IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i22p4691-d1282981.html
   My bibliography  Save this article

Fourier Transform of the Lippmann-Schwinger Equation: Solving Vectorial Electromagnetic Scattering by Arbitrary Shapes

Author

Listed:
  • Frederic Gruy

    (Ecole Nationale Supérieure des Mines de St. Etienne, Centre SPIN, F-42100 Saint-Etienne, France)

  • Victor Rabiet

    (Ecole Nationale Supérieure des Mines de St. Etienne, Centre SPIN, F-42100 Saint-Etienne, France
    Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France)

  • Mathias Perrin

    (Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France)

Abstract

In Electromagnetics, the field scattered by an ensemble of particles—of arbitrary size, shape, and material—can be obtained by solving the Lippmann–Schwinger equation. This singular vectorial integral equation is generally formulated in the direct space R n (typically n = 2 or n = 3 ). In the article, we rigorously computed the Fourier transform of the vectorial Lippmann–Schwinger equation in the space of tempered distributions, S ′ ( R 3 ) , splitting it in a singular and a regular contribution. One eventually obtains a simple equation for the scattered field in the Fourier space. This permits to draw an explicit link between the shape of the scatterer and the field through the Fourier Transform of the body indicator function. We compare our results with accurate calculations based on the T-matrix method and find a good agreement.

Suggested Citation

  • Frederic Gruy & Victor Rabiet & Mathias Perrin, 2023. "Fourier Transform of the Lippmann-Schwinger Equation: Solving Vectorial Electromagnetic Scattering by Arbitrary Shapes," Mathematics, MDPI, vol. 11(22), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4691-:d:1282981
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/22/4691/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/22/4691/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4691-:d:1282981. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.