New sets of eigenvalues in inverse scattering for inhomogeneous media and their determination from scattering data

Stekloff Eigenvalues in Inverse Scattering

We consider a problem in nondestructive testing in which small changes in the (possibly complex valued) refractive index n(x) of an inhomogeneous medium of compact support are to be determined from changes in measured far field data due to incident plane waves. The problem is studied by considering a modified far field operator F whose kernel is the difference of the measured far field pattern ...

Transmission eigenvalues in inverse scattering theory

In the past few years transmission eigenvalues have become an important area of research in inverse scattering theory with active research being undertaken in many parts of the world. Transmission eigenvalues appear in the study of scattering by inhomogeneous media and are closely related to non-scattering waves. Such eigenvalues provide information about material properties of the scattering m...

Inverse scattering theory and transmission eigenvalues

Theory of Thomson scattering in inhomogeneous media

Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. Thi...

Scattering and inverse scattering in one-dimensional nonhomogeneous media

The wave propagation in a one-dimensional nonhomogeneous medium is considered, where the wave speed and the restoring force depend on location. In the frequency domain this is equivalent to the Schrijdinger equation d2$/dx2 + k211, = k2P(x)II, + Q(x)Jt with an added potential proportional to energy. The scattering and bound-state solutions of this equation are studied and the properties of the ...