Single-photon scattering on Lambda-type three-level atoms in a one-dimensional waveguide

We investigate the quantum scattering involving a single photon and a chain of N polarized Lambda-type three-level atoms inside a one-dimensional waveguide. By using a transfer matrix method, we obtain analytic expressions of eigenvectors of the Hamiltonian, which determine the polarization dependent transmission and reflection spectra for a single photon. We show that the scattering is most significant when the interatomic distance equals an integer multiple plus a quarter of the resonance wavelength. In such a configuration, an incident photon with an unknown polarization can be converted into a specified polarization with a transmission probability higher than that in polarizers obeying Malus's law.