Counter-propagating 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 quasi-phase matching equations that describe counter-propagating guided signal and idler beams to be satisfied. We compare the tuning curves and spectral properties of such counter-propagating beams to those for co-propagating beams under typical experimental conditions. We find that the counter-propagating beams exhibit 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. 
Mark C. Booth, Mete Atature, Giovanni Di Giuseppe, Alexander V.   Sergienko, Bahaa E. A. Saleh, and Malvin C. Teich