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We investigate the persistent orientation of asymmetric-top molecules induced by time-delayed THz pulses that are either collinearly or cross polarized. Our theoretical and numerical results demonstrate that the orthogonal configuration outperforms the collinear one, and a significant degree of persistent orientation - approximately 10% at 5 K and nearly 3% at room temperature - may be achieved through parameter optimization. The dependence of the persistent orientation factor on temperature and field parameters is studied in detail. The proposed application of two orthogonally polarized THz pulses is both practical and efficient. Its applicability under standard laboratory conditions lays a solid foundation for future experimental realization of THz-induced persistent molecular orientation., Comment: 11 pages, 6 figures

We theoretically consider the phenomenon of field-free long-lasting orientation of symmetric-top molecules ionized by two-color laser pulses. The anisotropic ionization produces a significant long-lasting orientation of the surviving neutral molecules. The degree of orientation increases with both the pulse intensity and, counterintuitively, with the rotational temperature. The orientation may be enhanced even further by using multiple delayed two-color pulses. The long-lasting orientation may be probed by even harmonic generation or by Coulomb-explosion-based methods. The effect may enable the study of relaxation processes in dense molecular gases, and may be useful for molecular guiding and trapping by inhomogeneous fields., Comment: 7 pages, 4 figures

Ultrashort laser pulses are widely used for transient field-free molecular orientation -- a phenomenon important in chemical reaction dynamics, ultrafast molecular imaging, high harmonics generation, and attosecond science. However, significant molecular orientation usually requires rotationally cold molecules, like in rarified molecular beams, because chaotic thermal motion is detrimental to the orientation process. Here we propose to use the mechanism of the echo phenomenon previously observed in hadron accelerators, free-electron lasers, and laser-excited molecules to overcome the destructive thermal effects and achieve efficient field-free molecular orientation at high temperatures. In our scheme, a linearly polarized short laser pulse transforms a broad thermal distribution in the molecular rotational phase space into many separated narrow filaments due to the nonlinear phase mixing during the post-pulse free evolution. Molecular subgroups belonging to individual filaments have much-reduced dispersion of angular velocities. They are rotationally cold, and a subsequent moderate terahertz (THz) pulse can easily orient them. The overall enhanced orientation of the molecular gas is achieved with some delay, in the course of the echo process combining the contributions of different filaments. Our results demonstrate that the echo-enhanced orientation is an order of magnitude higher than that of the THz pulse alone. The mechanism is robust -- it applies to different types of molecules, and the degree of orientation is relatively insensitive to the temperature. The laser and THz pulses used in the scheme are readily available, allowing quick experimental demonstration and testing in various applications. Breaking the phase space to individual filaments to overcome hindering thermal conditions may find a wide range of applications beyond molecular orientation., Comment: 12 pages, 10 figures

We present a comprehensive study of enantioselective orientation of chiral molecules excited by a pair of delayed cross-polarized femtosecond laser pulses. We show that by optimizing the pulses' parameters, a significant (~ 10%) degree of enantioselective orientation can be achieved at zero and at five kelvin rotational temperatures. This study suggests a set of reasonable experimental conditions for inducing and measuring strong enantioselective orientation. The strong enantioselective orientation and the wide availability of the femtosecond laser systems required for the proposed experiments may open new avenues for discriminating and separating molecular enantiomers., Comment: 8 pages, 8 figures

Rotational dynamics of D$_2$ molecules inside helium nanodroplets is induced by a moderately intense femtosecond (fs) pump pulse and measured as a function of time by recording the yield of HeD$^+$ ions, created through strong-field dissociative ionization with a delayed fs probe pulse. The yield oscillates with a period of 185 fs, reflecting field-free rotational wave packet dynamics, and the oscillation persists for more than 500 periods. Within the experimental uncertainty, the rotational constant BHe of the in-droplet D$_2$ molecule, determined by Fourier analysis, is the same as Bgas for an isolated D$_2$ molecule. Our observations show that the D$_2$ molecules inside helium nanodroplets essentially rotate as free D$_2$ molecules.

