Topological charge of superposition of optical vortices described by a geometric sequence

Abstract

Here, we investigate coaxial superpositions of Gaussian optical vortices that can be described by a geometric sequence. For all superpositions analyzed, a topological charge (TC) is derived. In the initial plane, the TC can be either integer or half-integer, acquiring an integer value upon free-space propagation of the light field. Generally, the geometric sequence of optical vortices (GSOV) has three integer parameters and one real parameter. Values of these four parameters define the TC of the GSOV. Upon free-space propagation, the intensity pattern of the GSOV is not conserved, but can have intensity petals whose number is equal to one of the four beam parameters. If the GSOV has a unit real parameter, all constituent angular harmonics in the superposition have the same weight. In this case, the TC of the superposition is equal to the average index of the constituent angular harmonics. For instance, if the TC of the first and of the last angular harmonics, respectively, equals k and n, then the total TC of the superposition in the initial plane will be (n + k) /2, becoming equal to n upon free-space propagation.

The optical vortices focusing by subwavelength microelements with variable relief height using high-performance computer systems

“…The distinguishing feature of this structure is the presence of singular points at which the phase is not defined and the amplitude is zero. The special properties of vortex beams are of great interest [1][2][3][4][5][6][7][8][9][10][11][12][13] . This is manifested in the active use of this type of radiation for a number of applications, including optical transmission and information processing 3,[14][15][16][17] (including in wireless communication systems 18 ), sensing 5 , material processing and microscopy [19][20][21] , quantum informatics 22 , as well as optical capture and manipulation 4,[23][24][25][26][27] .…”