Light propagation in a planar dielectric slab waveguide with step discontinuities

The common matrix formalism for multi-layer systems is generalized to describe the optical field propagation along an arbitrary cascade of step discontinuities in a planar dielectric waveguide. The reflection and transmission properties of the step cascade are modelled by rigorous operator relations in a Hilbert-space calculus. In this way the complete propagation problem is reduced to two basic transformations. TE- and TM-polarized fields are treated simultaneously.