Generalized effective index series solution analysis of waveguide structures with positionally varying refractive index profiles

The use of a generalized series solution technique for analyzing semiconductor integrated-optic waveguide devices is presented. This technique can be employed to obtain TE and TM modes for any slab-waveguide structure with an arbitrary index variation, as long as the square of the index in each layer can be fitted to a polynomial function of position. The method is applied to a slab waveguide with a parabolic index profile, an AlGaAs heterostructure electrooptic phase modulator, heterostructure ridge-waveguide structures with sloped sidewalls, and an InGaAs-AlGaAs graded-index separate-confinement-heterojunction quantum-well structure.