Modeling of a Vertical Cavity Surface Emitting Laser Containing a Multi-QW Heterostructure

Abstract

A vertical cavity surface emitting laser (VCSEL) is an object of numerical study in the present paper.

The linear non-hermitian eigenvalue problem arises in the first stage when we consider a ”cold” cavity and neglect changes of material characteristics induced by electromagnetic field. The round-trip operator technique and Krylov subspace methods were used for determination of eigenfunctions, which represent intra-cavity wave field distributions. Corresponding complex eigenvalues determine the wavelength shifts relative to reference value and threshold gains.

The next stage of study relates to a case of a loaded cavity when self-consistent solving of a wave field equation and material equations is required. The eigenvalue problem for a non-linear operator must be solved to find the lasing electromagnetic field spatial profile and its frequency. The gain element of a typical VCSEL device comprises several quantum wells (QW). The charge carriers distributions in each of QW obey non-linear diffusion equation. The round-trip operator is a non-linear operator in this case, and its evaluation needs an iteration procedure. We propose the iteration procedure, which is applicable for a set of QW of any size and has computational costs growing linearly with number of QW.

The computational procedures and results of calculations for a cylindrical VCSEL will be reported.