We study the excitation of asymmetric-top (including chiral) molecules by two-color femtosecond laser pulses. In the cases of non-chiral asymmetric-top molecules excited by an orthogonally polarized two-color pulse, we demonstrate, classically and quantum mechanically, three-dimensional orientation. For chiral molecules, we show that the orientation induced by a cross-polarized two-color pulse is enantioselective along the laser propagation direction, namely, the two enantiomers are oriented in opposite directions. On the short time scale, the classical and quantum simulations give results that are in excellent agreement, whereas on the longer time scale, the enantioselective orientation exhibits quantum beats. These observations are qualitatively explained by analyzing the interaction potential between the two-color pulse and molecular (hyper-)polarizability. The prospects for utilizing the long-lasting orientation for measuring and using the enantioselective orientation for separating the individual enantiomers are discussed., Comment: 12 pages, 5 figures

Impulsive orientation of symmetric-top molecules excited by two-color femtosecond pulses is considered. In addition to the well-known transient orientation appearing immediately after the pulse and then reemerging periodically due to quantum revivals, we report the phenomenon of field-free long-lasting orientation. Long-lasting means that the time averaged orientation remains non-zero until destroyed by other physical effects, e.g. intermolecular collisions. The effect is caused by the combined action of the field-polarizability and field-hyperpolarizability interactions. The dependence of degree of long-lasting orientation on temperature and pulse's parameters is considered. The effect can be measured by means of second (or higher-order) harmonic generation, and may be used to control the deflection of molecules traveling through inhomogeneous electrostatic fields., Comment: 12 pages, 7 figures

Chirality and chiral molecules are key elements in modern chemical and biochemical industries. Individual addressing, and the eventual separation of chiral enantiomers has been and still is an important elusive task in molecular physics and chemistry, and a variety of methods has been introduced over the years to achieve this goal. Here, we theoretically demonstrate that a pair of cross-polarized THz pulses interacting with chiral molecules through their permanent dipole moments induces an enantioselective orientation of these molecules. This orientation persists for a long time, exceeding the duration of the THz pulses by several orders of magnitude, and its dependency on temperature and pulses' parameters is investigated. The persistent orientation may enhance the deflection of the molecules in inhomogeneous electromagnetic fields, potentially leading to viable separation techniques., Comment: 9 pages, 5 figures

Abstract We report the experimental observation of molecular unidirectional rotation (UDR) echoes, and analyze their origin and behavior both classically and quantum mechanically. The molecules are excited by two time-delayed polarization-twisted ultrashort laser pulses and the echoes are measured by exploding the molecules and reconstructing their spatial orientation from the detected recoil ions momenta. Unlike alignment echoes which are induced by linearly polarized pulses, here the axial symmetry is broken by the twisted polarization, giving rise to molecular unidirectional rotation. We find that the rotation sense of the echo is governed by the twisting sense of the second pulse even when its intensity is much weaker than the intensity of the first pulse. In our theoretical study, we rely on classical phase space analysis and on three-dimensional quantum simulations of the laser-driven molecular dynamics. Both approaches nicely reproduce the experimental results. Echoes in general, and the unique UDR echoes in particular, provide new tools for studies of relaxation processes in dense molecular gases.

Control of molecular rotations by laser fields is an active area of research focusing on the alignment/orientation of otherwise isotropic molecular samples. Oriented molecules are useful in many applications, such as molecular orbital tomography, femtosecond imaging of molecular structure, dynamics and chemical reaction control. In this work, we present a novel, previously unreported phenomenon appearing in thermal ensembles of non-linear polar molecules excited by a single THz pulse. We find that the induced orientation lasts long after the excitation pulse is over. In the case of symmetric-top molecules, the ensemble averaged orientation remains indefinitely constant after the pulse, whereas in the case of asymmetric-top molecules the orientation persists for a long time after the end of the pulse. We discuss the underlying mechanism, study its non-monotonous temperature dependence, and show that there exists an optimal temperature for the maximal residual orientation. The persistent orientation implies long lasting macroscopic dipole moment, which may be probed by second (or higher order) harmonic generation., Comment: 6 pages, 4 figures

