Abstract
The effective propagation constants and electric field profiles of the propagating modes in dielectric channel waveguides are solved through a modification of the finite-element method called the product method. A tensor product of two one-dimensional spline spaces is used as the basis set for the two-dimensional electric field profiles. Schwartz distributions are used to treat discontinuities in the normal component of the electric field at discontinuities in the index profile. Comparisons of this method with analytically computed waveguide modes show that the product method is highly accurate: to more than six significant figures for the fundamental TE mode and to five significant figures for the fundamental TM mode.
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