<title>Self-consistent calculation of two-dimensional diffusion equation for a modal gain analysis of lasing modes in cylindrical VCSELs</title>

A circular cylinder resonator modal analysis is applied to vertical cavity surface emitting lasers to obtain a resonance mode chart to identify possible lasing spectra. For the first time a 2D/ (radial and azimuthal) calculation of the inversion population distribution in the device is done, inclusive of current spreading, carrier diffusion, (bimolecular) spontaneous recombination, and stimulated recombination to account for above- threshold operation. Analysis of corresponding modal gain competition is used to indicate possible lasing mode selection.