4.1 Simulated Emission and Photon...

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Stimulated Emission Devices: LASERS

Kasap Chapter 4

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Contents4.1 Stimulated Emission and Photon Amplification4.2 Stimulated Emission Rate and Einstein Coefficients4.3 Optical Fiber Amplifiers4.4 Gas Laser4.5 The Output Spectrum of Gas Laser4.6 Laser Oscillation Conditions4.7 Principle of the Laser Diode4.8 Heterostructure Laser Diodes4.9 Elementary Laser Diode Characteristics4.10 Steady State Semiconductor Rate Equation4.11. Light Emitters for Optical Fiber Communications4.12 Single Frequency Solid State Lasers4.13 Quantum Well Devices4.14 Vertical Cavity Surface Emitting Lasers (VCSELs)4.15 Optical Laser Amplifiers4.16 Holography

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4.1 Simulated Emission and Photon Amplification

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E1

E2

h

(a) Absorption

h

(b) Spontaneous emission

h

(c) Stimulated emission

In hOut

h

E2 E2

E1 E1

Absorption, spontaneous (random photon) emission and stimulatedemission.

Spontaneous emission:random directionE1 is empty

As if e- is oscillating in freq. v

Stimulated emission: inducedTwo photons arein phase, same directionsame polarization, same energyIncoming e- couples to the e- in E2

Basis for photon amplificationRe-absorbed? => population inversion

not in two level systems

Fig. 4.1

(in steady state: R12= R21 )

Optical Cavity feedbackhigh optical intensity

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E1

h13E

2Metastablestate

E1

E3

E2

h32

E1

E3

E2

E1

E3

E2

h2h21

Coherent photons

OUT

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

E3

The principle of the LASER. (a) Atoms in the ground state are pumped up to the energy level E3 by

incoming photons of energy h13 = E3E1. (b) Atoms at E3 rapidly decay to the metastable state atenergy level E2 by emitting photons or emitting lattice vibrations; h32 = E3E2. (c) As the states at E2are long-lived, they quickly become populated and there is a population inversion between E2 and E1.

(d) A random photon (from a spontaneous decay) of energy h21 = E2E1 can initiate stimulatedemission. Photons from this stimulated emission can themselves further stimulate emissions leading to anavalanche of stimulated emissions and coherent photons being emitted.

IN

Pumping(optical)

e.g. ruby laser: chromium ions Cr3+ in Al2O3 crystalFeedback: silvered mirror and partially silvered mirror

LASER: Light Amplification by Stimulated Emission of Radiation

Fig. 4.2

(Note: usually, more efficient in four level systems )

Three level system

(long-lived state)

(See p.6)

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Theodore Harold Maiman was born in 1927 in Los Angeles, son of an electrical engineer. He studied engineering physics at Colorado University, while repairing electrical appliances to pay for college, and then obtained a Ph.D. from Stanford. Theodore Maiman constructed this first laser in 1960 while working at Hughes Research Laboratories (T.H. Maiman, "Stimulated optical radiation in ruby lasers", Nature, 187, 493, 1960). There is a vertical chromium ion doped ruby rod in the center of a helical xenon flash tube. The ruby rod has mirrored ends. The xenon flash provides optical pumping of the chromium ions in the ruby rod. The output is a pulse of red laser light. (Courtesy of HRL Laboratories, LLC, Malibu, California.)

http://www.llnl.gov/nif/library/aboutlasers/how.html

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4.2 Stimulated Emission Rate and Einstein Coefficients

A useful LASER medium must have a higher efficiency of stimulated emission compared with spontaneous emission and absorption.

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Upward transition rate

Downward transition rate

( ) hNBR 11212 =

( ) hNBNAR 22122121 +=

B12 B21, A21 : Einstein Coefficients

( )h : photon energy density / freq.= # photons / volume at hv

spontaneous stimulated

Thermal equilibrium: no change with time in the populations at E1 and E2

2112 RR =( )

=

TkEE

NN

B

12

1

2 expBoltzmann statistics

( )

=

1exp

8

3

3

Tkhc

hh

B

eq

(only) in thermal equilibrium, by Planks black body radiation distribution law

=> 2112 BB = 33

21

21 8ch

BA

= ( is much larger in laser operation)

Ni : atoms / unit volume at Ei

=>

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2112 BB = 33

21

21 8ch

BA

=

( ) ( )21

21

221

221

21

21

)()(

AhB

NAhNB

sponRstimR

== ( )3

38c hh

=

Ratio of stimulated to spontaneous emission

Ratio of stimulated emission to absorption

1

2

12

21

)()(

NN

absorpRstimR

=

R21(stim) > R12 (absorp) =>

Stim. emission >> spon. emission => large photon concentration achieved by optical cavity

Population inversion => depart from thermal equilibrium (negative abs. temp.)The laser principle is based on non-thermal equilibrium.

