin films within an all-fiber system. If we make the

SWCNTs concentration lower to isolate the nanotubes, thus the film thickness has

to increase to obtain the desired absorption. This will make the connector losses

too high. Increasing the concentration is not an option because the formation of

bundles is increased which have detrimental effects for the film as the intracavity

power is increased. We should also mention that in our experiments the maximum

modulation frequency was close to 4 GHz, but this frequency value was limited by

the available equipment. In principle, higher modulation frequencies should be

feasible. The key advantage of using this hybrid configuration is that we can obtain

pulse trains with higher repetition rates while maintaining the narrow pulses

achieved by passive SA. In fact, the pulses get narrower with the square root of

the period of the laser as we can see in Eq. (2.9), which will be also beneficial for

our hybrid system in order to obtain even narrower pulses.

5.4 Summary

In summary a hybrid mode-locked Erbium fiber laser was proposed and

implemented. This configuration has the advantage over current mode-locked

systems that can provide a high repetition rate while attaining ultrashort pulses

(with fs temporal duration). The SA was developed using a PDMS/SWCNTs thin

film composite, which is inexpensive and simple to fabricate. The hybrid

configuration (adding a SA inside active mode-locked laser) narrows the pulse-

width as compared to the active mode-locked laser by a factor of two, while also

reducing the SNS fluctuations on the RF noise. A pulse-width of 730 fs was

99

generated at a repetition rate of 4 GHz, and a maximum output power was 4 mW.

A reduction in the noise of the photo-detected RF spectrum was also observed in

the hybrid system.

5.5 References

[5.1] S. Yamashita, Y. Inoue, K. Hsu, T. Kotake, H. Yaguchi, D. Tanaka, M.

Jablonski, and S. Y. Set, “5-GHz Pulsed Fiber Fabry–Pérot Laser Mode-

Locked Using Carbon Nanotubes,” IEEE Photonics Technol. Lett. 17,

750-752 (2005).

[5.2] Y. W. Song, S. Yamashita, C. S. Goh, and S. Y. Set, “Passively mode-

locked lasers with 17.2-GHz fundamental-mode repetition rate pulsed by

carbon nanotubes,” Opt. Lett. 32, 430-432 (2007).

[5.3] A. Martinez and S. Yamashita, “Multi-gigahertz repetition rate passively

mode locked fiber lasers using carbon nanotubes,” Opt. Express 19,

6155-6163 (2011).

[5.4] I. Ozdur, M Akbulut, N Hoghooghi, D Mandridis, S Ozharar, F

Quinlan, and P.J. Delfyett, “A Semiconductor-Based 10-GHz Optical

Comb Source With Sub 3-fs Shot-Noise-Limited Timing Jitter and 500-

Hz Comb Linewidth,” IEEE Photonics Technol. Lett. 22, 431-433 (2010).

[5.5] A. E. Siegman, Lasers (University Science Books, Sausalito, California,

1986).

[5.6] M. Weiner, Ultrafast Optics (Wiley, USA, 2009).

[5.7] F. Rana, H. L. T. Lee, R. J. Ram, M. E. Grein, L. A. Jiang, E. P. Ippen,

and H. A. Haus, “Characterization of the noise and correlations in

harmonically mode-locked lasers,” J. Opt. Soc. Am. B 19, 2609-2621

(2002).

[5.8] T. H. Wu, K. Kieu, N. Peyghambarian, and R. J. Jones, “Low noise

erbium fiber fs frequency comb based on a tapered-fiber carbon

nanotube design,” Opt. Express 19, 5313-5318 (2011).

100

[5.9] J. K. Lim, K. Knabe, K. A. Tillman, W. Neely, Y. S. Wang, R. Amezcua-

Correa, F. Couny, P. S. Light, F. Benabid, J. C. Knight, K. L. Corwin, J.

W. Nicholson, and B. R. Washburn, “A phase-stabilized carbon nanotube

fiber laser frequency comb,” Opt. Express 17, 14115-14120 (2009).

