Chaos control and noise suppression in external-cavitysemiconductor lasers

Feedback-induced chaos and intensity noise enhancement in a laser diode with external optical feedback are studied by computer simulations. The enhancement of relative intensity noise (RIN) that is often observed in experiments is considered as a result of the feedback-induced deterministic chaos and the intensity noise suppression is treated from the viewpoint of chaos control. Especially, the conventional noise suppressing technique known as a high-frequency injection modulation is turned into a problem of stabilizing chaos through parameter modulations. We developed an analytical method which allows to optimize the modulation frequency from the linear stability analysis of the dynamical model that describes the laser diode with external feedback. The robustness of the modulation with respect to the modulation frequency and depth is verified and the results suggest the feasibility of applying our method to actual noise suppression. The RIN in the low-frequency region (up to 100 MHz) is shown to be reduced to the solitary laser level when the feedback-induced chaos is effectively controlled with the optimized modulation frequency     

Dynamics and chaos stabilization of semiconductor lasers withoptical feedback from an interferometer

This paper studies dynamical behaviors and noise properties of semiconductor lasers with optical feedback from an interferometer, i.e., two external cavities. Bifurcation diagrams versus external-cavity length and reflectivity reveal the existence of stable regions for fixed states and limit cycles. The steady-state analysis for a laser diode with two external feedbacks is performed, which shows that oscillation modes are locked at minimum excess gain modes. Oscillation frequencies of limit cycles show discrete transitions with the variation of ratios between two external-cavity lengths and reflectivities. It is proposed that such a model might be applied to stabilization of the feedback-induced chaos in external-cavity semiconductor lasers since the stable region is quite robust for wide parameter ranges. Intensity and phase noises are examined and the results indicate that the low-frequency relative intensity noise level and the linewidth can be greatly improved when the laser output is a fixed state or a limit cycle     

Chaos in semiconductor lasers with optical feedback: theory andexperiment

The authors present a detailed theoretical and experimental investigation of the nonlinear dynamics of a semiconductor laser with optical feedback. The results show that the coherence collapsed state is a chaotic attractor and that chaos is reached for increasing feedback level through a quasi-periodic route interrupted by frequency locking. Furthermore, the coexistence of two attractors, associated with the same external cavity mode, but having different relaxation oscillation frequencies, is demonstrated and explained     

Characteristics of a semiconductor laser coupled with a fiber Bragg grating with arbitrary amount of feedback

Stationary characteristics (such as laser frequency at threshold, light-intensity curve, etc.) and relative intensity noise of laser diodes coupled with an external Bragg reflector are studied for arbitrary amount of optical feedback. We put the stress on the interplay between external and internal cavities when the feedback strength is increased. For strong feedback, new stationary solutions that do not exist in the case of conventional feedback appear, while the ellipse, which usually contains the modes and so-called antimodes, collapse in the plane frequency-gain. Finally, analytical expressions are compared with numerical results obtained through a new approach that uses Green functions.     

Nonlinear dynamics of a laser diode with optical feedback systemssubject to modulation

The nonlinear dynamic behavior of a direct frequency-modulated diode laser with strong optical feedback is examined and compared to a laser diode subject to electro-optically modulated, strong optical feedback. Direct modulation is achieved by sinusoidal modulation of the diode laser injection current. Electro-optic modulation is achieved by applying a sinusoidal voltage to an intracavity phase modulating element. The output state (characterized by the output power versus time, the intensity noise spectrum and the optical frequency spectrum) for both types of modulation is dependent on the ratio of the modulation frequency to the external cavity resonant frequency, and the modulation power. A number of distinct states are observed: conventional amplitude modulation (with FM spectra); multimode, low-noise amplitude modulation; multimode, high-noise amplitude modulation; periodic limit-cycle operation; quasi-periodicity; chaos; low-frequency fluctuations; and mode-locking. There are significant differences between the direct and electro-optic frequency-modulation cases. The onset of the dynamic instability is characterized as a noisy period-one oscillation for direct modulation and a low-frequency fluctuation for intracavity electro-optic modulation. Phase portraits produced experimentally with the use of a digital phosphor oscilloscope are shown to agree well with those constructed from output power versus time data. This represents an experimental method for examining the dynamics phase portraits in real-time     

Nonlinear dynamics of vertical-cavity surface-emitting lasers

The dependence of the transient response of a vertical-cavity surface-emitting laser (VCSEL) on its aperture size is investigated subject to direct current modulation and external optical feedback. It is shown that lasers with small aperture size suppress higher order bifurcations and chaos even under large-signal modulation and external optical feedback. Furthermore, the noise characteristics of VCSELs under the influence of external optical feedback are studied via the calculation of relative intensity noise. It is found that the level of external optical feedback for the onset of coherence collapse is high for devices with small aperture size. On the other hand, the small-signal response of lasers is also analyzed through the calculation of third-order harmonic distortion. It is shown that harmonic distortion is minimized in small devices. Therefore, VCSELs with small aperture size have better immunity to irregular response under direct current modulation and external optical feedback     