Optical Cavity provides 1. feedback 2. high optical intensity

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4.3 Optical Fiber AmplifiersLong haul communication suffers attenuation.Regenerate signal by Optical-Electrical-Optical

Pros: Cons:

Amplify optical signal directly => optical amplifierPros: Cons:

EDFA: erbium (Er3+) doped fiber amplifierOther dopants: e.g. Nd3+Splicing: fibers are fused together

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Energy of the Er3+ ionin the glass fiber

E10

1.54 eV

1.27 eV

0.80 eV E2

E3

E3

1550 nm 1550 nm

InOut

980 nm

Non-radiative decay

Pump

Energy diagram for the Er3+ ion in the glass fiber medium and light amplificationby stimulated emission from E2 to E1. Dashed arrows indicate radiationlesstransitions (energy emission by lattice vibrations)

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Optically pumped (usu. by LD)

E2: long-lived ~ 10ms

1240 (eV nm)= (nm)

E hv

= ( )12 NNKGop =

Optical gain:

K: dep. on pumping intensity

Fig. 4.3

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Signal in Signal outSplice

Er3+-dopedfiber (10 - 20 m)

Wavelength-selective coupler

Pump laser diode

Splice

= 1550 nm = 1550 nm

= 980 nmTermination

Opticalisolator

Opticalisolator

A simplified schematic illustration of an EDFA (optical amplifier). Theerbium-ion doped fiber is pumped by feeding the light from a laser pumpdiode, through a coupler, into the erbium ion doped fiber.


E3 at 810 nm is less efficient.Photodetector: monitor the pumping levelClosely spaced collection of several levels:

1525-1565 nm (40nm) used in WDM systemgain flattening to overcome non-uniform gain

Pumping at 1480 nm is also usedGain efficiency: 8-10 dB/mW e.g. 103 gain by a few mW

Fig. 4.4

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Ali Javan and his associates William Bennett Jr. and Donald Herriott at Bell Labs were first to successfully demonstrate a continuous wave (cw) helium-neon laser operation (1960-1962).

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4.4 Gas LASERS: The He-Ne LASER

He-Ne laser @632.8nm (red) from Ne atoms, He used to excite Ne

Ne: 1s22s22p6 or 2p6 He: 1s2

excited Ne: 2p55s1 Excited He: 1s12s1

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Current regulated HV power supply

Flat mirror (Reflectivity = 0.999) Concave mirror (Reflectivity = 0.985)

He-Ne gas mixtureLaser beam

Very thin tube

A schematic illustration of the He-Ne laser


Using dc or RF high voltage: He atoms to become excited by collisions with drifting electrons

++ ee *HeHeExcited He*: 1s12s1 parallel spin, metastable,

not allowed to simply decay back to ground state,

** NeHeNeHe ++Excited He collides with a Ne atom

=> population inversion of Ne

Fig. 4.5

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(1s2)

(1s12s1)

0

20.61 eV

He

(2p6)

Ground states

(2p55s1)

Ne

(2p53p1)

(2p53s1)

Collisions

Lasing emission

632.8 nm

~600 nm

Collisions with the walls

Fast spontaneous decay

20.66 eV

Electron impact

The principle of operation of the He-Ne laser. He-Ne laser energy levels(for 632.8 nm emission).


Fig. 4.6

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(1s2)

(1s12s1)

0

20.6 eV

He

(2p6)

Ground states

Ne

(2p53p1)

Lasing emissions

Collisions with the walls

Various lasing transitions in the He-Ne laser

Electron impact

(1s12s1) (2p54s1)

(2p53s1)~600 nm

Fast spontaneous decay

(2p55s1)

1152 nm1118 nm

1523 nm19.8 eV

632.8 nm

543.5 nm

(2p54p1)

3.39 mCollisions


greenred

(metastable, requiring spin flip toreturn to 2p6)

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Ne(2p55s1): 4 closely spaced energy levels

Ne(2p53p1): 10 closely spaced energy levels

Also energy level -- Ne(2p54p1)

Red: 632.8 nmGreen: 543 nm

IR: 3.39 mprevented by freq. selective mirrors

Ne(2p53s1) is a metastable level, to ground state by colliding with the walls of laser tube=> narrow tube is better

Typ. He-Ne laserHe: Ne = 5:1 several torrs longer and narrower tube is better99.9% flat reflecting mirror, and 99% concave reflecting mirror, convergent lensdiameter: 0.5-1 mm divergence: 1 mrad few milliwattspolarized light by Brewster angle

Laser tube

Laser radiation

r

L

422 ow

=

( )

Gaussian beam

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Example 4.4.1 Efficiency of the HeNe laserTypical low-power He-Ne laser tube:

power = 5mWoperating dc voltage = 2000Vcurrent = 7 mA

What is the efficiency?

