| Abstract |
In the study of light interacting with a metallic nanoscale object, a
particular computational issue is that the problem includes sharp
discontinuities in the dielectric function along the surface of the
metallic object. In such cases, standard lower-order methods require
considerable computational work in order to achieve a certain expected
accuracy. The drawback comes from the slow rate of convergence of the
methods for discontinuous problems or problems whose solutions have less
regularity in smoothness. To avoid these difficulties, we propose to use
higher-order numerical techniques with phase-preserving nature,
specifically standard spectral methods with accuracy-enhancing
postprocessing techniques, and a spectral-element discontinuous Galerkin
method.
The standard pseudo-spectral Fourier time-domain method combined with
postprocessing techniques such as cost effective Gegenbauer
reconstructions has been developed to a nanophotonic problem that
simulates electromagnetic waves interacting with a metallic nanowire where
strong surface plasmon excitations can occur. Gegenbauer-postprocessed
results successfully capture reasonable profiles of the field response up
to the metal surface. Comparison to a finer-resolution FDTD
results will be demonstrated.
We have developed spectral-element discontinuous Galerkin (SEDG) code that
performs very accurate parallel computations of 3D structures without
stair-stepping phenomena. Exponential convergence of this method for
various mesh structures with various boundary conditions (periodic,
Dirichlet, PML) will be demonstrated. Our current developement of this
method to simulate metallic nanowires and photonic crystal waveguides will
be discussed. |
