Milan S. Petrović

Transverse modulational instabilities of counterpropagating solitons in photorefractive crystals

We study numerically the counterpropagating vector solitons in SBN:60 photorefractive crystals. A simple theory is provided for explaining the symmetry-breaking transverse instability of these solitons. Phase diagram is produced that depicts the transition from stable counterpropagating solitons to bidirectional waveguides to unstable optical structures. Numerical simulations are performed that predict novel dynamical beam structures, such as the standing-wave and rotating multipole vector solitonic clusters. For larger coupling strengths and/or thicker crystals the beams form unstable self-trapped optical structures that have no counterparts in the copropagating geometry.

Automatic Fourier transform and self-Fourier beams due to parabolic potential

Abstract We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.

Spatiotemporal optical instabilities in nematic solitons

We investigate numerically the propagation of self-trapped optical beams in nematic liquid crystals. Our analysis includes both spatial and temporal behavior. We display the formation of stable solitons in a narrow threshold region of beam intensities for fixed birefringence, and depict their spatiotemporal instabilities as the input intensity and the birefringence are increased. We demonstrate the breathing and filamentation of solitons above the threshold with increasing input intensity, and discover a convective instability with increasing birefringence. We consider the propagation of complex beam structures in nematic liquid crystals, such as dipoles, beam arrays, and vortices.

Counterpropagating self-trapped beams in photorefractive crystals

A time-dependent model for the formation of self-trapped optical beams in photorefractive media by counterpropagating laser beams is analysed. It is shown that dynamically the beams may form stable steady-state structures or display periodic and irregular temporal behaviour. Steady-state solutions of non-uniform cross section are found, representing a general class of self-trapped waveguides, that include counterpropagating spatial vector solitons as a particular case. Two critical curves are identified in the plane of parameters, the first one separating vector solitons from the stable bidirectional waveguides and the second one separating stable waveguides from the unstable ones. Dynamically stable rotating beam structures are discovered that have no analogues in the usual steady-state theory of spatial solitons.

Counterpropagating self-trapped beams in optical photonic lattices.

Dynamical properties of counterpropagating (CP) mutually incoherent self-trapped beams in optically induced photonic lattices are investigated numerically. A local model with saturable Kerr-like nonlinearity is adopted for the photorefractive media, and an optically generated two-dimensional fixed photonic lattice introduced in the crystal. Different incident beam structures are considered, such as Gaussians and vortices of different topological charge. We observe spontaneous symmetry breaking of the head-on propagating Gaussian beams as the coupling strength is increased, resulting in the splitup transition of CP components. We see discrete diffraction, leading to the formation of discrete CP vector solitons. In the case of vortices, we find beam filamentation, as well as increased stability of the central vortex ring. A strong pinning of filaments to the lattice sites is noted. The angular momentum of vortices is not conserved, either along the propagation direction or in time, and, unlike the case without lattice, the rotation of filaments is not as readily observed.

Dynamics of counterpropagating multipole vector solitons

Dynamical behavior of counterpropagating (CP) mutually incoherent vector solitons in a 5 x 5 x 23 mm SBN:60Ce photorefractive crystal is investigated. Experimental study is carried out, displaying rich dynamics of three-dimensional CP solitons and higher-order multipole structures, and a theory formulated that is capable of capturing such dynamics. We find that our numerical simulations agree well with the experimental findings for various CP beam structures. Linear stability analysis is also performed, predicting a threshold for the modulational instability of CP beams, and an appropriate control parameter is identified. We attempt at utilizing these results to CP solitons, but find only qualitative agreement with the numerical simulations and experimental findings. However, when broader hyper-Gaussian CP beams are used in simulations, an improved agreement with the theory is obtained.

Unified method for solution of wave equations in photorefractive media

A unified but simple method for solution of four-wave mixing equations in photorefractive crystals in both transmission and reflection geometries is presented. The method is applied to the problems of double phase conjugation and two-wave mixing with crossed polarizations in cubic crystals.

Counterpropagating mutually incoherent vortex-induced rotating structures in optical photonic lattices

Rotational properties of counterpropagating mutually incoherent self-trapped vortex beams in optically induced fixed photonic lattices are investigated numerically. Different lattice structures are considered, such as hexagonal/trigonal and circular photonic lattices. Periodically increasing propagation distance, regular nonlocal rotation of vortex filaments is observed for hexagonal photonic lattice. For circular photonic lattices with negative defect, we discover novel types of rotating beam structures that have no counterparts in the case without the lattice. Observed rotating structures are stable in the presence of noise.

Exact solution to photorefractive two-wave mixing with arbitrary modulation depth

We obtain analytical solution to the slowly varying envelope wave equations describing two-wave mixing in photorefractive crystals with arbitrary dependence of the gain and absorption on the two-wave fringe modulation depth. We introduce a novel form of the correction function for the space charge field that offers an improved agreement with the experiment.

Optical photorefractive flip-flop oscillator

Abstract Using two interconnected four-wave mixing ring resonators with two photorefractive crystals included as active and passive intracavity optical elements, we display the operation of an all-optical flip-flop oscillator.