synchronization of bandwidth-enhanced chaos in semiconductor lasers with optical feedback and...

Synchronization of bandwidth-enhanced chaos in semiconductor lasers with optical feedback

and injection

Hiroyuki Someya,1 Isao Oowada,

1 Haruka Okumura,

2 Takahiko Kida,

1 and Atsushi

Uchida2,*

1Department of Electronics and Computer Systems, Takushoku University, 815-1 Tatemachi, Hachioji, Tokyo 193-0985, Japan

2Department of Information and Computer Sciences, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama city, Saitama 338-8570, Japan

*[email protected]

Abstract: We experimentally investigate the generation and synchronization of bandwidth-enhanced chaos in a semiconductor laser (drive laser) that is subject to optical injection from another chaotic semiconductor laser (injection laser) with optical feedback. Effective bandwidth enhancement is achieved over 12 GHz, under the condition in which the optical wavelength of the drive laser is positively detuned with respect to that of the injection laser, outside the injection locking range. The bandwidth-enhanced chaotic signal of the drive laser is injected into a third semiconductor laser (response laser) for synchronization. Synchronization of chaos with a bandwidth greater than 12 GHz is observed between the drive and response lasers, under the condition in which the optical wavelength of the response laser is negatively detuned with respect to that of the drive laser, satisfying the injection locking condition. High-quality chaos synchronization is observed within the injection locking range between the drive and response lasers and under the condition of a low relaxation oscillation frequency of the response laser.

©2009 Optical Society of America

OCIS codes: (140.1540) Chaos; (190.3100) Instabilities and chaos; (140.5960) Semiconductor lasers; (060.4510) Optical communications.

References and links

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#115873 - $15.00 USD Received 18 Aug 2009; revised 26 Sep 2009; accepted 28 Sep 2009; published 13 Oct 2009

(C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS 19536

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1. Introduction

Synchronization of chaotic lasers has attracted a great deal of interest for applications involving secure optical communications and spread-spectrum communications [1–8]. For secure communications, a chaotic carrier is used to hide a data signal, and high-quality synchronization of chaos is required between the transmitter and receiver lasers in order to recover the hidden data. Several schemes of optical chaos communication, such as chaos masking, chaos modulation, and chaos shift keying, have been proposed and demonstrated [8]. Recently, high-speed long-distance communication based on chaos synchronization has been demonstrated over a commercial fiber-optic channel [7].

The transmission capacity in chaos communication is limited by the bandwidth of a chaotic carrier because a message is encoded within the frequency bandwidth of the chaotic carrier. Bandwidth enhancement of the chaotic carrier is therefore required for higher-speed chaos communications. The technique of bandwidth enhancement of chaos could also be useful for high-speed physical random number generators using chaotic semiconductor lasers [9–11]. Some schemes for bandwidth enhancement of chaos have been demonstrated using optical injection [12–16] and optoelectronic feedback [17]. Synchronization of bandwidth-enhanced chaos has been investigated in numerical simulations [14]. However, no experimental observation of synchronization of bandwidth-enhanced chaos over 10 GHz generated by optical injection has been reported so far. Chaotic signals with large spectral bandwidth over 10 GHz include high-frequency noise components both in laser devices and detection equipments, and it may become more difficult to obtain synchronization of high-bandwidth chaos than of slow chaotic oscillations around a few GHz.

In this study, we experimentally demonstrate the generation and synchronization of bandwidth-enhanced chaos in semiconductor lasers subject to optical feedback and injection over the frequency range of 12 GHz. The conditions of optical wavelength detuning are investigated for achieving bandwidth enhancement of chaos. We also experimentally observe synchronization of bandwidth-enhanced chaos in one-way coupled semiconductor lasers. We investigate the dependence of the synchronization quality on the optical wavelength detuning and the relaxation oscillation frequency.



