Photonic band gaps and photonic windows in cascaded optical waveguides: a complete analysis of the electromagnetic scattering properties

A procedure for obtaining the complete electromagnetic scattering properties of cascade discontinuities between arbitrary integrated optical waveguides is presented. The method involves a new Generalized Scattering Matrix concept, together with the Generalized Telegraphist Equations formulism and the Modal Matching Technique. Reflection and transmission coefficients between proper modes can be obtained. Numerical results of complex scattering coefficients for multiple discontinuities in planar optical wave-guides are given. Experimental evaluation was carried out for transitions in cylindrical dielectric waveguides. The possibilities of the method for analysing waveguide photonic crystals as well as optical devices in waveguide periodical structures are demonstrated.