Generation of Feedback-induced Chaos in a Semiconductor Ring Laser

doi:10.4236/opj.2013.32B039

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Optics and Photonics Journal, 2013, 3, 162-164

doi:10.4236/opj.2013.32B039 Published Online June 2013 (http://www.scirp.org/journal/opj)

Generation of Feedback-induced Chaos in a

Semiconductor Ring Laser

Xin Zhang, Guohui Yuan, Zhuoran Wang

School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu, Sichuan, China

Email: [email protected]

Received 2013

ABSTRACT

A scheme for chaotic signal generation in a semiconductor ring laser (SRL) with optical feedback is presented. Part of

the output is returned to the SRL, resulting in chaotic oscillation.

Keywords: (140.1540) Chaos; (140.5960) Semiconductor Lasers; (140.0140) Lasers and Laser Optics; (060.0060)

Fiber Optics and Optical Communications

1. Introduction

It is previously demonstrated that semiconductor lasers

are widely used in the chaotic Optical communications as

chaotic carrier source [1-2]. As a special case of semi-

conductor laser, semiconductor ring lasers (SRLs) can

also be utilized to chaotic communication systems.

In this paper, we demonstrate the chaotic signal gen-

eration in a SRL with an optical feedback. Simulated

results indicate the existence of chaotic oscillation in the

SRL with appropriate disturbance.

2. Feedback-induced Chaos Scheme

The feedback-induced scheme for the generation of

chaos is based on a SRL with a feedback waveguide as

shown in Figure 1. Part of the output of the SRL is in-

jected back to its cavity after a certain time delay, which

induces chaotic oscillation in the SRL with appropriate

feedback parameters. Simultaneously, the lasing direc-

tion of the drive SRL is set to the clockwise as a result of

mode competition.

Figure 1. Schematic illustration of a SRL with a feedback

waveguide.

The rate equations of the SRL with optical feedback

are described here as [3]:



 

1012

1111

cos()()

gsc

dE vG NNEEE

KEtt t

 







 





 

(1)



1012

111

()sin ()(

gsc

dvG NNEE

KEt tt





)









 







 



(2)



2021

2gsc

dE vG NNEEE

 



 





(3)



2021

()

gsc

dvG NNEE









 







(4)







222 22

121 212

scs c

dNN vG NN

dt eV

EEEE EE





 

 

 



(5)

where E is the electric field amplitude, Φ is the phase,

and N is the carrier density. The subscript 1 and 2 ac-

count for the clockwise and counter-clockwise directions

of the SRL; τ is the delay time of the feedback light. I is

the injection current of SRL; Kf is the feedback coeffi-

cient, the ratio of the feedback light to the light in SRL

controlled by the bias current of the couplers. The de-

tailed parameters of SRL are described in [3].

3. Simulation Results

The dynamics of the SRL with optical feedback depend

X. ZHANG ET AL. 163

on the adjustable system parameters including the delay

time of the feedback light τ, and the bias injection current

I of the SRL, the feedback coefficient Kf. In this paper, τ

is set to 179 fs, which means that the feedback waveguide

is about 15μm longer than that of the corresponding part

of the resonant cavity of the SRL. We focus on the effect

of the feedback coefficient and the bias injection current

of the SRL on the nonlinear system.

It is well known that any system containing at least

one positive lyapunov exponent is defined to be chaotic

and the larger the magnitude of the positive lyapunov

exponent is, the more chaotic the system is. The map of

largest lyapunov exponent of the system is presented in

Figure 2 as a function of the feedback coefficient and the

bias injection current of the SRL, which is approximately

computed based on the classic Wolf’s algorithm [4]. It is

clear that the system is chaotic for the most part of the

region in Figure 2. Figure 3 shows that the chaotic out-

put from the SRL when the feedback coefficient 0.25 and

the bias current of the SRL is 110 mA, where the largest

lyapunov exponent is about 0.14. Figure 3(a) is the

Random-like time series and Figure 3(b) is the impulse-

like autocorrelation, which also indicates a chaotic system.

Injection coefficient

Bias current of SRL (mA)

50 100 150

0.1

0.2

0.3

0.4

0.5

0.05

0.1

Figure 2. Largest lyapunov exponent map as a function of

the feedback coefficient and the bias current of the SRL.

01234

Time (ns)

Power (mW)

(a)

-1000 -5000500 1000

0.5

0.6

0.7

0.8

0.9

lags

arb.units

(b)

Figure 3. Time series (a) and autocorrelation (b) of SRL

when the feedback coefficients is 0.25 and the bias current

of the SRL is 110mA.

4. Conclusions

The generation of chaotic signal in a SRL with an optical

feedback is proposed in this paper. The positive lyapunov

exponent map, time series and autocorrelation of SRL

indicate the occurring of chaotic oscillation in our

nonlinear system with suitable system parameters, which

paves the way for the utilization of SRLs in the chaotic

Optical communication systems.

5. Acknowledgements

This work was sponsored in part by the National Natural

Science Foundation of China under Grant 61107061,

Grant 61107088, and Grant 61090393, Program for New

Century Excellent Talents in University under Grant

NCET-12-0092, Specialized Research Fund for the Doc-

toral Program of Higher Education (SRFDP) under Grant

20100185120016, Project of international sci-tech coop-

eration and exchange research of Sichuan Province under

Grant 2012HH0001, the Scientific Research Foundation

for the Returned Overseas Chinese Scholars of State

Education Ministry 2012GJ002, the State Key Labora-

tory of Electronic Thin Films and Integrated Devices

under Grant KFJJ201112, and State Key Laboratory on

Integrated Optoelectronics under Grant 2011KFB008.

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X. ZHANG ET AL.

164

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doi:10.1016/0167-2789(85)90011-9