Finding the polarizability of dielectric half-ellipse

Abstract

This article studies the electrostatic response of a two-dimensional dielectric half-ellipse. A semianalytical method is presented for solving the polarizability of a half-ellipse as a function of its relative permittivity. The polarizability depends on the direction of incident field, and therefore, it is written as a dyadic with two perpendicular components. These are called series and parallel polarizability, and they are solved separately. The solution requires a series expansion of the potential function, and the coefficients must be obtained numerically, through an inversion of a finite matrix equation. Numerical results are presented for the polarizability components of the half-ellipse as functions of its geometry and permittivity.

KEYWORDS:

• Laplace equation
• polarizability
• elliptic coordinates
• PEC

Acknowledgements

We would like to thank Dr. Henrik Kettunen for his expertise and valuable contribution to the theoretical analysis, especially during the initial studies.

Disclosure statement

The authors declare that they have no known competing interests that could have appeared to influence the work reported in this paper.

Additional information

Funding

The research is funded by Sapienza University of Rome, Italy.

Notes on contributors

Mehwish Nisar

Mehwish Nisar conducted this research and drafted the manuscript, Ari Sihvola and HenrikWallén contributed to the theoretical and numerical analysis as well as in finalizing the manuscript. Sidra Batool, Fabio Mangini and Fabrizio Frezza proofread the article.