Direct and inverse scattering problems play a central role in areas such as radar, sonar, geophysical exploration, and nondestructive testing and they have been widely studied in recent years. In particular, the uniqueness and existence of direct scattering problems, the reciprocity relation and completeness of electric far field patterns, etc. are basic in the inverse scattering theory.
In most applications as well as in geophysical exploration and nondestructive testing, it is, in general, assumed that the scattering obstacle is buried in a piecewise homogeneous medium and is partially coated by a dielectric. For example, underground mines and submarines are embedded in a piecewise homogeneous medium with air-earth and air-water interfaces and they consist of metallic and nonmetallic parts.
Kim Yun Chol, a section head at the Faculty of Applied Mathematics, has studied uniqueness and existence for a direct electromagnetic obstacle scattering problem in a piecewise homogeneous medium, some properties of a scattered field and a far field pattern, including boundedness, reciprocity relation and completeness, where it is assumed that the obstacle is a partially coated perfect conductor and the incident field is given by the electromagnetic plane wave.
He has conclusively proved that the electric far field pattern of the solution of the scattering problem of the electromagnetic plane wave as well as uniqueness and existence for the solution of the direct problem of scattering of time-harmonic electromagnetic waves by a partially coated obstacle buried in a piecewise homogeneous medium satisfies the reciprocity relation, and that the set of electric far-field patterns is complete in a Hilbert space.
These results are of great significance to the study on the solution of inverse electromagnetic scattering problems, i.e. determination of the location, shape and physical property of obstacles from the knowledge of electric far field patterns.
For further information, please refer to his paper “Electromagnetic wave scattering by a partially coated obstacle in a piecewise homogeneous medium” in “Mathematical Methods in the Applied Sciences” (SCI).
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