Controlling the phase of optical nonlinearity with plasmonic metasurfaces

Metasurfaces are ultrathin structured surfaces that are capable of manipulating the propagation of light in an arbitrary manner. It has been endowed with various functionalities ranging from imaging to holography. In contrast to linear optical processes, the control of wave propagation and diffraction over nonlinear optical processes such as harmonic generations had been much more limited until recently, when the concept of metasurfaces was extended from linear optics to the nonlinear optical regime for manipulating the generation of harmonic signals in an unprecedented level. The key to this recent development lies in the local control over the phase and/or the amplitude of nonlinear polarizability. This new development has led to an array of interesting optical phenomena and nonlinear optical devices that went beyond what had been achieved with traditional nonlinear optical elements. In this review, we summarize the latest progress in controlling the local phase of nonlinearity with plasmonic metasurfaces, with a focus on nonlinear geometric Berry phase and wavefront engineering, and various device applications with nonlinear metasurfaces.

Related papers:

title: Past achievements and future challenges in the development of three-dimensional photonic metamaterials
abstract: Photonic metamaterials are man-made structures composed of tailored micro- or nanostructured metallodielectric subwavelength building blocks. This deceptively simple yet powerful concept allows the realization of many new and unusual optical properties, such as magnetism at optical frequencies, negative refractive index, large positive refractive index, zero reflection through impedance matching, perfect absorption, giant circular dichroism and enhanced nonlinear optical properties. Possible applications of metamaterials include ultrahigh-resolution imaging systems, compact polarization optics and cloaking devices. This Review describes recent progress in the fabrication of three-dimensional metamaterial structures and discusses some of the remaining challenges.

title: From metamaterials to metadevices.
abstract: Metamaterials, artificial electromagnetic media that are structured on the subwavelength scale, were initially suggested for the negative-index 'superlens'. Later metamaterials became a paradigm for engineering electromagnetic space and controlling propagation of waves: the field of transformation optics was born. The research agenda is now shifting towards achieving tunable, switchable, nonlinear and sensing functionalities. It is therefore timely to discuss the emerging field of metadevices where we define the devices as having unique and useful functionalities that are realized by structuring of functional matter on the subwavelength scale. In this Review we summarize research on photonic, terahertz and microwave electromagnetic metamaterials and metadevices with functionalities attained through the exploitation of phase-change media, semiconductors, graphene, carbon nanotubes and liquid crystals. The Review also encompasses microelectromechanical metadevices, metadevices engaging the nonlinear and quantum response of superconductors, electrostatic and optomechanical forces and nonlinear metadevices incorporating lumped nonlinear components.

title: Transforming the optical landscape
abstract: Electromagnetism provides us with some of the most powerful tools in science, encompassing lasers, optical microscopes, magnetic resonance imaging scanners, radar, and a host of other techniques. To understand and develop the technology requires more than a set of formal equations. Scientists and engineers have to form a vivid picture that fires their imaginations and enables intuition to play a full role in the process of invention. It is to this end that transformation optics has been developed, exploiting Faraday’s picture of electric and magnetic fields as lines of force, which can be manipulated by the electrical permittivity and magnetic permeability of surrounding materials. Transformation optics says what has to be done to place the lines of force where we want them to be.

title: Topological photonic phase in chiral hyperbolic metamaterials.
abstract: Recently, the possibility of achieving one-way backscatter immune transportation of light by mimicking the topological properties of certain solid state systems, such as topological insulators, has received much attention. Thus far, however, demonstrations of nontrivial topology in photonics have relied on photonic crystals with precisely engineered lattice structures, periodic on the scale of the operational wavelength and composed of finely tuned, complex materials. Here we propose a novel effective medium approach towards achieving topologically protected photonic surface states robust against disorder on all length scales and for a wide range of material parameters. Remarkably, the nontrivial topology of our metamaterial design results from the Berry curvature arising from the transversality of electromagnetic waves in a homogeneous medium. Our investigation therefore acts to bridge the gap between the advancing field of topological band theory and classical optical phenomena such as the spin Hall effect of light. The effective medium route to topological phases will pave the way for highly compact one-way transportation of electromagnetic waves in integrated photonic circuits.

title: Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction
abstract: Light propagation can be controlled with plasmonic interfaces that introduce abrupt phase shifts along the optical path. Conventional optical components rely on gradual phase shifts accumulated during light propagation to shape light beams. New degrees of freedom are attained by introducing abrupt phase changes over the scale of the wavelength. A two-dimensional array of optical resonators with spatially varying phase response and subwavelength separation can imprint such phase discontinuities on propagating light as it traverses the interface between two media. Anomalous reflection and refraction phenomena are observed in this regime in optically thin arrays of metallic antennas on silicon with a linear phase variation along the interface, which are in excellent agreement with generalized laws derived from Fermat’s principle. Phase discontinuities provide great flexibility in the design of light beams, as illustrated by the generation of optical vortices through use of planar designer metallic interfaces.

title: Planar Photonics with Metasurfaces
abstract: (MMs) are smartly engineered structures with rationally designed, nanostructured building blocks that allow us to build devices with distinct responses to light, acoustic waves, and heat flows that are not attainable with naturally available materials. Plasmonic metasurfaces at work.  Subwavelength metallic nanoantenna arrays patterned onto a surface can provide the basis for planar optical devices, in which bulk optical elements that are typically thousands of wavelengths in size can be "flattened" into a two-dimensional sheet less than a wavelength thick. Kildishev et al. (10.1126/science.1232009) review progress in the optics of metasurfaces and discuss promising applications for surface-confined planar photonics components. Metamaterials, or engineered materials with rationally designed, subwavelength-scale building blocks, allow us to control the behavior of physical fields in optical, microwave, radio, acoustic, heat transfer, and other applications with flexibility and performance that are unattainable with naturally available materials. In turn, metasurfaces—planar, ultrathin metamaterials—extend these capabilities even further. Optical metasurfaces offer the fascinating possibility of controlling light with surface-confined, flat components. In the planar photonics concept, it is the reduced dimensionality of the optical metasurfaces that enables new physics and, therefore, leads to functionalities and applications that are distinctly different from those achievable with bulk, multilayer metamaterials. Here, we review the progress in developing optical metasurfaces that has occurred over the past few years with an eye toward the promising future directions in the field.

