Radial modal transitions of Laguerre-Gauss modes during parametric upconversion: towards the full-field selection rule of spatial modes
arXiv:1912.05585 · doi:10.1103/PhysRevA.101.063805
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.
arXiv comment10 pages, 6 figures
References in corpus (22)
- A quantum memory for orbital angular momentum photonic qubits
- Analysis and interpretation of high transverse entanglement in optical parametric down conversion
- Hypergeometric-Gaussian Modes
- Trans-spectral orbital angular momentum transfer via four wave mixing in Rb vapor
- Stimulated Raman and Brillouin backscattering of collimated beams carrying orbital angular momentum
- Physical meaning of the radial index of Laguerre-Gauss beams
- Sorting photons by radial quantum number
- Full-field quantum correlations of spatially entangled photons
- Lost and found: the radial quantum number of Laguerre-Gauss modes
- Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments
- Orbital angular momentum-entanglement frequency transducer
- Conservation of Orbital Angular Momentum in Stimulated Down-Conversion
- High orbital angular momentum harmonic generation
- Orbital angular momentum mixing in type II second harmonic generation
- Nonlinear Transformation of Orbital Angular Momentum through Quasi-phase Matching
- Coherent manipulation of a three-dimensional maximally entangled state
- Vectorial nonlinear optics: type-II second-harmonic generation driven by spin-orbit coupled fields
- Observation of reversible orbital angular momentum transfer based on photon-phonon coupling
- Radial coherent and intelligent states of paraxial wave equation
- Revealing photons' past via quantum twisted double-slit experiment
- Dynamic tomography of the spin-orbit coupling in nonlinear optics
- Generating strong cylindrical vector pulses via stimulated Brillouin amplification
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