Optics Communications 247 (2005) 319–323

www.elsevier.com/locate/optcom

The effect of the group delay ripple of chirped fiber gratingon composite second-order in optical fiber CATV system

Qing Ye *, Feng Liu, Ronghui Qu, Zujie Fang

Information Optics Laboratory, Shanghai Institute of Optics and Fine Mechanics, CAS, P.O. Box 800-211, Shanghai 201800, PR China

Received 20 July 2004; received in revised form 11 October 2004; accepted 18 November 2004

Abstract

The effect of group delay ripple of chirped fiber gratings on composite second-order (CSO) performance in optical

fiber CATV system is investigated. We analyze the system CSO performances for different ripple amplitudes, periods

and residual dispersion amounts in detail. It is found that the large ripple amplitude and small ripple period will dete-

riorate the system CSO performance seriously. Additionally, the residual dispersion amount has considerable effect on

CSO performance in the case of small ripple amplitude and large ripple period.

� 2004 Elsevier B.V. All rights reserved.

PACS: 42.81.-i; 07.60.Vg; 81.05.NiKeywords: Group delay ripple; Chirped fiber grating; Composite second-order; Optical fiber CATV system

1. Introduction

Long-distance transmission of 1550-nm AM-

VSB CATV systems based on the conventional

single-mode fiber (SMF) have become widespread

throughout the cable industry because of its large

number of distribution nodes and high video qual-ity [1,2]. However, fiber dispersion is one of the

most severe limiting factors in long fiber transmis-

0030-4018/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.optcom.2004.11.067

* Corresponding author. Tel.: +86 21 69918685; fax: +86 21

69918033.

E-mail address: yeqing@mail.siom.ac.cn (Q. Ye).

sion link. Fiber dispersion along with laser chirp-

ing generates composite second-order (CSO) in

multiple RF channels optical transmission sys-

tems. Higher chirp lasers over longer distances of

fiber have worst CSO performance. Up to now,

several compensation techniques have been pro-

posed to improve the system CSO performance.The most obvious one is the use of externally mod-

ulated transmitter because of its almost nonexis-

tent chirping generates very little fiber-induced

CSO distortion. Others include the dispersion

compensation fiber (DCF) and reverse dispersion

fiber (RDF) within the fiber transmission distance

ed.

320 Q. Ye et al. / Optics Communications 247 (2005) 319–323

[3] and the differential detection technique through

two fibers transmission to recombine the RF sig-

nals from the optical receiver in-phase [4]. How-

ever, it is difficult to obtain good CSO and

composite triple beat (CTB) performances due topoor carrier-to-noise ratio (CNR) resulted from

the use of DCF and RDF with their inherent high

power insertion losses in full channel loading.

In recent studies, chirped fiber grating (CFG)

has been used as a fiber dispersion compensation

device in digital and analog subcarrier-multiplexed

lightwave systems [5–7] due to its lots of advanta-

ges [8]. In order to improve the dispersion compen-sation performance of CFG, the apodization

technology is used in the process of the CFG fab-

rication and the side lobs in the reflective spectra

may be eliminated. However, there still remain

slight pseudo-periodic group-delay characteristics

(ripples). The period of the ripple depends on the

length of the grating and the transmitter wave-

length with respect to the grating bandwidth andhas roughly a range of �10 pm. In addition, the

imperfect fabrication process introduces stochastic

variation in the time delay and reflectivity re-

sponse. In some literatures [9,10], the effects of

the group delay ripple on the dispersion compen-

sations in digital lightwave systems have been

brought forward. In analog lightwave systems,

however, the effect of group delay ripple on CSOperformance still has not been studied although

its effect on dispersion induced intensity noise have

been pointed out [11]. In the present paper, we

investigate the effects of the group delay ripple of

1553.4 1553.7 1554.0 1554.3 1554.60

400

800

1200

1600

Wavelength (nm)

Gro

up d

elay

(ps

)

(a)

Fig. 1. The spectra of (a) group delay and (b

the CFG on the CSO performances in optical fiber

CATV system for different ripple amplitudes, peri-

ods and residual dispersion amounts. We find that

the large ripple amplitude and small ripple period

will deteriorate the CSO performance seriously.However, the effect of the residual dispersion

amount is considerable for small ripple amplitude

and large ripple period. Our analytic results are in

good agreement with the numerical simulations.