title: Plasmonic meta-atoms and metasurfaces
abstract: Metamaterials enable the tailoring of properties like dielectric permittivity and magnetic permeability. Electromagnetic excitations of metamaterial constituents and their interactions are reviewed, as well as promising future directions. Despite the extraordinary degree of interest in optical metamaterials in recent years, the hoped-for devices and applications have, in large part, yet to emerge. It is becoming clear that the first generation of metamaterial-based devices will most probably arise from their two-dimensional equivalents — metasurfaces. In this Review, we describe recent progress in the area of metasurfaces formed from plasmonic meta-atoms. In particular, we approach the subject from the perspective of the fundamental excitations supported by the meta-atoms and the interactions between them. We also identify some areas ripe for future research and indicate likely avenues for future device development.

title: Flat optics with designer metasurfaces.
abstract: Conventional optical components such as lenses, waveplates and holograms rely on light propagation over distances much larger than the wavelength to shape wavefronts. In this way substantial changes of the amplitude, phase or polarization of light waves are gradually accumulated along the optical path. This Review focuses on recent developments on flat, ultrathin optical components dubbed 'metasurfaces' that produce abrupt changes over the scale of the free-space wavelength in the phase, amplitude and/or polarization of a light beam. Metasurfaces are generally created by assembling arrays of miniature, anisotropic light scatterers (that is, resonators such as optical antennas). The spacing between antennas and their dimensions are much smaller than the wavelength. As a result the metasurfaces, on account of Huygens principle, are able to mould optical wavefronts into arbitrary shapes with subwavelength resolution by introducing spatial variations in the optical response of the light scatterers. Such gradient metasurfaces go beyond the well-established technology of frequency selective surfaces made of periodic structures and are extending to new spectral regions the functionalities of conventional microwave and millimetre-wave transmit-arrays and reflect-arrays. Metasurfaces can also be created by using ultrathin films of materials with large optical losses. By using the controllable abrupt phase shifts associated with reflection or transmission of light waves at the interface between lossy materials, such metasurfaces operate like optically thin cavities that strongly modify the light spectrum. Technology opportunities in various spectral regions and their potential advantages in replacing existing optical components are discussed.

title: Dielectric gradient metasurface optical elements
abstract: Extending the range of planar optics To build miniature optical devices, scientists are using silicon to replace bulky three-dimensional devices with flat versions. A patterned surface consisting of dense arrays of nanoscale silicon strips, which act as antennae, can be designed to work as transparent optical devices for the manipulation of light. Lin et al. used their versatile patterning technique to create a suite of planar optical elements. By patterning a 100-nm layer of silicon into a dense arrangement of nano-antennae, they were able to fabricate gratings, lenses, and axicons—a device that can add a shape to a propagating light beam. Science, this issue p. 298 Silicon-based metasurfaces can extend the range of planar optical devices. Gradient metasurfaces are two-dimensional optical elements capable of manipulating light by imparting local, space-variant phase changes on an incident electromagnetic wave. These surfaces have thus far been constructed from nanometallic optical antennas, and high diffraction efficiencies have been limited to operation in reflection mode. We describe the experimental realization and operation of dielectric gradient metasurface optical elements capable of also achieving high efficiencies in transmission mode in the visible spectrum. Ultrathin gratings, lenses, and axicons have been realized by patterning a 100-nanometer-thick Si layer into a dense arrangement of Si nanobeam antennas. The use of semiconductors can broaden the general applicability of gradient metasurfaces, as they offer facile integration with electronics and can be realized by mature semiconductor fabrication technologies.

title: Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter.
abstract: The polarization of light plays a central role in its interaction with matter, in situations ranging from familiar (for example, reflection and transmission at an interface) to sophisticated (for example, nonlinear optics). Polarization control is therefore pivotal for many optical systems, and achieved using bulk devices such as wave-plates and beam-splitters. The move towards optical system miniaturization therefore motivates the development of micro- and nanostructures for polarization control. For such control to be complete, one must distinguish not only between linear polarizations, but also between left- and right-circular polarizations. Some previous works used surface plasmons to this end, but these are inherently lossy. Other works used complex-layered structures. Here we demonstrate a planar dielectric chirality-distinguishing beam-splitter. The beam-splitter consists of amorphous silicon nanofins on a glass substrate and deflects left- and right-circularly polarized beams into different directions. Contrary to intuitive expectations, we utilize an achiral architecture to realize a chiral beam-splitting functionality.

title: Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control.
abstract: We experimentally demonstrate a functional silicon metadevice at telecom wavelengths that can efficiently control the wavefront of optical beams by imprinting a spatially varying transmittance phase independent of the polarization of the incident beam. Near-unity transmittance efficiency and close to 0-2π phase coverage are enabled by utilizing the localized electric and magnetic Mie-type resonances of low-loss silicon nanoparticles tailored to behave as electromagnetically dual-symmetric scatterers. We apply this concept to realize a metadevice that converts a Gaussian beam into a vortex beam. The required spatial distribution of transmittance phases is achieved by a variation of the lattice spacing as a single geometric control parameter.

