We present the spatially accelerating solutions of the Maxwell equations. Such nonparaxial beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams.For both TE and TM polarizations, the beams exhibit shape-preserving bending with subwavelength features, and the Poynting vector of the main lobe displays a turn of more than 90°.We show that these accelerating beams are self-healing, analyze their properties, and compare to the paraxial Airy beams. Finally, we present the new family of periodic accelerating beams which can be constructed from our solutions.

We show that the well-known Čerenkov effect contains new phenomena arising from the quantum nature of charged particles. The Čerenkov transition amplitudes allow coupling between the charged particle and the emitted photon through their orbital angular momentum and spin, by scattering into preferred angles and polarizations. Importantly, the spectral response reveals a discontinuity immediately below a frequency cutoff that can occur in the optical region. Near this cutoff, the intensity of the conventional Čerenkov radiation (ČR) is very small but still finite, while our quantum calculation predicts exactly zero intensity above the cutoff. Below that cutoff, with proper shaping of electron beams (ebeams), we predict that the traditional ČR angle splits into two distinctive cones of photonic shockwaves. One of the shockwaves can move along a backward cone, otherwise considered impossible for conventional ČR in ordinary matter. Our findings are observable for ebeams with realistic parameters, offering new applications including novel quantum optics sources, and opening a new realm for Čerenkov detectors involving the spin and orbital angular momentum of charged particles.

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We present shape-preserving spatially accelerating electromagnetic wavepackets in curved space: wavepackets propagating along non-geodesic trajectories while recovering their structure periodically. These wavepackets are solutions to the paraxial and non-paraxial wave equation in curved space. We analyze the dynamics of such beams propagating on surfaces of revolution, and find solutions that carry finite power. These solutions propagate along a variety of non-geodesic trajectories, reflecting the interplay between the curvature of space and interference effects, with their intensity profile becoming narrower (or broader) in a scaled selfsimilar fashion Finally, we extend this concept to nonlinear accelerating beams in curved space supported by the Kerr nonlinearity. Our study concentrates on optical settings, but the underlying concepts directly relate to General Relativity.

We discover long-lived (microsecond-scale) optical waveguiding in the wake of atmospheric laser filaments. We also observe the formation and then outward propagation of the consequent sound wave. These effects may be used for remote induction of atmospheric long-lived optical structures from afar which could serve for a variety of applications.* These authors contributed equally to this work. 2Propagation of self-guided laser filaments through air and other gases results in a rich variety of phenomena and applications [1][2][3]. A laser filament is formed when a femtosecond pulse, with peak intensity above the critical power for collapse (3 GW in air at an optical wavelength of 800 nm), is propagating in a transparent medium [1]. In air, the diameter of a filament is approximately 100 μm and it can propagate over distances much longer than the Rayleigh length, from 10 cm up to the kilo-meter range [4][5][6][7]. A filament is formed due to a dynamic balance between the linear diffractive and dispersive properties of the medium and its nonlinear features such as self-focusing optical Kerr effect and defocusing due to the free electrons which are released from molecules through multi-photon ionization. In the atmosphere, filaments can be initiated at predefined remote distances [4,5] and propagate through fog, clouds and turbulence [8,9]. Thus, filaments are attractive for atmospheric applications such as remote spectroscopy This mechanism was used for guiding properly delayed picosecond pulses [21,22], but at times larger than several nanosecond after the filamenting pulse, even this process does not leave behind any waveguiding effects. In fact, all processes resulting from plasma or molecular alignment in the wake of atmospheric laser filaments are limited to the first few nanoseconds period. Consequently, it was generally believed that ten nanoseconds after the filament, the medium does not exhibit any waveguiding effect. In contrast to that, it was recently discovered that 0.1-1 milliseconds after the filament, there is a circular negative index change that acts as an antiguide by defocusing a probe beam [23]. This effect was attributed to reduction in the air density at the center of the filament 4 as a result of heating. Altogether, to the best of our knowledge, thus far all experiments and theories on laser filamentation in the atmosphere concluded that there is no longlived (>10 nanosecond) waveguiding effect left behind the femtosecond filamenting pulse. This severely limits any CW application of laser filamentation, because the repetition rate of any high power laser used for creating the filament is low, hence for most of the time between pulses light would not be guided. Likewise, any other potential application would have to "live" on a picosecond scale, because at later times, waveguiding by the filament was thought to be nonexistent.Here, we show the exact opposite: we demonstrate theoretically and experimentally that the filament induces a transient positive index change which lasts for approximate...

We present, theoretically and experimentally, diffractionless optical beams displaying arbitrarily-shaped sub-diffraction-limited features known as superoscillations. We devise an analytic method to generate such beams and experimentally demonstrate optical superoscillations propagating without changing their intensity distribution for distances as large as 250 Rayleigh lengths. Finally, we find the general conditions on the fraction of power that can be carried by these superoscillations as function of their spatial extent and their Fourier decomposition. Fundamentally, these new type of beams can be utilized to carry sub-wavelength information for very large distances.

It is a long-standing goal to create light with unique quantum properties such as squeezing and entanglement. We propose the generation of quantum light using free-electron interactions, going beyond their already ubiquitous use in generating classical light. This concept is motivated by developments in electron microscopy, which recently demonstrated quantum free-electron interactions with light in photonic cavities. Such electron microscopes provide platforms for shaping quantum states of light through a judicious choice of the input light and electron states. Specifically, we show how electron energy combs implement photon displacement operations, creating displaced-Fock and displaced-squeezed states. We develop the theory for consecutive electron-cavity interactions with a common cavity and show how to generate any target Fock state. Looking forward, exploiting the degrees of freedom of electrons, light, and their interaction may achieve complete control over the quantum state of the generated light, leading to novel light statistics and correlations.

We show that light guided in a planar dielectric slab geometry incorporating a biaxial medium has lossless modes with group and phase velocities in opposite directions. Particles in a vacuum gap inserted into the structure experience negative radiation pressure: the particles are pulled by light rather than pushed by it. This effectively one-dimensional dielectric structure represents a new geometry for achieving negative radiation pressure in a wide range of frequencies with minimal loss. Moreover, this geometry provides a straightforward platform for experimentally resolving the Abrahams-Minkowski dilemma.