The phenomena occurring in semiconductor lasers due to weak external optical feedback are reviewed, including mode hopping and related mode-hopping noise, linewidth narrowing and broadening, and the transition to the coherence collapse regime. Guidelines are given for designing semiconductor lasers, both edge emitters and VCSEL's, with high endurance against external optical feedback. >

External optical feedback phenomena in semiconductor lasers

This paper presents a theoretical analysis and a comparison with experimental results on self-mixing interference inside a single-longitudinal-mode diode laser. A theoretical model, based on the steady-state equations of the lasing condition in a Fabry-Perot type laser cavity, is described, and through it a satisfactory analysis of self-mixing interference for optical sensing applications is given. In this work, the self-mixing interference produced by an external optical feedback is found to be due to the variations in the threshold gain and in the spectral distribution of the laser output. The gain variation results in an optical intensity modulation, and the spectral variation determines both the modulation waveform and the coherence properties of the interference. The theoretical analysis of the self-mixing interference is seen to yield a simulation of the laser power modulation which is in good agreement with the experiment results reported. >

Self-mixing interference inside a single-mode diode laser for optical sensing applications

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.

http://iopscience.iop.org/article/10.1088/1355-5111/7/2/003/pdf

Semiconductor lasers with optical injection and feedback

In optical fiber networks, the semiconductor laser source may be subjected to unavoidable optical feedback from fiber pigtails, fiber connectors and other components, unless expensive optical isolators are used. Therefore, a good understanding of external optical feedback phenomena in semiconductor lasers is required. This paper will review these phenomena, including linewidth narrowing and broadening, mode hopping phenomena and the transition to the so-called coherence-collapse regime. In particular, laser designs with high endurance against optical feedback will be discussed.

Chaotic pulsing and the route to chaos in a semiconductor laser with delayed, positive opto-electronic feedback are investigated numerically and experimentally. Both numerical simulation and experimental observation indicate that the laser enters a chaotic pulsing state at certain delay times of the feedback loop through a quasi-periodic route. The characteristics of each dynamical state are analyzed. The chaotic pulsing state is verified with a positive Lyapunov exponent and a fractal correlation dimension. The experimental results show very good qualitative agreement with the numerical results. Quantitative discrepancy between experimental and numerical results can be explained by the bandpass characteristics of the electronic feedback loop.

Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback

A novel and relatively simple expression is given for the optical spectrum of a single-mode semiconductor laser which, due to the presence of relaxation oscillations, consists of a strong central line with a broad weak sideband at each side. The coupling between phase and amplitude fluctuations is included in this derivation and is shown to result in an asymmetry between the relaxation oscillation sidebands. This asymmetry can be used to determine the linewidth enhancement factor. Using optical heterodyne detection, the spectrum of a Fabry-Perot-type AlGaAs laser has been measured as a function of output power. Information on the dynamics of the relaxation oscillations was thus obtained. The power dependence of the frequency and damping of the relaxation oscillations allowed the spontaneous lifetime and the dependence of the gain on both carrier density (differential gain) and intensity (gain saturation) to be separately determined. >

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Spectral signature of relaxation oscillations in semiconductor lasers

The visibility, i.e. the absolute value of the field-autocorrelation function, of a semiconductor laser subject to optical feedback has been measured. The feedback was provided by a mirror that was placed at a distance exceeding the coherence length of the emitted light. The amount of feedback varied between zero and the maximum feedback, for which the laser still operated in a single longitudinal mode of the semiconductor chip. The results are compared with numerical solutions of the Lang and Kobayashi equations. Over the whole range of feedback excellent agreement between experiment and theory was found. However. this agreement requires an unusually high value of the linewidth enhancement factor, i.e. a=10; the reason for this remains unclear. The self-sustained noise model, which is based on a statistical-analytical solution of the Lang and Kobayashi equations and which has been used in the past for analyzing feedback effects, is found to yield an inaccurate description of the experiments. Suggestions are given to explain this inadequacy. >

Coherence properties of a semiconductor laser with feedback from a distant reflector: experiment and theory

Nonuniform phase diffusion in a laser

In this paper we calculate the intensity and carrier-density distribution inside a Fabry-Perot-type semiconductor laser with arbitrary facet reflectivities. We derive an expression for the linewidth of such a laser operated well above threshold, when the inversion saturates and the carrier-density distribution becomes nonuniform. Results are given for the frequency and carrier-density dependence of the linewidth-enhancement factor of Al x Ga 1-x As lasers. We find that saturation results in substantial nonuniformity of the distributions of the spontaneous-emission factor and the linewidth-enhancement factor

Numerical study of the linewidth of a semiconductor laser: Effect of saturation.

A laser can be thought of as an amplitude-stabilized oscillator. Such an oscillator has a finite linewidth, due to phase-changing events. In most cases these events have a “technical” origin, such as fluctuations in the cavity length due to acoustic perturbations. However, even in a perfectly stable environment there is still phase diffusion due to spontaneous emission; this leads to the quantum-limited or fundamental linewidth as first discussed by Schawlow and Townes [1]. In recent years it has been shown by others [2,3,4,5] and by us [6,7,8,9] that the standard (Schawlow-Townes) formula for the fundamental linewidth must be modified if the outcoupling through the mirrors is large. In this paper we review our work [6,7,8,9] in this field, starting in section 2 with theory. In section 3 we report on the diagnostics of the semiconductor lasers used in the experiments. The technique of linewidth measurement is discussed in section 4 and actual results are given in section 5, together with a comparison with theory.

W. A. Hamel

Papers

Spectral signature of relaxation oscillations in semiconductor lasers

Coherence properties of a semiconductor laser with feedback from a distant reflector: experiment and theory

Nonuniform phase diffusion in a laser

Numerical study of the linewidth of a semiconductor laser: Effect of saturation.

Enhanced Fundamental Linewidth of a Laser Due to Outcoupling