Echo is a ubiquitous phenomenon found in many physical systems, ranging from spins in magnetic fields to particle beams in hadron accelerators. It is typically observed in inhomogeneously broadened ensembles of nonlinear objects, and is used to eliminate the effects of environmental-induced dephasing, enabling observation of proper, inherent object properties. Here, we report experimental observation of quantum wave packet echoes in a single isolated molecule. In contrast to conventional echoes, here the entire dephasing-rephasing cycle occurs within a single molecule without any inhomogeneous spread of molecular properties, or any interaction with the environment. In our experiments, we use a short laser pulse to impulsively excite a vibrational wave packet in an anharmonic molecular potential, and observe its oscillations and eventual dispersion with time. A second delayed pulsed excitation is applied, giving rise to an echo: a partial recovery of the initial coherent wavepacket. The vibrational dynamics of single molecules is visualized by time-delayed probe pulse dissociating them one at a time. Two mechanisms for the echo formation are discussed: ac Stark-induced molecular potential shaking and creation of depletion-induced "hole" in the nuclear spatial distribution. Interplay between the optically induced echoes and quantum revivals of the vibrational wave packets is observed and theoretically analyzed. The single molecule wave packet echoes may lead to the development of new tools for probing ultrafast intramolecular processes in various molecules., Comment: 9 pages, 7 figures

The nonlinear optical response of materials to exciting light is enhanced by resonances between the incident laser frequencies and the energy levels of the excited material. Traditionally, in molecular nonlinear spectroscopy one tunes the input laser frequencies to the molecular energy levels for highly enhanced doubly or triply resonant interactions. With metasurfaces the situation is different, and by proper design of the nanostructures, one may tune the material energy levels to match the incoming laser frequencies. Here we use multi-parameter genetic algorithm methodologies to optimize the nonlinear Four Wave Mixing response, and show that the intuitive conventional approach of trying to match the transmission spectrum to the relevant laser frequencies indeed leads to strong enhancement, but not necessarily to the optimal design. We demonstrate, experimentally and by direct nonlinear field calculations, that the near field mode distribution and spatial modes overlap are the dominant factor for optimized design.

Alignment and orientation of molecules by intense, ultrashort laser fields are crucial for a variety of applications in physics and chemistry. These include control of high harmonics generation, molecular orbitals tomography, control of molecular photoionization and dissociation processes, production of "molecular movies" with the help of X-ray free-electron laser sources and ultrafast electron diffraction of relativistic electrons. While the dynamics of laser-induced molecular alignment has been extensively studied and demonstrated, molecular orientation is a much more challenging task, especially for asymmetric-top molecules. Here we report the first experimental demonstration of a field-free, all-optical three-dimensional orientation of asymmetric-top molecules by means of phase-locked cross-polarized two-color laser pulses. In addition to the conventional integrated orientation factor, we report the differential degree of orientation which is not amenable to optical measurements, but is readily accessible in our angle-resolved imaging technique. Our scheme applies to a wide class of asymmetric molecules and opens new ways towards controlling their orientation, eventually leading to direct imaging of structure of gas-phase molecules using advanced free electron laser beams with extremely high spatiotemporal resolution.

Nanostructured metasurfaces offer unique capabilities for local control of the phase and amplitude of transmitted and reflected optical waves. Based on this potential, a large number of metasurfaces have been proposed in recent years as alternatives to standard optical elements. In most cases, however, these elements suffer from large chromatic aberrations, thus limiting their usefulness for multi-wavelength or broadband applications. Here, in order to alleviate and correct the chromatic aberrations of individual diffractive elements, we introduce dense vertical stacking of independent metasurfaces, where each layer comprises a different material, and is optimally designed for a different band within the visible spectrum. Using this approach, we demonstrate the first triply RGB achromatic metalens in the visible range and perform color imaging with this lens. We further demonstrate functional beam shaping by constructing a self-aligned integrated element for Stimulated Emission Depletion (STED) microscopy and a lens that provides anomalous dispersive focusing. These demonstrations lead the way to the realization of superachromatic ultrathin optical elements and multiple functional operations, all in in a single nanostructured ultrathin element.

