Radiation scattering by apertures in vertical-cavity surface-emitting laser cavities and its effects on mode structure

Microcavities with subwavelength features, such as oxide apertures and etched-mesa edges, suffer wide-angle scattering that cannot be captured by the paraxial propagation limit; hence the scattering cannot be fully accounted for by index guiding or by lenslike phase shifts. We present a systematic treatment by using the Born approximation in the vector Maxwell equations. We then introduce the scattering losses in the cavity round-trip matrix, by using a Gauss–Laguerre representation of the cavity modes. Optimization of the round-trip coefficient including confinement, diffraction, and scattering losses yields the mode waist in laterally open vertical cavity surface emitting laser (VCSEL) cavities. A simple equation relating the current aperture to mode spot size is obtained. The analytic results are applied to etched-mesa and oxide-confined VCSEL designs. Predictions for the mode waist and threshold current are comparable with experimental results in oxide-confined VCSELs.