2. Theoretical analysis

An ideal linear dispersion compensator would

exhibit a constant reflectivity and linear group de-

lay characteristic over a large operating bandwidth

and this has been the objective of recent develop-

ments in grating fabrication [12]. However, as dis-

cussed it is likely that all chirped fiber gratings will

exhibit pseudo-periodic deviations from ideal

characteristics (ripples) as is shown in Fig. 1. Thisfigure shows our experiment spectra of the group

delay and its ripple for a 10-cm CFG. Usually,

the group delay ripple amplitude of the chirped fi-

ber grating is below 50 ps (e.g. Fig. 1(b)). The

group delay may be investigated by adding peri-

odic functions to the group delay of an ideal linear

dispersion compensator and can be written as [9]:

s ¼ s0 þ Q0kþ ds sinð2pk=pÞ: ð1ÞHere, s0 is the initial group delay and Q0 is the

first-order dispersion value. ds and p are the group

1553.7 1554.0 1554.3 1554.6

0

60

120

-60

-120

-180

Wavelength (nm)

Gro

up d

elay

rip

ple

(ps)

(b)

) group delay ripple of a 10-cm CFG.

0 10 20 30-100

-80

-60

-40

p=0.1nmp=0.05nmp=0.02nmCS

O(d

Bc)

The amplitute of ripple δτ (ps)

numerical simulationeqn.7

Fig. 2. The CSO performance as a function of the ripple

amplitude with different ripple periods.

Q. Ye et al. / Optics Communications 247 (2005) 319–323 321

delay ripple amplitude and period, respectively.

The corresponding fiber grating dispersion is

Qg ¼osok

¼ Q0 þ2pdsp

cosð2pk=pÞ: ð2Þ

From the literature [13], we introduce the vari-

ation rate of the phase / (i.e., the chirping):

d/dt

¼ a2I

dIdt

; ð3Þ

where a = Dn 0/Dn00 is the relative change of the realpart Dn 0 and imaginary part Dn00 of the refractive

index. I = |E|2 is the instantaneous intensity. Atthe same time, we express frequency modulation

(FM) efficiency g (MHz/%) as the frequency chirp-

ing per modulation depth [14]

g ¼ 1

2p100md/dt

����max

: ð4Þ

Note that g is usually expressed as the maximum

value. Making use of the expression (4) and the lit-erature [15], the CSOi of the ith channel induced

by the dispersion of the fiber transmission link

may be written as

CSOi ¼ ð200pÞ2C2im2f 2i D

2fL

2f g

2k4=c2: ð5ÞHere, C2i and fi are the second harmonic count and

the RF signal frequency of the ith channel, respec-

tively. m is the optical modulation index. Df de-

notes the dispersion coefficient and Lf is the

optical signal transmission distance. k and c de-

note the wavelength and light velocity in the vac-

uum. When the dispersion compensation of CFGis considered, the upper description can be rewrit-

ten as

CSOi ¼ ð200pÞ2C2im2 fiðDfLf � QgÞgk2=c� �2

; ð6Þ

where Qg is the fiber grating dispersion described

by the expression (2). It is clear that if the group

delay ripple is negligible, Qg may be substitutedby the first-order dispersion Q0 . In the dispersion

compensation system, however, the group delay

ripple is non-neglected and its effect on the CSO

must be considered. In order to show the extent

of the group delay ripple effect on the CSO perfor-

mance, we first suppose that the dispersion

amount of the fiber transmission link is compen-

sated by the first-order dispersion of CFG com-

pletely (i.e., DfLf � Q0 = 0). Then the CSO may

be expressed as

CSOi ¼ ð200pÞ2C2im2 fi2pdsgk2

pccosð2pk=pÞ

� �2

:

ð7ÞFig. 2 shows theoretical analysis results (solid

line) and numerical simulations (dotted line) of

CSOi as a function of the group delay ripple

amplitude ds with different ripple periods. In the

following, parameters are taken to be: m = 0.04,k = 1550 nm, fi = 544.5 MHz, g = 2 MHz/%,

c = 3 · 108 m/s , and C2i = 21. The numerical sim-

ulation results are obtained by solving the wave-

envelope equations (i.e. the Eq. (3) of the literature

[16]) of the fiber and fiber grating using the itera-

tive method, wherein the output modulation signal

of the fiber is considered to be the initial input sig-

nal of the fiber grating. From the figure, one cansee clearly that the theoretical analysis result is in

good agreement with the numerical simulation.

