Surface impedance boundary conditions (SIBCs) for finite-difference time-domain (FDTD) are implemented with collocated H and E components in which first-order spatial finite difference have been used for the spatial derivatives. Transient error analysis is done for the reflected field for the whole possible range of modeled material conductivity. Magnitude and phase error analysis of the calculated reflection coefficients for wideband pulses is presented as well. The resulting numerical errors are compared with the errors of traditional SIBCs implementation when the tangential magnetic fields on the boundary are approximated with the neighboring FDTD magnetic field component located at half-cell size distance in space and half time step behind in time. It is shown that the collocated fields approach is considerably more accurate for both constant real resistive and dispersive complex lossy dielectric SIBCs, in both magnitude and especially phase. Unlike the traditional approach, it is stable for all values of modeled material conductivity. The collocated fields approach is also applied to SIBCs with coating, and the transient and reflection coefficient errors are studied. It is shown that in contrast to the traditional implementation, it is stable for arbitrarily thin coating and for any substrate conductivity, and requires storage only half of the auxiliary coefficients when computing the convolution integrals.Index Terms-Error analysis, finite-difference time-domain (FDTD) method, surface impedance boundary conditions (SIBCs).
A plethora of applications are grounded on the physics of electromagnetic interaction with a periodic arrangement of nanostructures. These range from metamaterials and negative index materials to photonic band-gap structures to surface plasmon polariton optics to nanofrequency selective surfaces. There is therefore a need for rigorous physics based methods that are both accurate and fast to enable rapid design and analysis. Difficulties that need to be overcome to realize such a simulation tool are twofold: (i) at wavelengths in the range 200-1300 nm metals behave as dielectrics with negative real permittivity. Their frequency response must be explicitly accounted for in the simulation. (ii) The computational cost to compute response over a broad band of frequencies is high. This paper develops an integral-equation-based analysis technique that addresses these challenges. This integral equation relies on a periodic layered medium formulation. The Green's dyad for this formulation is derived, and separated into a superposition of two contributions: direct and reflected components. The means to accelerate the computation of the Green's dyad and the evaluation of inner products is prescribed. The proposed technique is validated extensively against available analytical data for hypothetical materials as well as silver. It is shown that this solver can accurately predict the enhanced transmission from perforated silver films for several configurations. While the application domain in this paper is the study of enhanced transmission in perforated silver films, the method presented herein is sufficiently general and can be applied to several other application domains with little or no change.
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