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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 were found to have 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. In this work, we demonstrate that inverted pin beams carrying orbital angular momentum can further suppress intensity scintillations in moderate to strong irradiance fluctuation conditions. Our results can be useful in improving the performance and link availability of free-space optical communication systems., Comment: 4 pages, 4 figures

The statistical mechanical behavior of weakly nonlinear multimoded optical settings is attracting increased interest during the last few years. The main purpose of this work is to numerically investigate the main factors that affect the thermalization process in photonic lattices. In particular, we find that lattices with identically selected properties (such as temperature, coupling coefficient, lattice size, and excitation conditions) can exhibit very different thermalization dynamics and thus thermalization distances. Our investigation is focused on two different two-dimensional lattices: the honeycomb lattice and the triangular lattice. Our numerical results show that, independently of the excitation conditions, the honeycomb lattice always thermalizes faster than the triangular lattice. We mainly explain this behavior to the quasilinear spectrum that promotes wave-mixing in the honeycomb lattice in comparison to the power-like spectrum of the triangular lattice. In addition, we investigate the combined effects of temperature as well as the sign and magnitude of the nonlinearity. Switching either the sign of the Kerr nonlinear coefficient or the sign of the temperature can lead to significant differences in the thermalization dynamics, a phenomenon that can be physically explained in terms of wave instabilities. Larger absolute values of the temperature |T| result in more uniform distributions for the power occupation numbers and faster thermalization speeds. Finally, as expected, increasing the magnitude of the nonlinearity results in accelerated thermalization. Our findings provide valuable insights into optical thermalization in discrete systems where experimental realization may bring about new possibilities for light manipulation and applications., Comment: 11 pages, 4 figures

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 pressure-like intensive quantity ($\hat{p}$) 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. In this Letter, we elucidate the physical origin of the optical thermodynamic pressure and demonstrate its dual essence. In this context, we rigorously derive an expression that splits $\hat{p}$ into two distinct components, a term that is explicitly tied to the electrodynamic radiation pressure and a second entropic part that is responsible for the entropy change. We utilize this result to establish a formalism that simplifies the quantification of radiation pressure under nonlinear equilibrium conditions, thus eliminating the need for a tedious evaluation of the Maxwell stress tensor. Our theoretical analysis is corroborated by numerical simulations carried out in highly multimoded nonlinear optical structures. These results may provide a novel way in predicting and controlling radiation pressure processes in a variety of nonlinear electromagnetic settings.

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. Under thermal equilibrium conditions, we formally derive an equation that establishes a direct link between the partial thermodynamic pressures and the electrodynamic radiation pressures exerted by each polarization species. Our theoretical framework provides a straightforward approach for quantifying the total radiation pressures through the system's thermodynamics variables without invoking the Maxwell stress tensor formalism. In essence, we show that the total electrodynamic pressure in such arrangements can be obtained in an effortless manner from initial excitation conditions, thus avoiding time-consuming simulations of the utterly complex multimode dynamics. To illustrate the validity of our results, we carry out numerical simulations in multimoded nonlinear optical structures supporting two polarization species and demonstrate excellent agreement with the Maxwell stress tensor method.

Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear waves-settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to interactions between different frequencies and/or polarizations. The purpose of this work is to develop a thermodynamic theory that takes into account the synergistic action of multiple components. We find that the type of the nonlinearity involved can have important implications in the thermalization process and, hence, can lead to different thermal equilibrium conditions. Importantly, we derive closed-form expressions for the actual optomechanical pressure that is exerted on the system. In particular, the total optomechanical pressure is the sum of the partial pressures due to each component. Our results can be applied to a variety of weakly nonlinear optical settings such as multimode fibers, bulk waveguides, photonic lattices, and coupled microresonators. We present two specific examples, where two colors interact in a waveguide array with either a cubic or quadratic nonlinearity., Comment: 4 pages, 3 figures

We introduce a new 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 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., Comment: 4 pages, 4 figures, supplemental document

Optical forces are known to arise in a universal fashion in many and diverse physical settings. As such, they are successfully employed over a wide range of applications in areas like biophotonics, optomechanics and integrated optics. While inter-elemental optical forces in few-mode photonic networks have been so far systematically analyzed, little is known, if any, as to how they manifest themselves in highly multimoded optical environments. In this work, by means of statistical mechanics, we formally address this open problem in optically thermalized weakly nonlinear heavily multimode tight-binding networks. The outlined thermodynamic formulation allows one to obtain in an elegant manner analytical results for the exerted thermodynamic pressures in utterly complex arrangements-results that are either computationally intensive or impossible to obtain otherwise. Thus, we derive simple closed-form expressions for the thermodynamic optical pressures displayed among elements, which depend only on the internal energy as well as the coupling coefficients involved. In all cases, our theoretical results are in excellent agreement with numerical computations. Our study may pave the way towards a deeper understanding of these complex processes and could open up avenues in harnessing radiation forces in multimode optomechanical systems., Comment: 25 pages, 5 figures

