Radial coherent and intelligent states of paraxial wave equation

Abstract

Ladder operators for the radial index of the paraxial optical modes in the cylindrical coordinates are calculated. The operators obey the su(1,1) algebra commutation relations. Based on this Lie algebra, we found that coherent modes constructed as eigenstates of the destruction operator or resulting from the action of the displacement operator on the fundamental mode are different. Some properties of these two kinds of radial coherent modes are studied in detail.

arXiv comment3 pages, 3 figures

References in corpus (6)

• Entanglement of Orbital Angular Momentum States of Photons
• Hypergeometric-Gaussian Modes
• Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates
• Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence
• Light propagation in a birefringent plates with topological charge
• Polarization-controlled evolution of light transverse modes and associated Pancharatnam geometric phase in orbital angular momentum

Cited by in corpus (21)

• Laguerre-Gaussian mode sorter
• Generation and Confirmation of a (100x100)-dimensional entangled Quantum System
• High-dimensional quantum gates using full-field spatial modes of photons
• Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes
• Physical meaning of the radial index of Laguerre-Gauss beams
• Measuring azimuthal and radial modes of photons
• Lost and found: the radial quantum number of Laguerre-Gauss modes
• Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments
• State transfer based on classical nonseparability
• Gouy phase-matched angular and radial mode conversion in four-wave mixing
• Radial modal transitions of Laguerre-Gauss modes during parametric upconversion: towards the full-field selection rule of spatial modes
• Phenomenology of complex structured light in turbulent air
• Vector Laguerre-Gauss beams with polarization-OAM entanglement in a graded-index medium
• Full-field mode sorter using two optimized phase transformations for high-dimensional quantum cryptography
• Quantum state tomography of orbital angular momentum photonics qubits via a projection-based technique
• Full-mode Characterisation of Correlated Photon Pairs Generated in Spontaneous Downconversion
• Basis-neutral Hilbert-space analyzers
• Mitigating the effect of atmospheric turbulence on orbital angular momentum-based quantum key distribution using real-time adaptive optics with phase unwrapping
• Generation of High-Order Vortex States from Two-Mode Squeezed States
• Entangled ripples and twists of light: Radial and azimuthal Laguerre-Gaussian mode entanglement
• Digital sorting perturbed laguerre-gaussian beams by radial numbers via high order intensity moments