Collective effects of multiscattering on the coherent propagation of photons in a two-dimensional network

We study the collective phenomenon in the scattering of a single photon by one or two layers of two-level atoms. By modeling the photon dispersion with a two-dimensional coupled cavity array (2D CCA), we analytically derive the scattering probability of a single photon. We find that the translational symmetry of the atomic distribution leads to many important effects in the single-photon scattering. In the case with one layer of atoms, the atomic collective Lamb shift is related to the photonic density of states (DOS) of a 1D CCA, rather than the photonic DOS of a 2D CCA. As a result, the photon is effectively not cattered by the atoms when the incident momentum of the photon takes some special values. In the case with two layers of atoms, an effective coupling between two layers appears and induces an electromagnetically induced transparency like phenomenon. Our work provides a scheme of analyzing photon coherent transport in 2D and may help to understand recent experiments related to high-energy photon scattering by layered nuclei material.