Vortex inverted pin beams: mitigation of scintillations in strong atmospheric turbulence.

We recently introduced a new class of optical beams with a Bessel-like transverse profile and increasing beam width during propagation, akin to an "inverted pin." Owing to their specially engineered distribution, these beams have shown remarkable performance in atmospheric turbulence. Specifically, inverted pin beams (PBs) were found to have a reduced scintillation index as compared to collimated or focused Gaussian beams as well as other types of pin beams especially in moderate to strong turbulence.

Statistical mechanics and pressure of composite multimoded weakly nonlinear optical systems.

Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear-wave settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to interactions between different frequencies and polarizations. The purpose of this work is to develop a thermodynamic theory that takes into account the synergistic action of multiple components.

Dalton's law of partial optical thermodynamic pressures in highly multimoded nonlinear photonic systems.

We show that in highly multimoded nonlinear photonic systems, the optical thermodynamic pressures emerging from different species of the optical field obey Dalton's law of partial pressures. In multimode settings, the optical thermodynamic pressure is defined as the conjugate to the extensive variable associated with the system's total number of modes and is directly related to the actual electrodynamic radiation forces exerted at the physical boundaries of the system. Here, we extend this notion to photonic configuration supporting different species of the optical field.

Nature of Optical Thermodynamic Pressure Exerted in Highly Multimoded Nonlinear Systems.

The theory of optical thermodynamics provides a comprehensive framework that enables a self-consistent description of the intricate dynamics of nonlinear multimoded photonic systems. This theory, among others, predicts a pressurelike intensive quantity (p[over ^]) that is conjugate to the system's total number of modes (M)-its corresponding extensive variable. Yet at this point, the nature of this intensive quantity is still nebulous.

Inverted pin beams for robust long-range propagation through atmospheric turbulence.

We introduce a new, to the best of our knowledge, class of optical beams, which feature a spatial profile akin to an "inverted pin." In particular, we asymptotically find that close to the axis, the transverse amplitude profile of such beams takes the form of a Bessel function with a width that gradually increases during propagation. We examine numerically the behavior of such inverted pin beams in turbulent environments as measured via the scintillation index and show that they outperform Gaussian beams (collimated and focused) as well as Bessel beams and regular pin beams, which are all optimized, especially in the moderate and strong fluctuation regimes.

Tunable self-similar Bessel-like beams of arbitrary order.

We predict that Bessel-like beams of arbitrary integer order can exhibit a tunable self-similar behavior (that take an invariant form under suitable stretching transformations). Specifically, by engineering the amplitude and the phase on the input plane in real space, we show that it is possible to generate higher-order vortex Bessel-like beams with fully controllable radius of the hollow core and maximum intensity during propagation. In addition, using a similar approach, we show that it is also possible to generate zeroth-order Bessel-like beams with controllable beam width and maximum intensity.

Independent amplitude and trajectory/beam-width control of nonparaxial beams.

We show that it is possible to generate non-paraxial optical beams with pre-engineered trajectories and designed maximum amplitude along these trajectories. The independent control of these two degrees of freedom is made possible by engineering both the amplitude and the phase of the optical wave on the input plane. Furthermore, we come to the elegant conclusion that the beam width depends solely on the local curvature of the trajectory.

Observation of microscale nonparaxial optical bottle beams.

We predict and experimentally observe three-dimensional microscale nonparaxial optical bottle beams based on the generation of a caustic surface under revolution. Such bottle beams exhibit high contrast between the surrounding surface and the effectively void interior. Via caustic engineering, we can precisely control the functional form of the high-intensity surface to achieve microscale bottle beams with longitudinal and transverse dimensions of the same order of magnitude.

Spatiotemporal diffraction-free pulsed beams in free-space of the Airy and Bessel type.

We investigate the dynamics of spatiotemporal optical waves with one transverse dimension obtained as the intersections of the dispersion cone with a plane. We show that, by appropriate spectral excitations, the three different types of conic sections (elliptic, parabolic, and hyperbolic) can lead to optical waves of the Bessel, Airy, and modified Bessel types, respectively. We find closed form solutions that accurately describe the wave dynamics and unveil their fundamental properties.

Nonlinear imaging in photonic lattices.

We show that nonlinear imaging is possible in periodic waveguide configurations, provided that we use two different segments of nonlinear media with opposite signs of the Kerr nonlinearity with, in general, no other restriction about their magnitudes. The second medium is used to implement effective "reverse propagation." A main ingredient in achieving nonlinear imaging is the control of the sign and the amplitude of the coupling coefficient.

Nonparaxial abruptly autofocusing beams.