Fig. 1. Experimental setup for the generation and synchronization of bandwidth-enhanced chaos in three semiconductor lasers. The Injection and Drive lasers are used for bandwidth enhancement of chaos. The Drive and Response lasers are used for the synchronization of chaos. The abbreviations stand for the following: Amp, electronic amplifier; BS, beam splitter; FC, fiber collimator; ISO, optical isolator; L, lens; λ/2, half wave-plate; M, mirror; NDF, neutral density filter; PD, photodetector.

2. Experimental setup

Figure 1 shows the experimental setup for the bandwidth enhancement of optical chaos and its synchronization. We used three distributed-feedback (DFB) semiconductor lasers (NTT Electronics, NLK1555CCA, optical wavelength: 1547 nm) developed for optical fiber communications. The lasers were fabricated from the same wafer and so have similar characteristics. The first laser, which had optical feedback, (referred to hereinafter as the Injection laser) was used for injection, and the chaotic output of the Injection laser was used for the bandwidth enhancement of a second laser (referred to hereinafter as the Drive laser). The bandwidth-enhanced chaotic output of the Drive laser was injected into a third laser (referred to hereinafter as the Response laser) for synchronization. The injection current and the temperature of the semiconductor lasers were adjusted by a current-temperature controller (Newport, 8000-OPT-41-41-41-41). The optical wavelength of the lasers was precisely controlled by the temperature of the laser to a ratio of 0.097 nm/K. The resolution of the temperature control was 0.01 K. The lasing thresholds (Ith) of the injection current for the solitary lasers were 8.7 mA (Injection), 7.6 mA (Drive), and 9.2 mA (Response).

An external mirror was placed in front of the Injection laser at a distance of 1.40 m, corresponding to a feedback delay time (roundtrip) of 9.3 ns, whereas there was no external mirror for the Drive or Response lasers. A portion of the laser beam from the Injection laser was fed back to the cavity of the Injection laser to induce chaotic fluctuation of the laser output. The feedback power was adjusted by a neutral-density filter (a variable attenuator). The beam from the Injection laser was divided into two by a beam splitter, and one beam was injected into the Drive laser. An optical isolator and a half wave plate were used to achieve one-way coupling. The wavelengths of the Injection and Drive lasers were precisely adjusted in order to generate bandwidth-enhanced chaotic output of the Drive laser. The chaotic output of the Drive laser was also injected unidirectionally into the Response laser for synchronization. A portion of each laser output was extracted by a beam splitter, injected into a fiber collimator through an optical isolator and propagated through an optical fiber to be detected by a photodetector (New Focus, 1554-B, bandwidth: 12 GHz). The converted electronic signal at the photodetector was amplified by an electronic amplifier (New Focus, 1422-LF, bandwidth: 20 GHz) and sent to a digital oscilloscope (Tektronix, DPO71254, bandwidth: 12.5 GHz, 50 gigasamples/s) and a radio-frequency (RF) spectrum analyzer



(Advantest, R3172, 26.5 GHz bandwidth) to observe temporal dynamics and the corresponding RF spectra, respectively. The optical wavelength of the lasers was measured by an optical spectrum analyzer (Advantest, Q8384).

3. Experimental results

3.1 Bandwidth enhancement of chaos

We set the relaxation oscillation frequencies of the Injection and Drive lasers to 8.0 GHz by adjusting the injection current of the lasers. These values were similar to the maximum

Fig. 2. (a) Temporal waveforms of the Injection and Drive lasers, and (b) their corresponding RF spectra. (b) fpeak, peak frequency of the RF spectrum; BW, bandwidth of the RF spectrum. The bandwidth of the chaotic signals is defined as the range between DC and the frequency that contains 80% of the spectral power [16,17].

