  Fast surface integral equation (SIE) solvers seem to be ideal approaches for
simulating 3-D nanophotonic devices, as these devices generate fields both in
an interior channel and in the infinite exterior domain. However, many devices
of interest, such as optical couplers, have channels that can not be terminated
without generating reflections. Generating absorbers for these channels is a
new problem for SIE methods, as the methods were initially developed for
problems with finite surfaces. In this paper we show that the obvious approach
for eliminating reflections, making the channel mildly conductive outside the
domain of interest, is inaccurate. We describe a new method, in which the
absorber has a gradually increasing surface conductivity; such an absorber can
be easily incorporated in fast integral equation solvers. Numerical experiments
from a surface-conductivity modified FFT-accelerated PMCHW-based solver are
correlated with analytic results, demonstrating that this new method is orders
of magnitude more effective than a volume absorber, and that the smoothness of
the surface conductivity function determines the performance of the absorber.
In particular, we show 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.
