On effective index approximations of photonic crystal slabs

As a means to assess the quality of effective index approximations in simulations of photonic crystal slabs, we consider a reduction of 2-D Helmholtz problems for waveguide Bragg gratings to 1-D wave propagation, and compare with rigorous 2-D reference solutions. Variational procedures permit to establish a reasonable effective index profile even in cases where locally no guided modes exist