Optimizing biphoton generation via reconfigurable nonlinear waveguide arrays based on scattering tensor

Spontaneous parametric down-conversion (SPDC) plays a pivotal role in the field of quantum optics, especially in generating quantum entangled states. This study delves into utilizing the scattering tensor of nonlinear waveguide arrays to characterize the SPDC process and optimize its efficiency. By computing the pseudo-inverse of the third-order scattering tensor describing the nonlinear arrays for biphoton generation, we determine the optimal pump profile and array conditions that best approximate a desired output biphoton distribution. Counterintuitively, due to the diffraction of the pump beam, we find that the optimal biphoton correlation does not occur at positions corresponding to the maximum pumping in real space within the coupled nonlinear arrays. Our finding demonstrates that the scattering tensor method combined with universal beam-splitter meshes provides a promising route toward reconfigurable integrated quantum light sources.