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.Comment: 4 pages, 3 figures, submitted to referred journa

Twisted superfluids in moving frame

{Helical waveguide filled by superfluid is shown to transform the linear displacements of reference frame $\vec V$ into rotations of atomic ensemble and vise versa rotations of reference frame $\vec \Omega_{\oplus}$ are the cause of linear displacements of ensemble. In mean-field Gross-Pitaevskii equation with a weakly modulated gravitation the exact solutions for macroscopic wavefunction $\Psi$ demonstrate the emergence of $redshift$ phase factor being proportional to the population of condensate $N_a$. is shown to have}Comment: 6 pages, 2 figures , submitted to referred journa

Optical counterpart of the Foucault pendulum

The twin beam vortex interferometer with phase-conjugating mirror in rotating reference frame is analyzed. Using the concept of the $ideal$ phase-conjugating mirror it is shown that motion of helical interference pattern may be used for detection of the slow rotations. The pattern motion is due to exchange of angular momenta between photons and interferometer. The conditions of experimental realization of such rotation sensor are discussed and $scaling$ relations for geometric parameters, coherent backscattering and angular momenta transformations are obtained.Comment: 9 pages,3 figures, submitted to referred journa