Abstract

The aim of the present work is to show that the Laguerre–Gauss beams determine a Hamiltonian system with two degrees of freedom for a particle of mass $m = 1$ under the action of the quantum potential determined by these beams. We show that the integral curves of the Poynting vector constitute a particular subset of solutions to the corresponding Hamilton equations and that the geometrical light rays associated with these twisted beams turn out to be the tangent straight lines to the exact optics energy trajectories at the zeroes of the quantum potential. By using the Hamiltonian formulation, we determine the velocity, the linear momentum, the angular momentum, the torque, and the areal velocity characterizing the particle associated with the Laguerre–Gauss beams.

© 2022 Optica Publishing Group

Exact and geometrical optics energy trajectories in Bessel beams via the quantum potential

Gilberto Silva-Ortigoza, Israel Julián-Macías, Ernesto Espíndola-Ramos, and Ramón Silva-Ortigoza
J. Opt. Soc. Am. B 40(3) 620-630 (2023)

Properties of Hermite–Gaussian beams via the quantum potential

Gilberto Silva-Ortigoza, Ernesto Espíndola-Ramos, Edna Gabriela Gochicoa-Fuentes, and Ramón Silva-Ortigoza
J. Opt. Soc. Am. B 40(10) 2706-2715 (2023)

Self-interaction and mutual interaction of complex-argument Laguerre-Gauss beams

S. R. Seshadri
Opt. Lett. 31(5) 619-621 (2006)

Virtual source for a Laguerre–Gauss beam

S. R. Seshadri
Opt. Lett. 27(21) 1872-1874 (2002)

Polygonal Laguerre-Gauss beams

Job Mendoza-Hernández
Opt. Continuum 3(4) 607-614 (2024)