Mode Reduction for Efficient Modeling of Photonic Crystal Slab Structures

Rigorous numerical simulations for photonic crystal (PhC) slab structures and devices are difficult due to the complicated three-dimensional (3-D) geometry, high index-contrast, sharp edges, and possibly inhomogeneity at infinity. The approach based on expanding the field in 1-D vertical modes has great potential, but is currently limited by the relatively large number of modes needed for maintaining the accuracy of the solutions. In this paper, we show that if a single hole is first analyzed with the full set of vertical modes, the number of modes can be reduced to less than one third of the total in the main part of the computation. This leads to a speedup of more than 27 times. The method is illustrated by computing the transmission and reflection spectra for a PhC slab with a finite number of hole arrays.