Transverse energy redistribution upon edge diffraction of a paraxial laser beam with optical vortex

Abstract

We present the results of the numerical investigation of the transverse profile evolution for a beam obtained by the edge diffraction of a circular Laguerre-Gaussian mode. It is shown that the energy penetrates into the geometric shadow region asymmetrically, which testifies for the transverse energy circulation in the incident beam. The intensity profile shows the "overall" rotation in agreement with the energy circulation handedness. The phase profile of the diffracted beam is characterized by the system of singularities (optical vortices) that migrate over the beam cross section and participate in topological reactions of emergence and/or annihilation. In the far field, the beam profile structure is simplified and becomes symmetric with respect to the axis orthogonal to the screen edge. No matter which part of the Laguerre-Gaussian beam is stopped by the screen, the far-field profile contains the optical vortex of the same sense as the incident one.

Localization and migration of phase singularities in the edge-diffracted optical-vortex beams

“…For the single-charged input OV beam ( figure 2(a)), the presence of the screen edge causes the OV core displacement from its initial position at the z-axis; with growing screening (decreasing a, see figure 1(c)), the OV core evolves along the spiral-like trajectory oppositely to the beam profile rotation, which, in turn, agrees with the internal energy circulation shown by the grey arrow. Ultimately, the OV disappears in the shadow region (x > a) [21][22][23]33,35]. When the screen edge moves away from the z-axis, the spiral-like OV trajectory makes (theoretically) an infinite number of rotations until it restores the initial axial position.…”

“…In contrast, for the odd topological charge (m = -3), there are smooth minima of black and red curves in figures 3(e), (f). The evolution of the OV positions with the diffracted beam propagation is not the subject of the present work; for the LG beam diffraction, it was studied elsewhere [33,34]. However, comparison of the right and left columns of figures 3, 4 clearly demonstrates the main propagation-induced effects: the OV cores, generally, move away from the z-axis (the vertical scales are higher in the right column of figure 3), the spiral motion becomes slower (for each curve in the right column of figure 4, the range of  variation is smaller than for the same colour curve in the left column), and the small visually irregular oscillations ("ripples") in the r and  curves become smoother.…”

“…This equation was used many times for analysis of the OV beam diffraction (see, e.g., [32][33][34][35]). Frequently in practice, the OV beam is formed with the help of a special element (VG in figure 1(a)) -a helical phase plate or a diffraction grating with groove bifurcation ("fork" hologram), which introduces the phase singularity into an initially regular (Gaussian) beam.…”

“…A detailed study of these singularities and their evolution with the diffracted beam propagation was recently undertaken [32][33][34]; however, the theoretical discourse of these works was restricted to situations where the incident OV beam is described by the Laguerre-Gaussian (LG) model. This is the standard OV beam model but in practice, other sorts of OV beams are more appropriate.…”

“…), which can be used in diverse metrological applications. Besides the rich and impressive physical contents, including the phase singularities, internal energy circulation, specific features of the linear and angular momentum distributions [4][5][6], such beams offer a wide range of perspective applications in the micromanipulation techniques [7][8][9][10], information transfer and processing [11,12], sensitivity and resolution enhancement in optical observations and measurements [13][14][15][16][17][18][19].Among diverse manifestations of the specific "circulational" properties of optical vortices, an important place belongs to the edge diffraction phenomena [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. A series of experimental and theoretical researches has demonstrated that diffraction "reveals" the internal energy circulation, normally "hidden" in circular OV beams, and induces the essential transformation of their phase profile.…”