A High-Order-Accurate 3D Surface Integral Equation Solver for Uniaxial Anisotropic Media

This article introduces a high-order accurate surface integral equation (SIE) method for solving 3-D electromagnetic scattering for dielectric objects with uniaxially anisotropic permittivity tensors. The N-Muller formulation is leveraged, resulting in a second-kind integral formulation, and a finite-difference (FD)-based approach is used to deal with the strongly singular terms resulting from the dyadic Green's functions for uniaxially anisotropic media while maintaining the high-order accuracy of the discretization strategy. The integral operators are discretized via a Nystrom-collocation approach, which represents the unknown surface densities in terms of Chebyshev polynomials on curvilinear quadrilateral surface patches. The convergence is investigated for various geometries, including a sphere, cube, a complicated non-uniform rational basis spline (NURBS) geometry imported from a 3-D computer-aided design (CAD) modeler software, and a nanophotonic silicon waveguide, and the results are compared against a commercial finite-element (FE) solver. To the best of our knowledge, this is the first demonstration of high-order accuracy for objects with uniaxially anisotropic materials using SIEs.