Mixing Ince–Gaussian modes through sum-frequency generation

Abstract

We present a nonlinear mixing study of Ince–Gaussian (IG) beams in non-collinear sum-frequency generation, completing the fundamental analysis of all three families of paraxial wave equation solutions under this nonlinear process. Through theoretical and experimental results, we consider the nonlinear mixing of even and odd IG modes, and transition between the paraxial modes by controlling the eccentricity parameter $\epsilon$ and helical IG modes possessing arbitrary orbital angular momentum. Additionally, the selection rule of IG modes in the nonlinear mixing processes is determined. This work is important for optical communications and quantum protocols.