Theory of the bistable limit cycle behavior of laser diodes inducedby weak optical feedback

Weak optical feedback can transform the relaxation oscillations of the solitary laser diode in self-sustained pulsations. A bistability of such limit cycles supported by the same external cavity modes is investigated. Novel analytical expressions for the pulsation amplitudes, frequencies and the range of bistability are derived. They are in excellent agreement with numerical simulations     

Stable operation range for laser diodes with an integrated passivecavity in the presence of external optical feedback

It is shown that a laser diode with an integrated passive cavity yields higher tolerable levels of feedback from distant reflections than an equivalent long solitary laser diode. To ensure this high tolerance for external feedback, the internal feedback level in the integrated passive cavity must be of the order of about 10%. Then the laser diode remains stable up to external feedback levels in excess of 1% even if the internal reflection phase is not carefully adjusted. External reflections from a cleaved fiber end are then not sufficient to drive the laser into coherence collapse, if realistic coupling efficiencies between laser diode and fiber are taken into account. The low feedback sensitivity is explained by the combination of the long effective length of the laser and a high relaxation resonance frequency. Therefore, quantum-well laser diodes with a long length and a high relaxation resonance frequency are likewise expected to exhibit low feedback sensitivity     

Analysis of chromatic dispersion-induced second-harmonic distortions including laser dynamics to the second order

We perform analysis of chromatic dispersion-induced second-harmonic distortions including laser diode dynamics. Investigating laser diode dynamics fully to the second order, we derive analytical expressions for intensity and frequency modulation indices. Using these, we accurately model chromatic dispersion-induced second-harmonic distortions for signals produced by a directly modulated distributed feedback laser. The results agree well with numerical solutions, as well as with experimental results for a wide range of modulation frequencies and fiber lengths.     

Theory of dynamical relaxation oscillations and frequency lockingin a synchronously-pumped laser diode

It is shown that the rate equations for the plasma density and the light intensity, together with a delayed feedback of the light in the external resonator, can be used to describe the nonlinear dynamics of actively mode-locked laser diodes. In particular, the relaxation oscillations of the laser intensity and the plasma density around the stationary pulse solutions are calculated for a laser diode in a long resonator with a periodically pulsed pump current. For small negative detuning between the round-trip period and the pump period, slow dynamical relaxation oscillations that give rise to megahertz-sidemodes in the intensity correlation spectrum occur. For larger negative detuning the delayed feedback gives rise to a frequency locking between the light pulse frequency and the modulation frequency     

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     

Intermodulation and harmonic distortions of laser diodes withoptical feedback

Analytical expressions for the second-order harmonic and the third-order intermodulation distortions of laser diodes with optical feedback are derived. It is shown theoretically and experimentally that optical feedback from the transmission fiber considerably enhances intermodulation and harmonic distortions of laser diodes. Third-order intermodulation distortions up to -15 dBc must be expected for two-tone modulation and low-intensity modulation indexes m≈7% per carrier, which affects the performance of subcarrier multiplexed (SCM) communication systems. To avoid additional distortions the external feedback level must be two orders of magnitudes lower than the critical external feedback level of the laser diode     

High-frequency oscillations and self-mode locking in shortexternal-cavity laser diodes

An effect of compound-cavity mode competition for a laser diode with a short external cavity is investigated analytically and numerically on the basis of a round-trip approximation for emitted photons in the external cavity. Due to the noncoincidence of the compound-cavity modes with possible frequencies of stationary lasing, such competition may cause self-locking of two compound-cavity modes with deep high-frequency oscillations of the laser output for a short (typically ⩽5 mm) external cavity. Simple analytical expressions for critical feedback parameters and the frequencies of self-oscillations are given, as well as a generalized diagram of different dynamic regimes of a short external-cavity laser, which shows these regimes of high-frequency self-oscillations as well as coherence collapse instability. The results may be considered a guideline for the design of high-speed laser diodes with an integrated passive cavity. In particular, such a device may be a very efficient pulse source in the microwave (>20 GHz) region     

Mid-range coherent optical frequency domain reflectometry with aDFB laser diode coupled to an external cavity

The optical frequency of an external double cavity coupled laser diode was controlled via the phase of the feedback light. Strong linewidth and mode hopping reductions were obtained, extending coherent reflectometry with semiconductor sources to the range of hundreds of meters     

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.     

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.     

