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The World of Applied Electromagnetics pp 481–513Cite as

The Ewald–Oseen Extinction Theorem and the Extended Boundary Condition Method

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Abstract

Mathematical statements of the Ewald–Oseen extinction theorem have been formulated for a linear homogeneous medium with frequency-domain constitutive relations \(\underline{D} =\underline{\underline{\varepsilon }} \mbox{ $^{\bullet }$ }\underline{E} + [\underline{\underline{\xi }} + \left (\underline{K}-\underline{\varGamma }\right ) \times \underline{\underline{ I}}]\mbox{ $^{\bullet }$ }\underline{H}\) and \(\underline{B} =\underline{\underline{\mu }} \mbox{ $^{\bullet }$ }\underline{H} - [\underline{\underline{\xi }} -\left (\underline{K}+\underline{\varGamma }\right ) \times \underline{\underline{ I}}]\mbox{ $^{\bullet }$ }\underline{E}\). During the formulation, four dyadic Green functions were set up and their characteristics elucidated. The Ewald–Oseen extinction theorem has been exploited to set up the conceptual framework of the extended boundary condition method (EBCM) for scattering by a three-dimensional object made of a homogeneous medium. Implementation of the EBCM is also premised on the availability of bilinear expansions of the dyadic Green functions for both the scattering medium and the medium surrounding the scatterer.

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Acknowledgements

I am grateful to the Charles Godfrey Binder Endowment at Penn State for ongoing support of my research activities. I thank Drs. Cynthia M. Furse (University of Utah), Tom G. Mackay (University of Edinburgh), and Muhammad Faryad (Lahore University of Management Sciences) for going through the pre-final version of this chapter.

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  1. NanoMM – Nanoengineered Metamaterials Group, Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, 16802, USA

    Akhlesh Lakhtakia

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  1. NanoMM – Nanoengineered Metamaterials Group, Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, Pennsylvania, USA

    Akhlesh Lakhtakia

  2. Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, Utah, USA

    Cynthia M. Furse

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Lakhtakia, A. (2018). The Ewald–Oseen Extinction Theorem and the Extended Boundary Condition Method. In: Lakhtakia, A., Furse, C. (eds) The World of Applied Electromagnetics. Springer, Cham. https://doi.org/10.1007/978-3-319-58403-4_19

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