Nonparaxial electromagnetic Bragg scattering in periodic media with PT symmetry

The evolution of a pair of resonant Bragg modes situated at the edges of the Brillouin zone of a periodic photonic lattice, characterized by a complex one-dimensional PT-symmetric permittivity, is thoroughly investigated. Analytic solutions of Maxwell's equations are derived beyond the paraxial approximation to study Bragg oscillations, understood as the periodic energy exchange that occurs among Bragg modes in complex optical lattices. Three regimes defined by the symmetry breaking point are discussed: below, above and at the breaking point. These regimes are determined by the existence of four real eigenvalues in the symmetric phase, which collide and coalesce into a pair, at the breaking point. Above the critical value each member of the pair bifurcates into a pair of complex eigenvalues. Therefore, the complex lattice reveals a variety of wave dynamics depending on the gain/loss balance. In all regimes of the transition the signature of PT-symmetric systems is present, as the evolution is always nonreciprocal and unidirectional.