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The transfer matrix of a possibly complex and energy-dependent scatteringpotential can be identified with the $S$-matrix of a two-level time-dependentnon-Hermitian Hamiltonian H(t). We show that the application of the adiabaticapproximation to H(t) corresponds to the semiclassical description of theoriginal scattering problem. In particular, the geometric part of the phase ofthe evolving eigenvectors of H(t) gives the pre-exponential factor of the WKBwave functions. We use these observations to give an explicit semiclassicalexpression for the transfer matrix. This allows for a detailed study of thesemiclassical unidirectional reflectionlessness and invisibility. We examineconcrete realizations of the latter in the realm of optics.

Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility