Counterpropagating entangled photons from a waveguide with periodic nonlinearity

The conditions required for spontaneous parametric down-conversion in a waveguide with periodic nonlinearity in the presence of an unguided pump field are established. Control of the periodic nonlinearity and the physical properties of the waveguide permits the quasiphase matching equations that describe counterpropagating guided signal and idler beams to be satisfied. We compare the tuning curves and spectral properties of such counterpropagating beams to those for copropagating beams under typical experimental conditions. We find that the counterpropagating beams exhibit a narrow bandwidth, permitting the generation of quantum states that possess discrete-frequency entanglement. Such states may be useful for experiments in quantum optics and technologies that benefit from frequency entanglement.