Accelerating diffraction-free beams in photonic lattices

Propagation of waves in high Brillouin zones: Chaotic branched flow and stable superwires

We report unexpected classical and quantum dynamics of a wave propagating in a periodic potential in high Brillouin zones. Branched flow appears at wavelengths shorter than the typical length scale of the ordered periodic structure and for energies above the potential barrier. The strongest branches remain stable indefinitely and may create linear dynamical channels, wherein waves are not confined directly by potential walls as electrons in ordinary wires but rather, indirectly and more subtly by dynamical stability. We term these superwires since they are associated with a superlattice.

Interaction of Airy-Gaussian beams in photonic lattices with defects

We investigate numerically the interaction between two finite Airy-Gaussian (AiG) beams in different media with the defected photonic lattices in one transverse dimension. We discuss that the beams with different intensities and phases launch into the different lattice structures but accelerate in opposite directions. During interactions, the interference fringe, breathers, and soliton pairs are observed. In the linear media, the initial deflection direction of the accelerated beams is changed by adjusting the phase shift and the beam interval. For a certain lattice period, the periodic interference fringe can form. A constructive or destructive interference can vary with the defect depth and phase shift. While the nonlinearity is introduced, the breathers is generated. Especially in the self-defocusing media, the appropriate AiG beam amplitude and lattice depth may lead to the formation of soliton pairs, On the contrary, the interaction of two Gaussian beams is diffraction.

Trajectory variations of optical Bloch oscillations for Airy beams in transversely and longitudinally modulated photonic lattices

We consider four types of modulated photonic lattices and numerically study the optical Bloch oscillations of Airy beams in these periodic structures. Our results demonstrate that in transversely modulated photonic lattices, the oscillation period increases and the amplitude reduces as the separation variation index increases. However, the increasing of the width variation index could lead to a consistent reduction of oscillation period and amplitude. On the other hand, in three kinds of longitudinally bent photonic lattices, the optical Bloch oscillation trajectories of Airy beams follow the waveguide shape perfectly within the whole propagation length. For another three kinds of refractive index longitudinally varied lattices, the optical Bloch oscillation period and amplitude are limited with the increasing of refractive index, contributing to the presentation of dramatically different Airy propagation trajectories. Our study proposes a new view to manipulate the Airy trajectory in periodic structures.

Non-diffracting optical Bloch oscillations in hexagonal photonic lattices

Light beams undergoing optical Bloch oscillations (OBOs) in two-dimensional (2D) photonic lattices suffer from severe diffraction along the perpendicular direction to the oscillation plane. In this paper, we propose and demonstrate that such diffraction could be suppressed in hexagonal photonic lattices via sophisticated managements of the discrete diffraction. By positioning the Fourier spectrum of the beam to a special region in the Brillouin zone, the light driven by the OBO experiences normal and anomalous diffractions alternatively, leading to a non-diffracting propagation for a long distance. We show that non-diffracting OBOs can be implemented not only for Gaussian beam but also for other complex 2D beams including self-accelerating Airy beams and vortex beams. Our results provide novel insights into the diffraction or dispersion engineering of waves in periodic structures.

Nonlinear evolution of Airy-like beams generated by modulated waveguide arrays

We numerically study the formation of modulated waveguide generated Airy-like beams and their subsequent evolution in homogeneous medium. The results show that the Airy-like beams could be generated from narrow Gaussian beams propagating in one-dimensional transverse separation modulated unbent, cosine bent, or logarithm bent waveguide arrays, respectively. The waveguide-generated Airy-like beams maintain their characteristics when propagating without nonlinearity or under the self-defocusing nonlinearity in homogeneous medium, while the beams are distorted under the self-focusing nonlinearity. The deformation depends on the waveguide bending and the outgoing angles of the Airy-like beams. Our results provide a new way to generate and manipulate the Airy-like beam.

Soliton formation by decelerating interacting Airy beams

We demonstrate a new type of soliton formation arising from the interaction of multiple two-dimensional Airy beams in a nonlinear medium. While in linear regime, interference effects of two or four spatially displaced Airy beams lead to accelerated intensity structures that can be used for optical induction of novel light guiding refractive index structures, the nonlinear cross-interaction between the Airy beams decelerates their bending and enables the formation of straight propagating solitary states. Our experimental results represent an intriguing combination of two fundamental effects, accelerated optical beams and nonlinearity, together enable novel mechanisms of soliton formation that will find applications in all-optical light localization and switching architectures. Our experimental results are supported by corresponding numerical simulations.

Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient

We theoretically report the existence of optical Bloch oscillations (BO) of an Airy beam in a one-dimensional optically induced photonic lattice with a linear transverse index gradient. The Airy beam experiencing optical BO shows a more robust non-diffracting feature than its counterparts in free space or in a uniform photonic lattice. Interestingly, a periodical recurrence of Airy shape accompanied with constant alternation of its acceleration direction is also found during the BO. Furthermore, we demonstrate that the period and amplitude of BO of an Airy beam can be readily controlled over a wide range by varying the index gradient and/or the lattice period. Exploiting these features, we propose a scheme to rout an Airy beam to a predefined output channel without losing its characteristics by longitudinally modulating the transverse index gradient.