title: Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging
abstract: Multifunction planar optics Specially designed two-dimensional (2D) arrays of nanometer-scale metallic antennas, or metasurfaces, may allow bulky optical components to be shrunk down to a planar device structure. Khorasaninejad et al. show that arrays of nanoscale fins of TiO can function as high-end optical lenses. At just a fraction of the size of optical objectives, such planar devices could turn your phone camera or your contact lens into a compound microscope. Maguid et al. interleaved sparse 2D arrays of metal antennas to get multifunctional behavior from the one planar device structure (see the Perspective by Litchinitser). The enhanced functionality of such designed metasurfaces could be used in sensing applications or to increase the communication capacity of nanophotonic networks. Science, this issue pp. 1190 and 1202; see also p. 1177 A planar metasurface can function as a high-end optical lens. Subwavelength resolution imaging requires high numerical aperture (NA) lenses, which are bulky and expensive. Metasurfaces allow the miniaturization of conventional refractive optics into planar structures. We show that high-aspect-ratio titanium dioxide metasurfaces can be fabricated and designed as metalenses with NA = 0.8. Diffraction-limited focusing is demonstrated at wavelengths of 405, 532, and 660 nm with corresponding efficiencies of 86, 73, and 66%. The metalenses can resolve nanoscale features separated by subwavelength distances and provide magnification as high as 170×, with image qualities comparable to a state-of-the-art commercial objective. Our results firmly establish that metalenses can have widespread applications in laser-based microscopy, imaging, and spectroscopy.

title: Photonic Damascene process for integrated high-Q microresonator based nonlinear photonics
abstract: High confinement, integrated silicon nitride (SiN) waveguides have recently emerged as an attractive platform for on-chip nonlinear optical devices. The fabrication of high-Q SiN microresonators with anomalous group velocity dispersion has enabled broadband nonlinear optical frequency comb generation. Such frequency combs have been successfully applied in coherent communication and ultrashort pulse generation. However, the reliable fabrication of high confinement waveguides from stoichiometric, high stress SiN remains challenging. Here we present a novel photonic Damascene fabrication process enabling the use of substrate topography for stress control and thin film crack prevention. With close to unity sample yield we fabricate microresonators with 1.35 mu m thick waveguides and optical Q-factors of 3.7 x 10(6) and demonstrate single temporal dissipative Kerr soliton based coherent optical frequency comb generation. Our newly developed process is also interesting for other material platforms, photonic integration, and mid-infrared Kerr comb generation.

title: Gate-controlled diode structure based electro-optical interfaces in standard silicon-CMOS integrated circuitry.
abstract: In this paper, we discuss the emission of visible light by a monolithically integrated silicon gate-controlled diode with the p-n junction reverse-biased. Since the MOS-like diode utilizes the field effect to modulate the optical output, the modulation speed will benefit from this mechanism. Hence, a silicon gate-controlled diode structure for optical modulation analyzed its modulation principle, its dynamic characteristics are presented, and the bandwidth of the device is considered to approach GHz in theory due to the field-induced emission mechanism. The prototype MOS-like diode opens up the design of multiterminal silicon light emitting devices (LEDs), where gate electrodes with more than one gate contact overlap several junctions with different junction intersection geometries. The device appears as a good candidate for optical modulation within silicon technology.

title: Dual-polarity plasmonic metalens for visible light
abstract: Surface topography and refractive index profile dictate the deterministic functionality of a lens. The polarity of most lenses reported so far, that is, either positive (convex) or negative (concave), depends on the curvatures of the interfaces. Here we experimentally demonstrate a counter-intuitive dual-polarity flat lens based on helicity-dependent phase discontinuities for circularly polarized light. Specifically, by controlling the helicity of the input light, the positive and negative polarity are interchangeable in one identical flat lens. Helicity-controllable real and virtual focal planes, as well as magnified and demagnified imaging, are observed on the same plasmonic lens at visible and near-infrared wavelengths. The plasmonic metalens with dual polarity may empower advanced research and applications in helicity-dependent focusing and imaging devices, angular-momentum-based quantum information processing and integrated nano-optoelectronics.

title: Metasurface holograms reaching 80% efficiency.
abstract: Surfaces covered by ultrathin plasmonic structures--so-called metasurfaces--have recently been shown to be capable of completely controlling the phase of light, representing a new paradigm for the design of innovative optical elements such as ultrathin flat lenses, directional couplers for surface plasmon polaritons and wave plate vortex beam generation. Among the various types of metasurfaces, geometric metasurfaces, which consist of an array of plasmonic nanorods with spatially varying orientations, have shown superior phase control due to the geometric nature of their phase profile. Metasurfaces have recently been used to make computer-generated holograms, but the hologram efficiency remained too low at visible wavelengths for practical purposes. Here, we report the design and realization of a geometric metasurface hologram reaching diffraction efficiencies of 80% at 825 nm and a broad bandwidth between 630 nm and 1,050 nm. The 16-level-phase computer-generated hologram demonstrated here combines the advantages of a geometric metasurface for the superior control of the phase profile and of reflectarrays for achieving high polarization conversion efficiency. Specifically, the design of the hologram integrates a ground metal plane with a geometric metasurface that enhances the conversion efficiency between the two circular polarization states, leading to high diffraction efficiency without complicating the fabrication process. Because of these advantages, our strategy could be viable for various practical holographic applications.

title: Broadband Hybrid Holographic Multiplexing with Geometric Metasurfaces.
abstract: An effective way for broadband holographic multiplexing based on geometric metasurfaces is demonstrated by the integration of several recording channels into a single device. Each image can be individually addressed with a unique set of parameters, such as circular polarization, position, and angle. Such a technique paves the way for a wide range of applications related to optical patterning, encryption, and information processing.