Fig. 3. Center frequency (black solid curve) and bandwidth of the chaotic Drive laser (blue dotted curve) as a function of the optical wavelength detuning between the Drive and Injection lasers ∆λDI ( = λDrive - λInjection), where λDrive and λInjection denote the optical wavelength of the solitary Drive laser and the Injection laser with optical feedback, respectively. The injection locking range (region where λDrive matches λInjection due to coherent coupling) is shown in the region indicated by the red arrow.

relaxation oscillation frequencies that can be observed for solitary lasers using the RF spectrum analyzer in the experimental setup. The injection currents were 44.49 mA (5.1 Ith) for the Injection laser and 43.50 mA (5.7 Ith) for the Drive laser. In order to enhance the



bandwidth of the chaos, we detuned the optical wavelength of the Drive laser in the positive direction with respect to that of the Injection laser, i.e., we set the optical wavelength of the solitary Drive laser to 1547.418 nm and the optical wavelength of the Injection laser (with optical feedback) to 1547.333 nm by controlling the temperature of the two lasers. The optical wavelength detuning is defined as ∆λDI = λDrive - λInjection, where λDrive and λInjection denote the optical wavelength of the solitary Drive laser and the Injection laser with optical feedback, respectively. Here, ∆λDI was set to 0.073 nm (frequency: 9.1 GHz), which corresponds to the positive detuning condition in the literature [18–20]. For this condition, no injection locking was achieved between the Injection and Drive lasers, i.e., outside the injection locking range [18–20]. Here, injection locking is defined as the matching of optical wavelengths between the two lasers due to coherent unidirectional coupling.

Figure 2 shows the temporal waveforms of the Injection and Drive lasers and their corresponding RF spectra. The chaotic temporal waveforms are shown in Fig. 2(a), where it can be seen that waveform of the Drive laser oscillates faster than that of the Injection laser. The RF spectra in Fig. 2(b) show the bandwidth enhancement of the Drive laser by the optical injection of the Injection laser output, where the center frequencies of the Injection and Drive lasers are 8.66 and 12.64 GHz, respectively. We define the bandwidth of the chaotic signals as the range between DC and the frequency that contains 80% of the spectrum power [16,17]. The bandwidths of the Injection and Drive lasers are 9.48 and 12.96 GHz, respectively. The bandwidth enhancement is limited to approximately 13 GHz, as determined by the frequency bandwidth of the photodetectors. Effective bandwidth enhancement of chaotic signals is achieved for positive detuning conditions.

We investigated the characteristics of bandwidth enhancement when the optical wavelength detuning ∆λDI is varied. Figure 3 shows the center frequency and the bandwidth of the chaotic Drive laser as a function of the amount of the optical wavelength detuning ∆λDI. Both the center frequency and the bandwidth increase as ∆λDI increases from negative to positive values until ∆λDI = 0.073 nm, after which a decrease is observed. The center frequency of 12.64 GHz and the bandwidth of 12.96 GHz are obtained at ∆λDI = 0.073 nm. Note that the bandwidth enhancement is effectively achieved for positive ∆λDI outside the injection locking range, whereas the center frequency is almost constant within the injection locking range for negative ∆λDI due to the locking of the two optical wavelengths, as shown in Fig. 3. Therefore, for bandwidth enhancement of chaos, it is important to unlock the two optical wavelengths for positive (but not too large) values of ∆λDI outside the injection locking range. Note that bandwidth enhancement was observed up to approximately 13 GHz due to the bandwidth limitation of the photodetectors in the experimental equipment. Faster photodetectors are required to observe larger-bandwidth chaos.

