Dynamical characteristics of Laguerre–Gaussian vortex beams upon reflection and refraction

Abstract

Laguerre–Gaussian beams with vortex structure, as a special type of electromagnetic wave, can carry energy, momentum, and angular momentum, which is crucial for understanding of dynamical processes concerning light–matter interaction phenomena. In this paper, we theoretically investigate the local dynamical characteristics of Laguerre–Gaussian vortex beams upon reflection and refraction. Using a hybrid method based on the angular spectrum representation and vector potential in the Lorenz gauge, the explicit analytical expressions for the electric and magnetic field components of reflected and refracted Laguerre–Gaussian beams are derived in the form of a Hermite polynomial. A canonical approach is utilized to examine the energy, momentum, and spin and orbital angular momentum of the Laguerre–Gaussian vortex beams’ reflection and refraction at a plane interface between air and BK7 glass. The effects of the incidence angle, topological charge, and polarization state on these dynamical quantities are simulated and discussed in detail. This study may provide useful insights into the interactions of vortex beams with matter and their further applications.

Grating Design Methodology for Tailored Free-Space Beam-Forming

“…1) Design adaptations: To reverse-propagate the desired beam, we extend the analytical treatment of LG beam refraction in [45] to focused beams. The longitudinal grating parameters are still calculated from the fundamental Gaussian mode, thus the features of the higher orders are produced by the holographic phase matching-the phase contours alone will produce the central singularity and the circular intensity profile.…”

“…We restrict our consideration to the case where the radial mode index p is zero, so we do not discuss it here[45].This article has been accepted for publication in IEEE/OSA Journal of Lightwave Technology. This is the author's version which has not been fully edited and content may change prior to final publication.…”

Vortex beam manipulation through a tunable plasma-ferrite metamaterial

“…It is known that the VB calculations are accompanied by some complexity. This difficulties can be avoided in the frame of ASE 43 , 44 , in which the VB is decomposed into infinite plane waves in the spectral domain as follows Here, indicates the incident spectrum space. In this case, the transmitted electric field in the output plane can be calculated as where, is the total transmission coefficient, , , and .…”

A comparative study on the vector description of typical structured light beams

“…In recent years, considerable research interests have been attracted in the study of light fields with strong spatial inhomogeneity of amplitude, phase, polarization, and other parameters, such as the higher-order Hermite-Gaussian beams (Golla and Gupta 2011;Dong et al 2013;Lukowsk et al 2019;von Behren et al 2023), Laguerre-Gaussian vortex beams (Allen et al 1992;Allen and Padgett 2000;Wang et al 2016;Cui et al 2020), non-diffracting Bessel beams (McGloin and Dholakia 2005;Du et al 2014;Hu et al 2019;Fontaine et al 2019), self-accelerating Airy beams (Siviloglou, et al 2007;Singh et al 2015;Efremidis et al 2019), and so on. Such light fields are usually called structured light beams, which exhibit a series of interesting properties and have potential applications in many fields, especially in the field of optical trapping and manipulation of particles (Otte and Denz 2020;Yang et al 2021).…”

“…In theory, the vector potential method and VASR are suitable for describing any structured light beam, but both methods are more suitable for describing paraxial structured light beams due to their simple operation. To date, there have been some reports on the description of various structured light beams using the vector potential method and VASR (Hui et al 2020;Cui et al 2020;Ma et al 2023;Zhou 2006;Zhou and Zheng 2008;Liu and Zhou 2010;Li et al 2011;Jia et al 2016;Song et al 2020). However, most of the previous works only focused on one type of typical structured light beams, while few attentions have been paid to the systematic description of typical structured light beams.…”