Transverse modulational instabilities of counterpropagating solitons in photorefractive crystals

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.

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.

Counterpropagating solitons at boundary of photonic lattices

We study numerically the interaction of two counterpropagating (CP) optical beams near the boundary of a truncated one-dimensional photonic lattice. We demonstrate that the mutual coupling of beams suppresses the effective repulsion from the lattice edge, resulting in the formation of CP surface solitons. Such localized beams may propagate in the same, as well as in neighboring, waveguides. We also reveal that the lattice disorder reduces substantially the threshold power for the formation of CP surface states.

Counterpropagating nematicons in bias-free liquid crystals

We experimentally investigate the interaction of two counter-propagating spatial optical solitons (nematicons) in bias-free nematic liquid crystals. We demonstrate the existence of vector solitons composed of two nematicons propagating in opposite directions and analyze their stability versus relative distance and input power.We observe the dynamic instability of two counterpropagating nematicons in the form of time-dependent splitting and spatial entanglement.

Counterpropagating surface solitons in two-dimensional photonic lattices

We study interaction of counterpropagating beams in truncated two-dimensional photonic lattices induced optically in photorefractive crystals, and demonstrate the existence of counterpropagating surface solitons localized in the lattice corners and at the edges. We display intriguing dynamical properties of such composite optical beams and reveal that the lattice surface provides a strong stabilization effect on the beam propagation. We also observe dynamical instabilities for stronger coupling and longer propagation distances in the form of beam splitting. No such instabilities exist in the single beam surface propagation.

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.

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.

Two dimensional counterpropagating spatial solitons in photorefractive crystals

We demonstrate experimentally the existence of two transverse-dimensional counterpropagating (CP) incoherent spatial solitons in a 5 x 5 x 23 mm SBN:60Ce photorefractive crystal and investigate their dynamical behavior. We carry out numerical simulations that confirm our experimental findings. Substantially different behavior from the copropagating incoherent solitons is found. A symmetry breaking transition from stable overlapping CP solitons to unstable transversely displaced CP solitons is observed. We perform linear stability analysis that predicts the threshold for the split-up transition, in qualitative agreement with numerical simulations and experimental results.

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.

Dynamic instability of self-induced bidirectional waveguides in photorefractive media

We report on the experimental observation of a dynamic instability in the interaction of counterpropagating self-trapped beams in a photorefractive strontium barium niobate crystal. While the interaction of copropagating spatial optical solitons exhibits only transient dynamics, resulting in a final steady state, the counterpropagating geometry supports a dynamic instability mediated by intrinsic feedback. Experimental observations are compared with and found to be in qualitative agreement with numerical simulations.