-3

-3

output power 5 10Efficiency = = =0.036%input power 7 10 2000

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Example 4.4.2 Laser beam divergenceTypical He-Ne laser:

output beam diameter = 1 mmdivergence = 1 mrad

What is the diameter of the beam at a distance of 10m?

r

Laser output

L3

We assume the laser beam is a cone, as the below figure, with angle 2 =1 mrad.As the light is propagating, the spot size will be bigger,

rwith the relationship tan = ,L

1so r = (10m)tan 102

rad

=

5

so the diameter of the spot is 11mm.

mm

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4.5 The Output Spectrum of a Gas LaserAverage kinetic energy of molecules: (3/2)kBT

Doppler effect:

=

cvv xv101

+=

cvv xv102

moving away

moving toward

Doppler broadened linewidth: v approx. v2-v1

v = 2-5GHz for many gas lasers, He-Ne laser ~0.02

202/1)2ln(22

McTkvv B=Full width at half maximum

linewidth (FWHM)

Optical gain lineshape around 0= c/v0

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(a) Optical gain vs. wavelength characteristics (called the optical gain curve) of thelasing medium. (b) Allowed modes and their wavelengths due to stationary EM waveswithin the optical cavity. (c) The output spectrum (relative intensity vs. wavelength) isdetermined by satisfying (a) and (b) simultaneously, assuming no cavity losses.

(c)

Relative intensity

m

Optical Gain

Allowed Oscillations (Cavity Modes)

m

(b)

L

Stationary EM oscillationsMirrorMirror

Dopplerbroadening

m(/2) = L

(a)


Fig. 4.8

axial (longitudinal) modes

Finite width due to nonidealities of cavitiesacoustic and thermal fluctuations of Lnonideal end mirror (R

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Solution of Example 4.5.1

2314

1 2 0 2 26 8 2

121 2 1 22

9 60 0

2 ln 2 2(1.38 10 )(400)(ln 2)2 2(4.748 10 ) 1.51 .(3.35 10 )(3 10 )

From 2.02 10 .

And from ( / 2) , we know 2 / (2 0.4 ) /(632.8 10 ) 1.264 10 .

= = =

= = =

=

= = =

Bk T GHzMc

d c md

m Lm L m m

0

0

2

1 2

29 2 130

1 2

2 2 21 2

(632.8 10 ) /(2 0.4 ) 5.006 102

The number of modes in the FWHM of optical gain lineshape is:

4.03 There are 4 or 5 modes.

+

= = =+

= = =

m m m

m

m

L L Lm m m L

m m mL

m

m

5 modes case

4 modes case

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P+P

Laser medium

x

x

P

(a) A laser medium with an optical gain (b) The optical gain curve of the medium. Thedashed line is the approximate derivation in the text.

hE2

E1

Optical Gain

(a) (b)

g()

g(o)


Fig. 4.10

lineshape function: spectral shape of the gain curve

A. Optical Gain Coefficient g

4.6 LASER Oscillation Conditions

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4.6 LASER Oscillation Conditions

exp(-x) : absorption coefficient

exp(gx) g: optical gain coefficient

ph ph

ph ph

N NPP x N x cN t

= = =n

g

A. Optical Gain Coefficient g

( ) ( )( ) ( )

hBNN

hBNhBNdt

dN ph

2112

211212

emissionphoton stimulated of rateNet

==

=

(stimulated absorption)(considering directional wave=> spon. emission is neglected)

(Fig. 4.10)

(optical gain coefficient)

P proportional to Nph (concentration of coherent photons)

2112 BB =

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( )

00

hNh ph ( ) ( ) 21 00 2 1

B h N Nc

n

g

Radiation energy density per unit freq. at hv0 General optical gain coefficient at v0

ph ph

ph ph

N NPP x N x cN t

= = =n

g

( ) ( )( ) ( )

hBNN

hBNhBNdt

dN ph

2112

211212

emissionphoton stimulated of rateNet

==

=

2112 BB = 33

21

21 8ch

BA

=

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L

PiPf

R1R2

Steady state EM oscillations

Optical cavity resonator

Reflectingsurface

Reflectingsurface

Cavity axis x12

Ef Ei


B. Optical Threshold Gain gth

1==i

fop P

PG

Steady state conditions, no optical power loss in the round trip=> net round-trip optical gain Gop = 1.

Losses: R1, R2, absorption (e.g. by impurities, free carriers)scattering (defects and inhomogenities)others

Fig. 4.11

( ) ( )1 2 exp 2 exp 2f iP PR R L L = g

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Simplified description of a laser oscillator. (N2 N1) andcoherent output power (Po) vs. pump rate under continuouswave steady state operation.

Pump rate

Threshold pump rate

(N2 N1)th

N2 N1Threshold populationinversion

Po = Lasing output power(N2 N1) and Po

Fig. 4.12

( ) ( )1 2 exp 2 exp 2f iP PR R L L = g

1 2

1 1ln2th L R R

= +

g

( )2 121 0

thth

cN NB h

ng

Threshold optical gain

Threshold population inversion

( ) ( ) 21 00 2 1B h N N

c

ng

2 1, : fx of pumpingN N

1==i

fop P

PG

( )2 1 pumpingN N Note:

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C. Phase condition and Laser modes

( ) 2trip-round m=Ef = Ei in Fig. 4.11 Phase condition for laser oscillations

( ) ( )2 2mk L m nNeglect changes at mirrors

Lm m =

n2Approx. laser

cavity modeslongitudinal (axial) modes

Ideally, infinitely wide mirrors plane waves are assumedPractically, finite size mirrors Gaussian beams are the solutions

Off-axis modes can exist and replicate themselves=> transverse modes or transverse electric and magnetic (TEM) modesEach transverse mode with a given p,q has a set of longitudinal modes.

