Scattering losses from dielectric apertures in vertical-cavity lasers

In vertical-cavity lasers (VCLs) employing oxide or airgap apertures, the lasing mode typically travels unguided throughout most of the structure. For the aperture to exactly compensate for the diffraction of the mode in these regions, it would need to have a parabolic lateral index profile (i.e. that of an ideal thin lens). Although nonparabolic aperture shapes will partially compensate diffraction losses, some light will be scattered out of the mode. These scattering losses increase as the aperture size is reduced and will limit the performance of the smallest devices. We analyze these losses first using a semianalytic approach which allows us to frame the problem in terms of two parameters of the structure: the Fresnel number and the effective optical path length across the aperture. We compare the estimate with experimental results and with an iterative numerical calculation of the actual mode and losses. Lastly, we compare the loss reduction with different amounts of tapering that provide a better approximation to the ideal parabolic lens.