Abstract
We consider the electromagnetic inverse scattering problem for the Drude-Born-Fedorov model for periodic chiral structures known as chiral gratings both in $\mathbb{R}^2$ and $\mathbb{R}^3$. The Factorization method is studied as an analytical as well as a numerical tool for solving this inverse problem. The method constructs a simple criterion for characterizing shape of the periodic scatterer which leads to a fast imaging algorithm. This criterion is necessary and sufficient which gives a uniqueness result in shape reconstruction of the scatterer. The required data consists of certain components of Rayleigh sequences of (measured) scattered fields caused by plane incident electromagnetic waves. We propose in this electromagnetic plane wave setting a rigorous analysis for the Factorization method. Numerical examples in two and three dimensions are also presented for showing the efficiency of the method.
Highlights
We consider inverse scattering of time-harmonic electromagnetic waves from penetrable periodic chiral structures known as chiral gratings both in R2 and R3
The inverse problem of our interest is the shape reconstruction of chiral gratings from measured data consisting, in principle, of scattered electromagnetic waves, when plane electromagnetic waves are used as incident waves
Kirsch [21], as a tool for imaging the chiral scatterer. This Factorization method belongs to class of fast non-iterative methods, recently developed for solving inverse scattering problems
Summary
We consider inverse scattering of time-harmonic electromagnetic waves from penetrable periodic chiral structures known as chiral gratings both in R2 and R3. Additional degree of freedom β influences the possibilities for cloaking” Motivated by this conclusion and applications of non-destructive evaluation, we aim in the present work to study the Factorization method as a tool for reconstructing shape of a chiral grating from measurements of scattered electromagnetic waves. These measurements are the Rayleigh coefficients of evanescent and propagating modes of the scattered fields caused by incident electromagnetic plane waves. The rest of the paper has two main parts: we present in the first part the case of Helmholtz equations in R2 including setting of the problem, analysis of the Factorization method and numerical examples. A complete proof of the latter result can be found in [23]
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