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Maxwell's Equations in a Perturbed Periodic Structure

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Abstract

The paper is concerned with electromagnetic wave propagation in a perturbed periodic structure. Consider a time-harmonic electromagnetic plane wave incident on a biperiodic (grating) structure. A single inhomogeneous object is placed inside the biperiodic structure. The scattering problem is to study the electromagnetic field distributions. The problem arises in the study of near-field optics and has recently found many applications in physics and biology. In this paper, an integral representation approach is presented to solve the problem. Using the approach, well-posedness of the model problem is established. In addition, it is shown that the perturbation due to the object is exponentially decaying along the periodic directions of the structure, provided that no surface waves occur.

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Authors and Affiliations

  1. Centre de Mathématiques Appliquées, CNRS UMR 7641, Ecole Polytechnique, 91128, Palaiseau, France

    Habib Ammari

  2. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Gang Bao

Authors
  1. Habib Ammari
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  2. Gang Bao
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Ammari, H., Bao, G. Maxwell's Equations in a Perturbed Periodic Structure. Advances in Computational Mathematics 16, 99–112 (2002). https://doi.org/10.1023/A:1014402300371

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