Usu. m is very large ~ 106 in gas lasers

A mode with a certain field pattern at a reflector can propagate to the other reflector and back again and return the same field pattern.

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Wave fronts

Sphericalmirror

Optical cavityTEM00 TEM10

TEM01 TEM11

TEM00 TEM10

TEM01 TEM11

(b)

(c) (d)

Laser Modes (a) An off-axis transverse mode is able to self-replicate after one roundtrip. (b) Wavefronts in a self-replicating wave (c) Four low order transverse cavitymodes and their fields. (d) Intensity patterns in the modes of (c).

(a)


Transverse modes depend on: optical cavity dimensions, reflector sizes,..Cartesian (rectangular) or polar (circular) symmetry about the cavity axis

(Brewster angle)

highly desirable TEM00: lowest mode, radially symmetric, lowest divergence

Fig. 4.13

TEMpqm

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Example 4.6.1 Threshold population inversion for the He-Ne laserShow that the threshold population inversion Nth = (N2-N1)th :

where 0 = peak emission frequencyn = refractive indexsp = 1/A21 = mean time for spontaneous transition = optical gain bandwidth (frequency linewidth of optical gain lineshape)

Ex: He-Ne laser: operation wavelength = 623.8 nmtube length L = 50 cm tube diameter = 1.5 mmmirror reflectances: 100% and 90%linewidth = 1.5 GHzloss coefficient 0.05 m-1

spontaneous decay time constant sp = 1/A21 300 nsn 1

What is the threshold population inversion?

2 202

8 spth th

v vN g

c

n ( )2 1

21 0thth

cN NB h

g

n

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=

= =

= =

= + =

=

3321 21

2 20

2 1 3 221

03 30

8 1 1490

1

1 2

2 202

8/ ,

8 n( )

n8 n

3 10And 4.74 10 ,632.8 101 1from the given condition, ln 0.155

2

8 n(0.155

spth th th th

th

spth th

hA B ccN N N g g

A c chh

ms Hzm

g mL R R

N g mc

=

14 1 2 9 9 11

8 1 2

15 3

8 (4.74 10 )(1 )(300 10 )(1.5 10 ))(3 10 )

4.4 10

s s sms

m

( )2 121 0

thth

cN NB h

ng

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p+ n+

EF n

(a)

Eg

Ev

Ec

Ev

Ho les in V BElectro ns in C B

Junction

Electro nsEc

p+

Eg

V

n+

(b)

EF n

eV

EF p

The energy band diagram of a degenerately doped p-n with no bias. (b) Banddiagram with a sufficiently large forward bias to cause population inversion andhence stimulated emission.

In v ers io nreg io n

EF p

EcEc

eVo


Fig. 4.14

degenerate dopingn > Nc, p>Nv

4.7 Principle of the Laser Diode

EF= eV > Eg

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CB

g(E)

E

Impuritiesforming a band

(a) (b)

EFp

Ev

EcEFn

Ev

Ec

CB

VB

(a) Degenerate n-type semiconductor. Large number of donors form aband that overlaps the CB. (b) Degenerate p-type semiconductor.?1999 S O K O t l t i (P ti H ll)

E. Degenerate and Non-degenerate SemiconductorsNon-degenerate semiconductor:

The electron statistics ~the Boltzmann statistics (4)Pauli exclusion principle can be neglected.

vc NpNn

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1( )1 exp F

B

f EE E

k T

=

+

eVEF =

(1)

g ( ) ( )cc

E x

CBEn E f E dE

+=

(2)

(3)

B. Semiconductor Statistics

Probability of finding e-Fermi-Dirac function

Density of States (DOS) ( ) 21)( cEEEg

Electron concentration in CB

exp c FcB

E En Nk T

=

(4)

( ) ( ) ( ) StatisticsBoltzmann exp

>> Tk

EEEfTkEEB

fBfc

[ ] 2/32* /22 hTkmN Bec =Effective DOS at the CB edge

Non-degenerate Semiconductor(# of e-Nv

4.7 Principle of the Laser Diode

EF= eV > Eg

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No applied voltage, EFp = EFn

Fig. 4.14(a) degenerate doping

Fig. 4.14(b) applied voltage V, EF = eV > Eg

- Diminishes the built-in potential barrierSCL is no longer depleted

- In SCL, more electrons in the conduction band at energies near Ecthan electrons in the valence band near Ev

Fig. 4.15(a) Population inversion - occurs between energies near Ec and those near Ev around the junction- Called inversion layer or active layer- Incoming photons stimulate direct recombinations

More stimulated emission than absorption => optical gain

-

> -g Fn Fp

Fn Fp

E hv E Ehv E E

< < Stimulated emission

Absorption

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hEg

Optical gain EF n EF p

Optical absorption

0

Energy

Ec

Ev

CB

VB

(a) The density of states and energy distribution of electrons and holes inthe conduction and valence bands respectively at T 0 in the SCLunder forward bias such that EFn EFp > Eg. Holes in the VB are emptystates. (b) Gain vs. photon energy.

