Modelling of photonic crystal waveguides: a simple and accurate approach

We present an improved variational effective index method for reduction of 2-D Bragg grating problems to 1-D and show significant improvements particularly at smaller wavelengths. The method is based on the optimal variational (Vopt) method, which we have earlier used successfully for conventional waveguides. A 1-D transverse profile along with a longitudinal index variation are reduced to a 1-D longitudinal distribution, reflection and transmission spectra of which have been studied for both the TE and TM modes by transfer matrix methods. An accurate modeling for the out of plane scattering losses has been presented which occur when a guided wave propagating in a conventional waveguide impinges on a photonic crystal waveguide. Taking these losses into account brings the results pretty close to those of a rigorous 2-D Helmholtz solver QUEP, improving them remarkably over the variational EIM (vEIM) results.