Three-dimensional step discontinuities in planar waveguides: Angular-spectrum representation of guided wavefields and generalized matrix-operator formalism

For obliquely incident guided modes the light propagation in slab waveguides with step discontinuities can be described by means of an angular-spectrum representation of the electromagnetic fields together with a generalized matrix-operator formalism. By means of a discretization of the radiation and evanescent modes, the computation of the reflection and transmission coefficients can be reduced to the numerical solution of algebraic equations. The TE-TM coupling, which takes place for oblique incidence, and the different evanescent field effects are discussed in detail.