Inhomogeneous media characterization: a hybrid method of state space and frequency diversity

This paper presents an analytical method for the reconstruction of permittivity profile of an inhomogeneous slab. The proposed method which is based on state transition matrix combines state space formulation and frequency domain data. This methodology and formulation lead to an accurate inversion of complex inhomogeneous profiles. Comparing with other analytical methods, the proposed approach avoids solving the nonlinear integro-differential equation, which consequently yields mathematical implementation. In order to validate the algorithm, some inhomogeneous profiles with different levels of complexity are considered and analyzed. The results show that the proposed method can be considered as a robust technique for one-dimensional inverse scattering problems. The results are valuable for the study and electromagnetic characterization of inhomogeneous and planar layered media.