title: Geometric metasurface fork gratings for vortex‐beam generation and manipulation
abstract: In recent years, optical vortex beams possessing orbital angular momentum have received much attention due to their potential for high-capacity optical communications. This capability arises from the unbounded topological charges of orbital angular momentum (OAM) that provide infinite freedoms for encoding information. The two most common approaches for generating vortex beams are through fork diffraction gratings and spiral phase plates. While realization of conventional spiral phase plate requires complicated 3D fabrication, the emerging field of metasurfaces has provided a planar and facile solution for generating vortex beams of arbitrary orbit angular momentum. Among various types of metasurfaces, the geometric phase metasurface has shown great potential for robust control of light- and spin-controlled wave propagation. Here, we realize a novel type of geometric metasurface fork grating that seamlessly combine the functionality of a metasurface phase plate for vortex-beam generation, and that of a linear phase gradient metasurface for controlling the wave-propagation direction. The metasurface fork grating is therefore capable of simultaneously controlling both the spin and the orbital angular momentum of light.

title: Planar metasurface retroreflector
abstract: Metasurfaces are two-dimensional arrangements of subwavelength scatterers that control the propagation of optical waves. Here, we show that cascaded metasurfaces, each performing a predefined mathematical transformation, provide a new optical design framework that enables new functionalities not yet demonstrated with single metasurfaces. Specifically, we demonstrate that retroreflection can be achieved with two vertically stacked planar metasurfaces, the first performing a spatial Fourier transform and its inverse, and the second imparting a spatially varying momentum to the Fourier transform of the incident light. Using this concept, we fabricate and test a planar monolithic near-infrared retroreflector composed of two layers of silicon nanoposts, which reflects light along its incident direction with a normal incidence efficiency of 78% and a large half-power field of view of 60°. The metasurface retroreflector demonstrates the potential of cascaded metasurfaces for implementing novel high-performance components, and enables low-power and low-weight passive optical transmitters.

title: Metasurface Polarization Optics: Independent Phase Control of Arbitrary Orthogonal States of Polarization.
abstract: We present a method allowing for the imposition of two independent and arbitrary phase profiles on any pair of orthogonal states of polarization-linear, circular, or elliptical-relying only on simple, linearly birefringent wave plate elements arranged into metasurfaces. This stands in contrast to previous designs which could only address orthogonal linear, and to a limited extent, circular polarizations. Using this approach, we demonstrate chiral holograms characterized by fully independent far fields for each circular polarization and elliptical polarization beam splitters, both in the visible. This approach significantly expands the scope of metasurface polarization optics.

title: Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light.
abstract: Here, we investigate the spin-induced manipulation of orbitals using metasurfaces constructed from geometric phase elements. By carrying the spin effects to the orbital angular momentum, we show experimentally the transverse angular splitting between the two spins in the reciprocal space with metasurface, as a direct observation of the optical spin Hall effect, and an associated global orbital rotation through the effective orientations of the geometric phase elements. Such spin-orbit interaction from a metasurface with a definite topological charge can be geometrically interpreted using the recently developed high order Poincaré sphere picture. These investigations may give rise to an extra degree of freedom in manipulating optical vortex beams and orbitals using "spin-enabled" metasurfaces.

title: Quantal phase factors accompanying adiabatic changes
abstract: A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.

title: Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings.
abstract: Space-variant Pancharatnam-Berry phase optical elements based on computer-generated subwavelength gratings are presented. By continuously controlling the local orientation and period of the grating we can achieve any desired phase element. We present a theoretical analysis and experimentally demonstrate a Pancharatnam-Berry phase-based diffraction grating for laser radiation at a wavelength of 10.6microm.

title: Towards the origin of the nonlinear response in hybrid plasmonic systems.
abstract: Plasmonic systems are known for their distinct nonlinear optical properties when compared to purely dielectric materials. Although it is well accepted that the enhanced nonlinear processes in plasmonic-dielectric compounds are related to the excitation of localized plasmon resonances, their exact origin is concealed by the local field enhancement in the surrounding material and the nonlinearity in the metal. Here, we show that the origin of third-harmonic generation in hybrid plasmonic-dielectric compounds can be unambiguously identified from the shape of the nonlinear spectrum.

title: Linear and Nonlinear Fano Resonance on two-dimensional Magnetic Metamaterials
abstract: We demonstrate that both linear and nonlinear Fano resonances can be realized on two dimensional magnetic metamaterials. The Fano resonance comes from the interference between localized magnetic plasmon resonance and propagating surface plasmon polaritons. When studying the linear optical response of the metamaterial structure, this interference phenomenon was observed in the ellipsometric spectrum. By finely tailoring the geometrical parameters of the magnetic metamaterial device, the nonlinear Fano response was tuned to a near-infrared wavelength (1.61-1.8 {\mu}m) of femtosecond pump laser, and Fano-type modulation of the third harmonic generation was found and agrees well with our theoretical model.

