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A. Yu. Okulov

Publications and source records attributed to A. Yu. Okulov.

At least 19 recordsLinked to original sources
arXiv2025

Variational Principle for Optical Phase

{The problem of laser beam concentration in a focal spot via wavefront variations is formulated as a maximization of the $beam$ $propagation$ $functional$ defined as the light power passing through aperture of an arbitrary shape located in the far field. Variational principle provides the necessary and sufficient conditions for at least the $local$ $maximum$ of the $beam$ $propagation$ $functional$. The wavefront shape is obtained as an exact solution of nonlinear integral equation. }

nlin.PS↗
arXiv2023

Twisted superfluids in moving frame

Helical waveguide filled by superfluid is shown to transform rotations of the reference frame $\vec Ω_{\oplus}$ into linear displacements of the atomic ensemble and vise versa the linear displacements of the reference frame $\vec V$ initialize rotations $\vec Ω_{\oplus}$ of ensemble. In the mean-field Gross-Pitaevskii equation with a weakly modulated gravitation potential the exact solutions for macroscopic wavefunction $Ψ$ demonstrate the emergence of $redshift$ phase factor. For helical waveguides formed by phase-conjugated optical vortices with high angular momentum $L_z=\pm \ell \hbar \sim \pm \hbar \cdot 10^{3 ÷4}$ one may expect the significant improvement of the phase-sensitivity $δϕ$ by factor containing $2 \ell$ compared to the conventional nonsingular matter-wave interferometry.

nlin.PS↗
arXiv2022

Optical counterpart of the Foucault pendulum

The twin beam vortex interferometer with phase-conjugating mirror is analyzed in rotating reference frame.Circular motion of the interference pattern occurs due to exchange of the angular momenta between photons and interferometer. Using the concept of the $ideal$ phase-conjugating mirror it is shown that motion of the helical interference pattern of the interacting vortex photons with topological charge $\ell$ may be used for the detection of the slow rotations. The higher density of interference fringes may improve the sensitivity by factor containing $2 \ell$ compared to the conventional Michelson interferometry.

physics.optics↗
arXiv2020

Numerical investigation of coherent and turbulent structures of light via nonlinear integral mappings

The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of geometries relevant to typical problems of nonlinear optics, numerical modeling by reducing to dynamical systems with discrete time and continuous spatial variables to iterates of local nonlinear Feigenbaum and Ikeda mappings and nonlocal diffusion-dispersion linear integral transforms is equivalent to partial differential equations of the Ginzburg-Landau type in a fairly wide range of parameters. Such nonlocal mappings , which are the products of matrix operators in the numerical implementation, turn out to be stable numerical-difference schemes, provide fast convergence and an adequate approximation of solutions. The realism of this approach allows one to take into account the effect of noise on nonlinear dynamics by superimposing a spatial noise specified in the form of a multimode random process at each iteration and selecting the stable wave configurations. The nonlinear wave formations described by this method include optical phase singularities, spatial solitons, and turbulent states with fast decay of correlations. The particular interest is in the periodic configurations of the electromagnetic field obtained by this numerical method that arise as a result of phase synchronization, such as optical lattices and self-organized vortex clusters.

nlin.PS↗
arXiv2019

Structured light entities, chaos and nonlocal maps

Spatial chaos as a phenomenon of ultimate complexity requires the efficient numerical algorithms. For this purpose iterative low-dimensional maps have demonstrated high efficiency. Natural generalization of Feigenbaum and Ikeda maps may include convolution integrals with kernel in a form of Green function of a relevant linear physical system. It is shown that such iterative $nonlocal$ $nonlinear$ $maps$ are equivalent to ubiquitous class of nonlinear partial differential equations of Ginzburg-Landau type. With a Green functions relevant to generic optical resonators these $nonlocal$ $maps$ emulate the basic spatiotemporal phenomena as spatial solitons, vortex eigenmodes breathing via relaxation oscillations mediated by noise, vortex-vortex and vortex-antivortex lattices with periodic location of vortex cores. The smooth multimode noise addition facilitates the selection of stable entities and elimination of numerical artifacts.

physics.optics↗
arXiv2018

Configuration of vortex-antivortex lattices at output mirror of wide-area microchip laser

