Nonlinear differential equation for the reflection coefficient of an inhomogeneous lossy medium and its inverse scattering solutions

Nonlinear differential equations for the reflection coefficients of an inhomogeneous lossy medium illuminated by both TE-polarized and TM-polarized electromagnetic plane waves are derived using a microwave networking technique, which can be approximately solved by a nonlinear renormalization method. Considering the equivalent microwave network of the permittivity profile discontinuity at the interface of free space with the medium, two novel inverse scattering solutions for the permittivity profile and the conductivity profile are further investigated in closed forms. Closed-form and numerical reconstruction examples show the availability of this scheme.<
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