Parametric upconversion of Ince-Gaussian modes.

The Ince-Gaussian (IG) mode, a recently discovered type of structured Gaussian beam, corresponds to eigenfunctions of the paraxial wave equation in elliptical coordinates. This propagation-invariant mode is of significance in various domains, in particular, its nonlinear transformation; however, there have been few relevant studies to date. In this Letter, we report the parametric upconversion of IG modes and associated full-field selection rule for the first time, to the best of our knowledge. We demonstrate that IG signals can be perfectly upconverted by a flattop-beam pump; in contrast, significant mode distortion occurred when using the most common Gaussian pump. Particular attention was given to the origin of the distortion, i.e., radial-mode degeneration induced by the sum-frequency generation excited by a Gaussian pump. This proof-of-principle demonstration has great significance in relevant areas, such as high-dimensional quantum frequency interfacing and upconversion imaging.