Curvilinear coordinate method as an initial value problem: application to gratings.

We propose a C-method approach for the efficient calculation of the scattering matrix of a grating. We consider two horizontal planes above and below the grating and define a coordinate system such that the grating surface and both horizontal planes correspond to surface coordinates. Inside the area A delimited by the horizontal planes, the covariant formalism of Maxwell's equations leads to an initial value problem that is solved for independent initial conditions satisfying the boundary conditions. Outside the area A, the fields are represented by Rayleigh expansions. The scattering matrix is obtained by using continuity relations between different components of fields on the horizontal planes.

Multilevel fast multipole method based on a potential formulation for 3D electromagnetic scattering problems.

A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.