Self-pulsing, spectral bistability, with optoelectronic feedback Chang-Hee

and chaos in a semiconductor

laser diode

Leea) and Sang-Yung Shin

Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Gusung-Dong, Yusung-Ku, Taejon, Korea

(Received 5 June 1992; accepted for publication 6 December 1992) We observed experimentally self-pulsing, subharmonic generation, spectral bistability, and chaos in a stable semiconductor laser diode with delayed optoelectronic feedback. The laser diode emits 200 ps optical pulses with 1.1 GHz repetition rate in the self-pulsing region, and the bistable region is critically dependent on the closed loop gain of the system. Theoretical explanations of observed experimental results are also given. Effects of optoelectronic feedback on the dynamics of the semiconductor laser diode have attracted considerable attention.‘” The optoelectronic feedback narrows optical pulses emitted from the self-pulsed semiconductor laser.’ Delayed feedback is employed to generate optical short pulses.’ Recently, it has been shown theoretically that the stable semiconductor laser diode with negative optoelectronic feedback generates picosecond optical pulses.3 There also exist several types of optical bistable devices using a semiconductor laser diode with positive optoelectronic feedback.4-6 The advancement of optoelectronic integrated circuit technology offers a possibility of monolithic integration of these devices. However, there remains some lack of a full understanding of optoelectronic feedback effects on the dynamics of semiconductor laser diodes. In this letter, we report self-pulsing, subharmonic generation, spectral bistability, quasiperiodicity, and chaos in a stable semiconductor laser with delayed optoelectronic feedback. Our experimental system consists of a semiconductor laser diode, a photodiode, and an amplifier. The optical output from the semiconductor laser is detected by the photodiode and the photodiode current is negatively fed to the semiconductor laser after amplification, i.e., the feedback current decreases the injection current. The experimental setup is shown in Fig. 1. The optoelectronic feedback network is composed of an amplified photodiode (Ante1 model ARX-SP) and an MMIC amplifier (Avantek model MSA-0485). The 3 dB bandwidth of the designed bandpass feedback network is 300 MHz-l .7 GHz and the total delay time in the feedback network is 1 ns. The threshold current of the semiconductor laser (Hitachi model HLP 1400) is 57 mA. The measured resonance frequency of the semiconductor laser is 4.9 (Idr,, - 1) 1’2 GHz, where Ib is the bias current and Ith is the threshold current. The optical output detected by a high speed photodiode (Ortel model PDOSO-OM) is observed by using a sampling oscilloscope and a RF spectrum analyzer. The experiment is performed by varying the bias current of the semiconductor laser. The observed intensity spectra with the increase of the bias current are shown in Fig. 2. The closed loop gain of the feedback network is ‘ICurrent address: Optical Communication Section, Electronics and Telecommunications Research Institute, P. 0. Box 8, Daedok Science Town, Taejon, Korea.

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0.33. We use the L-I (light vs injection current) curve of the semiconductor laser in calculating the closed loop gain. Thus, we call it the frequency independent closed loop gain (FICLG) . It may be noted that the FICLG of our system, 0.33, is sufficient to initiate self-pulsing since there is a resonance peak in the modulation response of the semiconductor laser. The system is stable if the bias current is lower than 58.4 mA, at which the output of the semiconductor laser shows noise spectrum peaked at f = f t, as shown in Fig. 2(a). The oscillation frequency of f 1 increases as we increase the bias current of the semiconductor laser. The small signal resonance frequency of thesemiconductor laser is slightly lower than the frequency off r. As we increase the bias current, the amplitude of the spectrum f t grows, and it accompanies a precursor7 of the first subharmonic component as shown in Fig. 2(b). The subharmonic component grows rapidly while the fundamental component off I maintains a slow growth rate. At the bias current of 59.5 mA, the subharmonic component and the fundamental component have equal amplitude. As we increase the bias current further, the amplitude of the subharmonic component starts to decrease. Eventually, the subharmonic oscillation disappears at Ib= 60.6 mA. Then, the semiconductor laser shows self-pulsing at a single frequency ft. The typical pulse width is about 200 ps. The repetition rates are tuned from 1050 to 1150 MHz as the bias current increases from 60.6 to 63.5 mA, while the resonance frequency of the semiconductor laser is varied from 1231 to 1655 MHz. We show the intensity spectrum in Fig. 2(d). At 1,=63.5 mA, the intensity spectrum changes abruptly, as shown in Fig. 2(e). It has two fundamental frequencies f. and f t and the other spectral components are the combinations of beats off0 and ft. Here, it is noted that the resonance frequency of the semiconductor laser is about fo+fl. As we increase the bias current, the optical output becomes chaotic, as shown in Fig. 2(f). This sequence may be regarded as the two-frequency route to chaos. Through the chaotic state, locked states between f,-, and f t are observed. In other words, the frequency off, is three times that of fp The further increase of the bias current brings about the spectrum peaked at the resonance frequency of the semiconductor laser with the broadened noise peaks at f. and f ,. If we open the feedback loop, the system becomes stable and the output spectrum shows a

