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We analyze the occurrence of absolute instabilities in lasers that contain a dispersive host material with third-order nonlinearities. Starting from the Maxwell-Bloch equations, we derive general multimode equations to distinguish between convective and absolute instabilities. We find that both self-phase modulation and intensity-dependent absorption can dramatically affect the absolute stability of such lasers. In particular, the self-pulsing threshold (the so-called second laser threshold) can occur at few times the first laser threshold even in good-cavity lasers for which no self-pulsing occurs in the absence of intensity-dependent absorption.

We demonstrate experimentally that spatial effects of feedback are important in determining the operating characteristics of index-guided semiconductor lasers. It is in fact the inflexibility of the index-guided mode that makes the laser susceptible to small misalignments of the external cavity, which can induce power variations of nearly 40% of the solitary laser power with feedback levels of less than 2%.(-17 dB). With a simple model, we calculate the modification of the feedback wavefront as a function of the external cavity length and show that the power variations are induced through changes in the cavity loss brought on by the interference of the feedback field with the field reflected off the laser facet. By experimental comparison to a partly gain-guided laser, we conclude that these large-scale variations will be significantly reduced or absent in purely gain-guided lasers.

Weak optical-feedback effects on the statistical properties of self-pulsations in narrow-stripe semiconductor lasers are analyzed using Lang-Kobayashi-type equations. The self-pulsation features are compared with the characteristics of excited relaxation oscillations.We determine the operating regime in which the randomizing effect of spontaneous-emission noise destroys pulse coherence. In this regime, only phase-insensitive effects of optical feedback are possible, and optimum jitter reduction is achieved with delay times of the order of an integer-odd multiple of the free-running pulsation period. In the high-pump operating regime, interpulse coherence is retained and the optical-feedback phase is shown to be instrumental for pulse-jitter control. Our results show that for cavity lengths up to 10 cm, variations on the order of half an optical wavelength induce jitter variations of one order of magnitude., This work was supported in part by the European Union HCM Project CHRX- CT94-0594 and Direcci6n General de Investigacidn Cientifica y TCcnica Project PB94-I 167.

We report the first experimental observation of irregular picosecond light pulses within the coherence collapse of a semiconductor laser subject to delayed moderate optical feedback. This pulsing behavior agrees with the recent explanation of low frequency fluctuations as chaotic itinerancy with a drift. Theory and experiments show very good agreement.

We identify the various physical mechanisms in low frequency fluctuations, which occur when a semiconductor laser is subject to moderate optical feedback while operating close to its solitary laser threshold. In attempting to reach the maximum gain mode, which often is stable, the system forms short mode-locked pulses. In between pulses mode-slipping can occur, generally in the direction of maximum gain. Inevitably, the trajectory passes too close to one of the many saddle points, which will take the system back to the solitary laser state. >

In this review we discuss the theoretical framework needed for studying the dynamical behaviour of semiconductor lasers exposed to three kinds of optical modulation. We start by a derivation of the single-mode rate-equations for the slowly varying complex electric field and the inversion, and the necessary extensions for monochromatic optical injection and normal external optical feedback. The basic operating characteristics of the solitary semiconductor laser are analysed, including light-current curves and their dependence on the spontaneous emission level, as well as the optical spectrum. The effect of monochromatic injection is discussed in terms of locking and non-locking dynamics, including a thermodynamic potential for phase jumps. The basic ingredients for studying external optical feedback are given, including a derivation of the thermodynamic potential for phase-diffusion. After an introduction on optical phase conjugation, the field rate-equation for feedback from a phase-conjugate mirror is derived.

Resonant optical amplification is studied both theoretically and experimentally. Coupled rate equations for the signal field and the spontaneous emission field, valid for input signals with bit rates up to 10 Gb/s are derived. A special weighing procedure based on a dwell-time analysis is used to account for bistable filter operation. The measured amplification characteristics of a /spl lambda//4 DFB laser injected with a 2.5 Gb/s signal show good agreement with theory. >

A single-mode diode laser subject to reflections from an externally pumped phase-conjugate mirror is theoretically investigated by using a rate-equation approach. In the phase plane defined by the amount of feedback and the frequency detuning between diode laser and phase-conjugate mirror, we found an island of locked steady-state behavior, surrounded by another type of steady-state behavior, referred to as the frequency-difference solution, and a region of self-pulsating relaxation oscillations.

The single-mode, noise-free description of low frequency fluctuations (LFF) is reviewed by first discussing the nature of the solutions of the Lang-Kobayashi equations and their stability. Attention is focused on the stability of the so-called maximum gain mode because that plays a crucial role in the various ways of controlling LFF that are being pursued. After comparing numerical simulations with experiments the question is addressed as to whether there is a way to profit from LFF.

We report detailed measurements of the pump-current dependency of the self-pulsating frequency of semiconductor CD lasers. A distinct kink in this dependence is found and explained using a rate-equation model. The kink denotes a transition between a region where the self-pulsations are weakly sustained relaxation oscillations and a region where Q-switching takes place. Simulations show that spontaneous emission noise plays a crucial role in the cross-over., HCM CHRX-CT94-0594

Broad-area lasers exhibit complex spatiotemporal behavior due to multilateral mode operation, emitting filamented beams with low spatial coherence. Using weak external optical feedback we demonstrate that some degree of lateral mode selection and pattern stabilization of these lasers can be obtained under appropriate feedback conditions., This work has been partially supported by CICYT Projects No. TIC95/0563, PB94-1167 ~Spain!, and CHRXCT-94-0594. G.H.M.v.T. also acknowledges financial support by the Netherlands Organization for Scientific Research ~NWO!.

We show that, contrary to common wisdom, the maximum gain mode of semiconductor lasers subject to optical feedback is always stable. The minimum linewidth mode is shown to be subject to a Hopf bifurcation associated with destabilizing the relaxation oscillations. This explains the experimental observation of narrow-linewidth, single-mode diode lasers operating with high optical feedback. © 1995 The American Physical Society.

We report a new potential model for phase diffusion in class-B lasers exposed to external optical feedback. Excited relaxation oscillations cause the potential to be nonlocal. Analytical results using this new potential agree very well with the full system dynamics. We indicate the experimental conditions for which the nonlocal potential becomes manifest in semiconductor lasers.

The low facet reflectivity makes a diode laser very sensitive to external influences such as, e.g. weak feedback from a distant mirror. This sensitivity can succesfully be used in stabilization and line-narrowing schemes based on delayed external optical feedback (see refs. 1–8 in [1]). Recently, succesful frequency control of an AlGaAs diode laser using resonant phase- conjugate reflection was reported by Cyr et al.[2]. This experiment shows the possibility of locking the laser frequency through external optical feedback by the phase-conjugate reflection. A theory of phase-conjugate feedback in a semiconductor laser has been given by Agrawal and Klaus [1], but they formulated the problem for the case of a self-pumped mirror only. Therefore, in their theory the externally reflected signal does not provide a reference frequency to which the laser can lock.

The voltage of a current-driven optically injected semiconductor laser has been measured. The experiments not only show the well known phenomenon of injection locking but also reveal unprecedented dispersive-like structures around the relaxation oscillation frequencies. Based on the single-mode rate equations a theoretical explanation of both phenomena is given. The dispersive-like structures are shown to be caused by four wave mixing.

A single-mode laser subject to weak optical feedback may become a multistable system. When the hopping rate becomes appreciable, the output power spectrum will be modified by the hopping. By applying a novel spectral theory of frequency jumps on a two-mode external-cavity semiconductor laser, we give an explicit analytical expression for the power spectrum that consists of four contributions, two of which are a weighted sum of individual quasi-mode spectra and two of which express the additional spectral broadening that is due to the jumping process.