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The ability to tailor a specific electromagnetic field pattern along an arbitrary selected surface is interesting and of substantial importance, given its numerous immediate applications. It belong...

We demonstrate machine-learning assisted dynamic tracking of the shape of a multimode fiber whose spatial configuration is manipulated by the movement of three linear stages. The data source used for the analysis is the coherent speckle pattern of light that has made a round trip in the fiber.

The optical Archimedes screw is a structured beam of light shown to be useful in conveying airborne particles. Such beams were demonstrated propagating along straight and curved trajectories. Here we demonstrate an optical Archimedes screw where both its linear and angular momenta are accelerating—allowing to both control its trajectory and transverse profile during propagation.

Symmetries and their associated selection rules are extremely useful in all fields of science. In particular, for system that include electromagnetic (EM) fields interacting with matter, it has been shown that both of symmetries of matter and EM field's time-dependent polarization play a crucial role in determining the properties of linear and nonlinear responses. The relationship between the system's symmetry and the properties of its excitations facilitate precise control over light emission and enable ultrafast symmetry-breaking spectroscopy of variety of properties. Here. we formulate the first general theory that describes the macroscopic dynamical symmetries (including quasicrystal-like symmetries) of an EM vector field, revealing many new symmetries and selection rules in light-matter interactions. We demonstrate an example of multi-scale selection rules experimentally in the framework of high harmonic generation (HHG). This work waves the way for novel spectroscopic techniques in multi-scale system as well as for imprinting complex structures in EUV-X-ray beams, attosecond pulses, or the interacting medium itself., Comment: 27 pages, 5 figures

Phase mismatch and group velocity mismatch are two dispersion effects which limit the effectiveness of optical frequency conversion processes. Here we propose a condition for a high harmonic generation in which a phase mismatch and a group-velocity mismatch work together through constructive inter sub-cycle interference to provide an efficient, phase-matched optical frequency conversion. This condition, which we call an anomalous phase matching (APM) can be valuable to the emerging extreme non-linear optics regime of a long wavelength drive field and a high gas pressure. The APM condition is fulfilled once both phase mismatch and group velocity mismatch (GVM) are present in the optical system, which is the most general case to consider. The effect of a phase mismatch is that after a propagation of one coherence length the emission start to destruct coherently, leading to a decrease in the up-conversion efficiency. The effect of the GVM is that after a particular harmonic order is being generated by the fundamental pulse, it starts to drift away from its creation time in the reference frame moving with the pump pulse, due to different group velocities between the pump and that harmonic. If a harmonic emission arrives, due to GVM, to an emission with the opposite polarity after traversing a coherence length the interference of both emissions would be constructive. Actually, this condition ensures constructive interference over the whole interaction length allowing for an increased HHG flux. We derive a mathematical condition for an APM and show numerically that APM can be achieved and wavelength-tuned in several different setups: by varying the peak intensity of the pump laser in a pre-ionized gaseous medium, by varying the wave-guide radius in a hollow wave guide filled with a neutral gas and by varying the pressure of a neutral gas in a gas cell at moderate pressures and long fundamental beam wavelengths.

The possibility of employing the spatial degree of photons for communications is gaining interest in recent years due to its unbounded dimensionality. A natural basis to span the transverse profile of photons is comprised of Laguerre-Gaussian (LG) modes which are characterized with two topological numbers: l, the orbital index, describing the orbital-angular-momentum (OAM) in units of “h-bar” per photon in the beam and p, which is the radial index or radial quantum number. One of the main challenges for utilizing LG modes in communications is the ability to perform mode-sorting and demultiplexing of the incoming physical data-flow. Nowadays, there are two leading approaches to mode demultiplexing. The first approach uses intricate optical setups in which the l and p degrees of freedom are coupled to other degrees of freedom such as the angle of propagation or the polarization of the beam. Most of these methods address either the OAM or the radial index degrees of freedom. The second approach, which emerged recently, suggests using just a camera to detect the intensity of the incoming light beam and to utilize a deep neural network (DNN) to classify the beam. To date, demonstrated DNN-based demultiplexers addressed solely the OAM degree of light. We report on an experimental demonstration of state-of-the-art mode demultiplexing of Laguerre-Gaussian beams according to both their orbital angular momentum and radial topological numbers using a flow of two concatenated deep neural networks. The first network serves as a transfer function from experimentally-generated to ideal numerically-generated data, while using a unique "Histogram Weighted Loss" function that solves the problem of images with limited significant information. The second network acts as a spatial-modes classifier. Our method uses only the intensity profile of modes or their superposition with no need for any phase information.

