Abstract
We present a set of rate equations for the modal amplitudes and carrier-inversion moments that describe the deterministic multi-mode dynamics of a semiconductor laser due to spatial hole burning. Mutual interactions among the lasing modes, induced by high- frequency modulations of the carrier distribution, are included by carrier-inversion moments for which rate equations are given as well. We derive the Bogatov effect of asymmetric gain suppression in semiconductor lasers and illustrate the potential of the model for a two and three-mode laser by numerical and analytical methods.
Highlights
Numerical analysis of multi-mode operation in a semiconductor laser would benefit greatly from a set of coupled rate equations capable of describing the full deterministic dynamics of the lasing modes as well as their mutual interactions
We present a set of rate equations for the modal amplitudes and carrier-inversion moments that describe the deterministic multi-mode dynamics of a semiconductor laser due to spatial hole burning
In the absence of hole burning, i.e. no carrier induced grating ( Nm = 0,∀m = 1, 2,... ), the system is indifferent as to which mode will be excited: the total laser intensity is distributed over the two modes on a one-dimensional manifold and the choice of lasing mode is determined by initial conditions
Summary
Numerical analysis of multi-mode operation in a semiconductor laser would benefit greatly from a set of coupled rate equations capable of describing the full deterministic dynamics of the lasing modes as well as their mutual interactions. Our model is partly in line with the theory by Yamada [6], where a coupled system of ODEs for the mode intensities and a partial differential equation (PDE) for the carriers is introduced for the description of the laser which takes into account the material polarization derived from a density-matrix analysis In this theory no full optical spectrum can be derived and, the spatial interference pattern burned in the carrier distribution due to mode interaction is taken into account (by the “beating vibration on the injected carrier density”), no explicit rate equations for the corresponding oscillating inversion gratings are formulated. Most available models are either “too complicated” to be used when describing a device in a dynamical regime or “too simple” meaning that they lack mode-coupling mechanisms responsible for certain dynamical features
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