Modal frequencies of vertical-cavity lasers determined by an effective-index model

Previously, an effective-index optical model was introduced for the analysis of lateral waveguiding effects in vertical-cavity surface-emitting lasers. We show that the resultant transverse equation obtained in that model is almost identical to the one typically obtained in the analysis of dielectric waveguide problems, such as a step-index optical fiber. In this letter, we extend the effective-index model to obtain predictions of the discrete frequencies of the microcavity modes. As an example, we apply the analysis to vertical-cavity lasers that contain thin-oxide apertures. The model intuitively explains our experimental data and makes quantitative predictions in good agreement with a highly accurate numerical model.