101

Chapter 6

Passively Q-switched Erbium fiber laser using SU8/SWCNT as SA

6.1 Introduction

Up to now, it has been shown that passively mode-locked lasers can be

implemented by using SAs based on SWCNTs. These mode-locked lasers have

been extensible studied but little information regarding of passively Q-switching

has been mentioned [6.1], [6.2]. Zhou et al. constructed a passively Q-switched

fiber laser by using SWCNTs attached to a fiber angle connector as a SA [6.2]. The

implementation of this kind of SA has been shown to be reliable and reproducible.

However, the physical contact of the nanotubes with the connectors tends to

damage them. Moreover, since the nanotubes interact with air, they degrade much

faster. For that reason a passively Q-switched fiber laser was implemented and

tested by using a SU8-2075 thin film doped with SWCNTs as SA.

6.2 Passively Q-switched laser

A SA based on SU8-2075 doped with SWCNTs was developed using the technique

described in chapter 3, but the thickness of the sample and the quantity of the

tubes were 135 μm and 0.2 wt%, respectively. Different films that had diverse

concentration and thickness were tested in a Erbium fiber laser, as it was shown in

Chapter 3, and we found that the laser operation could change from self-passive

mode-locking to self-passive Q-switching by increasing the thickness and

concentration of the films. Hence, the concentration and thickness of these films

was chosen to observe just self-passive Q-switching operation. This film was

102

placed between two angle connectors in order to assembly an all-fiber SA and it

was then incorporated in a laser cavity, as shown in Fig. 6.1. The laser cavity was

pumped by a 980 nm laser diode through a WDM. A 3 m long EDF was used as the

laser gain medium (the peak absorption of the EDF was 94.59 dB at 1530 nm).

This WDM has an integrated isolator to guarantee unidirectional operation in the

laser cavity. Since the SU8-2075/SWCNT film exhibits slight polarization

dependence due to the random arrangement of the SWCNTs within the SU8-2075

polymer matrix, a polarization controller (PC) was inserted in the laser cavity.

Using a (90/10) coupler we extract 10% of the intracavity light while the remaining

90% is launched back into the laser cavity as feedback. The overall length of the

cavity laser was about 15 m, which corresponds to a frequency of 13.33 MHz.

Measurements of the laser dynamics was performed using a 3-dB coupler which

was used to split the output of the laser into two paths. One of the 50% ports was

connected to an Optical Spectrum Analyzer (OSA ANDO AQ6317B) while the other

50% was detected by a photo-detector and the signal was sent to an oscilloscope

to measure the pulse-width and the repetition rate of the laser.

Fig. 6.1 Schematic of the passively Q-switched fiber laser using a SU8-2075/SWCNT

film between two connectors.

103

6.3 Passively Q-switched fiber laser results

using a SU8-2075/SWCNT as a SA

The characteristics of the laser were evaluated by increasing the pump current and

monitoring the emission of the laser. Continuous-wave (CW) operation was

observed until 46 mA of pump current were applied. The laser is then switched to

a passive Q-switching mode when the pump current was increased to 47 mA. This

operation mode is confirmed by detecting a train of pulses in the oscilloscope.

When Q-switching started the spectrum is wider than the CW operation spectrum,

see Fig. 6.2 (a) and (b). The central wavelength of the CW mode was 1567.7 nm,

at a pump current of 75 mA, Fig. 6.2 (a). At the same pump current, this central

wavelength shifted to shorter wavelengths when the SU8-2075/SWCNT SA was

inserted in the laser cavity. The optical spectrum of Q-switched mode reveals a

peak wavelength of 1563.3 nm, with a spectral width at FWHM of 1.6 nm, as

shown in Fig. 6.2 (b). This shift in the central wavelength should be attributed to

the losses of the SA.

104

1557 1560 1563 1566 1569 15720

50

100

150

200

250

300

350

400

Po

we

r (m

W)

Wavelength (nm)

1557 1560 1563 1566 1569 15720

20

40

60

80

100

120

140

160

180

Wavelength (nm)

Po

we

r (W

)

(a) (b)

-100 -50 0 50 100 150

1

2

3

4

5

6

Time (s)

Ou

tpu

t P

ow

er

(a.u

.)