We study nonparaxial autofocusing beams with pre-engineered trajectories. We consider the case of linearly polarized electric optical beams and examine their focusing properties, such as contrast, beam width, and numerical aperture. Such beams are associated with larger intensity contrasts, can focus at smaller distances, and have smaller spot sizes as compared to the paraxial regime.

Modifying the optical path in a nonlinear double-slit experiment.

In this Letter, we study a nonlinear interferometric setup based on diffraction, rather than beam combining. It consists of a nonlinear analog of Young's double-slit experiment where a nonlinear material is placed exactly after one of the slits. The presence of nonlinearity breaks the transverse spatial symmetry of the system and, thus, modifies the optical path.

Curved singular beams for three-dimensional particle manipulation.

For decades, singular beams carrying angular momentum have been a topic of considerable interest. Their intriguing applications are ubiquitous in a variety of fields, ranging from optical manipulation to photon entanglement, and from microscopy and coronagraphy to free-space communications, detection of rotating black holes, and even relativistic electrons and strong-field physics. In most applications, however, singular beams travel naturally along a straight line, expanding during linear propagation or breaking up in nonlinear media.

Closed-form expressions for nonparaxial accelerating beams with pre-engineered trajectories.

In this Letter, we propose a general real-space method for the generation of nonparaxial accelerating beams with arbitrary predefined convex trajectories. Our results lead to closed-form expressions for the required phase at the input plane. We present such closed-form results for a variety of caustic curves: beside circular, elliptic, and parabolic, we find for the first time general power-law and exponential trajectories.

Composite multi-vortex diffraction-free beams and van-Hove singularities in honeycomb lattices.

We find diffraction-free beams for graphene and MoS-type honeycomb optical lattices. The resulting composite solutions have the form of multi-vortices, with spinor topological charges (n, n±1). Exact solutions for the spinor components are obtained in the Dirac limit.

Unveiling pseudospin and angular momentum in photonic graphene.

Pseudospin, an additional degree of freedom inherent in graphene, plays a key role in understanding many fundamental phenomena such as the anomalous quantum Hall effect, electron chirality and Klein paradox. Unlike the electron spin, the pseudospin was traditionally considered as an unmeasurable quantity, immune to Stern-Gerlach-type experiments. Recently, however, it has been suggested that graphene pseudospin is a real angular momentum that might manifest itself as an observable quantity, but so far direct tests of such a momentum remained unfruitful.

Accelerating diffraction-free beams in photonic lattices.

We study nondiffracting accelerating paraxial optical beams in periodic potentials, in both the linear and the nonlinear domains. In particular, we show that only a unique class of z-dependent lattices can support a true accelerating diffractionless beam. Accelerating lattice solitons, autofocusing beams and accelerating bullets in optical lattices are systematically examined.

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.

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.

Optical analogues for massless dirac particles and conical diffraction in one dimension.

We demonstrate that light propagating in an appropriately designed lattice can exhibit dynamics akin to that expected from massless relativistic particles as governed by the one-dimensional Dirac equation. This is accomplished by employing a waveguide array with alternating positive and negative effective coupling coefficients, having a band structure with two intersecting minibands. Through this approach optical analogues of massless particle-antiparticle pairs are experimentally realized.

Observation and optical tailoring of photonic lattice filaments.

We demonstrate, for the first time, that photonic lattices support a new type of laser filaments, called lattice filaments (LF). The LF attributes (length, width, and intensity) can be tailored by both varying the photonic lattice properties and also dynamically through the interaction between filaments. This opens the way for extensive all-optical control of the nonlinear propagation of intense ultrafast wave packets.

Reflection and refraction of an Airy beam at a dielectric interface.

Reflection and refraction of a finite-power Airy beam at the interface between two dielectric media are investigated analytically and numerically. The formulation takes into account the paraxial nature of the optical beams to derive convenient field evolution equations in coordinate frames moving along Snell's refraction and reflection axes. Through numerical simulations, the self-accelerating dynamics of the Airy-like refracted and reflected beams are observed.

Surface optical Bloch oscillations in semi-infinite waveguide arrays.

We predict that surface optical Bloch oscillations can exist in semi-infinite waveguide arrays with a linear index variation, if the array parameters close to the boundary are appropriately perturbed. The perturbation is such that the surface states obtain the Wannier-Stark ladder eigenvalues of the unperturbed infinite array. The number of waveguides, whose parameters need to be controlled, decreases with increasing ratio of index gradient over coupling.

Linear and nonlinear waves in surface and wedge index potentials.

We study optical beams that are supported at the surface of a medium with a linear index potential and by a piecewise linear wedge-type potential. In the linear limit the modes are described by Airy functions. In the nonlinear regime we find families of solutions that bifurcate from the linear modes and study their stability for both self-focusing and self-defocusing Kerr nonlinearity.