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@ 1993 American Institute of Physics

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FIG. 1. Experimental setup. LD and PD stand for laser diode and photodetector, respectively.

broad noise spectrum peaked at the resonance frequency of the semiconductor laser. For the observation of bistability, we increase the FICLG of the feedback network to 0.34 and observe the optical output. The system is stable when the bias current is lower than 57.8 mA. As we increase of the bias current, oscillation starts at frequency f. and its amplitude grows. Observed spectra are shown in Fig. 3 (a), which consist of the components of the spectrum fo, 2fc, 3fo, and precursor off t. With the increase of the bias current, both oscillation frequencies f. and f t increase. Also, the spectral width of f 1 broadens, as shown in Fig. 3 (b). Eventually, the amplitude off0 component starts to decrease and the intensity spectrum shows a single spectrum at f 1 when the bias current is higher than 59.6 mA. This spectrum changes abruptly at I,=61.6 mA to stable f0 oscillation. If we decrease the bias current, f. oscillation remains until 1,=60.2 mA. In other words, the semiconductor laser

I-

0

f%

..-. . ’ fl 1.7GHz 0

1.7GHz

FIG. 2. Observed optical output spectra with a FICLG of 0.33 at various bias currents: (a) 1,=58.4 mA, (b) 59 mA, (c) 60 mA, (d) 63 mA, (e) 64 mA, and (f) 64.4 mA. Vertical scale is 10 dB/div. 923

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0

’ ‘0

1:I WI2

FIG. 3. Observed optical output spectra and wave forms with a FICLG of 0.34. (a) Ib=58.3 mA, (b) 59.5 mA, and (c)-(f) 60.7 mA. The spectrum and the wave form of the f, oscillation state are shown in (c) and (d), respectively; the spectrum and the wave form of the fe oscillation state are shown in (e) and (f), likewise.

shows bistable characteristics between I,=60.2 mA and 1,=61.6 mA. The two stable states are f I oscillation and fc oscillation. Figures 3 (c) and 3 (d) show the spectrum and the wave form of the f I oscillation state, respectively; Figs. 3(e) and 3(f) show the spectrum and the wave form of the f. oscillation state, likewise. We also performed the experiment by changing the bias current of the feedback amplifier. The increase of the amplifier bias current enhances the FICLG of the feedback network. The bias current of the semiconductor laser is fixed at 1,=64.4 mA, where the intensity spectrum shows chaotic behavior, as shown in Fig. 2(f). When the amplifier bias current is decreased, the system shows a quasiperiodic state with fundamental frequencies of fc and f ,. The further decrease of the bias current brings about noise spectrum that have a sharp peak at the resonance frequency of the optoelectronic feedback system. On the other hand, when we increase the amplifier bias current from the amplifier bias current of the chaotic state, the laser diode shows a stable f. oscillation, like Fig. 3(e), through the oscillation spectrum, like Fig. 2 (e) . Similar behavior is also observed by changing the coupling efficiency of the semiconductor laser output to the photodiode. To understand the observed phenomena, we model our system that consists of a semiconductor laser, a photodiode, and an amplifier, using a rate-equation formulation.3 We use conventional rate equations for the semiconductor iaser. For the feedback network, a simple bandpass circuit ,vith an ideal amplifier is assumed. Stability of the system can be determined by the gain condition and the phase condition.’ The gain condition gives the required closed loop gain for oscillations. The phase condition gives the C.-H. Lee and S.-Y. Shin