-10 -8 -6 -4 -2 0 2 4 6 8 10

0.0

0.5

1.0

No

rma

lize

d I

nte

nsit

y (

a.u

.)

Delay Time (s)

(c) (d)

Fig. 6.2 Passively Q-switched fiber laser output characteristics at a pump current of 75 mA (a) CW

optical spectrum, (b) Q-switching optical spectrum, (c) Pulse train, and (d) Pulse.

The typical pulse train has a stable repetition rate and this stabilization was

optimized by playing with the PC. The repetition rate, the pulse duration at FWHM

and average power are 31.3 kHz, 2.5 μs and 91 μW, respectively, when the pump

current was 75 mA, see Fig. 6.2 (c) and (d). The peak power and the pulse energy

were 1.2 mW and 2.9 nJ, respectively. The long pulse duration is primary because

of the length of the laser cavity as it was explained in chapter 2.

105

Since this kind of laser presents long cavity and large gain, the repetition rate

and the output power are dependent on the pump current, as it was mention in

chapter 2. Fig. 6.3 shows the repetition rate of the Q-switched pulses and the

average output power as function of the pump current. A stable Q-switched mode

was observed with the range 47-115 mA of pump current. The pump current was

limited within this range to avoid optical power induced thermal damage of the

SWCNTs. The maximum average power, peak power, and pulse energy were 160

μW, 7.3 mW, and 5.1 nJ, respectively, at a pump current of 115 mA (pulse width

of 0.7 μs).

0 20 40 60 80 100 120

15

20

25

30

35

40

45

Current (mA)

Fre

qu

en

cy (

kH

z)

0

30

60

90

120

150

180

Ou

tpu

t P

ow

er

(W

)

Fig. 6.3 Average output power and pulse repetition rate as function of pump current.

6.4 Summary

A passively Q-switched Erbium fiber laser was implemented by using a thin film of

SU8-2075/SWCNT as a SA. The fabrication technique of the SA is simple and

reproducible, as was demonstrated in chapter 3. Moreover, the nanotubes are not

exposed to interact with air and they do not suffer physical damages due to the

connectors. It was shown that the repetition rate and the output power of the

laser vary with the pump current, as it was also mentioned in chapter 2. The

106

maximum average power, peak power, and pulse energy were 160 μW, 7.3 mW,

and 5.1 nJ, respectively, at a pump current of 115 mA.

6.5 References

[6.1] K. Kieu and M. Mansuripur, “Femtosecond laser pulse generation with a

fiber taper embedded in carbon nanotube/polymer composite,” Opt.

Lett. 32, 2242-2244 (2007).

[6.2] D.-P. Zhou, L. Wei, B. Dong, and W.-K. Liu, “Tunable passively Q-

switched erbium-doped fiber laser with carbon nanotubes as a saturable

absorber,” IEEE Photonics Technol. Lett 22, 9-11 (2010).

107

Chapter 7

Conclusions

7.1 Conclusions

This thesis is focused on the design and development of passively mode-

locked, hybrid mode-locked and Q-switched lasers by using thin films of polymer

doped with SWCNTs. In this thesis, the fabrication processes developed to

manufacture SAs using two different polymers doped with SWCNTs are explained

in detail. One of these polymers is PDMS and the other is SU8-2075; the

fabrication processes for both polymers are simple and reproducible. Not only do

these techniques not require expensive equipment or material, but also the films

do not require surface polish like other films [7.1], [7.2].

Using a PDMS/SWCNT film, a passively mode-locked Erbium fiber laser was

built up. This laser generated pulses as short as 1.26 ps, without taking care about

dispersion compensation, and having a repetition rate of 22.73 MHz with an output

power of 4.91 mW. A similar laser was built by using a SU8-2075/SWCNT film; the

pulse-width, the repetition rate, and the output power were 871 fs, 21.27 MHz, 1

mW, respectively. Since the optical features of the films are different, a direct

comparison is not possible; however, at first glance, the SU8-2075/SWCNT film can

support high temperature or the polymer has the ability of dissipate heat easily.

