A Spectral Volume Integral Method Using Geometrically Conforming Normal-Vector Fields

We present a method to simulate two-dimensional scattering by dielectric objects embedded in a dielectric layered medium with transverse magnetic polarization through a domain integral equation formulation. A mixed spatial-spectral discretization is employed with both a spatial and a spectral representation along the direction of the layer interfaces. In the spectral domain, a discretization on a path through the complex plane is used on which the Green function is well behaved. To calculate the field-material interaction in the spatial domain, an auxiliary field is employed similar to the Li factorization rules. Numerical results show that this auxiliary-field formulation significantly improves accuracy, compared to a formulation that directly employs the electric field.

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“…with Id the 2 × 2 identity matrix. We note that more general objects can in principle be treated by using normal-vector fields [8,9,23,24].…”

Section: E the Field-materials Interactionmentioning

confidence: 99%

2D TM scattering problem for finite dielectric objects in a dielectric stratified medium employing Gabor frames in a domain integral equation

2017

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“…In the papers [24] and [27], the 2-dimensional scattering problem of a 1-dimensionally periodic dielectric grating, embedded in a stratified medium is formulated as a spectral domain integral equation. We briefly outline both the TE and TM polarization.…”

Section: Illustration 2: Periodic Structurementioning

confidence: 99%

Scattered Field in Random Dielectric Inhomogeneous Media: A Random Resolvent Approach

Barzegar

Eijndhoven²,

Beurden

2015

PIER B

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Abstract-In modeling electromagnetic phenomena randomness of the propagation medium and of the dielectric object should be taken up. The usually applied Monte-Carlo based methods reveal true characteristics of the random electromagnetic field at the expense of large computation time and computer memory. Use of expansion based methods and their resulting algorithm is an efficient alternative. In this paper the focus is on characteristics of electromagnetic fields that satisfy integral equations where the integral kernel has a random component, typically, electromagnetic fields that describe scattering due to dielectric objects with an inhomogeneous random contrast field. The assumption is that the contrast is affinely related to a random variable. The integral equation is of second kind Fredholm type so that its solutions are determined by the resolvent, a random operator field. The key idea is to expand that operator field with respect to orthogonal polynomials defined by the probability measure on the underlying sample space and to derive the properties of the solution from that expansion. Two types of illustration are presented: an inhomogeneous dielectric slab and a 2D dielectric grating with 1D periodicity.

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A Spectral Volume Integral Method Using Geometrically Conforming Normal-Vector Fields

Cited by 2 publications

References 18 publications

2D TM scattering problem for finite dielectric objects in a dielectric stratified medium employing Gabor frames in a domain integral equation

2D TM scattering problem for finite dielectric objects in a dielectric stratified medium employing Gabor frames in a domain integral equation

Scattered Field in Random Dielectric Inhomogeneous Media: A Random Resolvent Approach

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