Abstract
Fast surface integral equation (SIE) methods seem to be ideal for
simulating 3-D nanophotonic devices, as such devices generate fields in both
the interior device volume and in the infinite exterior domain. SIE methods
were originally developed for computing scattering from structures with
finite surfaces, and since SIE methods automatically represent the infinite
extent of the exterior scattered field, there was no need to develop
numerical absorbers. Numerical absorbers are needed when SIE methods are
used to simulate nanophotonic devices that process or couple light, to
provide nonreflecting termination at the optical ports of such devices. In
this paper, we focus on the problem of developing an approach to absorbers
that are suitable for port termination, yet preserve the surface-only
discretization and the geometry-independent Green's function properties of
the SIE methods. Preserving these properties allows the absorber approach to
be easily incorporated in commonly used fast solvers. We describe our
solution to the absorber problem, that of using a gradually increasing
surface conductivity, and show how to include surface conductivity in SIE
methods. We also analyze numerical results using our absorber approach to
terminate a finite-length rectangular cross section dielectric waveguide.
The numerical results demonstrate that our surface-conductivity absorber can
easily achieve a reflected power of less than $10^{-7}$, and that the magnitude of the transition reflection is
proportional to $1/L^{2d+2}$, where $L$ is the absorber length and $d$ is the order of the differentiability of the surface conductivity
function.
© 2011 IEEE
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