利用光反馈半导体激光器产生超宽带混沌脉冲信号

提出了一种基于光反馈半导体激光器的混沌特性产生超宽带(UWB)信号的新方法。一个商用的通信波段半导体激光器在外腔光反馈下实现混沌振荡,输出连续波混沌激光,经由一个电吸收调制器后,被调制为一系列混沌脉冲信号。该混沌脉冲信号的频谱特性可通过调节半导体激光器的偏置电流和反馈强度进行控制。实验分别获得了中心频率为4.0 GHz、相对带宽为181%和214%的混沌脉冲UWB信号。进一步数值仿真了偏置电流和反馈系数对混沌脉冲UWB信号频谱特性的影响,实验结果与模拟验证相符。该方法实验装置简单,UWB信号频谱特性易控,可用作未来UWB光纤无线通信系统的光生微波信号发生装置。     

The effect of spurious intensity modulation in semiconductor diode lasers on the performance of optical heterodyne frequency shift-keyed communications systems

Analytical expressions are derived for the bit-error rate (BER) of anM-ary frequency shift-keyed (FSK), heterodyne, optical communication system with noncoherent demodulation in the presence of spurious intensity modulation (SIM) and frequency noise. The SIM degradation of an FSK system, implemented with semiconductor diode lasers, is estimated for lasers with zero and nonzero linewidths and will be discussed for a distributed feedback laser operating at 1.5μm and a channeled substrate planer laser operating at 0.83 μm. The SIM power penalty is typically less than 1 dB, but can exceed 1 dB for 2-, 4-, and 8-ary FSK at data rates above 1 Gbit/s.     

Intensity noise dependence on the injection current of laser diodeswith optical feedback

With increased injection current both low- and high-frequency intensity fluctuations shift toward higher frequencies. A comparison between the experimental results for an InGaAsP laser diode and a small-signal analysis of the laser rate equations shows that both types of frequency fluctuations can be interpreted as complex relaxation oscillations of a laser diode with external feedback. The simple model describes reasonably well the frequency shift and the spectral width of the fluctuations observed     

Experimental and theoretical study of filtered optical feedback ina semiconductor laser

We report on the systematical investigation of the steady-state regime and the dynamical behavior of a semiconductor laser subject to delayed filtered optical feedback. We study a Fabry-Perot (FP) interferometer type of filter placed in the external feedback loop of a diode laser. The effects of the filter on the locking of the diode laser frequency to the external cavity modes are described. We report and observe hysteresis, bistability, and multistability and show that all these are well described by a set of rate equations for the coupled laser and FP cavity system. We also present an experimental stability diagram that summarizes the dynamical behavior of the system     

Theory of noise in semiconductor lasers in the presence of optical feedback

We derive analytical expressions for the power spectral densities of intensity and frequency noise of single mode semiconductor lasers in the presence of an optical feedback. By explicitly taking into account the spontaneous emission processes into the laser mode, we obtain a behavior which, at high frequencies significantly differs from the usual one, and is in good agreement with recent experimental results. In particular, we are able to show in which way the intensity and frequency noise, besides being influenced by the external cavity length, are affected by the presence of the well known resonant peaks in the noise spectra of the solitary laser and how a substantial lowering and flattening in the noise spectra can be obtained with external cavity round trip times shorter than the inverse of the peak resonant frequency. We also present experimental results in good agreement with the theoretical ones.     

外部光反馈对强耦合外腔半导体激光器特性影响的理论分析

本文从理论上分析了外部光反馈对强耦合外腔半导体激光器特性的影响，对相干外部光反馈和非相干外部光反馈两种情形的分析结果均表明强耦合外腔半导体激光器可将半导体激光器所能容忍的临界光反馈强度提高大约２０ｄＢ以上，同时得出了长外腔和强耦合有利于提高外腔半导体激光器抗反馈能力的结论。     

Feedback sensitivity and coherence collapse threshold of semiconductor DFB lasers with complex structures

A general method for evaluating the feedback sensitivity of semiconductor lasers is proposed based on Green's functions approach. The rate equations derived in this paper generalize works already published to any type of laser cavities such as those with axially varying parameters. The variation of the lasing frequency occurring under external optical feedback is then used to predict the coherence collapse threshold. The approach is validated for conventional DFB lasers by comparing the calculated feedback sensitivity with those obtained from analytical expressions. Both feedback sensitivity and coherence collapse thresholds are then calculated and analyzed for DFB lasers with a chirped grating. A remarkable agreement on the critical feedback level between simulations and measurements is obtained for all the lasers under study.     

Root locus method for predicting the stability of laser diodes withoptical feedback

Optical feedback from an external reflector into a laser diode can render the output of the diode unstable. The critical feedback strength for a laser diode with external optical feedback is calculated using a computationally efficient root locus technique. Simulations reveal that for certain shorter feedback path lengths the critical feedback strength is elevated above the long path asymptotic value, leading to islands of increased stability     

Tuning characteristics of a tunable-single-frequencyexternal-cavity laser

The lasing characteristics of a tunable-single-frequency laser operated in conjunction with a tunable external cavity are investigated. The effect of phase error in the external cavity on the lasing frequency, linewidth, and output power is calculated by deriving the characteristic equation for the FP cavity as a traveling amplifier with an effective mirror concept. The analysis suggests that the diode laser and the external cavity may be successfully tuned open-loop if the feedback strength is appropriate and the tuning nonlinearities in the active and passive cavities are not too severe. This is demonstrated by maintaining a linewidth of 4 MHz while tuning continuously over 34 GHz