Bloch theory of entangled photon generation in nonlinear photonic crystals (11 pages)

Letizia Sciscione

Bahaa E. A. Saleh, A. Nick Vamivakas, Alexander V. Sergienko

William T. M. Irvine, M. J. A. de Dood, Dirk Bouwmeester

We present a quantum-mechanical description of parametric down conversion and phase matching of Bloch waves in nonlinear photonic crystals. We discuss the theory in one-dimensional Bragg structures giving a recipe for calculating the down-converted emission strength and direction. We exemplify the discussion by making explicit analytical predictions for the emission amplitude and direction from a one-dimensional structure that consists of alternating layers of ${\mathrm{Al}}_{0.4}{\mathrm{Ga}}_{0.6}\mathrm{As}$ and air. We show that the emission is suitable for the extraction of polarization-entangled photons.

William T. M. Irvine, M. J. A. de Dood, Dirk Bouwmeester

Yunxia Dong, Xiangdong Zhang

A rigorous quantum theory for the generation of multiphoton entangled states based on two consecutive three-frequency interactions of waves in a one-dimensional nonlinear photonic crystal is developed using the field expansion and differentiation methods. The three-photon correlation coefficient and the average photon numbers generated in the structure are calculated. All order expansion terms are included in the calculation. The generation conditions for multiphoton entangled states in such a structure are also analyzed. It is shown that the created photons in the present structures obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state. This means the nonlinear photonic crystal can be applied as a highly efficient source of an entangled multiphoton for highly integrated all-optical circuits.

William T. M. Irvine