Mountain echoes are a well-known phenomenon, where an impulse excitation is mirrored by the rocks to generate a replica of the original stimulus, often with reverberating recurrences. For spin echoes in magnetic resonance and photon echoes in atomic and molecular systems the role of the mirror is played by a second, time delayed pulse which is able to reverse the ow of time and recreate the original event. Recently, laser-induced rotational alignment and orientation echoes were introduced for molecular gases, and discussed in terms of rotational-phase-space filamentation. Here we present, for the first time, a direct spatiotemporal analysis of various molecular alignment echoes by means of coincidence Coulomb explosion imaging. We observe hitherto unreported spatially rotated echoes, that depend on the polarization direction of the pump pulses, and find surprising imaginary echoes at negative times., Comment: 9 pages, 8 figures and supplementary information

We report the observation of fractional echoes in a double-pulse excited nonlinear system. Unlike standard echoes which appear periodically at delays which are integer multiple of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide the first experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of CO2 molecules excited by a pair of femtosecond laser pulses.

A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multi-layer metamaterial holograms where by the nonlinear process of Third Harmonic Generation, a background free image is formed at a new frequency which is the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analyzed and prospects for future device applications are discussed.

Metasurfaces, and in particular those containing plasmonic-based metallic elements, constitute a particularly attractive set of materials. By means of modern nanolithographic fabrication techniques, flat, ultrathin optical elements may be constructed. However, in spite of their strong optical nonlinearities, plasmonic metasurfaces have so far been investigated mostly in the linear regime. Here we introduce full nonlinear phase control over plasmonic elements in metasurfaces. We show that for nonlinear interactions in a phase-gradient nonlinear metasurface a new anomalous nonlinear phase matching condition prevails, which is the nonlinear analog of the generalized Snell law demonstrated for linear metasurfaces. This phase matching condition is very different from the other known phase matching schemes. The subwavelength phase control of optical nonlinearities provides a foundation for the design of flat nonlinear optical elements based on metasurfaces. Our demonstrated flat nonlinear elements (i.e. lenses) act as generators and manipulators of the frequency-converted signal.

Optimizing the shape of nanostructures and nano antennas for specific optical properties has evolved to be a very fruitful activity. With modern fabrication tools a large variety of possibilities is available for shaping both nanoparticles and nanocavities; in particular nanocavities in thin metal films have emerged as attractive candidates for new metamaterials and strong linear and nonlinear optical systems. Here we rationally design metallic nanocavities to boost their Four Wave Mixing response by resonating the optical plasmonic resonances with the incoming and generated beams. The linear and nonlinear optical responses as well as the propagation of the electric fields inside the cavities are derived from the solution of Maxwell equations by using the 3D finite-differences time domain method. The observed conversion-efficiency of near infra-red to visible light equals or surpasses that of BBO of equivalent thickness. Implications to further optimization for efficient and broadband ultrathin nonlinear optical materials are discussed.

When two or more metallic nanoparticles are in close proximity, their plasmonic modes may interact through the near field, leading to additional resonances of the coupled system or to shifts of their resonant frequencies. This process is analogous to atom-hybridization, as had been proposed by Gersten and Nitzan and modeled by Nordlander et al. The coupling between plasmonic modes can be in-phase (symmetric) or out-of-phase (anti-symmetric), reflecting correspondingly, the "bonding" and "anti-bonding" nature of such configurations. Since the incoming light redistributes the charge distribution around the metallic nanoparticles, its polarization features play a major role in the nonlinear optical probing of the energy-level landscape upon hybridization. Thus, controlling the nature of coupling between metallic nanostructures is of a great importance as it enables tuning their spectral responses leading to novel devices which may surpass the diffraction limit., Comment: arXiv admin note: text overlap with arXiv:1303.0492

We consider optical properties of a gas of molecules that are brought to fast unidirectional spinning by a pulsed laser field. It is shown that a circularly polarized probe light passing through the medium inverts its polarization handedness and experiences a frequency shift controllable by the sense and the rate of molecular rotation. Our analysis is supported by two recent experiments on the laser-induced rotational Doppler effect in molecular gases, and provides a good qualitative and quantitative description of the experimental observations.