We examine the coupling process between the surface modes of a Su-Schrieffer-Heeger lattice both in the linear and the nonlinear regimes. We first develop a coupled-mode theory formalism for the modes of a finite lattice with zero boundary conditions. Our analysis relies on the closed-form expressions for the bulk and the surface eigenmodes of the system. The coupled-mode theory formalism is based on a decomposition of the supermodes into sublattice modes. In the case of the two zero sublattice surface modes, this leads to periodic oscillations between them without the involvement of the bulk modes. We analytically show that launching light only on the waveguide that is located at either edge of the array, can be very effective in successfully exciting the respective surface mode. We extend our analysis, in the case of Kerr nonlinearity, and develop a simplified model that accounts only for the surface modes. By direct numerical simulations, we find that this model can very accurately capture the dynamics of the surface modes when the nonlinearity is small or moderate. On the other hand, in the case of strong nonlinearity, wave mixing leads to the quasi-periodic excitation of the bulk modes, or even to a chaotic behavior where all the modes of the systems are excited, and no prominent signature of the surface modes can be detected., Comment: 8 pages, 6 figures

We study the statistical behavior of multimoded optical systems under equilibrium conditions. We investigate the role of variations of the system parameters in the thermodynamic description and derive, an optical analogue of the first law of thermodynamics, a generic expression for the work done to the system, and an optical Gibbs-Duhem equation. To demonstrate these effects, we focus in the case of two-dimensional photonic lattices. We study the conditions under which the entropy in such waveguide arrays can be considered as extensive. In this respect, small deviations from the extensive character of the entropy give rise to stress and strain terms. We examine how the conservation laws in such array configurations are affected by variations in the system parameters, and furthermore, we analyze the respective thermodynamic processes (isentropic and Joule-type expansions)., Comment: 12 pages, 2 figures

We examine the dynamics of electron beams that, in free space, are self-accelerating, in the presence of an additional magnetic field. We focus our attention in the case of Airy beams that follow parabolic trajectories and in generalized classes of beams associated with power-law trajectories. We study the interplay between beam self-acceleration and the circular motion caused by the magnetic field. In the case of Airy beams, using an integral representation, we find closed-form solutions for the electron wavefunction. We also derive asymptotic formulas for the beam trajectories both for Airy beams and for self-accelerating power-law beams. A ray optics description is rather useful for the interpretation of the beam dynamics. Our results are in excellent comparison with direct numerical simulations.

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. Our numerical results are in excellent agreement with our theoretical predictions.

Over the last dozen of years, the area of accelerating waves has made considerable advances not only in terms of fundamentals and experimental demonstrations but also in connection to a wide range of applications. Starting from the prototypical Airy beam that was proposed and observed in 2007, new families of accelerating waves have been identified in the paraxial and nonparaxial domains in space and/or time, with different methods developed to control at will their trajectory, amplitude, and beam width. Accelerating optical waves exhibit a number of highly desirable attributes. They move along a curved or accelerating trajectory while being resilient to perturbations (self-healing), and, are diffraction-free. It is because of these particular features that accelerating waves have been utilized in a variety of applications in the areas of filamentation, beam focusing, particle manipulation, biomedical imaging, plasmons, and material processing among others., Comment: 16 pages, 11 figures

We demonstrate valley-dependent vortex generation in a photonic graphene. Without breaking the inversion symmetry, excitation of two equivalent valleys leads to formation of an optical vortex upon Bragg-reflection to the third valley, with its chirality determined by the valley degree of freedom. Vortex-antivortex pairs with valley-dependent topological charge flipping are also observed and corroborated by numerical simulations. Furthermore, we develop a three-band effective Hamiltonian model to describe the dynamics of the coupled valleys, and find that the commonly used two-band model is not sufficient to explain the observed vortex degeneracy lifting. Such valley-polarized vortex states arise from high-band excitation without inversion symmetry breaking or synthetic-field-induced gap opening. Our results from a photonic setting may provide insight for the study of valley contrasting and Berry-phase mediated topological phenomena in other systems.

