Add to BibSonomy
Abstract
The state of polarization of a general form of an optical vortex mode is represented by the vector ${{\hat \epsilon}_m}$, which is associated with a vector light mode of order $m \gt 0$. It is formed as a linear combination of two product terms involving the phase functions ${e^{\pm im\phi}}$ times the optical spin unit vectors ${{\sigma}^ \mp}$. Any such state of polarization corresponds to a unique point $({\Theta _P},{\Phi _P})$ on the surface of the order $m$ unit Poincaré sphere. However, albeit a key property, the general form of the vector potential in the Lorenz gauge ${A} = {{\hat \epsilon}_m}{\Psi _m}$, from which the fields are derived, including the longitudinal fields, has neither been considered nor has had its consequences been explored. Here, we show that the spatial dependence of ${\Psi _m}$ can be found by rigorously demanding that the product ${{ \hat \epsilon}_m}{\Psi _m}$ satisfies the vector paraxial equation. For a given order $m$ this leads to a unique ${\Psi _m}$, which has no azimuthal phase of the kind ${e^{i\ell \phi}}$, and it is a solution of a scalar partial differential equation with $\rho$ and $z$ as the only variables. The theory is employed to evaluate the angular momentum for a general Poincaré mode of order $m$ yielding the angular momentum for right- and left- circularly polarized, elliptically polarized, linearly polarized and radially and azimuthally polarized higher-order modes. We find that in applications involving Laguerre–Gaussian modes, only the modes of order $m \ge 2$ have non-zero angular momentum. All modes have zero angular momentum for points on the equatorial circle for which $\cos {\Theta _P} = 0$.
© 2023 Optica Publishing Group
Full Article | PDF ArticleMore Like This
Gilberto Silva-Ortigoza, Israel Julián-Macías, Ernesto Espíndola-Ramos, and Ramón Silva-Ortigoza
J. Opt. Soc. Am. B 40(3) 620-630 (2023)
K. Koksal, M. Babiker, V. E. Lembessis, and J. Yuan
J. Opt. Soc. Am. B 39(2) 459-466 (2022)
Xiaorun Zang, Godofredo Bautista, Léo Turquet, Tero Setälä, Martti Kauranen, and Jari Turunen
J. Opt. Soc. Am. B 38(2) 521-529 (2021)