An analytical expression for the reflectivity between the active cavity of a circular symmetric pillar vertical cavity surface-emitting laser (VCSEL) and Bragg mirror, which takes account of diffraction at the interface, is derived. The method (mode-matching in Hankel space) is also used to determine the reflectivity with some of the Bragg layers embedded in the cavity region. The dependence of reflectivity upon Various parameters, including number of Bragg pairs, cavity radius and mode number, is discussed. The validity of using the plane wave reflectivity value (which ignores diffraction effects) is seen to depend significantly upon these parameters. As an indicator of the importance of taking these effects into account for pillar diameters of similar to 6 mu m and less, the variation of threshold gain with cavity radius is given for a commonly used type of VCSEL structure. References: 12
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