The nonlinear optical dynamics of nano-materials comprised of plasmons interacting with quantum emitters is investigated by a self-consistent model based on the coupled Maxwell-Liouville-von Neumann equations. It is shown that ultra-short resonant laser pulses significantly modify the optical properties of such hybrid systems. It is further demonstrated that the energy transfer between interacting molecules and plasmons occurs on a femtosecond time scale and can be controlled with both material and laser parameters., Comment: 15 pages, 9 figures, submitted to ACS Nano

When circularly polarized light is scattered from a rotating target, a rotational Doppler shift (RDS) emerges from an exchange of angular momentum between the spinning object and the electromagnetic field. Here, we used coherently spinning molecules to generate a shift of the frequency of a circularly polarized probe propagating through a gaseous sample. We used a linearly polarized laser pulse to align the molecules, followed by a second delayed pulse polarized at 45{\deg} to achieve unidirectional molecular rotation. The measured RDS is orders of magnitude greater than previously observed by other methods. This experiment provides explicit evidence of unidirectional molecular rotation and paves the way for a new class of measurements in which the rotational direction of molecular reagents may be monitored or actively controlled., Comment: Submitted also to Nature Photonics, current status: "under consideration"

Localized plasmonic modes of metallic nanoparticles may hybridize like those of atoms forming a molecule. However, the rapid decay of the plasmonic fields outside the metal severely limits the range of these interactions to tens of nanometers. Herein, we demonstrate very strong coupling of nanocavities in metal films, sparked by propagating surface plasmons and evident even at much larger distances of hundreds of nanometers for the properly selected metal/wavelength combination. Such strong coupling drastically changes the symmetry of the charge distribution around the nanocavities making it amenable to probing by the nonlinear optical response of the medium. We show that when strongly coupled, equilateral triangular nanocavities lose their individual three-fold symmetry to adopt the lower symmetry of the coupled system and then respond like a single dipolar entity. A quantitative model is suggested for the transition from individual to strongly coupled nanocavities.

Properly polarized and correctly timed femtosecond laser pulses have been demonstrated to create rotational states with a preferred sense of rotation. We show that due to conservation of angular momentum, collisional relaxation of these unidirectionally rotating molecules leads to the generation of macroscopic vortex flows in the gas. The emerging velocity field converges to a self-similar Taylor vortex, and repeated laser excitations cause a continuous stirring of the gas., Comment: 4 pages, 5 figures

The nonlinear response of sub wavelength nano-cavities in thin metal films is investigated. We report the resonant dependence of the Second Harmonic Generation by individual triangular and square holes on shape, size and wavelength. For cavities with internal nano-corrugations, giant field enhancements are observed, making them excellent candidates for high sensitivity spectroscopy.

We demonstrate strong coupling between molecular excited states and surface plasmon modes of a slit array in a thin metal film. The coupling manifests itself as an anti-crossing behavior of the two newly formed polaritons. As the coupling strength grows, a new mode emerges, which is attributed to long range molecular interactions mediated by the plasmonic field. The new, molecular-like mode repels the polariton states, and leads to an opening of energy gaps both below and above the asymptotic free molecule energy., Comment: 8 pages, 6 figures, submitted to PRL

We introduce a new scheme for controlling the sense of molecular rotation. By varying the polarization and the delay between two ultrashort laser pulses, we induce unidirectional molecular rotation, thereby forcing the molecules to rotate clockwise/counterclockwise under field-free conditions. We show that unidirectionally rotating molecules are confined to the plane defined by the two polarization vectors of the pulses, which leads to a permanent anisotropy in the molecular angular distribution. The latter may be useful for controlling collisional cross-sections and optical and kinetic processes in molecular gases. We discuss the application of this control scheme to individual components within a molecular mixture in a selective manner., Comment: 21 pages, 10 figures, Submitted to the New Journal of Physics for the "coherent control" special issue

