BANDWIDTH ENHANCEMENT IN CHAOTIC SEMICONDUCTOR LASERS WITH STRONG CHAOTIC OPTICAL INJECTION

April 16, 2012 15:2 WSPC/147-MPLB S021798491250073X 1–7

Modern Physics Letters BVol. 26, No. 12 (2012) 1250073 (7 pages)c© World Scientific Publishing Company

DOI: 10.1142/S021798491250073X

BANDWIDTH ENHANCEMENT IN CHAOTIC SEMICONDUCTOR

LASERS WITH STRONG CHAOTIC OPTICAL INJECTION

HUI-MIN YANG

Department of Physics, Heze University, Heze 274015, Shandong, China

[email protected]

Received 16 January 2012Revised 9 February 2012

The bandwidth properties of chaotic signals generated by semiconductor lasers subjectto strong chaotic optical injection (COI) are investigated numerically. The chaotic out-put of an injection master laser (ML) is injected into the slave laser (SL). The effectsof feedback strength, injection strength and bias current on the bandwidth propertiesare discussed in detail. Some novel results are found, the bandwidth for SL increaseswith the injection strength firstly until reaches a maximum, and then decrease to ap-proach the bandwidth of ML due to the injection-locking chaos synchronization. Largefeedback strength and bias current contributes to higher maximum chaotic bandwidthin the range of injection strength. That is to say, for given parameters, optimal injectionstrength exists contributing to highest chaotic bandwidth, and moves to a large valuefor a large feedback strength and bias current, which is extremely useful for increasingthe transmission rate of the optical chaotic communication system.

Keywords: Semiconductor laser; chaos; bandwidth; chaotic optical injection.

1. Introduction

Since the idea of chaos synchronization was first demonstrated by Pecora and

Carroll,1 the chaotic signal generated by semiconductor lasers has attracted consid-

erable attention In contrast to the conventional electric means, using semiconductor

lasers as chaotic source is beneficial to greatly enhance the system bandwidth in

virtue of the high-frequency oscillation in semiconductor lasers. Recently, optical

chaotic communications have attracted extensive attention from both theoretical

and experimental perspective.2–8 However, compared with the transformation rate

of the available optical network, the bandwidth of chaotic carrier still limits the

practical application of optical chaotic communication system.

So far, many efforts have been devoted to the study of bandwidth enhance-

ment for chaotic sources.9–14 The optical injection has been widely used to en-

hance the bandwidth of chaotic carrier. However, the majority works focused on

the continuous-wave (CW) optical injection. For example, Wang et al. employed

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http://dx.doi.org/10.1142/S021798491250073X

mailto:[email protected]


H.-M. Yang

a distributed feedback semiconductor laser with optical feedback as chaotic laser,

and experimentally demonstrated that the bandwidth was enhanced roughly three

times by injecting CW light.11,12 The detail bandwidth property of semiconductor

laser subject to chaotic optical injection (COI) still remains scarce. Takiguchi et al.

numerically studied the bandwidth-enhanced chaos synchronization in strongly

injection-locked semiconductor lasers with optical feedback.13 The bandwidth of

chaotic carrier was expanded roughly three times by strong optical injection com-

pared with the bandwidth when there was no optical injection, and by using a

bandwidth-enhanced semiconductor laser as chaotic transmitter and receiver, com-

plete chaos synchronization between the transmitter and the receiver lasers was

obtained. Besides, Someya et al. further experimentally investigated the generation

and synchronization of bandwidth-enhanced chaos in a semiconductor laser (drive

laser) that was subject to optical injection from another chaotic semiconductor laser

(injection laser) with optical feedback, where the effective bandwidth enhancement

was achieved over 12 GHz.14 However, it is still open to explore whether the optimal

injection strength exists to gain the highest bandwidth for given parameters.

It is known that, the injection-locking chaos synchronization to the master laser

(ML) would be realized for large injection strength,15 which is not desired for the

further increase of chaotic bandwidth of the slave laser (SL). Thus, increasing the

injection strength may not always lead to higher bandwidth. Hence, the bandwidth

enhancement for chaotic semiconductor lasers subject to COI, is still extremely

useful for the practical chaotic communication systems, and deserves extensive in-

vestigation. In this work, we consider the bandwidth enhancement properties of

SL subject to COI, and try to obtain an optimal selection of injection strength to

obtain highest bandwidth. The effects of injection strength, feedback strength and

bias current are discussed.

