Mathematical rigorous approach to simulate an over-threshold VCSEL operation

Mathematical rigorous approach to simulate an over-threshold steady-state operation of vertical-cavity surface-emitting diode lasers (VCSELs) is presented. The proposed approach does not require more parameters than the standard threshold one. With its aid, VCSEL operating conditions exceeding the lasing threshold may be examined. In particular, it enables a computer simulation of an excitation of successive transverse modes when the operation current (applied voltage) is gradually increased, taking into account the spatial hole-burning effect. Hence, using the proposed approach, VCSEL mode selectivity and conditions necessary to maintain a desired single-fundamental-mode operation may be examined for a VCSEL design under consideration.

► An iterative method of solving non-linear carrier diffusion equation in semicondutor lasers is presented.
► Its convergence is proven in the threshold case.
► An over-threshold model for VCSELs is proposed.
► Comparison with the experiment is given.