Modelling of photonic crystal waveguides: a simple and accurate approach

Abstract

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.

An Efficient Mode Reduction Technique for Modeling of Waveguide Gratings

“…In the third example, we consider a defect structure that has been studied in Section 5.3 in [21]. The defect waveguide contains 8 grooves with the central "tooth" be 1.515 µm width.…”

Semi-analytical model for a slab one-dimensional photonic crystal

“…Then, in case of piecewise constant media, the common transfer matrix method (quasi-0D) can be applied. However, performance of this method for TM (in-plane) modes was shown to be rather poor and iterative method was applied in [10] to address this issue. Here we use mode decomposition approach to show that in quasi-1D structures (both, 2D and 3D) the transfer matrix method actually can be applied.…”