The dynamics of the topological charge of a vortex optical beam propagating in turbulent air while accounting for the cubic nonlinearity is theoretically considered. In a number of examples, we show that the optical beam, self-focusing, manifests itself ambiguously depending on the optical wave power. At near-critical values of beam power, self-focusing leads to enhanced spatial localization of optical vortices and substantial suppression of vortex walk-off relative to the beam axis caused by air turbulence. However, with increasing optical intensity, the modulation instability imposed by cubic nonlinearity becomes significant and contributes jointly with medium turbulence and leads to faster divergence of vortex beams.

Laser beams converging at significant focusing angles have diverse applications, including quartz-enhanced photoacoustic spectroscopy, high spatial resolution imaging, and profilometry. Due to the limited applicability of the paraxial approximation, which is valid solely for smooth focusing scenarios, numerical modeling becomes necessary to achieve optimal parameter optimization for imaging diagnostic systems that utilize converged laser beams. We introduce a novel methodology for the modeling of laser beams sharply focused on the turbid tissue-like scattering medium by employing the unidirectional Helmholtz equation approximation. The suggested modeling approach takes into account the intricate structure of biological tissues, showcasing its ability to effectively simulate a wide variety of random multi-layered media resembling tissue. By applying this methodology to the Gaussian-shaped laser beam with a parabolic wavefront, the prediction reveals the presence of two hotspots near the focus area. The close-to-maximal intensity hotspot area has a longitudinal size of about 3–5 μm and a transversal size of about 1–2 μm. These values are suitable for estimating spatial resolution in tissue imaging when employing sharply focused laser beams. The simulation also predicts a close-to-maximal intensity hotspot area with approximately 1 μm transversal and longitudinal sizes located just behind the focus distance for Bessel-shaped laser beams with a parabolic wavefront. The results of the simulation suggest that optical imaging methods utilizing laser beams with a wavefront produced by an axicon lens would exhibit a limited spatial resolution. The wavelength employed in the modeling studies to evaluate the sizes of the focus spot is selected within a range typical for optical coherence tomography, offering insights into the limitation of spatial resolution. The key advantage of the unidirectional Helmholtz equation approximation approach over the paraxial approximation lies in its capability to simulate the propagation of a laser beam with a non-parabolic wavefront.

The inverse variational problem is solved for the nonlocal nonlinear Schrödinger equation modeling filamentation processes in various nonlinear media. The corresponding integral relations...

The dynamics of the topological charge of a vortex optical beam propagating in a turbulent air with accounting for the cubic nonlinearity is theoretically considered. On a number of examples, we show that the optical beam self-focusing manifests itself ambiguously depending on optical wave power. At near-critical values of beam power, self-focusing leads to enhanced spatial localization of optical vortices and substantial suppression of vortex walk-off relative to the beam axis caused by air turbulence. However, with increasing of optical intensity the modulation instability imposed by cubic nonlinearity becomes significant and contributes jointly with medium turbulence to faster divergence of vortex beams.

The general form of the kinetic equation for the filament number density with allowance for effects of their creation and decay is formulated—a nonlinear diffusion equation. The equation includes phen