2. Theory

The master–slave configuration is considered here, which is composed of two uni-

directionally coupled lasers, an injection ML with external optical feedback and a

SL without optical feedback, has been considered. Our rate equation models are

based on the well-known Lang–Kobayashi equations.16 The equations for the slowly

varying amplitude of the electric field E(t) and the carrier number N(t), assuming

single-mode operation and low to moderate feedback strengths, read:2,13,16

dEm(t)

dt=

(1 + iα)

2

(

ΓGm −1

τp

)

Em(t) + kdEm(t− τd) exp(iωmτd) , (1)

dEs(t)

dt=

(1 + iα)

2

(

ΓGs −1

τp

)

Es(t) + krEm(t− τr) exp(iωmτr) exp[i(ωm − ωs)t] ,

(2)

dNm,s(t)

dt=

I

qV−

Nm,s(t)

τe−Gm,s|Em,s(t)|

2 , (3)

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Bandwidth Enhancement in Chaotic Semiconductor Lasers

Gm,s = vgαN log[Nm,s(t)/N0]/[1 + εNL|Em,s(t)|2] . (4)

Here the subscripts m and s stand for the ML and SL. Note that, the last term

in Eq. (1) represents the feedback light for the master laser, kd and τd are the

feedback strength and feedback delay, respectively. The last term in Eq. (2) de-

notes the injection light from ML to SL, kr and τr are the injection strength

and injection delay, respectively. For simplicity, we have assumed identical inter-

nal laser parameters and operating conditions and neglected noise effects in the

lasers. α = 4.8 is the linewidth enhancement factor, Γ = 0.07 is the optical confine-

ment factor, vg = 8.1 × 109 cm s−1 is the group velocity, αN = 1.4 × 103 cm−1 is

the gain coefficient, and N0 = 1.3 × 1018 cm−3 is the transparent carrier density,

εNL = 1× 10−18 cm3 is the gain compression coefficient, τp = 2.2 ps is the photon

lifetime, ωm = 2.218× 106 rad/ns is the angular frequency of ML, q is the electric

charge, V = 1.885×10−12 cm3 is the volume of the laser active region, I is the bias

current, and τe = 2.7 ns is the carrier lifetime.

We numerically solve the equations by the fourth-order Runge–Kutta method

by using an integration step of 0.5 ps. Note that, we adopt the bandwidth definition

of chaotic signal as the span between the DC and the frequency where 80% of the

energy is contained within it.11

3. Results and Discussions

At first, we present the bandwidth enhancement for the case of SL subject to COI for

given feedback strengths and bias currents. Note that, the feedback strengths con-

sidered in this work are limited to low and moderate levels, as multiple reflections in

the external cavity have been neglected in Lang–Kobayashi equations.16 The band-

width as a function of injection strength is shown in Fig. 1. Here, three cases of

feedback strengths are considered, and the bandwidth for the ML is 12.7 GHz,

17.5 GHz and 20.05 GHz for kd = 5 ns−1, kd = 10 ns−1 and kd = 15 ns−1,

respectively. It can be observed that, for kd = 5 ns−1, the bandwidth of SL in-

creases with the injection strength at first and reaches its maximum about 30 GHz

at kr ≈ 190 ns−1, however, with the further increase of injection strength, the band-

width decreases abruptly toward to 12.7 GHz, which is the bandwidth of the ML.

For kd = 10 ns−1, similar trend is obtained; nevertheless, the maximum is 45 GHz

at about kr = 320 ns−1. When the injection strength is further increased, the band-

width of SL decreases dramatically until being close to 17.5 GHz. For the case of

kd = 15 ns−1, the maximum is about 58 GHz at about kr ≈ 470 ns−1. Further

increase of injection strength causes the bandwidth decrease toward 20.05 GHz.

Moreover, we can find that, for low and moderate feedback strength, with the in-

crease of feedback strength, the optimal injection strength leading to the maximum

bandwidth moves to a large value, and the corresponding maximum bandwidth also

increases.

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H.-M. Yang

Fig. 1. The chaotic bandwidth of SL with COI as a function of injection strength for differentfeedback strengths, with I = 2 mA.

Thus, we can conclude that, increasing the injection strength does not always

contribute to higher bandwidth; the optimal injection strength contributing to

highest chaotic bandwidth exists for given feedback strength and bias current.

