Using concept of an ideal phase-conjugating mirror we demonstrate that regardless to internal physical mechanism the phase-conjugation of singular laser beam is accompanied by excitation within mirror of internal waves which carry doubled angular momentum in order to match angular momentum conservation. For Brillouin hypersound wavefront-reversal mirror this means that each elementary optical vortex in a speckle pattern emits acoustical vortex wave with doubled topological charge. The exact spatial profiles of light intensity and intensity of hypersound in the vicinity of phase singularity are obtained. These spiral profiles have a form of a double helix which rotates with the speed of sound. The optoacoustic experiment is proposed for visualization of wavefront reversal of twisted optical beams and tunable twisted sound generation.The conservation of angular momentum (AM) J stems from isotropy of space [1]. In contrast to particles with nonzero rest mass m o , the decomposition of J for "spin" S and "orbital" L parts of photon's AM is referred to as ambiguous procedure [1,2]. The spin part S is related to polarization, i.e. time-dependent layout of electrical E and magnetic B fields of the "transverse" light wave. The orbital part (OAM) L is associated with helical staircase wavefront [2,3,4,5]. As a matter of fact a purely transverse light waves are abstraction because of a small but inevitable projections of E and B on direction of propagation, say Z-axis( fig.1). Indeed, the spin-orbital coupling of light occurs [6] due to vectorial interplay between longitudinal and transversal components of the fields E and B. The vectorial solutions of Maxwell's equations for propagation of a light spatially localized by a waveguide or emitted through finite aperture to free space give a strict relationship between longitudinal and transversal field components [7,8]. Nevertheless the approximate decomposition in the form J = S + L proved to be very fruitful for small curvatures of light wavefront, i.e. in paraxial wave approximation [2].The propagation of light in anisotropic medium changes the polarization and historically the spin of photon was observed firstly in Beth's experiment where

The rotational Doppler shift of a photon with orbital angular momentum ±ℓ 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. The one-arm phase-conjugating interferometer is considered. It 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)ℓ · Ω rotational Doppler shift appears and rotation of the helical interference pattern with angular frequency δω/2ℓ occurs. The accumulation of angular Doppler shift via successive passages 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. PACS numbers: 42.50.Tx 42.65.Hw 06.30.Gv 42.50.Dv

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 $\delta \omega$ 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.Comment: 6 pages, 1 figure, Physics Letters, A, November (2011), accepte

The spatiotemporal vortex lattices generated in high Fresnel number solid-state microchip lasers are studied in connection with Talbot phenomenon generic to spatially periodic electromagnetic fields. The spatial layout of light field is obtained via dynamical model based on Maxwell-Bloch equations for class-B laser, discrete Fox-Lee map with relaxation of inversion and static model based on superposition of copropagating Gaussian beams. The spatial patterns observed experimentally and obtained numerically are interpreted as nonlinear superposition of vortices with helicoidal phase dislocations. The usage of vortex labyrinths and Talbot lattices as optical dipole traps for neutral atoms is considered for the wavelength of trapping radiation in the range 0.98 $\div$ 2.79 $\mu m$. The separable optical trapping potential is mounted as a sum of array of vortex lines and additional parabolic subtrap. The factorization of macroscopic wavefunction have led to analytical solution of Gross-Pitaevski equation for ground state of ensemble of quantum particles trapped in vortex labyrinth and in spatially - periodic array of Gaussian beams.Comment: 10 pages 7 figure

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