title: Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna.
abstract: The ability to convert low-energy quanta into a quantum of higher energy is of great interest for a variety of applications, including bioimaging, drug delivery and photovoltaics. Although high conversion efficiencies can be achieved using macroscopic nonlinear crystals, upconverting light at the nanometre scale remains challenging because the subwavelength scale of materials prevents the exploitation of phase-matching processes. Light-plasmon interactions that occur in nanostructured noble metals have offered alternative opportunities for nonlinear upconversion of infrared light, but conversion efficiency rates remain extremely low due to the weak penetration of the exciting fields into the metal. Here, we show that third-harmonic generation from an individual semiconductor indium tin oxide nanoparticle is significantly enhanced when coupled within a plasmonic gold dimer. The plasmonic dimer acts as a receiving optical antenna, confining the incident far-field radiation into a near field localized at its gap; the indium tin oxide nanoparticle located at the plasmonic dimer gap acts as a localized nonlinear transmitter upconverting three incident photons at frequency ω into a photon at frequency 3ω. This hybrid nanodevice provides third-harmonic-generation enhancements of up to 10(6)-fold compared with an isolated indium tin oxide nanoparticle, with an effective third-order susceptibility up to 3.5 × 10(3) nm V(-2) and conversion efficiency of 0.0007%. We also show that the upconverted third-harmonic emission can be exploited to probe the near-field intensity at the plasmonic dimer gap.

title: Third Harmonic Mechanism in Complex Plasmonic Fano Structures
abstract: We perform third harmonic spectroscopy of dolmen-type nanostructures, which exhibit plasmonic Fano resonances in the near-infrared. Strong third harmonic emission is predominantly radiated close to the low energy peak of the Fano resonance. Furthermore, we find that the third harmonic polarization of the subradiant mode interferes destructively and diminishes the nonlinear signal in the far-field. By comparing the experimental third harmonic spectra with finite element simulations and an anharmonic oscillator model, we find strong indications that the source of the third harmonic is the optical nonlinearity of the bare gold enhanced by the resonant plasmonic polarization.

title: Symmetry-selective third-harmonic generation from plasmonic metacrystals.
abstract: Nonlinear processes are often governed by selection rules imposed by the symmetries of the molecular configurations. The most well-known examples include the role of centrosymmetry breaking for the generation of even harmonics, and the selection rule related to the rotational symmetry in harmonic generation for fundamental beams with circular polarizations. While the role of centrosymmetry breaking in second harmonic generation has been extensively studied in plasmonic systems, the investigation of selection rules pertaining to circular polarization states of harmonic generation is limited to crystals, i.e., symmetries at the atomic level. In this Letter we demonstrate the rotational symmetry dependent third harmonic generation from nonlinear plasmonic metacrystals. We show that the selection rule can be imposed by the rotational symmetry of metacrystals embedded into an isotropic organic nonlinear thin film. The results presented here may open new avenues for designing symmetry-dependent nonlinear optical responses with tailored plasmonic nanostructures.

title: Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response.
abstract: We observe enhanced third-harmonic generation from silicon nanodisks exhibiting both electric and magnetic dipolar resonances. Experimental characterization of the nonlinear optical response through third-harmonic microscopy and spectroscopy reveals that the third-harmonic generation is significantly enhanced in the vicinity of the magnetic dipole resonances. The field localization at the magnetic resonance results in two orders of magnitude enhancement of the harmonic intensity with respect to unstructured bulk silicon with the conversion efficiency limited only by the two-photon absorption in the substrate.

title: Continuous control of the nonlinearity phase for harmonic generations.
abstract: The capability of locally engineering the nonlinear optical properties of media is crucial in nonlinear optics. Although poling is the most widely employed technique for achieving locally controlled nonlinearity, it leads only to a binary nonlinear state, which is equivalent to a discrete phase change of π in the nonlinear polarizability. Here, inspired by the concept of spin-rotation coupling, we experimentally demonstrate nonlinear metasurfaces with homogeneous linear optical properties but spatially varying effective nonlinear polarizability with continuously controllable phase. The continuous phase control over the local nonlinearity is demonstrated for second and third harmonic generation by using nonlinear metasurfaces consisting of nanoantennas of C3 and C4 rotational symmetries, respectively. The continuous phase engineering of the effective nonlinear polarizability enables complete control over the propagation of harmonic generation signals. Therefore, this method seamlessly combines the generation and manipulation of harmonic waves, paving the way for highly compact nonlinear nanophotonic devices.

title: Nonlinear Fano-Resonant Dielectric Metasurfaces.
abstract: Strong nonlinear light-matter interaction is highly sought-after for a variety of applications including lasing and all-optical light modulation. Recently, resonant plasmonic structures have been considered promising candidates for enhancing nonlinear optical processes due to their ability to greatly enhance the optical near-field; however, their small mode volumes prevent the inherently large nonlinear susceptibility of the metal from being efficiently exploited. Here, we present an alternative approach that utilizes a Fano-resonant silicon metasurface. The metasurface results in strong near-field enhancement within the volume of the silicon resonator while minimizing two photon absorption. We measure a third harmonic generation enhancement factor of 1.5 × 10(5) with respect to an unpatterned silicon film and an absolute conversion efficiency of 1.2 × 10(-6) with a peak pump intensity of 3.2 GW cm(-2). The enhanced nonlinearity, combined with a sharp linear transmittance spectrum, results in transmission modulation with a modulation depth of 36%. The modulation mechanism is studied by pump-probe experiments.

title: Giant Nonlinear Optical Activity of Achiral Origin in Planar Metasurfaces with Quadratic and Cubic Nonlinearities.
abstract: 3D chirality is shown to be unnecessary for introducing strong circular dichroism for harmonic generations. Specifically, near-unity circular dichroism for both second-harmonic generation and third-harmonic generations is demonstrated on suitably designed ultrathin plasmonic metasurfaces with only 2D planar chirality. The study opens up new routes for designing chip-type biosensing platform, which may allow for highly sensitive detection of bio- and chemical molecules with weak chirality.

