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.
On the topological charge conservation in the three-dimensional ${\rm O}(3)$ $\sigma$-model.