Combined spectrally and time resolved measurements provide information not otherwise available if performed in either domain alone. We demonstrate a new approach to Four Wave Mixing spectroscopy, where spectral selectivity is achieved by phase matching filtering without a spectrometer, and the time resolved signal is obtained within a single pulse and without mechanically scanning any delays. We analyze the Degenerate Four Wave Mixing signal, and show that a counter-rotating Feynman diagram not previously considered is necessary in order to understand the measured frequency and time resolved spectrograms., Comment: 24 page article with 4 figures

We demonstrate noncontact, high quality surface modification with spatial resolution of ~20 nm. The nanowriting is based on the interaction between the surface and the tip of an Atomic force microscope illuminated by a focused laser beam and hovering 1-4 nanometers above the surface without touching it. The floating tip nanowriting is compared to mechanical surface scratching, and is found to be much more reproducible, and of higher quality. In an Apertureless Scanning Near Field Optical Microscope geometry the tip is illuminated by a focused femtosecond laser, leading to two different, clearly identifiable mechanisms for removing material from the surface: when heated by the laser beam, the hot-tip thermally patterns the surface of low melting temperature soft materials, and when focused right at the apex of the sharp tip, the enhanced electric field of the laser beam causes ablation in high melting temperature metal films., Comment: Version 2: new data added; PDF, 12 pages, 12 figures

Following excitation by a strong ultra-short laser pulse, molecules develop coordinated rotational motion, exhibiting transient alignment along the direction of the laser electric field, followed by periodic full and fractional revivals that depend on the molecular rotational constants. In mixtures, the different species undergo similar rotational dynamics, all starting together but evolving differently with each demonstrating its own periodic revival cycles. For a bimolecular mixture of linear molecules, at predetermined times, one species may attain a maximally aligned state while the other is anti-aligned (i.e. molecular axes are confined in a plane perpendicular to the laser electric field direction). By a properly timed second laser pulse, the rotational excitation of the undesired species may be almost completely removed leaving only the desired species to rotate and periodically realign, thus facilitating further selective manipulations by polarized light. In this paper, such double excitation schemes are demonstrated for mixtures of molecular isotopes (isotopologues) and for nuclear spin isomers., Comment: 23 pages, 13 figures

Single-shot time resolved Coherent Anti-Stokes Raman Scattering (CARS) is presented as a viable method for fast measurements of molecular spectra. The method is based on the short spatial extension of femtosecond pulses and maps time delays between pulses onto the region of intersection between broad beams. The image of the emitted CARS signal contains full temporal information on the field-free molecular dynamics, from which spectral information is extracted. The method is demonstrated on liquid samples of CHBr3 and CHCl3 and the Raman spectrum of the low-lying vibrational states of these molecules is measured.

We propose a generic approach to nonresonant laser cooling of atoms/molecules in a bistable optical cavity. The method exemplifies a photonic version of Sisyphus cooling, in which the matter-dressed cavity extracts energy from the particles and discharges it to the external field as a result of sudden transitions between two stable states.

Strong ultrashort laser pulses give rise to prompt molecular alignment followed by full, half and quarter quantum revivals of the rotational wave packets. In Four Wave Mixing (FWM) experiments, we make use of the long succession of repetitive alignment revivals to demonstrate isotope-selective alignment and time-resolved discrimination between different isotopic species. For two isotopes with a commensurate ratio of their moments of inertia, we observe constructive and destructive interferences of the FWM signals originating from different isotopes. Such destructive interference serves as an indication for distinct transient angular distributions of different isotopic species, paving the way to novel time-resolved analytic techniques, as well as to robust methods for isotope separation. When two pulses are used, enhancement or reduction of the degree of rotational excitation and of the corresponding molecular alignment is observed, depending on the delay between pulses. We implement the double pulse excitation scheme in a binary isotopic mixture, enhancing the rotational excitation of one isotopic component while almost totally reducing the rotational excitation of the other., Comment: 9 pages, 4 figures