Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays

We demonstrate that both the linear (diffraction) and the nonlinear dynamics of two-dimensional waveguide arrays are considerably more complex and versatile than their one-dimensional counterparts. The discrete diffraction properties of these arrays can be effectively altered, depending on the propagation Bloch k-vector within the first Brillouin zone of the lattice. In general, this diffraction behavior is anisotropic and therefore permits the existence of a new class of discrete elliptic solitons in the nonlinear regime.     

Observation of discrete solitons in optically induced real time waveguide arrays

We report the first experimental observation of discrete solitons in an array of optically induced waveguides. The waveguide lattice is induced in real time by illuminating a photorefractive crystal with a pair of interfering plane waves. We demonstrate two types of bright discrete solitons: in-phase self-localized states and the staggered (pi out-of-phase) soliton family. This experiment is the first observation of bright staggered solitons in any physical system. Our scheme paves the way for reconfigurable focusing and defocusing photonic lattices where low-power (mW) discrete solitons can be thoroughly investigated.     

Airy trajectory engineering in dynamic linear index potentials

We study the propagation of Airy beams in transversely linear index potentials with a gradient that is dynamically changing along the propagation direction. We find exact solutions in the case of Airy and apodized (Gaussian and exponentially) Airy beams in 1+1 and 2+1 dimensions. More important, we find that the Airy beam can follow any predefined path, in which case the potential gradient is determined as a function of this path.     

Exact X-wave solutions of the hyperbolic nonlinear Schrödinger equation with a supporting potential

We find exact solutions of the two- and three-dimensional nonlinear Schrödinger equation with a supporting potential. We focus in the case where the diffraction operator is of the hyperbolic type and both the potential and the solution have the form of an X-wave. Following similar arguments, several additional families of exact solutions can also can be found irrespectively of the type of the diffraction operator (hyperbolic or elliptic) or the dimensionality of the problem. In particular we present two such examples: The one-dimensional nonlinear Schrödinger equation with a stationary and a “breathing” potential and the two-dimensional nonlinear Schrödinger with a Bessel potential.     

Bessel X waves in two- and three-dimensional bidispersive optical systems

We show that new families of two- and three-dimensional nondiffracting Bessel X waves are possible in linear bidispersive optical systems. These X waves can be observed in both bulk and waveguide configurations as well as in photonic crystal lattices that simultaneously exhibit normal and anomalous dispersive-diffractive properties in different spatial or spatiotemporal coordinates.     

Fourier-space generation of abruptly autofocusing beams and optical bottle beams

We demonstrate analytically and experimentally that a circular abruptly autofocusing (AAF) Airy beam can be generated by Fourier-transforming an appropriately apodized Bessel beam whose radial oscillations are chirped by a cubic phase term. Depending on the relation between the chirp rate and the focal distance of the Fourier-transforming lens, it is possible to generate AAF beams with one or two foci, the latter case leading to the formation of an elegant paraboloid optical bottle.     

Reconfigurable 3D photonic lattices by optical induction for optical control of beam propagation

We report on our recent theoretical and experimental studies of three-dimensional (3D) photonic lattice structures which are established in a bulk nonlinear crystal by employing different optical induction techniques. These 3D photonic lattices bring about new opportunities for controlling the flow of light via coupling engineering originated from the lattice modulation along the beam propagation direction. By fine tuning the lattice parameters, we observe a host of unusual behaviors of beam propagation in such reconfigurable 3D lattices, including enhanced discrete diffraction, light tunneling inhibition—better known as coherent destruction of tunneling (CDT), anomalous diffraction, negative refraction, as well as CDT-based image transmission. In addition, we propose and demonstrate a new way of creating 3D ionic-type photonic lattices by controlled Talbot effect.     

White-light solitons

Optical spatial solitons made from incoherent white light were experimentally observed in 1997 by Mitchell and Segev [Nature (London) 387, 880 (1997)]. We present what is believed to be the first theory describing these solitons and find the characteristic features of their spatiotemporal coherence properties and their temporal power spectrum.     

Caustic design in periodic lattices

We study curved trajectory dynamics and design in discrete array settings. We find that beams with power law phases produce curved caustics associated with the fold and cusp type catastrophes. A parabolic phase produces a focus that suffers from spherical aberrations. More important, we find that by designing the initial phase or wavefront of the beam we can construct trajectories with pure power law caustics as well as aberration-free focusing of discrete waves.     

Trapping and guiding microparticles with morphing autofocusing Airy beams

We observe optical trapping and manipulation of dielectric microparticles using autofocusing radially symmetric Airy beams. This is accomplished by exploiting either the inward or outward transverse acceleration associated with their chirped wavefronts. We experimentally demonstrate, for the first time to our knowledge, that such Airy beams morph into nondiffracting Bessel beams in their far-field. Furthermore, the ability of guiding and transporting microparticles along the primary rings of this class of beams is explored.