3-D Vectorial Optical Model for High-Contrast Grating Vertical-Cavity Surface-Emitting Lasers

High-Contrast Gratings (HCG) are modeled in a rigorous way by a new mode-matching approach. They are highly attractive because they have recently proved suitable to replace distributed Bragg mirrors in Vertical-Cavity Surface-Emitting Lasers (VCSELs). Through a change of basis from plane to cylindrical waves, the generalized transmission matrix of the grating layer is obtained in a form that can be directly used within VCSEL ELectroMagnetic (VELM) code. This is the fully 3-D vectorial code developed at IEIIT-CNR (Turin, Italy) for a decade, which has proven to have the capability to reproduce the experimental details of the various structures investigated so far. The inclusion of HCG in VELM is performed on the same footing as all other geometrical details and in a way that preserves the code accuracy and numerical efficiency. A full set of modes of a large-size HCG VCSEL can be computed in a few minutes on an ordinary laptop.