3,016 research outputs found
The PML for rough surface scattering
In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough
surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution
of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved
Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures
We present a domain decomposition approach for the computation of the
electromagnetic field within periodic structures. We use a Schwarz method with
transparent boundary conditions at the interfaces of the domains. Transparent
boundary conditions are approximated by the perfectly matched layer method
(PML). To cope with Wood anomalies appearing in periodic structures an adaptive
strategy to determine optimal PML parameters is developed. We focus on the
application to typical EUV lithography line masks. Light propagation within the
multi-layer stack of the EUV mask is treated analytically. This results in a
drastic reduction of the computational costs and allows for the simulation of
next generation lithography masks on a standard personal computer.Comment: 24 page
JCMmode: An Adaptive Finite Element Solver for the Computation of Leaky Modes
We present our simulation tool JCMmode for calculating propagating modes of
an optical waveguide. As ansatz functions we use higher order, vectorial
elements (Nedelec elements, edge elements). Further we construct transparent
boundary conditions to deal with leaky modes even for problems with
inhomogeneous exterior domains as for integrated hollow core Arrow waveguides.
We have implemented an error estimator which steers the adaptive mesh
refinement. This allows the precise computation of singularities near the
metal's corner of a Plasmon-Polariton waveguide even for irregular shaped metal
films on a standard personal computer.Comment: 11 page
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