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

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.

10 pages, 6 figures

References in corpus (8)

• Hypergeometric-Gaussian Modes
• Trans-spectral orbital angular momentum transfer via four wave mixing in Rb vapor
• Sorting photons by radial quantum number
• Full-field quantum correlations of spatially entangled photons
• High orbital angular momentum harmonic generation
• Orbital angular momentum mixing in type II second harmonic generation
• Vectorial nonlinear optics: type-II second-harmonic generation driven by spin-orbit coupled fields
• Radial coherent and intelligent states of paraxial wave equation

Cited by in corpus (13)

• Conformal frequency conversion for arbitrary vectorial structured light
• Gouy-phase-mediated propagation variations and revivals of transverse structure in vectorially structured light
• Gouy phase-matched angular and radial mode conversion in four-wave mixing
• Spatial polarization independent parametric upconversion of vectorially structured light
• Parametric upconversion of Ince-Gaussian modes
• Real-time superresolution interferometric measurement enabled by structured nonlinear optics
• Heralded generation of vectorially structured photons with high purity
• Spatial distribution of two symmetric four-wave mixing signals induced by Gaussian beams
• Directly determining orbital angular momentum of ultrashort Laguerre-Gauss pulses via autocorrelation measurement
• Radial-angular coupling in self phase modulation with structured light
• Gouy-phase effects in the frequency combs of an optical parametric oscillator
• Propagation-invariant high-dimensional orbital angular momentum states
• Spin to orbital angular momentum transfer in nonlinear wave mixing