Density of states

Electronsin CB

Holes in VB= Empty states

EF n

EF p

eV

At T > 0

At T = 0

(a) (b)


Injection pumping: pumping by the forward diode current

Fig. 4.15

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LElectrode

Current

GaAs

GaAsn+

p+

Cleaved surface mirror

Electrode

Active region(stimulated emission region)

A schematic illustration of a GaAs homojunction laserdiode. The cleaved surfaces act as reflecting mirrors.

L


Fig. 4.16

Lm m =

n2

Optical Cavity: feedbackhigh optical intensity

Resonant frequencyMode

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Typical output optical power vs. diode current (I) characteristics and the correspondingoutput spectrum of a laser diode.

Laser

LaserOptical Power

Optical Power

I0

LEDOptical Power

Ith

Spontaneousemission

Stimulatedemission

Optical Power


Threshold current Ith: optical gain in the medium can overcome the photon losses from the cavity

Problems of homojunction LD: threshold current density Jth is too high for practical use~500 A/mm2 for GaAs, can only be operated at very low temperatureJth can be reduced by orders of magnitude by using heterojunction LD

Transparency current: stimulated emission = absorption

(g=gth)

I > Ith => coherent

(typ. 32% reflectingfor n=3.6)

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4.8 Heterostructure Laser DiodesReduction of the threshold current by improving:

A. Rate of stimulated emissioncarrier confinement => establish required e-h concentration for pop. inv.

B. Efficiency of the optical cavityphoton confinement by waveguide

Both can be achieved by heterostructured devicesLEDs vs LDs: stimulated emission > spontaneous emission (require good cavity)

Fig. 4.18p-GaAs and p-AlGaAs are degenerately doped

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Refractiveindex

Photondensity

Activeregion

n ~ 5%

2 eV

Holes in VB

Electrons in CB

AlGaAsAlGaAs

1.4 eV

Ec

Ev

Ec

Ev

(a)

(b)

pn p

Ec

(a) A doubleheterostructure diode hastwo junctions which arebetween two differentbandgap semiconductors(GaAs and AlGaAs).

2 eV

(b) Simplified energyband diagram under alarge forward bias.Lasing recombinationtakes place in the p-GaAs layer, theactive layer

(~0.1 m)

(c) Higher bandgapmaterials have alower refractiveindex

(d) AlGaAs layersprovide lateral opticalconfinement.

(c)

(d)


GaAs

Fig. 4.18

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Schematic illustration of the the structure of a double heterojunction stripecontact laser diode

Oxide insulator

Stripe electrode

SubstrateElectrode

Active region where J > Jth.(Emission region)

p-GaAs (Contacting layer)

n-GaAs (Substrate)

p-GaAs (Active layer)

Currentpaths

L

W

Cleaved reflecting surfaceEllipticallaserbeam

p-AlxGa

1-xAs (Confining layer)

n-AlxGa

1-xAs (Confining layer) 12 3

Cleaved reflecting surface

Substrate


Fig. 4.19

p-GaAs: 870-900 nm (dep. on doping, can also be AlyGa1-yAs for controlled wavelength)Stripe contact: define current densityGain guided => reduce Ith, better coupling to fiber W: few m, Ith: tens mA

small lattice mismatchnegligible strain inducedinterfacial defectsless nonradiative recomb.

(avoid Schottky junction)

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Oxide insulation

n-AlGaAs

p+-AlGaAs (Contacting layer)

n-GaAs (Substrate)

p-GaAs (Active layer)n-AlGaAs (Confining layer)

p-AlGaAs (Confining layer)

Schematic illustration of the cross sectional structure of a buriedheterostructure laser diode.

Electrode

Stripe geometry => poor optical confinement in lateral direction

Buried double heterostructureIndex guided: better lateral optical confinement

can be single mode by small V number

Efficiency can be further improved by higher reflection in the facet => dielectric mirror=> reduce threshold current Ith

1 2

1 1ln2th L R R

= +

g R=0.33 @ n=3.7 (GaAs)

~900nm GaAs/AlGaAs~1.3, 1.55m InGaGaP (InP substrate)

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Example 4.8.1 Modes in a laser and the optical cavity lengthAlGaAs based heterostructure laser diode

optical cavity length = 200 m peak radiation: 870 nmrefractive index of GaAs = 3.7FWHM wavelength width (gain vs. wavelength) = 6 nm

(a) What is the mode integer m of the peak radiation?(b) What is the separation between the modes of the cavity?(c) How many modes are there within the bandwidth?(d) How many modes are there if cavity length = 20 m?

