An analytical method to calculate the multi-transverse-mode static characteristics of index-guided vertical-cavity surface-emitting lasers is presented. The steady-state solution of a model that takes into account the spatial dependence of both the electrical field and the carrier-density profiles is calculated. Power of the transverse modes is then obtained by solving a linear set of equations of which the coefficients are simple integrals involving modal and injected-current-density profiles. Analytical expressions are then derived for threshold currents of the transverse modes. Finally, simple analytical expressions are derived for single- and two-mode operation.

Peer reviewed