At the same time, the group delay ripple may affect

the CSO performance of the optical fiber CATV

system seriously. When the ripple amplitude is

zero (without ripple), the CSO is very small

(<�100 dBc). This case may be considered as

CSO distortionless. As the ripple amplitude in-creases, the CSO performance of the system dete-

riorates quickly. For instance, in the case of

p = 0.05 nm, the CSO achieves �60 dBc when

the ripple amplitude increases into 7 ps. For larger

0 10 20 30-100

-80

-60

-40 (a)

CS

O(d

Bc)

The amplitude of ripple δτ (ps)

DfL

f-Q

0=50ps/nm

DfL

f-Q

0=200ps/nm

DfL

f-Q

0=500ps/nm

0 10 20 30-100

-80

-60

-40 (b)

CS

O(d

Bc)

The amplitude of ripple δτ (ps)

DfL

f-Q

0=50ps/nm

DfL

f-Q

0=200ps/nm

DfL

f-Q

0=500ps/nm

0 10 20 30-100

-80

-60

-40(c)

CS

O(d

Bc)

The amplitude of ripple δτ (ps)

DfL

f-Q

0=50ps/nm

DfL

f-Q

0=200ps/nm

DfL

f-Q

0=500ps/nm

Fig. 3. The CSO performance as a function of the ripple amplitude with different residual dispersion amounts. (a) p = 0.02 nm,

(b) p = 0.05 nm, (c) p = 0.1 nm.

322 Q. Ye et al. / Optics Communications 247 (2005) 319–323

ripple amplitudes, the CSO deteriorates more seri-ously and will not satisfy the requirement of the

usual CATV systems. On the other hand, the rip-

ple period also has effect on the CSO performance.

Consider the case of ds = 10 ps , the CSO distor-

tion achieves �50, �58 and �68 dBc for ripple

period of 0.02, 0.05 and 0.1 nm, respectively. It is

obvious that the smaller the ripple period is, the

worse the CSO performance of the system willbe. Therefore, we can say that small ripple ampli-

tude and large ripple period of CFG can improve

the CSO performance.

The preceding discussions show that the ripple

amplitude and period influence the system CSO

performance on condition that the system disper-

sion is compensated completely. However, in some

cases the dispersion of the CFG cannot completelycompensate the dispersion generated by the trans-

mission link (i.e., DfLf � Q0 6¼ 0) and there is some

residual dispersion in the system. Fig. 3 displays

the theoretical results of the CSO performance as

a function of the group delay ripple amplitude dswith different residual dispersion amounts and rip-

ple periods. Each plot of Fig. 3 shows that in the

case of small ripple amplitudes, the CSO perfor-mance deteriorates sharply with the increase of

the residual dispersion amount. However, for large

ripple amplitudes, the effects of the different resid-

ual dispersion amounts on CSO performance be-

comes slight. On the other hand, from Fig. 3 we

see that larger ripple period leads to better CSO

performance and this result is in consistent with

the case of without residual dispersion, as shownin Fig. 2. Meanwhile, it is also found that the effect

of residual dispersion amounts on the CSO perfor-

mance will be more distinct for larger rippleperiod. The main cause is that the large ripple

amplitude and small ripple period generates a large

CSO distortion which will play a primary role

compared with the CSO distortion induced by

the residual dispersion amount of the fiber trans-

mission link. Consequently, one should focus on

enhancing the ripple period, decreasing the ripple

amplitude and minimizing the residual dispersionamounts in order to achieve good CSO

performance.

3. Conclusion

We have investigated the effect of the group de-

lay ripple of the CFG on the composite second-order in optical fiber CATV system for different

ripple amplitudes, periods and residual dispersion

amounts of the transmission link in detail. It is

found that the large ripple amplitude and small

period will deteriorate the CSO performance seri-

ously. Additionally, the residual dispersion

amount has obvious effect on CSO performance

in the case of small ripple amplitude and large rip-ple period. In a word, we should enhance the rip-

ple period, decrease the ripple amplitude and

minimize the residual dispersion amounts in order

to achieve good CSO performance.

Acknowledgements

This work is supported by the pre-research item

of �973� of China under Grant No. 2001CCA04600

Q. Ye et al. / Optics Communications 247 (2005) 319–323 323

and the Science and Technology Development

Fund of Shanghai Science Committee (02dj14001).

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