# Transfer matrices as nonunitary S matrices, multimode unidirectional invisibility, and perturbative inverse scattering

@article{Mostafazadeh2014TransferMA, title={Transfer matrices as nonunitary S matrices, multimode unidirectional invisibility, and perturbative inverse scattering}, author={Ali Mostafazadeh}, journal={Physical Review A}, year={2014}, volume={89}, pages={012709} }

We show that in one dimension the transfer matrix M of any scattering potential v coincides with the S-matrix of an associated time-dependent non-Hermitian 2 x 2 matrix Hamiltonian H(\tau). If v is real-valued, H(\tau) is pseudo-Hermitian and its exceptional points correspond to the classical turning points of v. Applying time-dependent perturbation theory to H(\tau) we obtain a perturbative series expansion for M and use it to study the phenomenon of unidirectional invisibility. In particular…

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