We develop two inverse scattering schemes for locating multiple electromagnetic (EM) scatterers by the electric far-field measurement corresponding to a single incident/detecting plane wave. The first scheme is for locating scatterers of small size compared to the wavelength of the detecting plane wave. The multiple scatterers could be extremely general with an unknown number of components, and each scatterer component could be either an impenetrable perfectly conducting obstacle or a penetrable inhomogeneous medium with an unknown content. The second scheme is for locating multiple perfectly conducting obstacles of regular size compared to the detecting EM wavelength. The number of the obstacle components is not required to be known in advance, but the shape of each component must be from a certain known admissible class. The admissible class may consist of multiple different reference obstacles. The second scheme could also be extended to include the medium components if a certain generic condition is satisfied. Both schemes are based on some novel indicator functions whose indicating behaviors could be used to locate the scatterers. No inversion will be involved in calculating the indicator functions, and the proposed methods are every efficient and robust to noise. Rigorous mathematical justifications are provided and extensive numerical experiments are conducted to illustrate the effectiveness of the imaging schemes. and sonar, non-destructive testing, remote sensing, geophysical exploration and medical imaging to name just a few; see [4,5,10,11,15,20,25,31,33] and the references therein. In the current article, we shall mainly consider the reconstruction scheme for this inverse scattering problem. There are extensive studies in the literature in this aspect and many imaging schemes have been developed by various authors, and we would like to refer to [1-6, 9, 12, 14, 17-19, 21, 30, 32] and the references therein. However, we would like to remark that in those schemes, one either needs to make use of many wave measurements or if only a few wave measurements are utilized, then one must require that the underlying scatterer is of small size compared to the detecting wavelength. In this work, we shall consider our study in a very practical setting by making use of a single electric far-field measurement. That is, we shall consider the reconstruction by measuring the far-field electric wave corresponding to a single time-harmonic plane wave. From a practical viewpoint, the inverse scattering method with a single far-field measurement would be of significant interests, but is highly challenging with very limited progress in the literature; we refer to [15,20,[24][25][26]33] for related discussion and surveys on some existing development. For more practical considerations, we shall work in a even more challenging setting by assuming very little a priori knowledge of the underlying scattering object, which might consist of multiple components, and both the number of the components and the physical property of each...

We consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain Ω ⊂ R N (N ≥ 2). In a subregion D ⋐ Ω, the medium is supposed to be lossy and have a large mass density. We study the asymptotic development of the wave field as the mass density ρ → +∞ and show that the wave field inside D will decay exponentially while the wave filed outside the medium will converge to the one corresponding to a sound-hard obstacle D ⋐ Ω buried in the medium supported in Ω\D. Moreover, the normal velocity of the wave field on ∂D from outside D is shown to be vanishing as ρ → +∞. We derive very accurate estimates for the wave field inside and outside D and on ∂D in terms of ρ, and show that the asymptotic estimates are sharp. The implication of the obtained results is given for an inverse scattering problem of reconstructing a complex scatterer.

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