Solution of the vector wave equation for general dielectricwaveguides by the Galerkin method

Numerical guided mode solutions for vector waves of general dielectric waveguides are obtained by expanding the unknown field vectors in a double series consisting only of sine functions. The authors formulate solutions by series expansion for the electric and magnetic vector wave equations that yield different matrix equations but identical eigenvalues. The general results are applied to a simple step-index fiber with a large core-cladding index difference and to a fiber core in proximity to a semiinfinite dielectric half space