Modal analysis of step discontinuities in graded-index dielectric slab waveguides

The modal solutions of the TE- and TM-modes of an arbitrary graded-index dielectric slab waveguide have been derived by applying the generalized telegraphist´s equations to the equivalent inhomogeneous parallel-plate waveguide model with electric or magnetic walls. These modal solutions have been employed in a mode-matching procedure to calculate the transmission properties of step discontinuities in arbitrarily graded-index dielectric slab waveguides such as diffused optical waveguides having exponential, Gaussian and complementary error-function index profiles. For slab waveguides containing an abrupt offset, the radiated power is found to increase smoothly with increasing displacement. Power loss calculations for an abrupt change in diffusion depth for which the dominant mode is in the vicinity of cutoff, exhibit a sharp transition from almost zero loss to nearly total radiation loss