An active mode-locked Erbium fiber laser was implemented. This laser

generated pules as short as 1.39 ps, without taking care about dispersion

compensation, at a repetition rate of 4GHz with an output power of 8 mW. The

peak power that was inside the cavity was 1.43 W. Furthermore, the energy per

pulse, the fluence, and the peak intensity were 1.989 pJ, 3.96 μJ/cm2, 2.85

MW/cm2, respectively. By adding a SA (PDMS/SWCNT film), this laser became a

108

hybrid mode-locked laser that generated pules as short as 730 fs, without taking

care about dispersion compensation, at a repetition rate of 4 GHz with an output

power of 4 mW. The peak power that was inside the cavity was 1.36 W.

Furthermore, the energy per pulse, the fluence, and the peak intensity were 0.995

pJ, 1.98 μJ/cm2, 2.7 MW/cm2, respectively. This peak intensity was a little higher

than the saturation intensity (2.4 MW/cm2) showed by this film. The hybrid

configuration (adding a SA inside active mode-locked laser) narrows the pulse

width as compared to the active mode-locked laser by a factor of two, while also

the SNS was improved by approximately 5 dB. Nonetheless more important is the

fact that the SNS fluctuations were considerably reduced, potentially due to the

fact that the SA acts as an amplified spontaneous emission suppressor outside the

pulse window.

It is feasible to suppress the self-passive mode-locked and to observe self-

passive Q-switching by increasing the thickness of the film and the concentration

of the nanotubes. Thus, using a SU8-2075/SWCNT film whose thickness and

concentration of nanotubes were 135 μm and 0.2 wt%, respectively; a passively

Q-switched laser was implemented. The maximum average power, peak power,

and pulse energy were 160 mW, 7.3 mW, and 5.1 nJ, respectively, at a pump

current of 115 mA (pulse width of 0.7 μs). It was also shown that the repetition

rate of the train of pulses increased when the pump current increased.

7.2 Future work

Optimizing the performance of the film should be an important task to achieved

shorter and more stable pulses. For this purpose testing films that have different

modulation depths can give insight about stabilization and pulse formation. This

can be done not only by varying the thickness of the films for a fixed

concentration, but also by changing the concentration of the SWCNTs by

maintaining the film thickness. A paper related with this kind of work has been

109

already published [7.3], but for PDMS and SU8-2075 there is nothing about it. The

absorption of the film depends on the polarization of the light that is hitting the

sample for that reason it should be developed a film in which the tubes are aligned

respect to the electrical field. Some work related to how to align SWCNTs in a

polymer has done [7.4], but there is nothing applied to mode-locked laser. Since

the film is between two angle connector, the divergence of the beam (when the

light travels though the film) generates nonsaturable absorption. This degrades the

performance of the films and can be minimized by making the thickness smaller.

Trying to find the smaller thickness should reduce the nonsaturable absorption and

hence the performance of the film.

7.3 References

[7.1] M. Nakazawa, S. Nakahara, T. Hirooka, and M. Yoshida, “Polymer

saturable absorber materials in the 1.5 μm band using poly-methyl-

methacrylate and polystyrene with single -wall carbon nanotubes and

their application to a femtosecond laser,” Opt. Lett. 31, 915-917 (2006).

[7.2] F. Shohda T. Shirato, M. Nakazawa, K. Komatsu, and T. Kaino, “A

passively mode-locked femtosecond soliton fiber laser at 1.5 μm with a

CNT-doped polycarbonate saturable absorber,” Opt. Express 16, 21191-

21198 (2008).

[7.3] J.-C. Chiu, Y.-F. Lan, C.-M. Chang, X.-Z. Chen, C.-Y. Yeh, C.-K. Lee, G.-

R. Lin, J.-J. Lin, and W.-H. Cheng, “Concentration effect of carbon

nanotube based saturable absorber on stabilizing and shortening mode-

locked pulse,” Opt. Express 18, 3592-3600 (2010).

[7.4] L. Jin, C. Bower, and O. Zhou, “Alignment of carbon nanotubes in a

polymer matrix by mechanical stretching,” Appl. Phys. Lett. 73, 1197-

1199(1998).