  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, we establish the possibility of
having multimode unidirectional invisibility with wavelength-dependent
direction of invisibility and construct various physically realizable optical
potentials possessing this property. We also offer a simple demonstration of
the fact that the off-diagonal entries of the first Born approximation for M
determine the form of the potential. This gives rise to a perturbative inverse
scattering scheme that is particularly suitable for optical design. As a simple
application of this scheme, we construct an infinite-range unidirectionally
invisible potential.
