Inter-modal interference of arbitrary orbital angular momentum modes in nonlinear frequency conversion

Nonlinear interaction between orbital angular momentum (OAM) modes provides an enticing promise for realizing high-dimensional quantum states and multimodal communications. Here, we demonstrate the inter-modal interference of OAM modes based on the nonlinear frequency conversion of perfect vortex beams, permitting the arbitrary spatial intensity and phase information to be transformed and manipulated from 778 nm input beam to 420 nm output beam. The conversion of single OAM state obeys the typical arithmetic operation. In contrast, the conversion of superposition state is predicted and revealed as the inter-modal interference of full spatial complex amplitude. For the allowed OAM modes, the probability amplitude is quantitatively analyzed by the intensity overlap of input OAM modes, which determines the degree of degradation in the intensity and phase. As a result, the output beam exhibits the nonuniform petal-shaped intensity and phase distributions under the conditions of phase matching and OAM conservation. Furthermore, the inherent transverse structure invariance of perfect vortex beams enables them to accommodate and support larger OAM values and more superposition states.