Effects of Losses and Nonlinearities on the Generation of Polarization Entangled Photons

We investigate the effects of waveguide loss and nonlinearities on the generation of polarization entangled photon-pairs through spontaneous four-wave mixing (FWM) in X⁽³⁾ materials. We quantify those effects through the analysis of the coincidence-to-accidental ratio (CAR), and through the Clauser, Horne, Shimony, and Holt (CHSH) inequality. Two distinct cases are analyzed. First, we consider a fixed fiber length. Second, we admit that the fiber length decreases with the increase of the waveguide loss coefficient. Results show that for the first case, for a fixed value of waveguide loss the CHSH parameter tends to decrease with the increase of the nonlinear parameter. This is due to the increase generation of multiphotons on the signal and idler fields, which leads to an increase on the rate of accidental counts. This is also verified by the analysis of the CAR. Results also show that for a fixed value of nonlinear parameter, increasing the value of the loss coefficient leads to a strong violation of the CHSH inequality. In the second scenario, results show that a strong violation of the CHSH inequality is observed for short waveguide lengths. Our findings also show that a high value of coincidence counting rate does not necessarily leads to a strong violation of the CHSH inequality.