Unified fractional Laguerre–Gaussian beams
Abstract
We introduce a Fourier-Laplace fractional framework that unifies the standard and elegant Laguerre-Gaussian families through exact paraxial solutions. By imposing a Gaussian-type envelope constraint, we recover the integer-indexed standard modes and simultaneously generate a bounded, elegant branch with fractional-radial order. The azimuthal dependence is explored with Chebyshev structures and realized physically through a Shannon-sinc superposition of integer orbital-angular-momentum (OAM) modes, which preserves single-valuedness yet enables continuously tunable mean OAM. We derive closed-form normalized fields, numerically validate their free-space propagation, and uncover an OAM degeneracy between the standard and elegant branches, each exhibiting distinct transverse robustness.
Fields of Study & Subjects
Orbital Angular Momentum in Optics
Quantum Mechanics and Non-Hermitian Physics
Nonlinear Photonic Systems
Publication details
- Journal / source
- Optics Letters
- Publisher
- Optica Publishing Group
- Volume
- 51
- Issue
- 3
- Pages
- 640–640
- Publication date
- 9 January 2026
- Language
- EN