Discrete light localization in one dimensional nonlinear lattices with arbitrary non locality

We model discrete spatial solitons in a periodic nonlinear medium encompassing any degree of transverse non locality. Making a convenient reference to a widely used material -nematic liquid crystals-, we derive a new form of the discrete nonlinear Schrodinger equation and find a novel family of discrete solitons. Such self-localized solutions in optical lattices can exist with an arbitrary degree of imprinted chirp and a have breathing character. We verify numerically that both local and non local discrete light propagation and solitons can be observed in liquid crystalline arrays.Comment: Extended version with 6 pages and 4 Figures, to appear in Phys. Rev.

Breather solitons in highly nonlocal media

We investigate the breathing of optical spatial solitons in highly nonlocal media. Generalizing the Ehrenfest theorem, we demonstrate that oscillations in beam width obey a fourth-order ordinary differential equation. Moreover, in actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell [Science \textbf{276}, 1538 (1997)] cannot accurately describe the dynamics of self-confined beams as the transverse size oscillations have a period which not only depends on power but also on the initial width. Modeling the nonlinear response by a Poisson equation driven by the beam intensity we verify the theoretical results against numerical simulations.Comment: 7 pages, 4 figures, resubmitted to Physical Review

Electromagnetic confinement via spin-orbit interaction in anisotropic dielectrics

We investigate electromagnetic propagation in uniaxial dielectrics with a transversely varying orientation of the optic axis, the latter staying orthogonal everywhere to the propagation direction. In such a geometry, the field experiences no refractive index gradients, yet it acquires a transversely-modulated Pancharatnam-Berry phase, that is, a geometric phase originating from a spin-orbit interaction. We show that the periodic evolution of the geometric phase versus propagation gives rise to a longitudinally-invariant effective potential. In certain configurations, this geometric phase can provide transverse confinement and waveguiding. The theoretical findings are tested and validated against numerical simulations of the complete Maxwell's equations. Our results introduce and illustrate the role of geometric phases on electromagnetic propagation over distances well exceeding the diffraction length, paving the way to a whole new family of guided waves and waveguides which do not rely on refractive index tailoring.Comment: 16 pages, 4 figure

Incoherent interaction of nematicons in bias-free liquid-crystal cells

We study experimentally the propagation dynamics and interaction of a pair of mutually incoherent nematicons: spatial optical solitons in nematic liquid crystals. In contrast to earlier studies, we consider a bias-free liquid-crystal cell and compare the soliton interaction in copropagating and counterpropagating geometries. We analyze the dependence of nematicon interaction on input power and observe a direct manifestation of a long-range nonlocal nonlinearity. Attraction of counterpropagating solitons requires higher powers and longer relaxation times than that of copropagating nematicons due to losses-induced power asymmetry of counterpropagating nematicons.Comment: 5 pages, z figure

Quadratic phase matching in slot waveguides

We analyze phase matching with reference to frequency doubling in nanosized quadratic waveguides encompassing form birefringence and supporting cross-polarized fundamental and second-harmonic modes. In an AlGaAs rod with an air void, we show that phase-matched second-harmonic generation could be achieved in a wide spectral range employing state-of-the-art nanotechnology.Comment: 3 pages, 4 figure