To show more insight into the abrupt decrease of bandwidth when the injection

strength is beyond the optimal value, we take the case of kd = 10 ns−1 as an

example, present the outputs in the time and frequency domain for the ML, and

SL with COI for different injection strengths in Fig. 2. It can be seen that, for

kd = 10 ns−1, the ML exhibit chaotic dynamics. For SL, when kr = 100 ns−1, the

output is also chaotic, moreover, the spectrum is expanded significantly, and the

chaotic time series is not synchronized to that of ML, the bandwidth enhancement

is due to the interaction between the injection light and the chaotic laser field by

beating.11,12,14,17 However, for kr = 800 ns−1, the output of SL is well synchronized

to that of ML, and thus the bandwidth of SL is also close to that of ML1. From

physical point of view, for large injection strength, the injected light consumes

most of the carriers in SL through stimulated radiation and become the dominant

output until suppress the SL field completely, leading to the injection locking chaos

synchronization.15,18 That is to say, as the injection strength is large enough, the

injection-locking chaos synchronization is achieved, and hence the output of SL is

well synchronized to that of ML, leading to the abrupt decrease of bandwidth.

Next, we fix the feedback strength as kd = 10 ns−1, and also check the effects of

bias currents on the chaotic bandwidth. The bandwidths as functions of injection

strengths for different bias currents are shown in Fig. 3. The bandwidth of the

chaotic injection ML is 13.15 GHz, 17.5 GHz and 23.3 GHz for the case of I = 1 mA,

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Fig. 2. The outputs in the time (left column) and frequency (right column) domains, (a) and(b) are for the ML with kd = 10 ns−1, (c) and (d) are for the SL with COI and kr = 100 ns−1,(e) and (f) are for SL with COI and kr = 800 ns−1, with I = 2 mA.

Fig. 3. The chaotic bandwidth of SL with COI as a function of injection strength for differentbias currents, with kd = 10 ns−1.

I = 2 mA and I = 3 mA, respectively. It can be seen from Fig. 3 that, the trends for

bandwidth of SL are similar to those in Fig. 1. The bandwidth increases with the

injection strength initially and reaches its maximum at optimal value of injection

strength, and then decreases toward that of bandwidth of the chaotic injection ML.

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H.-M. Yang

Fig. 4. The outputs in the frequency domain for the SL with COI, (a) I = 1 mA and kr =240 ns−1, (b) I = 2 mA and kr = 320 ns−1, (c) I = 3 mA and kr = 380 ns−1. The black linescorrespond to the SL and the gray lines correspond to the chaotic injection ML.

For I = 1 mA, the optimal injection strength is at about kr = 240 ns−1 leading to

the maximum bandwidth as 33.9 GHz. When I = 2 mA, the best choice of injection

strength is kr = 320 ns−1 contributing to the bandwidth of 42.55 GHz. While for

I = 3 mA, the optimal injection strength kr = 380 ns−1 leading to the highest

bandwidth as 53.7 GHz. That is to say, a large bias current also leads to larger

optimal injection strength, and higher maximum bandwidth.

At last, to better show the bandwidth enhancement for different optimal injec-

tion strength at different bias current, we further present the spectrum of the chaotic

output of SL corresponding to the optimal injection strength mentioned in Fig. 3.

It can be seen that, for these optimal injection strength, the chaotic bandwidth is

expanded significantly and large bias current leading to higher bandwidth.

These results provide valuable information for choosing optimal injection

strength to obtain the highest chaotic bandwidth of SL with COI, which promotes

the increase of transmission rate for the optical chaotic communication systems.

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4. Conclusion

In summary, the bandwidth enhancement property of a SL with strong COI is

investigated in detail. For given bias current and feedback strength, the chaotic

bandwidth increases first with the injection strength, and optimal injection strength

exists which leads to the highest chaotic bandwidth, further increase of injection

strength beyond the optimal value would cause injection-locking chaos synchroniza-

tion, and hence reduce the bandwidth of SL toward that of injection ML. Moreover,

a large feedback strength and bias current contributes to larger optimal injection

strength and higher maximum chaotic bandwidth. These results obtain the opti-

mal injection strength to obtain highest chaotic bandwidth, which promotes the

increase of transmission rate for the optical chaotic communication systems.

Acknowledgments

This work was supported by Colleges Science and Technology Program Projects of

Shandong Province (No. J11LA52), and the Science Research Foundation of Heze

University (No. XY10XX01).

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BANDWIDTH ENHANCEMENT IN CHAOTIC SEMICONDUCTOR LASERS WITH STRONG CHAOTIC OPTICAL INJECTION

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