Fast oscillations of orbital angular momentum and Shannon entropy caused by radial numbers of structured vortex beams.

We address theoretical and experimental considerations of two-parameter excitation of each Hermite-Gaussian (HG) mode in composition of a structured Laguerre-Gaussian (sLG) beam. The complex amplitude of the sLG beam is shaped in such a way that the radial and azimuthal numbers of eigenmodes are entangled with each other. As a result, variations in the amplitude and phase parameters of mode excitation, although dramatically changing the intensity and phase patterns, do not change the structural stability of the beam. We reveal that the radial number of the sLG beam can cause fast oscillations of the orbital angular momentum and Shannon entropy, dramatically increasing the uncertainty of detecting the beam in some particular state. We found that despite the fast oscillations, the sLG beam has an invariant in the form of a module of the total topological charge (TC), with the exception of narrow intervals of the phase parameter, where the measurement error does not allow us to accurately measure the sign of the TC. The difference between the interpretation of informational entropy as a measure of uncertainty and a measure of information capacity is considered on the example of the measurement of Shannon entropy in the bases of LG and HG modes.

Control of the orbital angular momentum via radial numbers of structured Laguerre-Gaussian beams.

We found that the internal perturbations of the structured Laguerre-Gaussian beam in the form of two-parametric harmonic excitations of the Hermite-Gaussian (HG) modes in its composition mix up the radial and azimuthal numbers. The harmonic excitation is characterized by two parameters, one of them controls the amplitude of the HG modes, and the second parameter controls the phases of each HG mode. It was revealed that this mixing of the beam quantum numbers leads to the possibility of controlling the orbital angular momentum (OAM) by means of radial numbers. Non-zero radial numbers lead to rapid OAM oscillations as the phase parameter changes, while oscillations disappear if the radial number is zero. We have also shown that the variation of the phase parameter in a wide range of values does not change the modulus of the total topological charge of the structured beam, despite the fast OAM oscillations.

Super bursts of the orbital angular momentum in astigmatic-invariant structured LG beams.

A structured Laguerre-Gaussian (sLG) beam in an optical system with an astigmatic element acquires additional degrees of freedom in the form of changing the fine structure of the beam, its orbital angular momentum (OAM), and topological charge. We have theoretically and experimentally revealed that at a certain ratio between the beam waist radius and the focal length of the cylindrical lens, the beam turns into an astigmatic-invariant one, and such a transition does not depend on the beam radial and azimuthal numbers. Moreover, in the vicinity of the OAM zero, its sharp bursts occur, the magnitude of which significantly exceeds the initial beam OAM and grows rapidly as the radial number increases.

Fine structure of perturbed Laguerre-Gaussian beams: Hermite-Gaussian mode spectra and topological charge.

We found that small perturbations of the optical vortex core in Laguerre-Gaussian (LG) beams generate a fine structure of the Hermite-Gaussian (HG) mode spectrum in the form of weak variations of amplitudes and phases of the HG modes. We developed and implemented the intensity moments technique for measuring the HG mode spectra. We also theoretically justified and experimentally implemented a technique for measuring the topological charge of the LG beams with an arbitrary number of ring dislocations. Theoretical discussion and experimental study are accompanied by examples of estimating the orbital angular momentum and the topological charge of perturbed LG beams as well as the algorithm for plotting the HG mode spectra.

Partially coherent stable and spiral beams.

Stable and spiral coherent beams, which do not change the form of their intensity distribution apart from possible scaling and rotation during propagation and therefore possess self-healing properties, are widely applied in science and technology. On the other hand, it has been found that partially coherent light often provides better output than coherent light. Here we consider two methods for the design and experimental generation of partially coherent stable and spiral beams.