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. Although, in general, the phase profile at the input plane can be computed numerically, we find closed form expressions for bottle beams with various type of surfaces both in real and in the Fourier space., Comment: Optics Letters 43, 3878 (2018)

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 input plane. Furthermore, we come to the elegant conclusion that the beam width depends solely on the local curvature of the trajectory. Thus, we can generate beams with pre-defined amplitude and beam-width by appropriately selecting the local curvature. Our theoretical results are in excellent agreement with numerical simulations. We discuss about methods that can be utilized to experimentally generate such beam. Our work might be useful in applications where precise beam control is important such as particle manipulation, filamentation, and micromachining.

We show that it is possible to independently control both the trajectory and the maximum amplitude along the trajectory of a paraxial accelerating beam. This is accomplished by carefully engineering both the amplitude and the phase of the beam on the input plane. Furthermore, we show that the width of an accelerating beam is related only on the curvature of the trajectory. Therefore, we are able to produce beams with predefined beam widths and amplitudes. These results are useful in applications where precise beam control is important. In addition we consider radially symmetric abruptly autofocusing beams. We identify the important parameters that affect the focal characteristics. Consequently, we can design autofocusing beams with optimized parameters (such as sharper focus and higher intensity contrast). In all our calculations the resulting formulas are presented in an elegant and practical form in direct connection with the geometric properties of the trajectory. Finally we discuss methods that can be utilized to experimentally realize such optical waves.

We investigate the dynamics of spatiotemporal optical waves with one transverse dimension that are 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 type, respectively. We find closed form solutions that accurately describe the wave dynamics and unveil their fundamental properties.

We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory., Comment: Published version, 15 pages, 7 figures

We show that the velocity and thus the frequency of a signal pulse can be adjusted by the use of a control Airy pulse. In particular, we utilize a nonlinear Airy pulse which, via cross-phase modulation, creates an effective potential for the optical signal. Interestingly, during the interaction, the signal dispersion is suppressed. Importantly, the whole process is controllable and by using Airy pulses with different truncations leads to predetermined values of the frequency shifting. Such a functionality might be useful in wavelength division multiplexing networks.

We find exact solutions describing bidirectional pulses propagating in fiber Bragg gratings. They are derived by solving the coupled-mode theory equations and are expressed in terms of products of modified Bessel functions with algebraic functions. Depending on the values of the two free parameters the general bidirectional X-wave solution can also take the form of a unidirectional pulse. We analyze the symmetries and the asymptotic properties of the solutions and also discuss about additional waveforms that are obtained by interference of more than one solutions. Depending on their parameters such pulses can create a sharp focus with high contrast.

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. We numerically test our results in one and two dimensional square arrangement of waveguides.

We consider an optical nonlinear interferometric setup based on Young's double-slit configuration where a nonlinear material is placed exactly after one of the two slits. We examine the effects of Kerr nonlinearity and multi-photon absorption in the resulting interference pattern. The presence of nonlinearity breaks the transverse spatial symmetry of the system, resulting to a modified intensity pattern at the observation plane as a function of the incident intensity. Our theoretical model, based on the modification of the optical path due to the presence of nonlinearity, is surprisingly accurate in predicting the intensity profile of the main lobes for a wide range of parameters. We discuss about potential applications of our model in nonlinear interferometry. Specifically, we show that it is possible to measure both the multi-photon and the Kerr coefficients of a nonlinear material based on the spatial translation of the interference pattern as a function of the incident intensity.

Motivated by recent experiments on Bose-Einstein condensed atoms which rotate in annular/toroidal traps we study the effect of the finiteness of the atom number $N$ on the states of lowest energy for a fixed expectation value of the angular momentum, under periodic boundary conditions. To attack this problem, we develop a general strategy, considering a linear superposition of the eigenstates of the many-body Hamiltonian, with amplitudes that we extract from the mean field approximation. This many-body state breaks the symmetry of the Hamiltonian, it has the same energy to leading order in $N$ as the mean-field state and the corresponding eigenstate of the Hamiltonian, however it has a lower energy to subleading order in $N$ and thus it is energetically favorable.

