This paper discusses a numerical method for computing the electromagnetic modes supported by multilayer planar optical waveguides constructed from lossy or active media, having in general a diagonal permittivity tensor. The method solves the dispersion equations in the complex plane via the Cauchy integration method. It is applicable to lossless, lossy and active waveguides, 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 reduces the time required to compute the derivatives is given. This has a double 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 the literature; excellent agreement is noted for all comparisons made.

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Journal Optics Express
Chen, C, Berini, P. (Pierre), Feng, D. (Dazeng), Tanev, S, & Tzolov, V.P. (Velko P.). (2000). Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media. Optics Express, 7(8), 260–272. doi:10.1364/OE.7.000260