Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media

This paper discusses a numerical method for computing the electromagnetic m odes supported by multilayer planar optical waveguides constructed from los sy or active media, having in general a diagonal permittivity tensor. The m ethod solves the dispersion equations in the complex plane via the Cauchy i ntegration method. It is applicable to lossless, lossy and active waveguide s, and to AntiResonant Reflecting Optical Waveguides (ARROW's). Analytical derivatives for the dispersion equations are derived and presented for what is believed to be the first time, and a new algorithm that significantly r educes the time required to compute the derivatives is given. This has a do uble impact: improved accuracy and reduced computation time compared to the standard approach. A different integration contour, which is suitable for leaky modes is also presented. Comparisons are made with results found in t he literature; excellent agreement is noted for all comparisons made. (C) 2 000 Optical Society of America.