We demonstrate both experimentally and theoretically controlled acceleration of one- and two-dimensional Airy beams in optically induced refractive-index potentials. Enhancement as well as reduction of beam acceleration are realized by changing the index gradient, while the beam shape is maintained during propagation through the linear optical potential. Our results of active acceleration manipulation in graded media are pertinent to Airy-type beam propagation in various environments.

We study both numerically and experimentally the acceleration and propagation dynamics of 2D Airy beams with arbitrary initial angles between their "two wings." Our results show that the acceleration of these generalized 2D Airy beams strongly depends on the initial angles and cannot be simply described by the vector superposition principle (except for the normal case of a 90° angle). However, as a result of the "Hyperbolic umbilic" catastrophe (a two-layer caustic), the main lobes of these 2D Airy beams still propagate along parabolic trajectories even though they become highly deformed. Under such conditions, the peak intensity (leading energy flow) of the 2D Airy beams cannot be confined along the main lobe, in contrast to the normal 90° case. Instead, it is found that there are two parabolic trajectories describing the beam propagation: one for the main lobe, and the other for the peak intensity. Both trajectories can be readily controlled by varying the initial wing angle. Due to their self-healing property, these beams tend to evolve into the well-known 1D or 2D Airy patterns after a certain propagation distance. The theoretical analysis corroborates our experimental observations, and explains clearly why the acceleration of deformed Airy beams increases with the opening of the initial wing angle.

Abstract:We demonstrate self-trapping of singly-charged vortices at the surface of an optically induced two-dimensional photonic lattice. Under appropriate conditions of self-focusing nonlinearity, a singly-charged vortex beam can self-trap into a stable semi-infinite gap surface vortex soliton through a four-site excitation. However, a single-site excitation leads to a quasi-localized state in the first photonic gap, and our theoretical analysis illustrates that such a bandgap surface vortex soliton is always unstable. Our experimental results of stable and unstable topological surface solitons are corroborated by direct numerical simulations and linear stability analysis.

We report the first experimental demonstration of the so-called three-Airy beams. Such beams represent a two-dimensional field that is a product (rather than simple superposition) of three Airy beams. Our experiments show that, in contrast to conventional Airy beams, this new family of Airy beams can be realized even without the use of truncation by finite apertures. Furthermore, we study linear and nonlinear propagation of the three-Airy beams in a photorefractive medium. It is found that a three-Airy beam tends to linearly diffract into a super-Gaussian-like beam, while under nonlinear propagation it either turns into three intensity spots with a self-defocusing nonlinearity or evolves into a self-trapped channel with a self-focusing nonlinearity.

We demonstrate both theoretically and experimentally that a nonlinear beam can be reflected by a negative defect in a photonic lattice if the incident angle is below a threshold value. Above this threshold angle, the beam simply passes through the defect. This phenomenon occurs in both one-and two-dimensional photonic lattices, and it provides a way to use the incident angle to control beam propagation in a lattice network. If the defect is absent or positive, no evident transition from reflection to transmission occurs. These nonlinear phenomena are also compared with linear nondiffracting-beam propagation in a photonic lattice with a defect, and both similarities and differences are observed. In addition, some important features in linear and nonlinear beam propagations are explained analytically by using a linear model with a delta-function defect.