Vertical-cavity surface-emitting lasers (VCSELs) yield single-longitudinal-mode operation, low-divergence circular output beam, and low threshold current. This paper gives an overview on theoretical, self-consistent modelling of physical phenomena occurring in a VCSEL. The model has been experimentally confirmed. We present versatile numerical methods for nitride, arsenide, and phosphide VCSELs emitting light at wavelengths varying from violet to near infrared. We also discuss different designs with respect to optical confinement: gain guidance using tunnel junctions and index guidance using oxide confinement or photonic crystal and we focus on the problem of single-transverse-mode operation. 1. Introduction Currently there are two distinctly different classes of Fabry-Perot semiconductor diode lasers: edge-emitting lasers (EELs) and vertical-cavity surface-emitting lasers (VCSELs). Because of the details of their structure, VCSELs have a number of unique features that distinguish them from conventional EELs [1]: inherent single-longitudinal-mode operation, low-divergence nonastigmatic circular output beams, low threshold current at room-temperature (RT) continuous-wave (CW) operation, device geometry suitable for integration into two-dimensional laser arrays, compatibility with vertical-stacking architecture, the ability to be modulated at very high frequencies, and the possibility of in situ testing. While EELs usually emit many longitudinal modes around the maximal optical gain wavelength, VCSELs emit a single longitudinal mode at the wavelength determined by the cavity design. Therefore, EEL cavities are always tuned to their maximal optical gain but those of VCSELs may be intentionally detuned, which gives an additional degree of freedom to the VCSEL design. As a result, designers of EELs can propose devices emitting radiation of wavelength solely determined by their activeregions. In the case of VCSELs, however, it is possible to design a device emitting radiation at wavelength somewhat different (practically always longer) from that associated with their active-region structure. Computer simulations of laser operation enable anticipating the laser performance in more efficient and inexpensive way than the trial-and-error method. However, VCSEL modelling is a very involved task because of its multilayered structure (sometimes containing as many as several hundred layers) often of nonplanar or buried-type architecture, with many heterojunctions, graded layers, strained layers, quantum wells (QWs), quantum dots (QDs) or quantum wires, superlattices,
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