Hermite-Gauss functions in the analysis of a category of optical devices

It is shown in this paper that the Hermite-Gauss functions may be systematically used in an eigenfunction expansion procedure to solve for field propagation characteristics in the devices of interest. This quasi-analytic approach, coupled with the naturally suited collocation numerical procedure, is demonstrated to be a very efficient and effective scheme for analysing optical fields in non-uniform, inhomogeneous media. It is proposed as a method. of solution for active semiconductor optical devices where it is also necessary to calculate the optical field in conjunction with the diffusion-dominated carrier density equation. Self-consistent solutions are normally obtained only after several iterations, hence the need to achieve an efficient computation scheme is paramount.