# Laser Beam Positioning by Using a Broken-Down Optical Vortex Marker
## 1 Introduction  
Light beams with a special intensity and their phase structures have attracted attention in modern technology in recent years. Beams carrying an optical vortex are of special interest as they contain a characteristic isolated point of zero intensity and singular phase. When traversing the closed path around the singular point, the phase increases by 2 pm, where \(m=1,2,3\dots\) denotes the topological charge (TC). The use of such beams in optical fiber communication was considered and described in [1]. The spatial characteristics of optical fields such as polarization, amplitude, and phase structures have been extensively studied in optical fiber communication to facilitate a significant increase in transmission throughput and the efficient use of frequency-limited resources thanks to a promising technique; i.e., space division multiplexing [2; 3]. Optical vortex (OV) beams have already found application in fiber optic communication or in free space [4; 5; 6; 7; 8; 9]. Weather conditions affect the propagation of information in free space. However, it has been shown that, by means of a beam with optical vortices, it is possible to encode and transmit a message at a distance exceeding 100 km [10].  
The orbital angular momentum (OAM) in the vortex beams (VBs), where OV propagates in the paraxial beams, can be used to increase optical communication throughput as well as to develop new approaches to quantum coding [11; 12].  
An optical vortex is an isolated point or singularity in an optical field. An example of a beam transmitting an optical vortex is the Laguerre-Gauss (LG) beam [13; 14]. Many methods characterize a vortex beam regarding its intensity profile. The bright ring of the ideal vortex beam is circular, with a diameter that encapsulates the information of the beam size [15]. In the case of optical imperfections, the intensity profile loses a spherical symmetry, changing for example into the elliptical one [16; 17].  
Optical communication uses optical vortices with higher topological charges (TC), and these break up during propagation, so it is important to know the stability and dynamics of the vortex core propagation [18; 19]. A vortex with a higher charge in a superfluid is energetically unfavorable compared to vortices with a unit charge. Thus, a vortex with a higher charge always tends to break up into unit charge vortices [20; 21]. The breaking up of optical vortices can be controlled by several external parameters [22; 23]. Currently,many methods for the determination of the TC [24; 25; 26; 27; 28; 29] are known and used, but to obtain the best efficiency of TC determination, a beam positioning method should be used.  
In the article, we propose the use of the phenomenon of breaking optical vortices with higher topological charges for beam position control. First, we present a numerical simulation method to obtain a beam with a higher TC segmented to a few units of charged optical vortices. Next, novel vortex location finding methods are described. In the last step, the results of the experiment are shown. The experiment was conducted in the conditions of atmospheric turbulence. Under such conditions, the splitting of higher charge optical vortices is observed [30].  
The positioning method described in this article may be useful in optical communication channels with digital signal processing but is not limited to this application.