Topological Charge of Multi-Color Optical Vortices

Victor Victorovich Kotlyar,Alexey Andreevich Kovalev,Anton Gennadyevich Nalimov,Sergey Sergeevich Stafeev

doi:10.3390/photonics9030145

Victor Victorovich Kotlyar, Alexey Andreevich Kovalev + Show 2 more

Open Access

https://doi.org/10.3390/photonics9030145

Copy DOI

Abstract

The topological charge of an optical vortex is a quantity rather stable against phase distortions, for example, turbulence. This makes the topological charge attractive for optical communications, but for many structured beams it is unknown. Here, we derive the topological charge (TC) of a coaxial superposition of spatially coherent Laguerre–Gaussian beams with different colors, each beam with its own wavelength and its own TC. It turns out that the TC of such a superposition equals the TC of the LG beam with a longer wavelength, regardless of the weight coefficient of this beam in the superposition and regardless of its TC. It is interesting that the instantaneous TC of such a superposition is conserved on propagation, whereas the time-averaged intensity distribution of the colored optical vortex changes its gamut; if, in the near field, the colors of the light rings arrange along the radius according to their TCs in the superposition from lower to greater, then, on space propagation, the colors of the light rings in the cross-section are arranged in reverse order from the greater TC to the lower TC. We also demonstrate that, by choosing appropriate wavelengths (blue, green, and red) in a three-color superposition of single-ringed LG beams, it is possible to generate, at some propagation distance, a time-averaged light ring of the white color. If all the beams in a three-color superposition of single-ringed LG beams have the same TC, then there is a single ring of nearly white light in the initial plane. Then, on propagation in space, light rings of different colors acquire different radii: a smaller ring radius for a shorter wavelength.

Highlights

It is interesting that the instantaneous topological charge (TC) of such a superposition is conserved on propagation, whereas the time-averaged intensity distribution of the colored optical vortex changes its gamut; if, in the near field, the colors of the light rings arrange along the radius according to their TCs in the superposition from lower to greater, on space propagation, the colors of the light rings in the cross-section are arranged in reverse order from the greater TC to the lower TC
Vortex beams, or optical vortices, have been known in optics since the 1980s, but many fundamental, theoretical issues about these beams still have not been addressed. Some of these unsolved problems are related to the important quantity of the optical vortices, their topological charge (TC) [1], due to its discreteness, it demonstrates a significant stability when coherent vortex beams propagate in turbulence [2–4] and can be used for identifying incoming optical signals. It was only recently discovered [5] that the TC of a superposition of two parallel, monochromatic Laguerre–Gaussian (LG) beams with their azimuthal indices of different parity can be different depending on which of these two beams is on the left and which is on the right
In work [12], a spiral phase plate (SPP) was illuminated by a white-light beam, and it was demonstrated that a rainbow is generated since the different wavelengths in the white-light beam generate, after passing through the SPP, light rings of different radii

Summary

Introduction

Optical vortices, have been known in optics since the 1980s, but many fundamental, theoretical issues about these beams still have not been addressed. Some of these unsolved problems are related to the important quantity of the optical vortices, their topological charge (TC) [1], due to its discreteness, it demonstrates a significant stability when coherent vortex beams propagate in turbulence [2–4] and can be used for identifying incoming optical signals It was only recently discovered [5] that the TC of a superposition of two parallel, monochromatic Laguerre–Gaussian (LG) beams with their azimuthal indices of different parity can be different depending on which of these two beams is on the left and which is on the right. There are few works on the multi-color optical vortices (COV) and even fewer (or almost no) works which derive the TC of a superposition of COVs. In this work, we study, as an example, a spatial coherent coaxial superposition of single-ringed (i.e., with zero radial index) LG beams with the same waist radius but with different weight coefficients, TCs, and wavelengths. Both theoretically and numerically, that the topological competition is won by a more “red” LG beam, i.e., the common TC of the whole superposition is equal to the TC of the constituent LG beam with a longer wavelength

Topological Charge of a Two-Color Superposition of Optical Vortices

Numerical

Numerical Simulation of Paraxial Free-Space Space Propagation of a Three-Color

Topological Charge of a White Optical Vortex

Experiment