Hybrid Computational Algorithms for the Problem of Scattering from Grating Structures

Abstract

Modeling of wave scattering from grating couplers has become increasingly important due to extensive recent research interest in the problem of plasmonic resonance. Computational algorithms which are specially used to model the problem of scattering from the grating surfaces suffer from several drawbacks such as accuracy, computational efficiency, and generality. To address the challenges of the previous methods, this work presents a novel hybrid Finite Element-Boundary Integral Method (FE-BIM) solution to the problem of scattering from grating surfaces consisting of finite or infinite array of two-dimensional cavities and holes in an infinite metallic walls covered with a stratified dielectric layer.

To solve the scattering problem from finite number of cavities or holes engraved in a perfectly conducting screen (PEC), the solution region is divided into interior regions containing the cavities or holes and the region exterior to them. The finite element formulation is applied inside the interior region to derive a linear system of equations associated with nodal field values. Using two-boundary formulation, the surface integral equation employing free-space Green's function is then applied at \emph{only} the opening of the cavities or holes to truncate the computational domain and to connect the matrix subsystem generated from each cavity or hole.

The hybrid FE-BIM method is extended to solve the scattering problem from an infinite array of cavities or holes in a PEC screen by deriving the quasi-periodic Green's function. In the scattering problem from an infinite array of cavities, the finite element formulation is first used inside a single cavity in the unit-cell. Next, the surface integral equation employing the quasi-periodic Green's function is applied at the opening of \emph{only} a single cavity as a boundary constraint to truncate the computational domain. Effect of the infinite array of cavities is incorporated into the system of the nodal equations by the quasi-periodic Green's function.

Finally, the method based on the hybrid FE-BIM is developed to solve the scattering problem from grating surfaces covered with a stratified dielectric layer. In this method, the surface integral equation employing grounded dielectric slab Green's function is applied at the opening of the cavities or holes inside the dielectric coating to truncate the solution region efficiently. An accurate algorithm is presented to derive the grounded dielectric slab Green's function in spatial domain incorporating the effects of the surface-waves and leaky-waves excited and propagated inside the dielectric slab. Numerical examples of near and far field calculations for finite or infinite array of cavities or holes are presented to validate accuracy, versatility, and efficiency of the algorithm presented in this thesis.