title: Enhanced Third Harmonic Generation in Single Germanium Nanodisks Excited at the Anapole Mode.
abstract: We present an all-dielectric germanium nanosystem exhibiting a strong third order nonlinear response and efficient third harmonic generation in the optical regime. A thin germanium nanodisk shows a pronounced valley in its scattering cross section at the dark anapole mode, while the electric field energy inside the disk is maximized due to high confinement within the dielectric. We investigate the dependence of the third harmonic signal on disk size and pump wavelength to reveal the nature of the anapole mode. Each germanium nanodisk generates a high effective third order susceptibility of χ((3)) = 4.3 × 10(-9) esu, corresponding to an associated third harmonic conversion efficiency of 0.0001% at an excitation wavelength of 1650 nm, which is 4 orders of magnitude greater than the case of an unstructured germanium reference film. Furthermore, the nonlinear conversion via the anapole mode outperforms that via the radiative dipolar resonances by about 1 order of magnitude, which is consistent with our numerical simulations. These findings open new possibilities for the optimization of upconversion processes on the nanoscale through the appropriate engineering of suitable dielectric materials.

title: Multipolar Third-Harmonic Generation Driven by Optically Induced Magnetic Resonances
abstract: We analyze third-harmonic generation from high-index dielectric nanoparticles and discuss the basic features and multipolar nature of the parametrically generated electromagnetic fields near the Mie-type optical resonances. By combining both analytical and numerical methods, we study the nonlinear scattering from simple nanoparticle geometries such as spheres and disks in the vicinity of the magnetic dipole resonance. We reveal the approaches for manipulating and directing the resonantly enhanced nonlinear emission with subwavelength all-dielectric structures that can be of particular interest for novel designs of nonlinear optical antennas and engineering the magnetic optical nonlinear response at nanoscale.

title: Nonlinear metamaterials for holography
abstract: 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 multilayer metamaterial holograms. A background free image is formed at a new frequency—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 analysed and prospects for future device applications are discussed.

title: Third Harmonic Generation Enhanced by Multipolar Interference in Complementary Silicon Metasurfaces
abstract: Nonlinear harmonic generation in metasurfaces has shown great promises for applications such as novel light sources, nonlinear holography and nonlinear imaging. In particular, dielectric metasurfaces have shown multi-fold enhancement of the harmonic efficiency in comparison to their plasmonic counterparts due to lower optical loss and much higher damage threshold. In this work, we propose to enhance the efficiency of the third harmonic generation in a complementary silicon nonlinear metasurface, consisting of nanoapertures of cross-like shape in the silicon film. The efficiency enhancement is based on a multipolar interference between the magnetic dipole and electric quadrupole, resulting in significant near-field enhancement and a large mode volume of the nonlinear interaction. The measured efficiency of third harmonic generation from the silicon metasurface is 100 times higher than that from a planar silicon film of the same thickness. Numerical analysis of the near-field resonant modes confirms the mul...

title: Surface-enhanced nonlinear four-wave mixing.
abstract: We report on a particularly strong third-order nonlinear response from nanostructured gold surfaces. Two incident laser beams with frequencies omega{1} and omega{2} give rise to four-wave mixing (4WM) fields with frequencies 2omega{1}-omega{2} and 2omega{2}-omega{1}. We demonstrate that the nonlinear response can be purely evanescent and that nanostructured surfaces convert the evanescent energy into propagating radiation, thereby increasing the efficiency of frequency conversion. The emitted 4WM radiation is found to be directional, polarized, coherent, and both frequency and angle tunable. The ability to perform efficient frequency conversion in reduced dimensions provides new opportunities for nanophotonics and active plasmonics.

title: Subwavelength imaging using phase-conjugating nonlinear nanoantenna arrays.
abstract: We investigate the use of nonlinear metasurfaces formed by plasmonic nanoantennas loaded with χ(3) nonlinear elements, in order to realize subwavelength imaging based on phase conjugation and time reversal. The nanoantennas' plasmonic resonance is used to boost the nonlinear response over an ultrathin surface, meeting the conditions for efficient phase conjugation necessary for imaging applications. Pairing two such surfaces, we put forward a realistic design for a time-reversal 'perfect lens', which can overcome the limitations in resolution and sensitivity to losses typical of negative-index lenses.

title: Optical negative refraction by four-wave mixing in thin metallic nanostructures.
abstract: The law of refraction first derived by Snellius and later introduced as the Huygens-Fermat principle, states that the incidence and refracted angles of a light wave at the interface of two different materials are related to the ratio of the refractive indices in each medium. Whereas all natural materials have a positive refractive index and therefore exhibit refraction in the positive direction, artificially engineered negative index metamaterials have been shown capable of bending light waves negatively. Such a negative refractive index is the key to achieving a perfect lens that is capable of imaging well below the diffraction limit. However, negative index metamaterials are typically lossy, narrow band, and require complicated fabrication processes. Recently, an alternative approach to obtain negative refraction from a very thin nonlinear film has been proposed and experimentally demonstrated in the microwave region. However, such approaches use phase conjugation, which makes optical implementations difficult. Here, we report a simple but different scheme to demonstrate experimentally nonlinear negative refraction at optical frequencies using four-wave mixing in nanostructured metal films. The refractive index can be designed at will by simply tuning the wavelengths of the interacting waves, which could have potential impact on many important applications, such as superlens imaging.