The transverse field profile of light is being recognized as a resource for classical and quantum communications for which reliable methods of sorting or demultiplexing spatial optical modes are required. Here, we demonstrate, experimentally, state-of-the-art mode demultiplexing of Laguerre-Gaussian beams according to both their orbital angular momentum and radial topological numbers using a flow of two concatenated deep neural networks. The first network serves as a transfer function from experimentally-generated to ideal numerically-generated data, while using a unique "Histogram Weighted Loss" function that solves the problem of images with limited significant information. The second network acts as a spatial-modes classifier. Our method uses only the intensity profile of modes or their superposition, making the phase information redundant.

Symmetry-based analysis is very useful in many fields of science. In the case of time-dependent systems, the symmetries of interest are dynamical, and are maintained during the system's evolution in time. Interestingly, such symmetries may manifest over several length scales, e.g. both microscopically and macroscopically. For example, in high harmonic generation (HHG), micro-scale dynamical symmetries (DSs) yield selection rules that forbid some harmonic orders and determine the polarizations of the allowed harmonics [1], as was formulated recently in a consistent group theory [2]. Macroscopically, DSs of the wave equation may induce selection rules with respect to phase-matching conditions and conservation of angular or linear momentum [3]. However, the DSs of these different length scales are generally thought to be non-interacting, and have so far only been described separately. Here we formulate and explore plethora of multi-scale dynamical symmetries (MSDS), where the symmetry operations involve both microscopic and macroscopic length scales. We derive all possible MSDS operations and their resulting selection rules in HHG, and experimentally demonstrate non-trivial selection rules of the new theory.

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding - still being explored - recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments.

We propose a simple quasi-phase-matching (QPM) scheme in high-order harmonic generation (HHG) based on the approximately linear dependence of the phase mismatch on harmonic order. With this scheme, essentially all the harmonic orders are phase matched simultaneously, with harmonic order $q$ experiencing a $q\mathrm{th}$-order QPM. We validate this proposal by simulations using a semiclassical numerical model of HHG.

We suggest a macroscopic scheme for generating circularly polarized high harmonics. The scheme uses a superposition of circularly polarized pump beams with different spatial modes, realizing a perturbed linearly polarized field which rotates along the propagation axis due to virtual circular birefringence. This method provides a spectral selectivity for the harmonic orders which are generated efficiently and for their spacing. The scheme is investigated numerically with a good agreement with the theory.

Light propagation in optical fibers is accompanied by random omnidirectional scattering. The small fraction of coherent guided light that escapes outside the cladding of the fiber forms a speckle pattern. Here, visual information imaged into the input facet of a multimode fiber with a transparent buffer is retrieved, using a convolutional neural network, from the side-scattered light at several locations along the fiber. This demonstration can promote the development of distributed optical imaging systems and optical links interfaced via the sides of the fiber.

It is shown theoretically that the use of accelerating spatiotemporal quasi-phase-matching (QPM) modulation patterns in media with parametric optical interactions makes it possible to generate a time-reversed replica of the pump pulse envelope in a frequency converted signal. The conversion is dependent on the group-velocity mismatch between the fundamental and up-converted harmonics, and controlled by the acceleration rate (chirp) of the QPM phase pattern. Analytical results are corroborated by numerical simulations., Comment: ACS Photonics, in press

We demonstrate both theoretically and experimentally the generation of a tunable two-dimensional superoscillating optical field through the interference of multiple Airy beams. The resulting pattern exhibits self-healing properties for a set of sub-Fourier diffraction spots with decreasing dimensions. Such spatial optical fields might find applications in microscopy, particle manipulation, and nonlinear optics.

In this tutorial we discuss the macroscopic aspects of the extreme nonlinear frequency conversion process of high-order harmonic generation. For most, this entails describing the phase mismatch of the process and the means to mitigate it by tuning global parameters or by modulations perturbing the process. Additionally, we consider applications of phase matching in general for probing and for controlling different parameters of the emitted radiation.

Using a superposition of shifted Bessel beams with different longitudinal wave vectors and orbital angular momenta, we realize an optical beam having simultaneous axial, angular, and radial focusing narrower than the Fourier limit. Our findings can be useful for optical particle manipulation and high-resolution microscopy.

High harmonic generation has been considered for many years to be a coherent source of upconverted laser radiation. We propose a method for the generation of essentially incoherent high harmonic generation with a controlled degree of temporal coherence, obeying random-walk statistics. This is achieved by a unique combination of single-atom and macroscopic effects involving preparation of the medium in an excited state with coordinate-dependent population inversion and using an intense off-resonant and phase-mismatched pumping.

