Impedance boundary method of moments with extended boundary conditions

An improved impedance boundary method of moments is proposed to accurately and efficiently determine the propagation characteristics of multilayer planar optical waveguides whose refractive index profiles contain large step index changes or a graded-index region combined with step index changes. Extended impedance boundary conditions are used in the impedance boundary method of moments to replace regions in the waveguide structure which have refractive index discontinuities. Two methods for determining the extended boundary conditions include the standard transfer matrix method and a procedure utilizing a cascaded transmission line representation with successive calculation of input impedances. Simulation results show significantly improved convergence rates in the determination of propagation constants.