We discuss a possibility of a pinning of quantized matter wave vortices by optical vortices in specially arranged optical
dipole traps. The vortex-antivortex optical arrays of rectangular symmetry are shown to transfer angular orbital
momentum to support "antiferromagnet-like" matter waves. The separable Hamiltonian for matter waves is proposed
which allows to factorize of the 3D - wavefunction exactly in a product of 1D - harmonic oscillator's ground state and 2D
- vortex-antivortex wavefunction. The wavefunction's phase gradient field associated with the field of classical
velocities via Madelung transformation forms labyrinth-like structure. The macroscopic wavefunction of periodically
spaced BEC superfluid vortices appears to be less influenced by decoherence.
.It is well known that ciode-pumped solid-state lasers exibit a high efficiency at low and moderate powers elny pumped by single laser diode aioig optical axis of the resonator. The futher lncreaslng c)f the power s being achieved now by diode array side--pumpiiig of neodilriiulrL rods. But the efficiency of this type of pumping iS somewhat smaller because of nonideal overlapping of the inversion profile and the desirable iasnn rnode(TEM )."i.. This drawback could be 0 0 avoided at moderate powers by the use of the end-pumping by diode-arrays or several diodes that results in a highly efficient fundamental-mode operation/2/. Nevertheless this kind of the end-pumping leads to significant heating of the active elelrient/3/, because the pumped region of the crystal should be sufficiently small to select TEM mode. These are the reasons 00 which limits the output power in the standard end-pumping scheme, although the use of the moving slabs and rotating disks could overcome the some of the above difficulties //3/ The alternative approach is to refuse from Gaussian beams paradigm and to select spatially periodic modes using the phenomenon of the seif-imaging/4/.
Il is shown numerically that in Talbot cavity being formed by a thin nonlinear amplifying layer and a pair of a flat imperfect mirrors the small phase distortions put a fundamental limitation on the size of aperture with in-phase lasing. This effect results in spreading of the far field distribution and it is not suppressed by plane wave injection.
Transverse effects in nonlinear optical devices are being widely investigated. Recently, synchronization of a laser set by means of the Talbot effect has been demonstrated experimentally. This paper considers a Talbot cavity formed by a solid-state amplifying laser separated from the output mirror by a free space interval. This approach involves the approximation of the nonlinear medium as a thin layer, within which the diffraction is negligible. The other part of a resonator is empty, and the wave field is transformed by the Fresnel-Kirchoff integral. As a result, the dynamics of the transverse (and temporal) structure is computed by a successively iterated nonlinear local map (one- or two-dimensional) and a linear nonlocal map (generally speaking, infinitely dimensional).
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