title: Phase Mismatch–Free Nonlinear Propagation in Optical Zero-Index Materials
abstract: Nonlinear Optics Made Easier Nonlinear optical materials can change their optical properties in the presence of light. The nonlinearity results from the constructive addition of interacting photons, but the amount of nonlinear light produced is crucially dependent on meeting strict phase-matching conditions of the interacting photon fields. Suchowski et al. (p. 1223; see the Perspective by Kauranen) now show that metamaterials can be designed with optical properties that relax the phase-matching requirements. At a specific wavelength where the metamaterial exhibits zero refractive index, the photons are found to interact nonlinearly with the phasematching done automatically. Metamaterials relax the requirement for phase matching in nonlinear optics. Phase matching is a critical requirement for coherent nonlinear optical processes such as frequency conversion and parametric amplification. Phase mismatch prevents microscopic nonlinear sources from combining constructively, resulting in destructive interference and thus very low efficiency. We report the experimental demonstration of phase mismatch–free nonlinear generation in a zero-index optical metamaterial. In contrast to phase mismatch compensation techniques required in conventional nonlinear media, the zero index eliminates the need for phase matching, allowing efficient nonlinear generation in both forward and backward directions. We demonstrate phase mismatch–free nonlinear generation using intrapulse four-wave mixing, where we observed a forward-to-backward nonlinear emission ratio close to unity. The removal of phase matching in nonlinear optical metamaterials may lead to applications such as multidirectional frequency conversion and entangled photon generation.

title: Coherent Fano resonances in a plasmonic nanocluster enhance optical four-wave mixing
abstract: Plasmonic nanoclusters, an ordered assembly of coupled metallic nanoparticles, support unique spectral features known as Fano resonances due to the coupling between their subradiant and superradiant plasmon modes. Within the Fano resonance, absorption is significantly enhanced, giving rise to highly localized, intense near fields with the potential to enhance nonlinear optical processes. Here, we report a structure supporting the coherent oscillation of two distinct Fano resonances within an individual plasmonic nanocluster. We show how this coherence enhances the optical four-wave mixing process in comparison with other double-resonant plasmonic clusters that lack this property. A model that explains the observed four-wave mixing features is proposed, which is generally applicable to any third-order process in plasmonic nanostructures. With a larger effective susceptibility χ(3) relative to existing nonlinear optical materials, this coherent double-resonant nanocluster offers a strategy for designing high-performance third-order nonlinear optical media.

title: Plasmon-enhanced four-wave mixing for superresolution applications.
abstract: We introduce a nonlinear optical approach to transform spatial information stored in evanescent waves into propagating ones: we study analytically the use of partially degenerate four-wave mixing in thin metallic film to map a band of evanescent waves at a given frequency into a propagating-wave band at a different one. The relatively low efficiency of this process is compensated by setting the pump beam, mediating this transformation, to be a surface plasmon polariton, whose field enhancement increases the nonlinear interaction strength. This setting can be utilized for nonresonant plasmon-assisted superresolution applications that support transverse-electric polarization, in contrast to linear plasmonic imaging (such as superlens) that can only transfer transverse-magnetic waves.

title: Giant nonlinear response at a plasmonic nanofocus drives efficient four-wave mixing
abstract: A plasmonic route for mixing waves Nonlinear optics typically requires photons to interact over distances spanning hundreds or thousands of wavelengths. Nonlinear optical devices therefore tend to be bulk components. Nielsen et al. used a polymer material with a high nonlinear coefficient that they embedded within a plasmonic cavity to show that the interaction length scale could be reduced dramatically. The plasmonic cavity focused the light down to the nanoscale, providing an intense electromagnetic field that induced the nonlinear process of four-wave mixing in the polymer. The technique provides a versatile platform for compact nonlinear optical devices. Science, this issue p. 1179 Efficient wave mixing in plasmonic waveguides provides a versatile platform for compact nonlinear optical devices. Efficient optical frequency mixing typically must accumulate over large interaction lengths because nonlinear responses in natural materials are inherently weak. This limits the efficiency of mixing processes owing to the requirement of phase matching. Here, we report efficient four-wave mixing (FWM) over micrometer-scale interaction lengths at telecommunications wavelengths on silicon. We used an integrated plasmonic gap waveguide that strongly confines light within a nonlinear organic polymer. The gap waveguide intensifies light by nanofocusing it to a mode cross-section of a few tens of nanometers, thus generating a nonlinear response so strong that efficient FWM accumulates over wavelength-scale distances. This technique opens up nonlinear optics to a regime of relaxed phase matching, with the possibility of compact, broadband, and efficient frequency mixing integrated with silicon photonics.

title: Nonlinear plasmonics
abstract: Nonlinear optical effects (Box 1) have an important role in modern photonic functionalities, including control over the frequency spectrum of laser light, generation of ultrashort pulses, all-optical signal processing and ultrafast switching1. Optical nonlinearities are inherently weak, because they are governed by photon–photon interactions enabled by materials. They are superlinearly dependent on the electromagnetic field and can be strengthened in material environments that provide mechanisms for field enhancement. An increased effective nonlinear optical response can be achieved through plasmonic effects. Such effects arise from coherent oscillations of conduction electrons near the surface of noblemetal structures2,3 (Box 2). For extended metal surfaces, this gives rise to surface plasmon polaritons (SPPs), which are surface electromagnetic waves propagating at the metal–dielectric interface. For metal nanoparticles, the response arises from localized surface plasmons (LSPs), whose resonances depend on the particle size and shape. New concepts, including SPP crystals2 and waveguides4, nano-antennas5 and plasmonic metamaterials6, can be used to tailor the optical responses further through the resonances of the individual units and their mutual electromagnetic coupling. Plasmonic excitations can boost nonlinear optical effects in several ways. First, the coupling of light to surface plasmons can result in strong local electromagnetic fields2,5, significantly enhancing optical processes. A prime example is surface-enhanced Raman scattering, where plasmonic excitations at rough or engineered metal surfaces can enhance the inherently weak Raman process by orders of magnitude, allowing even single-molecule detection7. In nonlinear optics, this naturally translates to higher effective nonlinearities of the metal itself or the surrounding dielectric material. Second, plasmonic excitations can be extremely sensitive to dielectric properties of the metal and the surrounding medium. This is the basis for label-free plasmonic sensors: minute modifications of the refractive index near the metal surface result in significant modifications of the plasmonic resonance8. In nonlinear optics, this extraordinary sensitivity can be exploited to control light with light, using a control beam to induce a nonlinear change in the dielectric properties of one of the materials, thus modifying the plasmonic resonances and the propagation of a signal beam. Finally, plasmonic excitations can respond on the timescale of a few femtoseconds, allowing ultrafast processing of optical signals3. Nonlinear effects in plasmonics could therefore lead to several interesting nanophotonic functionalities, and we are now seeing the emergence of metal nanostructures designed to favour specific nonlinear processes. Nonlinear plasmonics

