Generalised impedance boundary method of moments for multilayer graded-index dielectric waveguide structures

A generalisation of the impedance boundary method of moments (IBMOM) for application to multilayer graded-index dielectric waveguides is proposed. The transverse field in each layer is expanded in local basis functions and matched at the interfaces between the layers. Exact impedance boundary conditions are applied at the two interfaces between the guiding region and cladding regions. Comparison with the IBMOM shows that the generalised impedance boundary method of moments (GIBMOM) is more efficient in calculating the propagation constants of structures with discontinuous refractive index distributions. Numerical results for a two-layer graded-index structure and a step-index coupler are presented to illustrate the improvement in the rate of convergence.