Effects of band non-parabolicity on cavity modes in photonic crystals

Abstract

We include the effect of band non-parabolicity on photonic defect states within the Wannier theory, which improves the quadratic approximation adopted by Painter et al. [Phys. Rev. B 68, 035214 (2003)] for large-size defects, as well as extends the theory to a wider range of defect size. A 2D hexagonal photonic crystal is considered, and analyzed for the origin and degree of non-parabolicity in the 1st TE band around J-point, and for the effect of non-parabolicity on acceptor type cavity modes. The non-parabolicity is shown to derive primarily from the inherent anisotropy of band dispersion around the point. Overall, with the inclusion of non-parabolicity, (i) mode degeneracy is lowered, (ii) the “binding energy” of a cavity mode is increased, and (iii) the cut-off of defect size for a given cavity mode is reduced, by as much as 35% in certain cases, in comparison with that calculated without the non-parabolicity. A simple “overall effective mass” picture is provided for the understanding of non-parabolicity effects.