3.2 Synchronization of bandwidth-enhanced chaos

Next, we investigate the synchronization of bandwidth-enhanced chaos between the Drive and Response lasers. The optical wavelength of the Drive laser was shifted from 1547.418 to 1547.476 nm due to the optical injection from the Injection laser for bandwidth enhancement. We set the injection current to 13.84 mA (1.5 Ith) and the relaxation oscillation frequency to 3.0 GHz for the Response laser. A bandwidth-enhanced chaotic signal from the Drive laser was injected into the Response laser unidirectionally. In contrast to the case for bandwidth enhancement, the optical wavelength of the Response laser was detuned in the negative direction with respect to that of the Drive laser. The optical wavelength of the solitary Response laser was set to 1547.264 nm. The optical wavelength detuning between the Drive and Response lasers is defined as ∆λRD = λ Response - λDrive, where λ Response and λDrive are the optical wavelengths of the solitary Response laser and the Drive laser with optical injection

from the Injection laser, respectively. Here, ∆λRD was set to −0.212 nm (frequency: −26.5 GHz), which corresponds to negative detuning, so that injection locking (matching of optical wavelengths) was achieved between the Drive and Response lasers.

Figure 4 shows the temporal waveforms, cross correlation, RF spectra, and the optical spectra of the Drive and Response lasers. The temporal waveforms of the bandwidth-



enhanced chaotic signals are synchronized between the Drive and Response lasers, as shown in Figs. 4(a) and 4(b). The center frequencies of the two chaotic waveforms are very similar (12.22 and 12.12 GHz for the Drive and Response lasers, respectively, as shown in Fig. 4(c)). In addition, the bandwidth of the Response laser of 12.16 GHz is similar to that of the Drive laser of 12.28 GHz. In Fig. 4(d), the optical spectrum of the Response laser is shifted to a longer wavelength and matched to the optical spectrum of the Drive laser due to injection locking. In contrast, the optical spectrum of the Injection laser is not matched to that of the Drive laser to maintain bandwidth enhancement. Synchronization of bandwidth-enhanced chaos over 12 GHz can be achieved for negative detuning within the injection locking range.

Fig. 4. (a) Temporal waveforms, (b) cross correlation, (c) RF spectra, and (d) optical spectra of the Drive and Response lasers. (c) fpeak, peak frequency of the RF spectrum; BW, bandwidth of the RF spectrum. Synchronization of bandwidth-enhanced chaos is achieved between the Drive and Response lasers. The cross correlation value in (b) is C = 0.954.

We quantitatively define the quality of synchronization as the cross correlation between two temporal waveforms normalized by the product of their standard deviations, as follows:

1 1 2 2

1 2

( )( )I I I IC

σ σ

− −

= (1)

where I1 and I2 are the total intensities of the two temporal waveforms, 1

I and 2

I are their

respectively mean values, and σ1 and σ2 are their respectively standard deviations. The angle brackets denote time averaging. The best synchronization is obtained at a cross-correlation coefficient of C = 1. The cross correlation value of Fig. 4(b) is C = 0.954 (calculated from Eq.



(1)), and high-quality synchronization of bandwidth-enhanced chaos is achieved in the experiment.

Fig. 5. (a) Cross correlation of the temporal waveforms between the Drive and Response lasers as a function of ∆λRD ( = λResponse - λDrive), where λResponse and λDrive are the optical wavelengths of the solitary Response laser and the Drive laser with optical injection from the Injection laser, respectively. (b) Cross correlation between the Drive and Response lasers (black solid curve) and bandwidths of the Drive (blue dotted curve) and Response (red dashed curve) lasers as a function of ∆λDI, where ∆λDI ( = λDrive - λInjection) denotes the optical wavelength detuning between the solitary Drive laser and the Injection laser with optical feedback. The change in ∆λDI affects the bandwidth of chaos in the Drive laser.

Fig. 6. Cross correlation of the temporal waveforms between the Drive and Response lasers as a function of the relaxation oscillation frequency of the Response laser fR, where fR increases monotonically with the increase in the injection current of the Response laser. The cross correlation value decreases slightly as fR is increased.