Square vortex lattices predicted theoretically and experimentally observed in diode-pumped solid state microchip lasers are shown to have a remarkable symmetry. These lattices are formed by counter-rotating vortices. The interaction of vortices with nonlinear gain medium leads to precession of vortices and collective excitations with dynamics identical to acoustical and optical vibrations of atomic lattices.

nlin.PS↗
arXiv2017

Helical containers with classical and quantum fluids in rotating frame

The examples of the classical liquids confined by rotating helical boundaries are considered and these examples are compared with rotating helical reservoir filled by ultracold bosonic ensemble. From the point of view of observer who co-rotates with classical liquid trapped by reservoir the quantum fluid will move translationally alongside rotation axis while in laboratory frame the quantum fluid will stay in rest. This behavior of quantum ensemble which is exactly opposite to the classical case might be interpreted as a helical analog of Hess-Fairbank effect.

nlin.PS↗
arXiv2014

Coherency Tuning via Phase Conjugation in Fiber Laser Networks

Phase-locking of large mode area Yb photonic crystal fiber amplifiers via stimulated Brillouin scattering phase conjugation is analyzed. The wavefront reversing mirrors are proposed for chirped pulse fiber laser networks. The chirp control via both nonresonant Kerr and resonant index is considered.

physics.optics↗
arXiv2014

Phase-conjugation of the isolated optical vortex using a flat surfaces

The robust method for obtaining the helical interference pattern due to the phase-conjugation of an isolated optical vortex by means of the non-holographic technique is proposed. It is shown that a perfect wavefront-reversal of the vortex in a linear polarization state via even number of reflections is achievable due to the turn of the photon's momentum $\vec p \approx \hbar \vec k$ with respect to the photon's orbital angular momentum projection $L_z$. The possible experimental realization is based upon $catseye-prism$ like reflections inside the confocal optical $loop$ cavity. The alternative scheme contains the Dove prism embedded in the optical $loop$ with the odd number of reflections from mirrors. This $confocal$ interferometric technique is applicable to the optical tweezers, atomic traps, Sagnac laser loops and metamaterials fabrication.

physics.optics↗
arXiv2014

Coherent chirped pulse laser network in Mickelson phase conjugating configuration

The mechanisms of nonlinear phase-locking of a large fiber amplifier array are analyzed. It is shown that Michelson phase conjugating configuration with double passage through array of fiber amplifiers have the definite advantages compared to one-way fiber array coupled in a Mach-Zehnder configuration. Regardless to amount of synchronized fiber amplifiers Michelson phase-conjugating interferometer is expected to do a perfect compensation of the phase-piston errors and collimation of backwardly amplified fiber beams on entrance/output beamsplitter. In both configurations the nonlinear transformation of the stretched pulse envelope due to gain saturation is capable to randomize the position of chirp inside envelope thus it may reduce the visibility of interference pattern at output beamsplitter. A certain advantages are inherent to the $sech$-form temporal envelope because of exponential precursor and self-similar propagation in gain medium. The Gaussian envelope is significantly compressed in a deep gain saturation regime and frequency chirp position inside pulse envelope is more deformed.

physics.optics↗
arXiv2013

Vortex-antivortex wavefunction of a degenerate quantum gas

A mechanism of a pinning of the quantized matter wave vortices by optical vortices in a specially arranged optical dipole traps is discussed. The vortex-antivortex optical arrays of rectangular symmetry are shown to transfer angular orbital momentum and form the "antiferromagnet"-like matter waves. The separable Hamiltonian for matter waves in pancake trapping geometry is proposed and 3D-wavefunction is factorized in a product of wavefunctions of the 1D harmonic oscillator and 2D vortex-antivortex quantum state. The 2D wavefunction's phase gradient field associated via Madelung transform with the field of classical velocities forms labyrinth-like structure. The macroscopic quantum state composed of periodically spaced counter-rotating BEC superfluid vortices has zero angular momentum and nonzero rotational energy.

nlin.PS↗
arXiv2012

Superfluid rotation sensor with helical laser trap

The macroscopic quantum states of the dilute bosonic ensemble in helical laser trap at the temperatures about $10^{-6}\bf {K}$ are considered in the framework of the Gross-Pitaevskii equation. The helical interference pattern is composed of the two counter propagating Laguerre-Gaussian optical vortices with opposite orbital angular momenta $\ell \hbar$ and this pattern is driven in rotation via angular Doppler effect. Macroscopic observables including linear momentum and angular momentum of the atomic cloud are evaluated explicitly. It is shown that rotation of reference frame is transformed into translational motion of the twisted matter wave. The speed of translation equals the group velocity of twisted wavetrain $V_z= Ω\ell/ k$ and alternates with a sign of the frame angular velocity $Ω$ and helical pattern handedness $\ell$. We address detection of this effect using currently accessible laboratory equipment with emphasis on the difference between quantum and classical fluids.