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2

m 2

9 2

m 6

The relationship between the free-space wavelength of cavity mode

and the length of the cavity is: 2

2 1644.4 1644

2 2 2And 1 2

(900 10 )When 200 , 2(3.7)(200 10

m Ln

nLm

nL nL nLm m m nL

L m

=

= =

= =+

= =

m

1 2

m

0.547)

When 20 , 5.47

There are modes in the optical gain linewidth,

when =200 , there are 10 modes in the linewidth,when =20 , there is only one mode in the linewidth.

nm

L m nm

L mL m

=

= =

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(a) Optical gain vs. wavelength characteristics (called the optical gain curve) of thelasing medium. (b) Allowed modes and their wavelengths due to stationary EM waveswithin the optical cavity. (c) The output spectrum (relative intensity vs. wavelength) isdetermined by satisfying (a) and (b) simultaneously, assuming no cavity losses.

(c)

Relative intensity

m

Optical Gain

Allowed Oscillations (Cavity Modes)

m

(b)

L

Stationary EM oscillationsMirrorMirror

Dopplerbroadening

m(/2) = L

(a)


Fig. 4.8

axial (longitudinal) modes

Finite width due to nonidealities of cavitiesacoustic and thermal fluctuations of Lnonideal end mirror (R single mode, TEM00divergence: smaller aperture => larger diffraction (e.g. H in Fig. 4.21)

B. Optical Gain Curve

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Height, H Width W

Length, L

The laser cavity definitions and the output laser beamcharacteristics.

Fabry-Perot cavity

Dielectric mirror

Diffractionlimited laserbeam


Fig. 4.21

alternating n1 & n2 with thicknesses in quarter wavelengths

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778 780 782

Po = 1 mW

Po = 5 mW

Relative optical power

(nm)

Po = 3 mW

Output spectra of lasing emission from an index guided LD.At sufficiently high diode currents corresponding to highoptical power, the operation becomes single mode. (Note:Relative power scale applies to each spectrum individually andnot between spectra)


Red shift: temperature-induced gain shifting due to heating

Fig. 4.22

Index guidedmay become single mode at high I

Gain guidedstill multimode even at high I(no lateral optical confinement)

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901 37500

Fig. 4.24

Temp. Refractive Index center wavelength cavity length

o(nm)

Mode hopping

20 30 40 50Case temperature ( C)

Single mode

776

778

780

782

784

786

788

20 30 40 50Case temperature ( C)

Single mode

20 30 40 50

Multimode

Case temperature ( C)

Peak wavelength vs. case temperature characteristics. (a) Mode hops in the outputspectrum of a single mode LD. (b) Restricted mode hops and none over the temperaturerange of interest (20 - 40 C). (c) Output spectrum from a multimode LD.

(a) (b) (c)


Avoid mode hopssufficiently separated modes to reduce the chance of mode hoppingthermoelectric (TE) cooler to control device temp.

Slope efficiency P/(I-Ith)Conversion efficiency: output optical power / input electric power

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0 20 40 60 800

2

4

6

8

10

Po (mW)

I (mA)

0 C25 C

50 C

Output optical power vs. diode current as three different temperatures. Thethreshold current shifts to higher temperatures.


Fig. 4.23

thIIP

= 0slope

Slope efficiency

Threshold current increases exponentially with the absolute temperature.

Conversion efficiency

=

may be as high as 30-40%

output optical powerinput electrical power

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901 37500

4.10 Steady State Semiconductor Rate Equation

phph

ph CnNN

=

Steady state: Rate of the coherent photon loss = Rate of stimulated emission

ph: due to trans. thru end-faces, scattering, absorption

Rate of electron inject by current= Rate of spontaneous emission + Rate of stimulated emission

C: constant dep. on B21Nph: coherent photon encouraged

by the optical cavity (mode)

Consider double heterojunction (DH) laser diode (LD) (Fig. 4.19)

Under steady state operation

n: injected electron concentration

(neglect non-radiative recombination)

phsp

I n CnNedLW

= + (1)

Active layer

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901 37500

Threshold: simulated emission just overcomes the spontaneous emission + total loss mechanisms in ph

Schematic illustration of the the structure of a double heterojunction stripecontact laser diode

Oxide insulator

Stripe electrode

SubstrateElectrode

Active region where J > Jth.(Emission region)

p-GaAs (Contacting layer)

n-GaAs (Substrate)

p-GaAs (Active layer)

Currentpaths

L

W

Cleaved reflecting surfaceEllipticallaserbeam

p-AlxGa

1-xAs (Confining layer)

n-AlxGa

1-xAs (Confining layer) 12 3

Cleaved reflecting surface

Substrate

phth C

n1

=

thth

sp

n edLWI I

= =

At threshold

Right before lasing, coherent photon by the cavity: Nph = 0

Smaller Ith: heterostructureand stripe geometry

Stimulated emission just balanced by (all loss + spontaneous emission)

From phph

ph CnNN

=

from

dLW Ith

Scattering, absorption, out-coupling(steady state)

phsp

I n CnNedLW

= +

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901 37500

Simplified and idealized description of a semiconductor laserdiode based on rate equations. Injected electron concentrationn and coherent radiation output power Po vs. diode current I.

