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

  title={Transfer matrices as nonunitary S matrices, multimode unidirectional invisibility, and perturbative inverse scattering},
  author={Ali Mostafazadeh},
  journal={Physical Review A},
  • A. Mostafazadeh
  • Published 7 November 2013
  • Physics, Mathematics
  • Physical Review A
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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