A theory for filamentation in semiconductor lasers including the dependence of dielectric constant on injected carrier density

A model for the self-focusing mechanism in semiconductor lasers is analysed and applied to the formation of lasing filaments in p-n junction devices. The self-focusing is attributed to an increase of dielectric constant in the semiconductor in regions of high light intensity due to a depletion of the injected carrier concentration. Two mechanisms are postulated for the dependence of dielectric constant on carrier concentration; the free carrier effect and the band-to-band interaction. The band-to-band interaction is computed as a function of photon energy, and found to give the major contribution to a total dielectric constant perturbation of typically −0.05 at threshold. This agrees with experiment. A single-mode solution is obtained for the waveguide equation of an isolated filament or a set of coupled filaments. This shows that the filament width contracts with current. Expressions are obtained for the optical intensity distribution, for the guided wavelength, for the effect of carrier diffusion, and for the higher-order mode cut-offs. The calculated filament width at 300 K varies typically between 12 and 3 microns for currents from 1 to 60% above threshold; at 77 K the width is almost doubled. This agrees reasonably with experiment. In general the analysis shows that the strength of self-focusing in heterostructure lasers depends on the number of carriers injected at threshold per cm2 per micron thickness of the optical confinement region.

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