IIth

nth

n

nThreshold populationinversion

Po

Po = Lasing output power Nph

?1999 S O Kasap Optoelectronics (Prentice Hall)

phthth NCn

edLWII

= ( )thphph JJedN =

( )( )( )R

t

NP

ph

= 1energyPhoton VolumeCavity

21

0

( ) ( )2

0

12

phth

hc W RP J J

e

= n

Above threshold J=I/WL =>

O/P opticalpower t=nL/c

=> Laser diode equation

Fig. 4.25 Nph: coherent photon concentratoin

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4.11 Light Emitters for Optical Fiber Communications

Short haul: LED larger simpler to drive, economic, longer lifetimeusually with multimode graded index fibers

Long haul: LDnarrow linewidth and high output power

A laser diode pigtailed to a fiber. Two of the leads are fora back-facet photodetector to allow the monitoring of thelaser output power (Courtesy of Alcatel)

Comparison, see Fig. 4.26 and Table 4.1

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901 37500

Typical optical power output vs. forward currentfor a LED and a laser diode.

Current0

Light powerLaser diode

LED

100 mA50 mA

5 mW

10 mW


Fig. 4.26

rise time: light output 10% to 90%LD has very short r used when wide bandwidth (bit rate) is required

Short haul

Long haul

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901 37500

< 0.01 nm in single frequency LD

One mode by suppressing unwanted mode through design, ~ 0.01~0.1nm

Laser diode

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Corrugateddielectric structure

Distributed Braggreflector

(a) (b)

AB

q(B/2n) =

Active layer

(a) Distributed Bragg reflection (DBR) laser principle. (b) Partially reflected wavesat the corrugations can only constitute a reflected wave when the wavelengthsatisfies the Bragg condition. Reflected waves A and B interfere constructive whenq(B/2n) = .


4.12 Single Frequency Solid State Lasers

Fig. 4.27

B: Bragg wavelengthq: diffraction order

2Bq =n

Distributed Bragg reflector (DBR) laser

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901 37500

Active layer

Corrugated grating

Guiding layer

(a)

(a) Distributed feedback (DFB) laser structure. (b) Ideal lasing emission output. (c)Typical output spectrum from a DFB laser.

Optical power

(nm)

0.1 nm

Ideal lasing emission

B(b) (c)


Distributed feedback (DFB) laser

Fig. 4.28

( )2

12

Bm B mL

= +n

Right and left traveling waves are coupledset up a standing wave if they are coherently coupled(round-trip phase change =2)

m=0 dominatesbecause relative threshold gain of higher modes is higherIdeally, perfectly symmetric (b) Practically, asymmetry induced on purpose (c)

L>> m~B Commercially available 1.55m ~0.1nm

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Activelayer

L D

(a)

Cleaved-coupled-cavity (C3) laser

Cavity Modes

In L

In D

In bothL and D

(b)


Cleaved-coupled-cavity (C3) laser

Two lasers are pumped by different currentsOnly those waves that can exist as modes in both cavities are allowed

Wide separation between the modes => single mode operation

Fig. 4.29

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901 37500

Example 4.12.1 DFB LaserDFB laser has: corrugation period = 0.22 m

grating length = 400 meffective refractive index of the medium = 3.5

For a first order grating, calculate:(a) Bragg wavelength(b) mode wavelength(c) mode separation

B

2B

B

0

The Bragg wavelength is :2 2(0.22 )(3.5) 1.540

1(1.54 )( 1) 1.54 (0 1)

2 2(3.5)(400 )The wavelength of the mode with 0 is:

1.5392 or 1.5408 .

= = =

= + = +

==

m

n m mq

mmnL m

mm m

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901 37500

4.13 Quantum Well Devices

Fig. 4.30Ultra thin, typ. < 50nm, narrow bandgap semiconductor devicesLattice match is required

d

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901 37500

Ec

Ev

E1

E1

h = E1 ? E1

E

In single quantum well (SQW) lasers electrons areinjected by the forward current into the thin GaAslayer which serves as the active layer. Populationinversion between E1 and E 1 is reached even with asmall forward current which results in stimulatedemissions.


Fig. 4.31

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901 37500

Active layer Barrier layerEc

Ev

E

A multiple quantum well (MQW) structure.Electrons are injected by the forward currentinto active layers which are quantum wells.


A 1550 nm MQW-DFB InGaAsPlaser diode pigtail-coupled to a fiber. (Courtesy of Alcatel.)

Fig. 4.32

Multiple quantum well (MQW) laser

Larger volumeMQW spectrum < bulk spectrum, but MQW still not necessarily single mode=> MQW +DFB

SQW: power not largeEnhancement by MQW

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Example 4.13.1 A GaAs quantum wellElectron effective mass: 0.07me (me: electron mass in vacuum)Hole effective mass: 0.5me Quantum well thickness = 10 nmFind: (a) first two electron energy levels

(b) hole energy (below Ev)(c) change in the emission wavelength w.r.t. bulk GaAs

(energy gap of bulk GaAs = 1.42 eV)

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901 37500


1

2 2

* 2

1 22 2

'* 2

'

, where is the quantum number,8

from the given conditions, we get 0.0537 , 0.215 .

