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
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]:


 
22
1012
1111
11
1
2
cos()()
gsc
P
f
in
dE vG NNEEE
dt
KEtt t
 



 


 
1
(1)




22
1012
1
111
1
11
1
2
()sin ()(
gsc
P
f
th
in
dvG NNEE
dt
KEt tt
E



1
)




 



  
(2)


22
2021
11
1
2gsc
P
dE vG NNEEE
dt
 

 


2
(3)


22
2021
2
11
1
2
()
gsc
P
th
dvG NNEE
dt




 



(4)

 
0
222 22
121 212
11
ig
s
scs c
I dNN vG NN
dt eV
EEEE EE


 
 
 

2
(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
0.1
0.2
0.3
0.4
0.5
0
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
0
1
2
3
4
5
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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164
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