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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