Nikolaos K. Efremidis

Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices

Nonlinear periodic lattices occur in a large variety of systems, such as biological molecules, nonlinear optical waveguides, solid-state systems and Bose–Einstein condensates. The underlying dynamics in these systems is dominated by the interplay between tunnelling between adjacent potential wells and nonlinearity. A balance between these two effects can result in a self-localized state: a lattice or ‘discrete’ soliton. Direct observation of lattice solitons has so far been limited to one-dimensional systems, namely in arrays of nonlinear optical waveguides. However, many fundamental features are expected to occur in higher dimensions, such as vortex lattice solitons, bright lattice solitons that carry angular momentum, and three-dimensional collisions between lattice solitons. Here, we report the experimental observation of two-dimensional (2D) lattice solitons. We use optical induction, the interference of two or more plane waves in a photosensitive material, to create a 2D photonic lattice in which the solitons form. Our results pave the way for the realization of a variety of nonlinear localization phenomena in photonic lattices and crystals. Finally, our observation directly relates to the proposed lattice solitons in Bose–Einstein condensates, which can be observed in optically induced periodic potentials.

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.

Observation of abruptly autofocusing waves

We report on the experimental observation of abruptly autofocusing waves. This interesting family of wave packets has been realized by using a radially symmetric Airy intensity distribution. As demonstrated in our experiments, these waves can exhibit unusual features, such as the ability to autofocus by following a parabolic trajectory toward their focus.

Spatial photonics in nonlinear waveguide arrays

The recent proposal of optical induction for producing nonlinear photonic lattices has revolutionized the study of nonlinear waves in waveguide arrays. In particular, it enabled the first observation of (2+1) dimensional lattice solitons, which were the first 2D solitons observed in any nonlinear periodic system in nature. Since then, progress has been rapid, with many fundamental discoveries made within the past two years. Here, we review our theoretical and experimental contributions to this effort.

Pre-engineered abruptly autofocusing beams

We introduce a new family of (2+1)D light beams with pre-engineered abruptly autofocusing properties. These beams have a circularly symmetric input profile that develops outward of a dark disk and oscillates radially as a sublinear-chirp signal, creating a series of concentric intensity rings with gradually decreasing width. The light rays involved in this process form a caustic surface of revolution that bends toward the beam axis at an acceleration rate that is determined by the radial chirp itself. The collapse of the caustic on the axis leads to a large intensity buildup right before the intended focus. This ray-optics interpretation provides valuable insight into the dynamics of abruptly autofocusing waves.

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.

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.

Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories

We experimentally demonstrate self-accelerating Bessel-like optical beams propagating along arbitrary trajectories in free space. With computer-generated holography, such beams are designed to follow different controllable trajectories while their main lobe transverse profiles remain nearly invariant and symmetric. Examples include parabolic, snake-like, hyperbolic, hyperbolic secant, and even three-dimensional spiraling trajectories. The self-healing property of such beams is also demonstrated. This new class of optical beams can be considered as a hybrid between accelerating and nonaccelerating nondiffracting beams that may find a variety of applications.

Bessel-like optical beams with arbitrary trajectories

A method is proposed for generating Bessel-like optical beams with arbitrary trajectories in free space. The method involves phase-modulating an optical wavefront so that conical bundles of rays are formed whose apexes write a continuous focal curve with pre-specified shape. These ray cones have circular bases on the input plane; thus their interference results in a Bessel-like transverse field profile that propagates along the specified trajectory with a remarkably invariant main lobe. Such beams can be useful as hybrids between non-accelerating and accelerating optical waves that share diffraction-resisting and self-healing properties.

Self-accelerating Airy Beams: Generation, Control, and Applications

Recently, a specific type of nondiffracting beams named self-accelerating Airy beams has attracted a great deal of interest due to their unique properties and many proposed applications in areas such as optical micromanipulation, plasma guidance, vacuum electron acceleration, and routing surface plasmon polaritons. In contradistinction with Bessel beams, Airy beams do not rely on simple conical superposition of plane waves, and they possess the properties of self-acceleration in addition to nondiffraction and self-healing. For the past few years, tremendous research work has been devoted to the study of Airy beams, from theoretical predictions to experimental observations, from linear control to nonlinear self-trapping, and from fundamental aspects to demonstrations of potential applications. In this chapter, we provide an overview on generation and control of Airy beams and recent developments in the area.