Vortex avalanche in the perturbed singular beams

Volyar, A. V.; Bretsko, M.; Akimova, Yana; Egorov, Yu. V.

doi:10.1364/josaa.36.001064

Cited by 23 publications

(12 citation statements)

References 25 publications

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“…This makes the dips in the OAM spectrum more distinct. The complex amplitude (12) corresponds to the OAM in the form For large parameters Ω >>20, the OAM is doubled ℓ z ¼ 2M in range of the initial topological charges M. As was shown in [47,48], a perturbation δp causes a local distortion of the forked grating defect for the large values parameter p shown in Figure 3(a).…”

Section: Degenerate Case and Vortex Avalanchementioning

confidence: 79%

“…This effect is accompanied by a sharp restructuring of the vortex spectrum. For small perturbations of the singular beam, additional vortex modes arise only near the initial value of the topological charge m ¼ M (see [47]). However, in general case of the hologram perturbation, vortex modes with opposite signs of topological charges appear.…”

Section: Nondegenerate Casementioning

confidence: 99%

See 1 more Smart Citation

Digital Sorting of Optical Vortices in Perturbed Singular Beams

Volyar¹,

Bretsko²,

Akimova³

et al. 2021

Nonlinear Optics - From Solitons to Similaritons

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The chapter provides a brief overview of shaping and measuring techniques of the vortex spectra (squared amplitudes and initial phases of vortex modes) including radial indices. The main physical mechanisms causing the formation of laser beams with a complex vortex composition, in particular, in biological media, are indicated, and the need for a digital analysis of vortex spectra is substantiated. It is the analysis of vortex spectra that allows us to find the orbital angular momentum and informational entropy (Shannon's entropy) of perturbed laser beams in real time. In the main part of the chapter, we consider in detail a new approach for measuring vortex spectra without cuts and gluing of the wavefront, based on digital analyzing high-order intensity moments of complex beams and sorting the vortex beam in computer memory sells. It is shown that certain types of weak local inhomogeneities cause a vortex avalanche causing a sharp dips and bursts of the orbital angular momentum spectra and quick ups and downs of the informational entropy. An important object of analysis is also the vortex spectra of beams scattered by simple opaque obstacles such as a hole, a disk, and a sector aperture.

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Section: Degenerate Case and Vortex Avalanchementioning

confidence: 79%

Section: Nondegenerate Casementioning

confidence: 99%

Digital Sorting of Optical Vortices in Perturbed Singular Beams

Volyar¹,

Bretsko²,

Akimova³

et al. 2021

Nonlinear Optics - From Solitons to Similaritons

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“…As we have shown in Ref. [19][20][21], the analysis of the vortex spectrum (dependence of the vortex mode intensity ( ) 2 , m n C α on the topological charge n ) enable us recovering the initial beam shape and finding its OAM. In our studies, we select two vortex beams with topological charges 5 m = and 15 m = that most clearly reflect properties of the sector perturbation.…”

mentioning

confidence: 94%

Orbital angular momentum and informational entropy in perturbed vortex beams

et al. 2019

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The first simple experiments of self-reconstructing or self-healing Bessel vortex beams after being obscured by symmetric obstacles [1,2] caused a flow of publications, for example, on microscopy with self-reconstructing beams [3], the information transmission and data processing systems [4,5]. Self-healing properties were also found in other types of vortex beams [6][7][8]. However, a more careful analysis of the self-healing showed [9] that Bessel beams do not always self-heal from transparent obstacles, and never self-heal from turbulence. This article caught our attention because it raises the question: what parameters of the beam characterize its selfreconstruction? The answer to this question depends on the use of feature properties of the vortex beam in various optical devices. For example, the sector obstacles inject some measure of uncertainty into the vortex beam [12][13][14] between the orbital angular momentum (OAM) and the angle of the sector obstacle, which, in turn, triggers a chain of vortex birth and annihilation events that increases a number of new vortex states. But such a perturbation although causing irreversible destruction of the wavefront, allows one to determine the topological charge of the optical vortex [10] and the orbital angular momentum [11]. On the other hand, the information properties of the vortex beam as a whole deteriorate significantly. Indeed, the growth of internal uncertainty in the wave structure induced by the sector aperture iindicates significant changes in such physical characteristics as informational entropy [15] and spatial coherence [16]. The fundamental problems of analyzing informational entropy (or Shannon's entropy) in light beams were considered in detail by Francis [15] and applied to vortex beams by the authors of Ref. [17,18]. The authors of Ref.[17] theoretically estimated the informational entropy and pointed out the relationship between entropy and spatial coherence for the 1D case of an unperturbed quasi-monochromatic vortex beam while the authors of Ref.[18] presented experimental confirmation of these theoretical predictions. We paid attention to the fact that, in the general case, informational entropy characterizes the vortex beam as a whole rather than its 1D projection onto the observation plane, as in Ref. [17,18]. Besides, the main contribution to information entropy is made by changes in the number of vortex states in the beam subjected to external perturbations. It is such an approach allowed the authors of Ref.[13] to investigate the relationship between the uncertainty of the angular position inside the vortex beam and the OAM. These studies point out the relationship between the vortex spectrum of the perturbed beam, the OAM, and the information entropy. Thus, the purpose of our letter is both a computer simulation and experimental measurement of informational entropy and the OAM of the perturbed vortex beam on the base of analyzing their vortex spectra.

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“…One of the possible approaches to solving this problem has been recently proposed and implemented in the articles [40][41][42][43]. The key idea of this technique is to use the intensity moments of higher-orders (see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…[40] considered specifics of employing the intensity moments technique for measuring the vortex spectrum (squared amplitudes and mode phases) and using them to calculating the total OAM of the combined beam containing LG modes with different topological charges m of the same signs ( 0 m or 0 m ) but zero radial number 0 n . This technique allowed analyzing structure of the vortex avalanche [41] caused by small local perturbations of the holographic grating. The use of the astigmatic transformation of the combined beam by means of a cylindrical lens [42] has expanded this technique to the beams with different signs of topological charges ( 0 m and 0 m ), but a zero radial number.…”

Section: Introductionmentioning

confidence: 99%

Sorting Laguerre-Gaussian beams by radial numbers via intensity moments

et al. 2020

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We propose and experimentally implement a new technique for digitally sorting Laguerre-Gaussian (LG) modes by radial number at a constant topological charge, resulting from the pertur-bation of the original LG beam, or superposition thereof, by passing them through a thin dielectric diaphragm with various aperture radii. The technique is based on a digital analysis of higher-order intensity moments. Two types of perturbed beams are considered: non-degenerate and degenerate beams with respect to the initial radial number of the LG beam superposition. A diaphragm with a circular pinhole causes the appearance of a set of secondary LG modes with different radial num-bers, which are characterized by an amplitude spectrum. The digital amplitude spectrum makes it possible to recover the real LG modes and find the measure of uncertainty due to perturbation by means of information entropy. It is found that the perturbation of a complex beam leads to the appearance of a degenerate am-plitude spectrum since a single spectral line corresponds to a set of modes generated by M original Laguerre-Gaussian beams with different radial numbers. For the spectrum to be deciphered, we use M keys represented by the amplitude spectra of the nondegenerate perturbed beams in our ex-periment. However, the correlation degree decreases to 0.92.

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Vortex avalanche in the perturbed singular beams

Cited by 23 publications

References 25 publications

Digital Sorting of Optical Vortices in Perturbed Singular Beams

Digital Sorting of Optical Vortices in Perturbed Singular Beams

Orbital angular momentum and informational entropy in perturbed vortex beams

Sorting Laguerre-Gaussian beams by radial numbers via intensity moments

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