Simulation of Guided Wave Structures of Arbitrary Geometry Using Boundary Integral Method

Guided wave structures with increasing complexity have been a persistent challenge to integrated photonic device modeling. Direct approaches to solving wave equations, either in the finite difference or the finite element scheme, lead to excessive consumption of computational resources. This is because large number of nodes over the domains of interest are needed in order to accurately represent the differential equations. The number of nodes can be enormous even in some moderately complex structures, therefore device modeling based on wave analysis can be extremely costly. Although many special techniques have been developed for specific structures, generic and accurate simulations are often difficult. Beam propagation method (BPM) [1] is very efficient in studying paraxial propagation problems but is not suitable for structures with reflections or large angle bends. The boundary integral method we introduce in this paper, instead of solving the wave equations in the whole domain, only solves boundary values through integration. In most applications it significantly reduces computation time and storage because nodes on the boundaries are much less than nodes needed for the whole domain. Other advantages of the method include the flexibility of treating arbitrary boundaries, easy implementation of boundary conditions, and the simplicity of mesh setup.