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We present a second kind integral equation (SKIE) formulation for calculatingthe electromagnetic modes of optical waveguides, where the unknowns are only onmaterial interfaces. The resulting numerical algorithm can handle opticalwaveguides with a large number of inclusions of arbitrary irregular crosssection. It is capable of finding the bound, leaky, and complex modes foroptical fibers and waveguides including photonic crystal fibers (PCF),dielectric fibers and waveguides. Most importantly, the formulation is wellconditioned even in the case of nonsmooth geometries. Our method is highlyaccurate and thus can be used to calculate the propagation loss of theelectromagnetic modes accurately, which provides the photonics industry areliable tool for the design of more compact and efficient photonic devices. Weillustrate and validate the performance of our method through extensivenumerical studies and by comparison with semi-analytical results and previouslypublished results.

Second Kind Integral Equation Formulation for the Mode Calculation of Optical Waveguides