The mathematical phenomenon of super-oscillation, in which a spectrally bound function oscillates locally at a rate faster than its fastest Fourier component, has found use in both theoretical and applied areas of optical research. We show the existence of a complementary phenomenon we term sub-oscillation, in which a spectrally lower bound limited function oscillates locally at an arbitrarily low frequency beyond the lower band limit. We construct a spatially sub-oscillatory optical beam to experimentally demonstrate optical super defocusing i.e. a very fast, exceptional, expansion of a partially blocked light beam. The relevance of super-oscillations to varied fields such as quantum measurement, optical beam shaping and super-resolution, particle manipulation, electron beam shaping and radio frequency antenna design, suggest that sub-oscillations could find interesting uses in varied fields as well. Our demonstration of super defocusing by itself might be relevant for optical dark-field microscopy. [1] Y. Eliezer and A. Bahbad, Optica 4, 440 (2017)

We propose and demonstrate experimentally an optical analogue of the famous Archimedes' screw where airborne particles are conveyed down or upstream the photons momentum ow through the rotation of a helical optical beam. We also report on the action of such a rotating screw on low-absorbing particles in a solution.

High harmonic generation (HHG) is an extreme nonlinear frequency up-conversion process during which extremely short duration optical pulses at very short wavelengths are emitted. A major concern of HHG is the small conversion efficiency at the single emitter level. Thus ensuring that the emission at different locations are emitted in phase is crucial. At high pump intensities it is impossible to phase match the radiation without reverting to ordered modulations of either the medium or the pump field itself, a technique known as Quasi-Phase-Matching (QPM). To date, demonstrated QPM techniques of HHG were usually complicated and/or lacked tunability. Here we demonstrate experimentally a relatively simple, highly and easily tunable QPM technique by using a structured pump beam made of the interference of different spatial optical modes. With this technique we demonstrate on-the-fly, tunable quasi-phase-matching of harmonic orders 25 to 39 with up to 30 fold enhancement of the emission., 13 pages, 4 figures

Quantum backflow is a counterintuitive phenomenon in which a forward-propagating quantum particle propagates locally backwards. The actual counter-propagation property associated with this delicate interference phenomenon has not been observed to date in any field of physics, to the best of our knowledge. Here, we report the observation of an analog optical effect, namely, transverse optical backflow where a beam of light propagating to a specific transverse direction is measured locally to propagate in the opposite direction. This observation is relevant to any physical system supporting coherent waves.

We introduce the one-dimensional PT-symmetric Schrodinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatory-like potential always generates an entirely real eigenvalue spectrum, its counterpart based on the superoscillatory wave function gives rise to an intricate pattern of PT-symmetry-breaking transitions, controlled by the parameters of the superoscillatory function. One scenario of the transitions proceeds smoothly via a set of threshold values, while another one exhibits a sudden jump to the broken PT symmetry. Another noteworthy finding is the possibility of restoration of the PT symmetry, following its original loss, in the course of the variation of the parameters., Comment: Phys. Rev. A, to be published

We demonstrate experimentally the generation of an optical beam having an axial focusing that is narrower than the Fourier limit. The beam is constructed from a superposition of Bessel beams with different longitudinal wave vectors, realizing a super-oscillatory axial intensity distribution. Such beams can be useful for microscopy and for optical particle manipulation.

We show that it is possible to construct spectrally lower bound limited functions which can oscillate locally at an arbitrarily low frequency. Such sub-oscillatory functions are complementary to super-oscillatory functions which are band-limited yet can oscillate locally at an arbitrarily high frequency. We construct a spatially sub-oscillatory optical beam to experimentally demonstrate optical super defocusing., 14 pages, 4 figures

Trapping and manipulation of particles using laser beams has become an important tool in diverse fields of research. In recent years, particular interest is given to the problem of conveying optically trapped particles over extended distances either down or upstream the direction of the photons momentum flow. Here, we propose and demonstrate experimentally an optical analogue of the famous Archimedes' screw where the rotation of a helical-intensity beam is transferred to the axial motion of optically-trapped micro-meter scale airborne carbon based particles. With this optical screw, particles were easily conveyed with controlled velocity and direction, upstream or downstream the optical flow, over a distance of half a centimeter. Our results offer a very simple optical conveyor that could be adapted to a wide range of optical trapping scenarios., Comment: 10 pages, 5 figures

A first-principles tutorial account is given for the diffraction of either light or free, non-relativistic, massive particles from a moving grating. Discussion on the properties of the moving grating including non-reciprocity is followed by considering both Raman-Nath (thin grating) diffraction and Bragg (thick grating) diffraction in either transmission or reflection geometry. Use of four-momentum conservation with dispersion relations yield the angles of diffraction. The increase in the angle of diffraction for grazing incident by using a moving grating relative to using a static grating is calculated. It is shown that this increase is possible only for Raman-Nath geometry.