Mode partition in semiconductor lasers with optical feedback

The authors point out that random noise processes induce mode partition fluctuations in semiconductor lasers. Mode partition depends on laser parameters and modulation current. However, external optical feedback can also increase mode partition noise. Here, a numerical solution of multimode noise-driven rate equations with time-delayed terms is utilized to investigate mode partition in semiconductor lasers with reflecting feedback. Photon statistics of the main and side modes in semiconductor lasers under both CW operation and dynamic operation are considered. Probability-density curves for the main and side modes are shown. The feedback-induced change of photon statistics of the main and side modes is clearly seen. Numerical results indicate that, if the laser used is exposed to reflections, a more stringent mode discrimination requirement for suppressing the buildup of laser-cavity longitudinal side modes may result. If mode discrimination is insufficient for avoiding the excitation of side modes, the feedback-induced power penalty depends on the fiber dispersion     

Microwave modulation of laser diodes with optical feedback

It is shown theoretically and experimentally that significant variations in the microwave modulation responses of laser diodes occur due to optical feedback from the transmission fiber. These variations decrease if the laser spectrum is less coherent; this can be achieved, for example, by increasing the intensity modulation index. In a recent letter the authors (1989) discussed the small-signal transfer functions; large deviations in the amplitude and the phase response resulted from optical feedback. For large-signal modulation, weaker feedback-induced deviations of the transfer function were predicted by W.I. Way and M.M. Choy (1988). The microwave modulation characteristics are considered in more detail, including the effects of higher modulation indexes. For a typical intensity modulation index of 26%, variations of up to 3 dB in amplitude and 60° in phase were observed     

Synchronized chaotic optical communications at high bit rates

Basic issues regarding synchronized chaotic optical communications at high bit rates using semiconductor lasers are considered. Recent experimental results on broadband, high-frequency, phase-locked chaos synchronization, and message encoding-decoding at 2.5 Gb/s are presented. System performance at a bit rate of 10 Gb/s is numerically studied for the application of three encryption schemes, namely chaos shift keying, chaos masking, and additive chaos modulation, to three chaotic semiconductor laser systems, namely the optical injection system, the optical feedback system, and the optoelectronic feedback system. By causing synchronization error in the forms of synchronization deviation and desynchronization bursts, the channel noise and the laser noise both have significant effects on the system performance at high bit rates. Among the three laser systems, the optoelectronic feedback system has the best performance while the optical feedback system has the worst. Among the three encryption schemes, only the performance of additive chaos modulation with low-noise lasers is acceptable at high bit rates.     

External optical feedback effects on intensity noise ofvertical-cavity surface-emitting lasers

The authors have experimentally evaluated the effect of external optical feedback on the relative intensity noise (RIN) of a vertical-cavity surface-emitting laser (VCSEL) diode. In the absence of optical feedback, the smallest RIN is found to be -135 dB/Hz. For optical feedback levels approaching -25 dB, the RIN is degraded by about 20 dB. The authors have measured feedback-induced power penalties in a 500-Mb/s intensity-modulation/direct-detection (IM/DD) link and determined that the penalty exceeds 1 dB if the optical feedback ratio is larger than -30 dB     

Dynamics in a compound cavity semiconductor laser induced by smallexternal-cavity-length change

For the short-range variations of the external cavity length, the dynamic behaviors of a semiconductor laser with optical feedback are investigated by the numerical simulations and experiments. Under the condition of a single-mode oscillation, the laser output power shows periodic undulation along the external cavity length whose period is equal to half of the optical wavelength. At weak to moderate external optical feedback, stable, periodic, quasi-periodic, and chaotic oscillations of the laser output power are observed within the periodic undulation. Experimental results of periodic and quasi-periodic oscillations obtained by the laser output power and the optical spectrum support the predictions from the numerical analysis based on the rate equations     

Stability analysis for a semiconductor laser in an external cavity

A detailed theoretical analysis of stability is presented for a semiconductor laser in an external cavity. The limits of stable operation are determined as a function of the external cavity parameters and the linewidth enhancement factor α. Instability is related to jumps of the laser frequency between external cavity modes (frequency bistability) or to feedback-induced intensity pulsations due to the carrier density dependence of the refractive index. The limit of bistability is derived from the steady-state solutions of the rate equations and the intensity pulsation limit is obtained from a small-signal analysis. This analysis also gives the location of zeros in the system determinant and the resulting FM noise spectrum. For practical applications we emphasize the determination of the stable tuning range for the phase in the external cavity and the classification of the possible types of instability for various feedback levels.     

