![]() This effect occurs even when the numbers of injected carriers are constant. The first mechanism is beating vibration (i.e., pulsing modulation) on spectral distributions of injected carriers (i.e., electrons and holes) due to lasing frequencies, which is observed as the spectral hole burning effect and whose relaxation is characterized with the intraband relaxation time on the order of 10-13 s. Nonlinear optical phenomena in semiconductor lasers are induced by two types of mechanisms. We also observe switching and hopping of the lasing modes in accordance with the experiments. In our model the origin of modal oscillations is spatial hole burning in the envelope of the carrier grating, which is due to the interaction of different longitudinal modes. These oscillations become faster as the injection current increases, in good agreement with recent experimental observations. We find deterministic out-of-phase modal oscillations which leave the sum of total modal intensities nearly constant. The model considers key ingredients describing the semiconductor medium, such as the spatial variations of the carriers and optical fields in the longitudinal direction, a parabolic frequency-dependent gain and phase-amplitude coupling, and does not assume a priori a fixed number of active longitudinal modes. The multi-longitudinal-mode dynamics of a semiconductor laser is studied theoretically, based on traveling-wave equations for the slowly varying amplitudes of the counterpropagating optical fields in the laser cavity, coupled to an equation for the carrier population dynamics. We demonstrate that this approximation is very good when the underlying carrier diffusion is fast, thus leading to a weakly developed carrier grating. We assess the validity of an existing approximation scheme that has dealt with spatial inhomogeneities by expanding the carrier density into a truncated hierarchy of moments. In these two regimes, the total output of the laser has the properties of a single-mode laser for nondispersive applications. For larger feedback we observe in-phase fast oscillations at a frequency close to the relaxation oscillation frequency of the solitary laser. This result is largely independent of the value of the diffusion coefficient. We find that in the weak feedback regime the longitudinal modes display antiphase oscillations that lead to a nearly constant output intensity. ![]() We also consider the effect of carrier diffusion. ![]() Our model takes into account explicitly spatial effects, which are included by considering spatial profiles for N longitudinal modes coupled to the space-dependent gain. We study the dynamics of multimode semiconductor lasers with optical feedback. ![]()
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