Band-limited functions can oscillate locally at an arbitrarily fast rate through an interference phenomenon known as superoscillations. Using an optical pulse with a superoscillatory envelope we experimentally break the temporal Fourier-transform limit having a temporal feature which is approximately three times shorter than the duration of a transform-limited Gaussian pulse having a comparable bandwidth while maintaining $29.5\%$ visibility. Numerical simulations demonstrate the ability of such signals to achieve temporal super-resolution., Comment: 9 pages, 6 figures, supplementary sections included

It is shown theoretically and numerically that a metal-dielectric or an all-dielectric side-by-side gratings structure can support non-degenerate guided modes coupled to the same radation mode. This realizes an easy to fabricate, simple system supporting a nearly degenerate, efficiently coupled, double Fano resonance. The ensuing relatively narrow and high-visibility spectral line-shape can be useful for realizing ultra-thin optical filters.

Quasi-phase-matching (QPM) has always been thought of as a purely spatial phenomenon. Now, scientists show that QPM can be extended to the temporal domain, introducing temporal and spatiotemporal modulations of the nonlinear susceptibility. This concept paves the way for the manipulation of light through nonlinear interactions, and may have unique applications in nonlinear optics.

We demonstrate experimentally a generic method for the synthesis of optical femtosecond pulses based on Gaussian, Airy and Hermite-Gauss functions, which are transformed to exhibit fringes with tunable width. The width of the fringes is set in some cases to be much narrower than the inverse of the spectral bandwidth. Such pulses might be useful for ultrafast spectroscopy, coherent control and nonlinear optics.

Standard quasi-phase-matching (QPM) schemes assume exact momentum relations between the interacting beams, thus necessitating the direct use of a reciprocal lattice vector to satisfy momentum balance. Usage of finite width beams for colinear interactions permits to use a projection of the reciprocal lattice vector along the propagation direction of the beams. We analytically derive this result and exam the new options given by this projection-based QPM for the analysis and design of nonlinear optical devices.

We analyze quasi-phase-matched (QPM) conversion efficiency of the five possible types of periodic two-dimensional nonlinear structures: Hexagonal, square, rectangular, centered-rectangular, and oblique. The frequency conversion efficiency, as a function of the two-dimensional quasi-phase-matching order, is determined for the general case. Furthermore, it is demonstrated for two basic feasible motifs, a circular motif and a rectangular motif. This enables to determine the optimal motif dimensions for achieving the highest conversion efficiency. We find that a rectangular motif is more efficient than a circular motif for quasi-phase-matched processes that rely on a single reciprocal lattice vector (RLV), and that under optimal choice of motif dimensions, it converges into a one-dimensional periodic structure. In addition, in a few specific cases we found that higher order QPM can be significantly more efficient than lower order QPM.

We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity-dispersion (GVD) in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity ($\mathcal{CP}$) symmetry, while the addition of the intra-core cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons., Physical Review A, in press

We propose a paradigm for macroscopic control of high-order harmonic generation by modulating the bound-state population of the medium atoms. A unique result of this scheme is that apart from regular spatial quasi-phase-matching (QPM), also purely temporal QPM of the emitted radiation can be established. Our simulations demonstrate temporal QPM by inducing homogenous Rabi oscillations in the medium and also spatial QPM by creating a grating of population inversion using the process of rapid adiabatic passage. In the simulations a scaled version of high-order harmonic generation is used: a far off-resonance $2.6\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ source generates UV-visible high-order harmonics from alkali-metal-atom vapor, while a resonant near IR source is used to coherently control the medium.

A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions involving a dynamic modulation of the interaction parameters such as non-reciprocal phenomena, time reversal of signals and spatiotemporal quasi phase matching, Comment: 9 pages

It is shown that pairs of solitary pulses (SPs) in a linearly-coupled system with opposite group-velocity dispersions form robust breathing bound states. The system can be realized by temporal-modulation coupling of SPs with different carrier frequencies propagating in the same medium, or by coupling of SPs in a dual-core waveguide. Broad SP pairs are produced in a virtually exact form by means of the variational approximation. Strong nonlinearity tends to destroy the periodic evolution of the SP pairs., Comment: Optics Letters, in press

Particle swarm optimization is used to design optical nano-antennas for nonlinear optical interactions in a gas medium adjacent to the nano-antenna. The optimization is specifically designed to address broad band pumping.

It is theoretically shown that coherent control of atomic bound states can achieve macroscopic control over the process of High-order Harmonic Generation. In particular purely temporal Quasi-Phase-Matching is numerically demonstrated.