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Ali Mostafazadeh
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A dynamical formulation of scattering theory, inverse scattering, and unidirectional invisibility
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For a given scattering potential v(x) in one
dimension, we construct a two-level non-Hermitian
Hamiltonian whose S-matrix coincides with
the transfer matrix of v(x). For a real scattering
potential this Hamiltonian is pseudo-Hermitian
and has exceptional points at the classical
turning points. We use this approach to give
a through perturbative analysis of the phenomenon
of unidirectional invisibility, develop a
dynamical theory of scattering where the
reflection and transmission amplitudes are
given as solutions of a set of dynamical
equations, and offer an inverse scattering
scheme for construction scattering potentials
with desirable properties at a prescribed
wavelength.
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