G.H.M. van Tartwijk

Semiconductor lasers with optical injection and feedback

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.

Sisyphus effect in semiconductor lasers with optical feedback

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. >

Theory of a diode laser with phase-conjugate feedback

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 steadystate behavior, surrounded by another type of steady-state behavior, referred to as the frequency-difference solution, and a region of self-pulsating relaxation oscillations.

Optical feedback on self-pulsating semiconductor 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.

Resonant optical amplification in a laser diode: theory and experiment

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. >

Absolute instabilities in lasers with host-induced nonlinearities and dispersion

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.

Power spectrum of a bistable external-cavity diode laser

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.

Spatial feedback effects in narrow-stripe index-guided semiconductor lasers

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.

Spatial effects of feedback in narrow-stripe semiconductor lasers

0 0 indicating that it is composed of a superposition of spatially overlapping degenerate polarization states; this also correlates well with the observed minimum in the RIN. (Modal analysis shows that there are four degenerate polarization states for the LP,, mode in a cylindrical waveguide-tangential, radial, and 2 pincushion.) Above 12 mA, beam profile geometry and optical spectrum analysis show that the total beam and each polarized component are multi-transverse mode. We are continuing to investigate the degenerate polarization states of the LP,, mode and how they influence the correlations between beam geometry and RIN. This work is expected to have important implications in low-noise VCSEL applications that use polarization-selective components. -

Dispersion-tailored active-fiber solitons: errata.

In Ref. 1, owing to an editorial error, the acronym EDDF was defined as electronic data display fiber.This expression should be replaced with exponentially dispersion-decreasing fiber throughout the text [after Eq. (5)].