Transmission eigenvalues with artificial background for explicit material index identification

Abstract : We are interested in the problem of retrieving information on the refractive index $n$ of a penetrable inclusion embedded in a reference medium from farfield data associated with incident plane waves. Our approach relies on the use of transmission eigenvalues (TEs) that carry information on $n$ and that can be determined from the knowledge of the farfield operator $F$. In this note, we explain how to modify $F$ into a farfield operator $F^{art}=F-\tilde{F}$, where $\tilde{F}$ is computed numerically, corresponding to well chosen artificial background and for which the associated TEs provide more accessible information on $n$.
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Lorenzo Audibert, Lucas Chesnel, Houssem Haddar. Transmission eigenvalues with artificial background for explicit material index identification. Comptes Rendus Mathématique, Elsevier Masson, 2018, 356 (6), pp.626-631. ⟨10.1016/j.crma.2018.04.015⟩. ⟨hal-01631062⟩

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