cond-mat.other↗
arXiv2011

Cold matter trapping via slowly rotating helical potential

We consider the cold bosonic ensemble trapped by a helical interference pattern in the optical \textit{loop} scheme. This rotating helical potential is produced by the two slightly detuned counter propagating Laguerre-Gaussian laser beams with counter directed orbital angular momenta $\pm \ell\hbar $. The detuning $δω$ may occur due to rotational Doppler effect. The superfluid hydrodynamics is analysed for the large number of trapped atoms in Thomas-Fermi approximation. For the highly elongated trap the Gross-Pitaevskii equation is solved in a slowly varying envelope approximation. The speed of axial translation and angular momenta of interacting atomic cloud are evaluated. In the $T \rightarrow 0$ limit the angular momentum of the helical cloud is expected to be zero while toroidal trapping geometry leads to $2\ell \hbar$ angular momentum per trapped atom.

physics.atom-ph↗
arXiv2011

Rotational Doppler shift of the phase-conjugated photon

The rotational Doppler shift of a photon with orbital angular momentum $\pm \ell \hbar$ is shown to be an even multiple of the angular frequency $Ω$ of the reference frame rotation when photon is reflected from the phase-conjugating mirror. We consider the one-arm phase-conjugating interferometer which contains $N$ Dove prisms or other angular momentum altering elements rotating in opposite directions. When such interferometer is placed in the rotating vehicle the $δω=4 (N+1/2) \ell \cdot Ω$ rotational Doppler shift appears and rotation of the helical interference pattern with angular frequency $δω/{2 \ell}$ occurs. The accumulation of angular Doppler shift via successive passage through the $N$ image-inverting prisms is due to the phase conjugation, for conventional parabolic retroreflector the accumulation is absent. The features of such a vortex phase conjugating interferometry at the single photon level are discussed.

quant-ph↗
arXiv2010

Laser Singular Theta-Pinch

The interaction of the two counter-propagating ultrashort laser pulses with a singular wavefronts in the thin slice of the underdense plasma is considered. It is shown that ion-acoustic wave is excited via Brillouin three-wave resonance by corkscrew interference pattern of a paraxial singular laser beams. The orbital angular momentum carried by light is transferred to plasma ion-acoustic vortex. The rotation of the density perturbations of electron fluid is the cause of helical current which produce the kilogauss axial quasi-static magnetic field. The exact analytical configurations are presented for an ion-acoustic current field and magnetic induction. The range of experimentally accessible parameters is evaluated.

nlin.PS↗
arXiv2009

Twisted speckle entities inside wavefront reversal mirrors

The previously unknown property of the optical speckle pattern reported. The interference of a speckle with an oppositely moving phase-conjugated speckle wave produces a randomly distributed ensemble of a twisted entities (ropes) surrounding optical vortex lines. These entities appear in a wide range of randomly chosen speckle parameters inside the phase-conjugating mirrors regardless to an internal physical mechanism of the wavefront reversal. These numerically generated interference patterns are relevant to a Brillouin $\bf PC$-mirrors and to a four-wave mixing $\bf PC$-mirrors based upon laser trapped ultracold atomic cloud.

nlin.PS↗
arXiv2008

Angular Momentum of a Photon and Phase Conjugation

Using the concept of an ideal phase-conjugating mirror we demonstrate that regardless of internal physical mechanism the phase-conjugation of a singular laser beam is accompanied by excitation within the mirror of internal waves which carry doubled angular momentum in order to match angular momentum conservation. For a Brillouin hypersound wavefront-reversal mirror this means that each elementary optical vortex belonging to a speckle pattern emits an acoustical vortex wave with doubled topological charge. The exact spatial profiles of light intensity and the intensity of hypersound in the vicinity of the phase singularity are obtained. These spiral profiles have a form of double helix which rotates with the frequency of sound. An optoacoustic experiment is proposed for visualization of the wavefront reversal of twisted optical beams and tunable twisted sound generation.

nlin.PS↗