Mode selection in GaAs injection lasers resulting from fresnel reflection

In several recent papers, attention has been given to the Fresnel reflectivity associated with cleaved facets of the laser. The small dimensions of the heterostructure waveguide give rise to a considerable angular spread in the energy incident on the facet. As a result, the mode reflectivity is not given simply by the Fresnel equation, which is only valid for an infinite plane wave. Rather, it is a properly weighted average over the plane-wave distribution of the mode. The differences in mode reflectivity with respect to TE and TM modes, as well as the variations with mode number, have been offered as a possible explanation for the predominant appearance of TE modes and preference for higher order modes in the large optical-cavity (LOC) geometry. However, the considerations to date have ignored the finite extent of the field in the junction plane. This situation is rectified in this paper. It is shown that the splitting in the mode reflectivity values between TE (electric field in the junction plane) and TM (electric field perpendicular to the junction plane) modes is reduced, and under certain conditions TM modes can be favored. In particular, it is shown that if a TE mode is oscillating, then there is a preference for a lowest order mode in the plane of the junction and a highest order mode in the transverse plane. Conversely, if for some reason a TM mode is oscillating, then the preference is for highest order modes in the plane of the junction and lowest order modes in the transverse plane.