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 (transverse electric)-polarized and TM (transverse magnetic)-polarized electromagnetic plane waves are derived by 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 investigated in closed forms. Further investigations show that under the lossless condition the results presented here will reduce to those of H. D. Ladouceur and A. K. Jordan (1985) and D. L. Jaggard and Y. Kim (1985).<
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