Radial modal transitions of Laguerre-Gauss modes during parametric upconversion: towards the full-field selection rule of spatial modes

TL;DR

This paper investigates the radial modal transitions of Laguerre-Gauss modes during parametric upconversion, providing a comprehensive theoretical framework and experimental validation for full-field spatial mode selection rules, including both azimuthal and radial components.

Contribution

It introduces a general solution for predicting the sum-frequency generation field of arbitrary LG modes, enabling full-field spatial mode transformation analysis in nonlinear optics.

Findings

Validated the theoretical model experimentally

Derived full-field selection rules for radial and azimuthal modes

Enhanced understanding of complex structured light in nonlinear interactions

Abstract

Optical orbital angular momentum transformation and corresponding azimuthal-mode selection rules have been studied exhaustively for various nonlinear optical interactions. However, nonlinear transformation of radial mode has not been systematically studied since the pioneering work [Phys. Rev. A 56, 4193, 1997]. In this paper, we theoretically study and experimentally verify the radial modal transitions of Laguerre-Gauss (LG) modes in parametric upconversion. Specifically, we provide a general solution that describes the sum-frequency generation (SFG) field excited by two arbitrary LG modes. Based on the solution, one can predict the full spatial complex amplitude of SFG fields upon propagation precisely and readily obtain the associated full-field selection rule including both azimuthal and radial modes. This work provides a theoretical basis for quantum and nonlinear optical research involving parametric upconversion of complex structured light, and paves the way for future work on full-field transformation of spatial modes in other nonlinear interactions.