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., Comment: 5 pages, 8 figures. To be published in Optics Letters

In this letter, we study a nonlinear interferometric setup based on diffraction rather than beam combining. It consists of a nonlinear analogue 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. For moderate nonlinearities this leads to a self-induced shift of the intensity pattern in the transverse plane. A simple theoretical model is developed which is surprisingly accurate in predicting the intensity profile of the main lobes for a wide range of parameters. We discuss about possible applications of our model in nonlinear interferometry, for example in measuring the nonlinearities of optical materials., Comment: 4 pages, 6 figures

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: besides circular, elliptic, and parabolic, we find for the first time general power-law and exponential trajectories. Furthermore, by changing the initial amplitude we can design different intensity profiles along the caustic., Comment: Accepted for publication in Optics Letters

We find diffraction-free beams for graphene and MoS$_2$-type honeycomb optical lattices. The resulting composite solutions have the form of multi-vortices, with spinor topological charges ($n$, $n\pm1$). Exact solutions for the spinor components are obtained in the Dirac limit. The effects of the valley degree of freedom and the mass are analyzed. Passing through the van-Hove singularity the topological structure of the solutions is modified. Exactly at the singularity the diffraction-free beams take the form of strongly localized one-dimensional stripes., Comment: 4 pages, 6 figures, accepted for publication in Optics Letters

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. Here, by selective excitation of two sublattices of an artificial photonic graphene, we demonstrate pseudospin-mediated vortex generation and topological charge flipping in otherwise uniform optical beams with Bloch momentum traversing through the Dirac points. Corroborated by numerical solutions of the linear massless Dirac-Weyl equation, we show that pseudospin can turn into orbital angular momentum completely, thus upholding the belief that pseudospin is not merely for theoretical elegance but rather physically measurable., Comment: 12 pages, 5 figures

We consider a Bose-Einstein condensed cloud of atoms which rotate in a toroidal/annular potential. Assuming one-dimensional motion, we evaluate the critical frequencies associated with the effect of hysteresis and the critical coupling for stability of the persistent currents. We perform these calculations using both the mean-field approximation and the method of numerical diagonalization of the many-body Hamiltonian which includes corrections due to the finiteness of the atom number., Comment: 7 pages, 5 figures, section on experimental relevance added, final version

We present variational and numerical solutions for the problem of stability of persistent currents in a two-component Bose-Einstein condensate of distinguishable atoms which rotate in a ring potential. We consider the general class of solutions of constant density in the two components separately, thus providing an alternative approach of the solution of the same problem given recently by Zhigang Wu and Eugene Zaremba [Phys. Rev. A {\bf 88}, 063640 (2013)]. Our approach provides a physically transparent solution of this delicate problem. Finally, we give a unified and simple picture of the lowest-energy state of the system for large values of the coupling., Comment: Published version

We analyze the mean-field yrast spectrum of a two-component Bose gas in the ring geometry with arbitrary interaction asymmetry. Of particular interest is the possibility that the yrast spectrum develops local minima at which persistent superfluid flow can occur. By analyzing the mean-field energy functional, we show that local minima can be found at plane-wave states and arise when the system parameters satisfy certain inequalities. We then go on to show that these plane-wave states can be yrast states even when the yrast spectrum no longer exhibits a local minimum. Finally, we obtain conditions which establish when the plane-wave states cease to be yrast states. Specific examples illustrating the roles played by the various interaction asymmetries are presented., Comment: Final version, one revised figure, to appear in Phys. Rev. A

A new class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept expands on our previous proposal of paraxial accelerating Bessel-like beams to include beams with subwavelength lobes and/or large trajectory angles. Such waves are produced when the phase at the input plane is engineered so that the interfering ray cones are made to focus along the prespecified path. When the angle of these cones is fixed, the beams possess a diffraction-free Bessel profile on planes that stay normal to their trajectory, which can be considered as a generalized definition of diffractionless propagation in the nonparaxial regime. The analytical procedure leading to these results is based on a ray optics interpretation of Rayleigh-Sommerfeld diffraction and is presented in detail. The evolution of the proposed waves is demonstrated through a series of numerical examples and a variety of trajectories., Comment: submitted work

The system of coupled discrete equations describing a two-component superlattice with interlaced linear and nonlinear constituents is revisited as a basis for investigating binary waveguide arrays, such as ribbed AlGaAs structures, among others. Compared to the single nonlinear lattice, the interlaced system exhibits an extra band-gap controlled by the, suitably chosen by design, relative detuning. In more general physics settings, this system represents a discretization scheme for the single-equation-based continuous models in media with transversely modulated linear and nonlinear properties. Continuous wave solutions and the associated modulational instability are fully analytically investigated and numerically tested for focusing and defocusing nonlinearity. The propagation dynamics and the stability of periodic modes are also analytically investigated for the case of zero Bloch momentum. In the band-gaps a variety of stable discrete solitary modes, dipole or otherwise, in-phase or of staggered type are found and discussed.

We demonstrate that families of vortex solitons are possible in a bi-dispersive three-dimensional nonlinear Schrodinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity. Such vortex solitons can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity., Comment: 4 pages, 4 figures