Simulating spatial distribution of spontaneously down converted photon pairs in nonlinear crystals

  Sivan Trajtenberg Mills  ,  Noa Voloch-Bloch [2]  ,  Hagai Eisenberg [2]  ,  Ady Arie [1]  
[1] Tel-Aviv University
[2] Hebrew University of Jerusalem

Spontaneous parametric down conversion (SPDC) in nonlinear photonic crystals is widely used for generating single photon and entangled photon states, readily useable for a variety of quantum applications. Even so, no simulation tool has been available for predicting the spatial distribution of these photons for arbitrarily modified photonic crystals. We present an algorithm, based on the classical non linear coupled-wave equations with a seed signal beam having a wide distribution of wave-vectors, for calculating the spatial distribution of the output state. The algorithm correctly reproduces the spatial distribution as measured in different experiments and with different nonlinear crystals, among them one-dimensional and two-dimensional periodically poled crystals and birefringently phase matched crystals.  Furthermore, SPDC with special structured beams such as vortex beams that carry orbital angular momentum can be also accurately calculated. We believe that this tool will open new possibilities in designing sophisticated nonlinear photonic crystals for quantum optics applications.