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small signal oscillation frequencies in the system. Hence, the phase condition is derived from a condition of 2mr (m is an integer) round trip phase shift. Since the semiconductor laser has a resonance peak at the small signal resonance frequency, the required FICLG for oscillation is minimum at that frequency. It is about 0.2 for our system. The small signal modulation response of the semiconductor laser is well known. It has a resonance peak and the phase of the optical output power is shifted rr radian with respect to the phase of modulation signal at the small signal resonance frequency. The delay time of 1 ns implies a phase shift of r at 500 MHz. The feedback network also provides an additional phase shift. If the small signal resonance frequency of the semiconductor laser is about 500 MHz, the system has a single frequency that satisfies the phase condition. The required FICLG for oscillation is less than unity. The oscillation frequency is less than the resonance frequency of the semiconductor laser due to the additional phase shift in the feedback network. With the increase of the semiconductor laser bias current, the resonance frequency increases, and thus, the phase shifts due to the time delay and the feedback network increases too. Then, our system has at least two frequencies that satisfy the phase condition with a reasonable FICLG that is required for oscillation. Our experimental results may be explained by the following argument. If the bias current of the semiconductor laser is close to the lasing threshold current, the system shows only stable self-pulsing with a single spectra ft [see Fig. 2(b)]. The oscillation frequency f, is about the resonance frequency of the semiconductor laser. The oscillation frequency f i is the second spectrum that satisfies the phase condition. Since the closed loop gain is not enough at the lowest possible oscillation frequency fe (i.e., the first spectrum that satisfies the phase condition) that is about 500 MHz, the oscillation starts at frequency fi. It may be noted that if the FICLG of the system is sufficiently large, the system usually shows self-pulsing with the fundamental frequency f. instead of fi. With the increase of the bias current, the oscillation frequency fl increases and it be-

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comes about 2 f a. Then, the first subharmonic of frequency f i can be generated by the parametric interaction of these two frequencies [see Fig. 2(c)]. The amplitude of the subharmonic component increases with the bias current and starts to decrease. And it disappears if the oscillation frequency f i moves away from 2fp In that case, the system shows a single stable oscillation at frequency f 1. As we increase the bias current further, the oscillation frequency of f 1 increases and it becomes about 3f w Since the frequency f. is not equal to one-third of f, and the increase rate of the oscillation frequency f 1 is larger than that of fo, the system shows quasiperiodicity, chaos, and a locking state between the two frequencies f. and f i. If the FICLG adjusts in a certain range, the system shows bistability between two different oscillation states. One is the oscillation with a frequency about the resonance frequency of the semiconductor laser [see Figs. 3(c) and 3(d)]. The other is the oscillation at the lowest frequency that satisfies the phase condition [see Figs. 3(e) and 3(f)]. In conclusion, we observed experimentally self-pulsing, subharmonic generation, spectral bistability, and chaos in a stable semiconductor laser with delayed optoelectronic feedback. We also described the observed experimental results theoretically based upon the rate-equation model. The authors thank Sung-Ho Lee for his technical assistance. They are also grateful to researchers at the Applied Optics Laboratory in the Korea Institute of Science and Technology for kindly lending a RF spectrum analyzer. ‘K. A. Lau and A. Yariv, Appl. Phys. Lett. 45, 124 (1984). ‘T. C. Damen and M. A. Dunuav, Electron. Lett. 16, 166 (1980). 3C.-H. Lee, K.-H. Cho, S.-Y:Sdin, and S.-Y. Lee, Opt. Lett. 13, 464 (1988). 4K. Y. Lau and A. Yariv, Appl. Phys. Lett. 45, 719 (1984). ‘K. Okumura, Y. Ogawa, H. Ito, and H. Inaba, IEEE J. Quantum Electron. QE21, 377 (1985). “C.-H. Lee, K.-H. Cho, S.-Y. Shin, and S.-Y. Lee, IEEE J. Quantum Electron. QE-24, 2063 ( 1988). ‘C. Jeffries and K. Wiesenfeld, Phys. Rev. A 31, 1077 ( 1985). “C.-H. Lee, Ph.D. dissertation, Korea Advanced Institute of Science and Tech., 1989.

C.-H. Lee and S.-Y. Shin

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