And the energy of holes is ,8

from the given conditions, we get 0.0075 .

No

n

n n ce

h

h nE E nm d

eV eVh nm d

eV

= =

= =

=

=

1

QW '1

w we calculate the emission wavelength of bulk GaAs,

from =1.42eV, we get 874 .

Now for GaAs quantum well,

839 ,

The emission wavelength shifts 35nm.

g gg

g

hcE nmE

hc nmE

= =

= =+ +

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4.14 Vertical Cavity Surface Emitting Lasers (VCSELs)

See Fig. 4.33Dielectric mirrors

21

2211 =+ dd nn

(DBR structure)

High reflectance end mirrors are needed due to short cavity length20-30 or so layers to obtain the required reflectance (99%)

Active layer: very thin single mode longitudinally (maybe not laterally)

(pumping EDFA)

Maybe not laterally, dep. on lateral size In practice, single lateral modeDiameter < 8 m spectrum width ~0.5 nm

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A simplified schematic illustration of a vertical cavitysurface emitting laser (VCSEL).

Contact

Surface emission

Dielectric mirror

Contact

Substrate

/4n1

Active layer

/4n2 Dielectric mirror


Fig. 4.33

21

2211 =+ dd nn

(MQW)

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An 850 nm VCSEL diode.(Courtesy of Honeywell.)

SEM (scanning electron microscope) of the first low-threshold VCSELsdeveloped at Bell Laboratories in 1989. The largest device area is 5 m in diameter (Courtesy of Dr. Axel Scherer Caltech.)

Microlaser: cavity dimension in the microns rangeMatrix emitter: arrayed microlaser, broad area surface emittiner laser sourse

optical inter connect, optical computinghigher optical power than conventional laser, few watts

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Simplified schematic illustrations of two types of laser amplifiers

Pump current

Active region

AR = Antireflectioncoating

AR

Signal in Signal out

(a) Traveling wave amplifier (a) Fabry-Perot amplifier

Partial mirror Partial mirror


Fig. 4.34

4.15 Optical Laser AmplifiersAmplified by induced stimulated emissionPumped to achieve optical gain

(i.e. population inversion)Random spontaneous emission

=> noise => filtered outTyp. ~20dB, dep. on the AR coating

Under threshold currentAmplified by stim. EmissionMultiple reflectionHigher gain, less stable

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4.16 Holography A technique of reproducing three dimensional (3D) optical image of an objectby using a highly coherent radiation from a laser source

Fig. 4.35

Ecat: both amplitude and phase variations representing the cats surfaceReflected Ecat interferes with Eref at photographic plateInterference pattern depends on the magnitude and phase variations in Ecat.Hologram: recorded interference patter in the photographic film

Diffracted beam: virtual image (Bragg condition d sin = m )

Thru beam: real image

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Incidentlight wave

m = 0

m = -1

m = 1

Zero-order

First-orde

First-order

(a) Transmission grating (b) Reflection grating

Incidentlight wave

Zero-orderFirst-order

First-order

(a) Ruled periodic parallel scratches on a glass serve as a transmission grating. (b) Areflection grating. An incident light beam results in various "diffracted" beams. Thezero-order diffracted beam is the normal reflected beam with an angle of reflection equalto the angle of incidence.


(sin sin ) m 0, 1, 2,...m id m = ; = (8)

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Real cat imagVirtual cat image(b)

Photographic plate(a)

Hologram

Laserbeam Through beam

Observer

Cat

Mirror

Laserbeam

Ecat(x,y)

Eref(x,y)

Ecat(x,y)Eref(x,y)

A highly simplified illustration of holography. (a) A laser beam is made to interfere withthe diffracted beam from the subject to produce a hologram. (b) Shining the laser beamthrough the hologram generates a real and a virtual image.


Fig. 4.3580

901 37500

( ) ( ) tjr eyxUyxE ,,ref = ( ) ( ) tjeyxUyxE ,,cat =( ) ( )( )**22catref, UUUUUUEEyxI rrr ++=+=+=

( ) ****, UUUUUUUUyxI rrrr +++=

( ) ( )****, UUUUUUUUUyxIUU rrrrrrt +++=( ) ( ) ( ) *2***, UUUUUUUUUUyxIUU rrrrrrrt +++=( ) ( )yxcUyxbUaUt ,, *++

Pattern on the hologram

Illuminating the hologram with reference beam

i.e.

a = Ur(UU*+UrUr*) constant: through beambU: scaled version of U: virtual imagecU*: complex conjugate of U: real image, conjugate image

Eye can not detect phase shift. Observer always sees the positive image.

Holography is a method of wavefront reconstruction.

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Dennis Gabor (1900 - 1979), inventor of holography, is standing next to his holographic portrait. Professor Gabor was a Hungarian born British physicist who published his holography invention in Nature in 1948 while he as at Thomson-Houston Co. Ltd, at a time when coherent light from lasers was not yet available. He was subsequently a professor of applied electron physics at Imperial College, University of London. (From M.D.E.C. Photo Lab, Courtesy AIP Emilio SegrVisual Archives, AIP.)

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