Guiding mode expansion of a TE and TM transverse-mode integral equation for dielectric slab waveguides with an abrupt termination

We propose a rigorous transverse-mode integral equation formulation for ana lyzing TE and TM electromagnetic radiation fields on the facet of dielectri c slab waveguides with an abrupt termination in free space. Both exact wave guide guiding modes and discretized radiation modes are included in the ker nels of the integral equation. Tb reduce the size of the matrix that approx imates the exact integral equation, we expand the unknown field at the junc tions in terms of guiding modes of a selected waveguide with sufficiently l arge normalized frequency and core thickness. By direct matrix inversion, w e obtain numerical solutions of the scattered fields at the junctions. Our method can be used to study the field distribution as well as the energy re flection and transmission coefficients of dielectric waveguides with multip le step discontinuities. (C) 2001 Optical Society of America.