Dragana M. Jović

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.

Anderson localization of light in PT -symmetric optical lattices

Anderson localization (AL) of light is investigated numerically in a disordered parity-time (PT)-symmetric potential, in the form of an optical lattice. The lattice is recorded in a nonlinear medium with Kerr nonlinearity. We demonstrate enhancement of light localization in a PT-symmetric lattice, as compared to the localization in the corresponding real lattice. The effect of strength of the gain-loss component in the PT lattice on various regimes of AL is also discussed. It is found that the localization exists and is further enhanced above the threshold strength of the imaginary part of the potential. The influence of nonlinearity and disorder level on the transverse localization of light in such a complex-valued potential is addressed.

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.

Counterpropagating beams in nematic liquid crystals.

The behavior of counterpropagating self-trapped optical beam structures in nematic liquid crystals is investigated. A time-dependent model for the beam propagation and the director reorientation in a nematic liquid crystal is numerically treated in three spatial dimensions and time. We find that the stable vector solitons can only exist in a narrow threshold region of control parameters. Below this region the beams diffract, above they self-focus into a series of focal spots. Spatiotemporal instabilities are observed as the input intensity, the propagation distance, and the birefringence are increased. We demonstrate undulation, filamentation, and convective dynamical instabilities of counterpropagating beams. Qualitatively similar behavior as of the copropagating beams is observed, except that it happens at lower values of control parameters.

Gaussian-induced rotation in periodic photonic lattices

We numerically investigate time-dependent rotation of counterpropagating mutually incoherent self-trapped Gaussian beams in periodic optically induced fixed photonic lattices. We demonstrate the relation between such rotation and less confined discrete solitonic solutions.

Counterpropagating optical vortices in photorefractive crystals.

We present a comprehensive numerical study of (2+1)D counterpropagating incoherent vortices in photorefractive crystals, in both space and time. We consider a local isotropic dynamical model with Kerr-type saturable nonlinearity, and identify the corresponding conserved quantities. We show, both analytically and numerically, that stable beam structures conserve angular momentum, as long as their stability is preserved. As soon as the beams loose stability, owing to radiation or non-elastic collisions, their angular momentum becomes non-conserved. We discover novel types of rotating beam structures that have no counterparts in the copropagating geometry. We consider the counterpropagation of more complex beam arrangements, such as regular arrays of vortices. We follow the transition from a few beam propagation behavior to the transverse pattern formation dynamics.

Vortex solitons at the boundaries of photonic lattices.

Using numerical analysis we demonstrate the existence of vortex solitons at the edge and in the corners of two-dimensional triangular photonic lattice. We develop a concise picture of their behavior in both single-propagating and counterpropagating beam geometries. In the single-beam geometry, we observe stable surface vortex solitons for long propagation distances only in the form of discrete six-lobe solutions at the edge of the photonic lattice. Other observed solutions, in the form of ring vortex and discrete solitons with two or three lobes, oscillate during propagation in a way indicating the exchange of power between neighboring lobes. For higher beam powers we observe dynamical instabilities of surface vortex solitons and study orbital angular momentum transfer of such vortex states. In the two-beam counterpropagating geometry, all kinds of vortex solutions are stable for propagation distances of the order of typical experimental crystal lengths.

Defect-controlled Anderson localization of light in photonic lattices

The transverse localization of light in a disordered photonic lattice with a central defect is analyzed numerically. The effect of different input beam widths on various regimes of Anderson localization is investigated. The inclusion of a defect enhances the localization of both narrow and broad beams, as compared to the lattice with no defect. But, in the case of a broad beam a higher disorder level is needed to reach the same localization as for a narrow input beam. It is also investigated how the transverse localization of light in such geometries depends on both the strength of disorder and the strength of nonlinearity in the system. While in the linear regime the localization is most pronounced in the lattice with the defect, in the nonlinear regime this is not the case.