Approximate boundary conditions for homogeneous dielectric bodies

Abstract

Using a method based on the asymptotic expansion of the field inside a homogeneous dielectric body in inverse powers of N, where N is the complex refractive index, a boundary condition is developed accurate to the third order in 1/N applicable at the surface γ = constant of the body, where α, β, γ are orthogonal curvilinear coordinates. In contrast to the standard (first order) condition, the boundary condition involves tangential field derivatives through the second order, and is an example of a second order generalized impedance condition. The superior accuracy that it provides is demonstrated, and the result has important consequences in connection with absorbing boundary conditions used to terminate the computational domain in a finite element or finite difference solution of the wave equation.