Inverse scattering problems in absorbing media

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Abstract
We study inverse scattering problems which occur in various fields of physics (transmission lines theory, electromagnetism, elasticity theory), and in which the inhomogeneous media considered are absorbing. We suppose that waves propagate in a z direction from z=0 to z=∞ and are totally reflected at z=0, the input data being the values of the reflection coefficient to the right S+(k) for all frequencies k (note that the case where waves propagate from z=−∞ to z=∞ can be studied in a similar way). These problems are reduced to an inverse scattering problem for the radial s‐wave Schrödinger equation with an energy‐dependent potential. The case where S+(k) is close to 1 and the case where the absorption is weak are specially investigated, and a class of exactly solvable examples is given.