Uniqueness of the scatterer for electromagnetic field with one incident plane wave

Abstract

In this paper, we solve a longstanding open problem for determining the shape of an obstacle from the knowledge of the electric (or magnetic) far field pattern for the scattering of time-harmonic electromagnetic field. We show that the electric (or magnetic) far field patten ${\mathbf{E}}^{\infty }(\mathbf{\beta },{\mathbf{\alpha }}_0,k_0)$ (or ${\mathbf{H}}^{\infty }(\mathbf{\beta },{\mathbf{\alpha }}_0,k_0)$), known for all $\mathbf{\beta }\in {\mathbb{S}}^2$, where ${\mathbb{S}}^2$ is the unit sphere in ${\mathbb{R}}^3$, ${\mathbf{\alpha }}_0\in {\mathbb{S}}^2$ is fixed, $k_0>0$ is fixed, determines the obstacle $D$ and the boundary condition on $\partial D$ uniquely. The boundary condition on $\partial D$ is either the perfect conductor or the impedance one.

there is a gap in the proof of main theorem

References in corpus (1)

• A Global Uniqueness for Formally Determined Inverse Electromagnetic Obstacle Scattering

Cited by in corpus (1)

• Uniqueness in inverse elastic scattering with one incident wave