3.3 Parameter dependence

Next, we investigate the dependence of the synchronization of bandwidth-enhanced chaos on laser parameter values. We first change the degree of optical wavelength detuning between the Drive and Response lasers (∆λRD). Figure 5(a) shows the cross correlation of the temporal waveforms between the Drive and Response lasers as a function of ∆λRD. The maximum cross

correlation of 0.954 is obtained at ∆λRD = −0.212 nm. The cross correlation is larger than 0.85

in the range of −0.26 nm < ∆λRD < −0.05 nm, which roughly corresponds to the injection locking range between the Drive and Response lasers. Therefore, the region for high-quality synchronization of chaos is approximately equivalent to the injection locking range.

Figure 5(b) shows the cross correlation between the Drive and Response lasers as a function of the amount of the optical wavelength detuning between the Injection and Drive lasers ∆λDI. The change in ∆λDI affects the bandwidth of the chaos in the Drive laser.



Therefore, the bandwidths of the Drive and Response lasers are also plotted in Fig. 5(b). Cross correlation values between 0.91 and 0.95 are obtained and high-quality synchronization is observed over a wide range of ∆λDI. However, at approximately ∆λDI = 0.08 nm, there exists a discrepancy in the bandwidth between the Drive and Response lasers, and the cross correlation value decreases slightly. In this condition, the high-frequency oscillation of the Response laser of over 12 GHz cannot follow that of the Drive laser, and a degradation of the degree of synchronization is observed. We speculate that this discrepancy may result from the different frequency characteristics of the two 12-GHz-bandwidth photodetectors at the edge of the high cut-off frequency. Further investigations will be conducted in the future.

Next, we investigate the influence of the relaxation oscillation frequency of the Response laser fR on the synchronization quality. Note that fR increases monotonically with the increase in the injection current of the Response laser. Figure 6 shows the cross correlation of the temporal waveforms between the Drive and Response lasers as a function of fR. The cross correlation value decreases slightly as fR is increased. The maximum cross correlation value of 0.964 is obtained at fR = 2.83 GHz. This indicates that the synchronization quality is decreased for a highly-pumped Response laser with a large injection current. The relative power of the injected chaotic signal to the Response laser field in the Response laser cavity is increased as the injection current of the Response laser is decreased. Therefore, the dynamics of the Response laser with a lower injection current (smaller relaxation oscillation frequency) is more susceptible to the injected chaotic signals, and high-quality synchronization is achieved at the condition of a low injection current and small relaxation oscillation frequency of the Response laser.

4. Conclusion

We have experimentally investigated the generation and synchronization of bandwidth-enhanced chaos in the Drive semiconductor laser subject to optical injection from the chaotic Injection laser with optical feedback. Effective bandwidth enhancement is achieved over 12 GHz when the optical wavelength of the Drive laser is positively detuned from that of the Injection laser. We found that it is important for bandwidth enhancement of chaos to unlock the two optical wavelengths of the Drive and Injection lasers under positive optical detuning conditions outside the injection locking range.

The bandwidth-enhanced chaotic signal of the Drive laser is injected into the Response laser for synchronization. Synchronization of the chaos with a bandwidth over 12 GHz is observed between the Drive and Response lasers under the condition in which the optical wavelength of the Response laser is negatively detuned with respect to that of the Drive laser, satisfying the injection locking condition. The optimum wavelength-detuning parameter is found to be different for synchronization of chaos than for bandwidth enhancement of chaos. High-quality chaos synchronization with a bandwidth of over 12 GHz is achieved within the injection locking range between the Drive and Response lasers and under the condition of a low relaxation oscillation frequency of the Response laser.

The techniques of bandwidth enhancement of chaos and its synchronization appear promising for applications such as ultra-fast physical random number generators with chaotic lasers and high-capacity optical chaos communications.

Acknowledgments

The authors would like to thank Peter Davis and Kazuyuki Yoshimura for their helpful discussions. This study was supported in part by the JGC-S Scholarship Foundation, the Mazda Foundation, the CASIO Science Promotion Foundation, the TEPCO Research Foundation, and the Ministry of Education, Culture, Sports, Science and Technology through a Grant-in-Aid for Young Scientists.



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