Vertical-cavity surface-emitting lasers (VCSELs) yield single-longitudinal-mode operation, low-divergence circular output beam,\r\nand low threshold current. This paper gives an overview on theoretical, self-consistent modelling of physical phenomena occurring\r\nin a VCSEL. The model has been experimentally confirmed. We present versatile numerical methods for nitride, arsenide, and\r\nphosphide VCSELs emitting light at wavelengths varying from violet to near infrared.We also discuss different designs with respect\r\nto optical confinement: gain guidance using tunnel junctions and index guidance using oxide confinement or photonic crystal and\r\nwe focus on the problem of single-transverse-mode operation.
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