Wave propagation of transient electromagnetic waves in (inic-vnryin|j media is considered, The medium, which is assumed to he inhoniogeneous and dispersive, hicks Invarinnee under time translations. The spatial variation of ihe medium i.s assumed tn he in (he depth coordinate, i.e. it is stratified. The constitutive relations ol die medium ure a lime integral of a generalized .susceptibility kernel and (he held. The p'lieiali/ctl susceptibility kernel depends on one spatial and two lime coordiante. The concept of wave spltllinj! is inlmdiiccd. The direct and Inverse scattering problems are solved hy ihe use of an imbedding or n (liven function approach. The direct titttl (he inverse scattering problems are solved for a homogeneous semi-inlinite medium. Explicit algorithms are developed. In this inverse scullciiiitf problem, a function depending on two lime coordinates is leconstiuclrd. Several mimetical lompulalions illustrate the performance of the algorithms.
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