Modelling investigations of DBRs and cavities with photonic crystal holes for application in VCSELs

We investigate the reflection spectra of distributed Bragg reflectors (DBRs) and DBR cavities with and without photonic crystal holes fabricated within them. A finite-difference time domain (FDTD) electromagnetic model which is considered to provide the exact solution of Maxwell equations is used as a reference model. Two simplified modelling approaches are compared to the FDTD results: an effective index model where the individual DBR constituent layers penetrated by holes possess an effective index and a spatial loss model where optical losses are introduced spatially where the holes are fabricated. Results of the FDTD and the spatial loss model show that optical loss determines the properties of an etched DBR and DBR cavity when the lattice constant of the holes of exceeds 1 μm and the hole depth is small. The spatial loss model compares well to the FDTD results for holes with a lattice period exceeding 1 μm. We also consider the realistic effect of angling the sides of the etched holes.