Mode description of routes to chaos in external-cavity coupledsemiconductor lasers

The nonlinear behaviors of routes to chaos in semiconductor lasers with external optical feedback were explored in this work. It was indicated that the relaxation oscillation was the origin of the first nonlinear instability of optical intensity under a short delay. Three types of transition routes with quasi-periodic, subharmonic oscillation, and periodic doubling to optical chaos were distinguished in terms of the delay time normalized to the inverse of the relaxation oscillation frequency of a solitary laser diode. The linearized mode theory and small-signal response were confirmed as part of the phenomena in the transitions to chaos     

Transverse-mode dynamics in directly modulated vertical-cavity surface-emitting lasers with optical feedback

Vertical-cavity surface-emitting lasers (VCSELs) with optical feedback are known to exhibit different transverse-mode regimes depending on the injection current. Close to threshold a VCSEL operates on the fundamental transverse mode, while for larger injection the dynamics is often multimode, with the optical feedback inducing either in-phase or anti-phase transverse mode oscillations. In this paper, we study numerically the influence of current modulation on these different feedback-induced transverse-mode regimes. The modulation amplitude and period are taken as control parameters. We find that the in-phase and anti-phase regimes are robust under weak modulation. As the modulation amplitude increases, there is a transition to a dynamics governed by the current modulation, where the total output power follows the injection current and there is either single-mode or in-phase multimode behavior. However, the effect of the current modulation depends on the modulation period. Under fast modulation, the laser cannot follow the modulation and the optical-feedback-induced effects are dominant. On the contrary, under slow modulation there is a superposition of modulation and feedback effects, with the total output following the modulated current and an underlying transverse-mode behavior mainly determined by the optical feedback. A resonant behavior was observed for modulation periods close to the internal oscillation period. In this case, current modulation induces pulsing output intensity with single-mode or in-phase multimode behavior.     

Oscillation frequency, linewidth reduction and frequency modulation characteristics for a diode laser with external grating feedback

Simple analytical expressions are given for the oscillation frequency, linewidth, FM noise spectrum and frequency modulation characteristics of a diode laser with external grating feedback. The analytical expressions are found to be in good agreement with experimental results and to be useful for quantitative predictions and optimisations of the external feedback controlled diode laser performance.     

The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers

Theory and experiments on optical feedback effects in index-guided single-mode semiconductor lasers are presented. Evidence is found for the existence of a characteristic parameterCwhich indicates the relative strength of the optical feedback. Near the transition (C approx 1.0) from low to high feedback, the feedback-induced low-frequency intensity noise shows a maximum. At higher feedback hysteresis and instabilities are dominant, whereas the feedback-induced noise is low again.     

多次外光反馈下垂直腔面发射激光器非线性动态特性理论研究

在SIMULINK平台下建立了垂直腔面发射激光器(VCSEL)动态仿真模型，利用该模型对多次外光反馈下垂直腔面发射激光器的非线性行为进行了研究。结果表明，短外腔时，光子密度随外腔长呈周期为半激射波长的余弦关系；长外腔时，随外腔长增加，垂直腔面发射激光器依次经历混沌、多周期、倍周期和单周期区域，增大外腔反射率时同样存在这些非线性区域，但出现顺序相反。进一步得出：考虑单次反馈时由于忽略了占有较多能量的高次反馈导致上述非线性效应偏弱；增大自发辐射因子或减小线性展宽因子可抑制系统的非线性行为。     

Oscillation center frequency tuning, quantum FM noise, and direct frequency characteristics in external grating loaded semiconductor lasers

Simple analytical expressions for the oscillation frequency, quantum FM noise spectrum, oscillation power spectrum, spectral linewidth, and direct optical frequency modulation efficiency in semiconductor lasers with external grating feedback are presented. Experimental results for the grating loaded AlGaAs lasers are in good agreement with the theoretical predictions. Remarkable reduction in spectral linewidth to less than 50 kHz is achieved by feeding back only 10^-3of the output power. Oscillation frequency stabilization, frequency jump behavior, and reduction in direct optical frequency modulation efficiency are also discussed.     

外部光注入分布反馈激光器的非线性动力学特性

实验研究了外部光注入分布反馈(DFB)激光器的非线性动力学行为,并给出了其输出特性随注入光强度和频率失谐量变化的动力学特征图.实验结果表明,激光器的动力学行为对外部的微扰十分敏感;在不同外部光注入条件下,激光器可以呈现出单周期、倍周期、多周期以及混沌等多种非线性动力学特征;在注入光强度和频率失谐量变化空间存在三个复杂动力学区域;激光器表现出的复杂动力学行为总是与周期行为有关;当激光器处于复杂动力学区域时,其频谱为连续谱,在连续谱上存在多个明显的峰,所对应的频率定义为特征频率,特征频率的大小不随注入光的强弱以及频率变化.     

Stability and noise properties of diode lasers with phase-conjugatefeedback

For a diode laser subjected to filtered feedback from a phase-conjugating mirror, we present the first exact stability analysis and various noise spectra. The stability properties are intermediate between those of the injection laser and the laser with conventional optical feedback. The role of a finite response-time is to drastically enhance the steady-state stability For moderate feedback, the frequency noise is suppressed by several orders of magnitude, and the main relaxation frequency of the laser shows a crossover from the usual relaxation oscillation frequency to a new frequency determined by the amount of feedback. This may be of technological importance since it is expected to improve the modulation bandwidth