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We experimentally realize higher-order catastrophic structures in light fields presenting solutions of the paraxial diffraction catastrophe integral. They are determined by potential functions whose singular mapping manifests as caustic hypersurfaces in control parameter space. By addressing different cross-sections in the higher-dimensional control parameter space, we embed swallowtail and butterfly catastrophes with varying caustic structures in the lower-dimensional transverse field distribution. We systematically analyze these caustics analytically and observe their field distributions experimentally in real and Fourier space. Their spectra can be described by polynomials or expressions with rational exponents capable to form a cusp.

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate here a paraxial vector Gaussian beam with an infinite number of polarization singularities residing evenly on a straight line. The intensity distribution is derived analytically and the polarization singularities are shown to exist only in the initial plane and in the far field. The azimuthal angle of the polarization singularities is shown to increase in the far field by π/2. We obtain the longitudinal component of the spin angular momentum (SAM) density and show that it is independent of the azimuthal angle of the polarization singularities. Upon propagation in free space, an infinite number of C-points is generated, where polarization is circular. We show that the SAM density distribution has a shape of four spots, two with left and two with right elliptic polarization. The distance to the transverse plane with the maximal SAM density decreases with decreasing distance between the polarization singularities in the initial plane. Generating such alternating areas with positive and negative SAM density, despite linear polarization in the initial plane, manifests the optical spin Hall effect. Application areas of the obtained results include designing micromachines with optically driven elements.

We studied paraxial light beams, obtained by a continuous superposition of off-axis Gaussian beams with their phases chosen so that the whole superposition is invariant to free-space propagation, i.e., does not change its transverse intensity shape. Solving a system of five nonlinear equations for such superpositions, we obtained an analytical expression for a propagation-invariant off-axis elliptic Gaussian beam. For such an elliptic beam, an analytical expression was derived for the orbital angular momentum, which was shown to consist of two terms. The first one is intrinsic and describes the momentum with respect to the beam center and is shown to grow with the beam ellipticity. The second term depends parabolically on the distance between the beam center and the optical axis (similar to the Steiner theorem in mechanics). It is shown that the ellipse orientation in the transverse plane does not affect the normalized orbital angular momentum. Such elliptic beams can be used in wireless optical communications, since their superpositions do not interfere in space, if they do not interfere in the initial plane.

A new analytical solution of the nonparaxial Helmholtz equation for the Gaussian beam has been obtained. It is shown that the beam retains the Gaussian distribution of the amplitude at propagation in space. The scale transformation of the beam has been determined. The Kogelnik–Li law applies to a nonparaxial Gaussian beam.

The beam parameters of fundamental mode in MQW waveguide including mode-field half-width, divergence half-angle and beam propagation factor are analyzed according to the non-paraxial vectorial moment theory of light beam propagation as well as waveguide mode theory and some new conclusions are proposed.

Behaviour of Laguerre-Gaussian beams impinged at a dielectric interface under distinct angles is discussed. For different incident angles the beams interact with the interface differently. Two ranges of incident angles, specified by a position of a spectral cone of beam field and related to a cross-polarization effect, are analyzed. Boundary between these two ranges is defined. Cases of critical incidence and total internal reflection are also discussed. Paraxial beams near the lower paraxial limit are considered. Theoretical predictions are confirmed by numerical simulations.

Wave beams, packets or pulses are known to be subject to a drift if the properties of the medium change across their extension. This effect is often analyzed considering the dispersive properties of the oscillation, related to the real part of the dispersion relation. The evolution of Gaussian beams/packets/pulses in nonuniform media in the presence of gain or damping is investigated in detail, with particular emphasis on the role of dispersion on both the real and the imaginary part of the dispersion relation. In the paraxial limit, the influence of a non-Hermitian medium on the evolution of the wave can be treated employing the equations derived by Graefe and Schubert in the frame of non-Hermitian quantum mechanics ( Phys. Rev. A 83 060101(R)). Analytic solutions of the corresponding paraxial equations are obtained here for a one-dimensional complex dispersion relation characterized by a linear or quadratic dependence on the transverse coordinate (a space coordinate for beams and packets, the time in the co-moving frame for a pulse). In the presence of a constant gradient in both the real and the imaginary part of the dispersion relation, the contribution of the latter can lead to a faster or slower propagation with respect to the Hermitian case, depending on the parameters. In focusing media, a constant gain can counteract dispersive or inhomogeneous damping producing packets of asymptotically constant shape. The analytic formulas derived in this paper offer a way to predict or control the properties of beams/packets/pulses depending on their initial conditions and on the characteristics of the medium.

The head-on scattering of electrons with energies from a few MeV to 5 GeV off ultrashort and ultra-intense laser pulses at petawatt intensities is investigated. Radiation reaction (RR) effects are included through the correction terms given by the Landau–Lifshitz equation. Full paraxial fields for the laser are used, including their longitudinal electric and magnetic components, and both the fundamental Gaussian TEM00 mode as well as the orbital angular momentum (OAM) mode with (l,p)=(1,0) are studied. We compare the expected behavior, as regards the influence of RR, at near-infrared (NIR) and at vacuum ultraviolet (VUV) or X-ray wavelengths.

We obtain a transform that relates the standard Bessel–Gaussian (BG) beams with BG beams described by the Bessel function of a half-integer order and quadratic radial dependence in the argument. We also study square vortex BG beams, described by the square of the Bessel function, and the products of two vortex BG beams (double-BG beams), described by a product of two different integer-order Bessel functions. To describe the propagation of these beams in free space, we derive expressions as series of products of three Bessel functions. In addition, a vortex-free power-function BG beam of the mth order is obtained, which upon propagation in free space becomes a finite superposition of similar vortex-free power-function BG beams of the orders from 0 to m. Extending the set of finite-energy vortex beams with an orbital angular momentum is useful in searching for stable light beams for probing the turbulent atmosphere and for wireless optical communications. Such beams can be used in micromachines for controlling the movements of particles simultaneously along several light rings.