MODELING OF DIFFRACTION IN PILLAR VERTICAL-CAVITY SURFACE-EMITTING LASERS WITH EMBEDDED BRAGG LAYERS

An analytical expression for the reflectivity between the active cavit y of a circular symmetric pillar vertical cavity surface-emitting lase r (VCSEL) and Bragg mirror, which takes account of diffraction at the interface, is derived. The method (mode-matching in Hankel space) is a lso used to determine the reflectivity with some of the Bragg layers e mbedded in the cavity region. The dependence of reflectivity upon Vari ous parameters, including number of Bragg pairs, cavity radius and mod e number, is discussed. The validity of using the plane wave reflectiv ity value (which ignores diffraction effects) is seen to depend signif icantly upon these parameters. As an indicator of the importance of ta king these effects into account for pillar diameters of similar to 6 m u m and less, the variation of threshold gain with cavity radius is gi ven for a commonly used type of VCSEL structure.