Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides

We present a stable and efficient method for the Bloch-mode computation of one-dimensional grating waveguides. The approach uses the Fourier modal method and the S-matrix algorithm to remove numerical instabilities. The use of perfectly matched layers provide a high accuracy. Numerical results obtained for different lamellar grating waveguides and for both TE and TM polarizations illustrate the performance of the approach.