1. Semiconductor Laser Diodes 2. Basic Concepts 3. Free-Carrier Theory 4. Coulomb Effects 5. Many-Body Gain 6. Band Mixing and Strain in Quantum Wells 7. Semiclassical laser Theory 8. Multimode Operation 9. Quantum Theory of the Laser 10. Propagation Effects 11. Beyond Quasiequilibrium Theory, Appendices A-e, Index

Semiconductor-Laser Physics

The study of the effects of noise and fluctuations is a well established subject in several different disciplines ranging from pure mathematics (stochastic processes) to physics (fluctuations) and electrical engineering (noise and radiophysics). In traditional statistical physics, fluctuations are of thermal origin giving rise to small departures from a mean value. They tend to zero as one approaches the thermodynamic limit in which different statistical descriptions (different ensembles) become equivalent. Likewise, in more applied contexts fluctuations or noise are usually regarded as small corrections to a deterministic (noise free) behavior that degrades a signal-to-noise ratio or can cause transmission errors. In such framework fluctuations are a correction that can be usually dealt with through some sort of linearization of dynamics around a mean or noise free dynamics. A different point of view about fluctuations emerges, for example, in the study of critical phenomena in the 1970’s. The statistical physics description of these phenomena requires a formulation appropriate for a system dominated by fluctuations and nonlinear it ies. A linear theory only identifies the existence of a critical point by a divergence of fluctuations.

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Stochastic effects in physical systems

We theoretically study the dynamics and the mode-locking properties of semiconductor Fabry-Perot lasers with intracavity saturable absorber by using a travelling-wave model and a time-domain description of the optical response of the semiconductor materials. Our description enables us to incorporate important features as for instance the abrupt spectral variations of the absorption in the saturable absorber. We analyze the influence of several key parameters that affect the stability of the mode-locking regime and show that this modelling approach can be used, upon proper fitting of the material parameters, for optimization of the design of semiconductor mode-locked lasers.

Mode-Locking in Semiconductor Fabry-Pérot Lasers

We use a traveling-wave model for explaining the experimentally observed changes in the directionality of the emission of semiconductor ring lasers and its different behavior when current is increased or decreased. The modulation of the cavity losses imposed by the light extraction sections together with the thermal shift of the gain spectrum and spatial hole burning in the carrier density play a crucial role in the directionality of the emission and its changes with operation current. The differences as the current is increased or decreased correspond to the different role played by spatial hole burning.

Emission Directionality of Semiconductor Ring Lasers: A Traveling-Wave Description

This work reports on the existence of deterministic nonlinear dynamics in a free-running multimode semiconductor laser. The main dynamical effects found in a set of experiments realized with several edge-emitting lasers are: (i) periodic fluctuations, in the MHz range, of each modal output, (ii) compensation in the total output which remains practically flat, (iii) the modal switching sequence follows the modal optical frequencies sequence from blue to red; when the reddest mode switches off, the sequence restarts from the bluest mode. These effects are robust against a change of the control parameters which mostly affects the number of oscillating modes. Experimentally, the pump current of the lasers was increased and it was verified that the property of regular modal switching with flat total output is independent of the mode number, up to seven oscillating modes. For large number of modes, the fluctuations persist but they can lose regularity in phase and amplitude. The authors have always noticed the almost complete extinction (more than -40 dB) of the modal switching frequency in the total intensity and the switching sequence that progresses from the blue side of the optical spectrum to the red side. The frequency of the modal switching tends to increase with pumping current and with the number of active modes but it remains in the range 5 to 15 MHz. No significant difference between the power spectra of the different modal amplitudes was observed.

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Dynamics of multimode semiconductor lasers

We report the results of a numerical study of multimode behaviour of a Fabry-Perot laser. The model is based on travelling-wave equations for the slowly varying amplitudes of the counterpropagating waves in the cavity, coupled to equations for spatially dependent population inversion and polarization of a two-level active medium. Variations in the material variables on the scale of a wavelength are taken into account by means of an expansion in a Fourier series. Results are given for typical semiconductor laser parameters. Spatially distributed spontaneous emission noise and carrier diffusion are taken into account. The competing roles of spatial hole burning (SHE), spontaneous emission noise, and carrier diffusion in determining multimode behaviour are elucidated; with no carrier diffusion, spontaneous emission noise excites a large number of modes close to threshold, while SHE leads to a fixed number of significant lasing modes well above threshold. Carrier diffusion washes out the gratings in the material variables, and the resulting strengthening of the inter-mode coupling (cross-saturation) restores dominant single-mode emission well above threshold. We have also studied the effects of optical feedback and opportunities for mode selection with short external cavities; for an external cavity much shorter than the laser cavity length and a small field amplitude reflectivity coefficient, a single mode can be selected. For a large reflectivity coefficient, two groups of intracavity modes separated by the external cavity mode interspacing are selected. For an external cavity with a round trip time half that of the laser cavity, the laser can be forced with modest feedback to operate on two modes that are both quasiresonant with the external cavity. Mode selection is not found, even for weak feedback, when the external mode spacing is about 90% of the laser mode spacing.

Travelling wave model of a multimode Fabry-Perot laser in free running and external cavity configurations

Mode competition in a Fabry-Perot semiconductor laser: travelling wave model with asymmetric dynamical gain

The spectrum of single-mode laser pulses generated by fast pseudorandom word modulation is studied numerically for return-to-zero and nonreturn-to-zero control signals. We analyze both statistics and the worst cases for the frequency chirp during each optical pulse, and we study the connection between these frequency chirps and the turn-on times. We show that patterns in the modulation signal sequences contribute to chirp noise. The worst case values of the turn-on time and the chirp range are very similar in the two modulation schemes, hence, the optimum choice depends mainly on the characteristics of the decision circuit and on the driver and detector bandwidths. >

Statistical properties of the spectrum of light pulses in fast pseudorandom word modulation of a single-mode semiconductor laser

The authors have studied the numerical response of a singlemode semiconductor laser under modulation of the injection current in the presence of optical feedback for different external cavity lengths. They have restricted the experiment to the nonreturn-to-zero modulation scheme and a modulation frequency of 10 Gbit/s. Observations are made that for short cavities (a few millimetres) the eye diagram aperture and the frequency chirp depend strongly on the phase of the reinjected field. Conversely, for cavity lengths of a few centimetres (pig-tail sizes) neither the eye aperture nor the frequency chirp are appreciably affected by the feedback.

Effect of optical feedback on fast modulated semiconductor lasers

We theoretically investigate the influence of optical feedback on the modulation response of quantum-well lasers. Controlled weak optical feedback is shown to be useful to improve the high frequency performance, compensating the limitations imposed by carrier-transport effects.

M. Homar

Papers

Travelling wave model of a multimode Fabry-Perot laser in free running and external cavity configurations

Mode competition in a Fabry-Perot semiconductor laser: travelling wave model with asymmetric dynamical gain

Statistical properties of the spectrum of light pulses in fast pseudorandom word modulation of a single-mode semiconductor laser

Effect of optical feedback on fast modulated semiconductor lasers

Modulation response of quantum-well lasers with carrier transport effects under weak optical feedback