title: Colloquium : Nonlinear metamaterials
abstract: This Colloquium presents an overview of the research on nonlinear electromagnetic metamaterials. The developed theoretical approaches and experimental designs are summarized, along with a systematic description of various phenomena available with nonlinear metamaterials.

title: Nonlinear photonic metasurfaces
abstract: Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the ‘meta-atoms’), enable the manipulation of light–matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing. Photonic metasurfaces can be used to control the polarization, phase and amplitude of light. Nonlinear metasurfaces enable giant nonlinear optical chirality, realization of the geometric Berry phase, wavefront engineering, and optical switching and modulation, and hold potential for on-chip applications.

title: All-dielectric meta-optics and non-linear nanophotonics
abstract: Most optical metamaterials fabricated and studied to date employ metallic components resulting in significant losses, heat and overall low efficiencies. A new era of metamaterial physics is associated with all-dielectric meta-optics, which employs electric and magnetic Mie resonances of subwavelength particles with high refractive index for an optically induced magnetic response, thus underpinning a new approach to design and fabricate functional and practical metadevices. Here we review the recent developments in meta-optics and subwavelength dielectric photonics and demonstrate that the Mie resonances can play a crucial role in the realization of the unique functionalities of meta-atoms, also driving novel effects in the fields of metamaterials and nanophotonics. We discuss the recent research frontiers in all-dielectric meta-optics and uncover how Mie resonances can be employed for a flexible control of light with full phase and amplitude engineering, including unidirectional metadevices, highly transparent metasurfaces, non-linear nanophotonics and topological photonics.

title: Harmonic generation and selection rules in nonlinear optics
abstract: A simple procedure, based on the transformation properties of the nonlinear susceptibility tensors of different ranks referred to appropriate coordinate systems, is given for studying the selection rules and polarization characters in regard to all orders of harmonics. By this procedure, results covering both linearly and circularly polarized incident light for all the 32 crystal classes with some simplifying restrictions are obtained and listed in the paper. Attention is drawn to special features in each case. There is complete agreement with what has been reported earlier by Tang and Herbert Rabin for circularly polarized incident light.

title: Second-Harmonic Generation from Magnetic Metamaterials
abstract: We observe second-harmonic generation from metamaterials composed of split-ring resonators excited at 1.5-micrometer wavelength. Much larger signals are detected when magnetic-dipole resonances are excited, as compared with purely electric-dipole resonances. The experiments are consistent with calculations based on the magnetic component of the Lorentz force exerted on metal electrons—an intrinsic second-harmonic generation mechanism that plays no role in natural materials. This unusual mechanism becomes relevant in our work as a result of the enhancement and the orientation of the local magnetic fields associated with the magnetic-dipole resonances of the split-ring resonators.

title: Collective effects in second-harmonic generation from split-ring-resonator arrays.
abstract: Optical experiments on second-harmonic generation from split-ring-resonator square arrays show a nonmonotonic dependence of the conversion efficiency on the lattice constant. This finding is interpreted in terms of a competition between dilution effects and linewidth or near-field changes due to interactions among the individual elements in the array.

title: Predicting nonlinear properties of metamaterials from the linear response.
abstract: The discovery of optical second harmonic generation in 1961 started modern nonlinear optics. Soon after, R. C. Miller found empirically that the nonlinear susceptibility could be predicted from the linear susceptibilities. This important relation, known as Miller's Rule, allows a rapid determination of nonlinear susceptibilities from linear properties. In recent years, metamaterials, artificial materials that exhibit intriguing linear optical properties not found in natural materials, have shown novel nonlinear properties such as phase-mismatch-free nonlinear generation, new quasi-phase matching capabilities and large nonlinear susceptibilities. However, the understanding of nonlinear metamaterials is still in its infancy, with no general conclusion on the relationship between linear and nonlinear properties. The key question is then whether one can determine the nonlinear behaviour of these artificial materials from their exotic linear behaviour. Here, we show that the nonlinear oscillator model does not apply in general to nonlinear metamaterials. We show, instead, that it is possible to predict the relative nonlinear susceptibility of large classes of metamaterials using a more comprehensive nonlinear scattering theory, which allows efficient design of metamaterials with strong nonlinearity for important applications such as coherent Raman sensing, entangled photon generation and frequency conversion.

title: Controlling light with metamaterial-based nonlinear photonic crystals
abstract: Nonlinearity engineering is demonstrated by the construction of metamaterial-based photonic crystals. Nonlinear emission and diffraction are controlled and intense focusing is reported.

title: Multipole interference in the second-harmonic optical radiation from gold nanoparticles.
abstract: We provide experimental evidence of higher multipole (magnetic dipole and electric quadrupole) radiation in second-harmonic (SH) generation from arrays of metal nanoparticles. Fundamental differences in the radiative properties of electric dipoles and higher multipoles yield opposite interference effects observed in the SH intensities measured in the reflected and transmitted directions. These interference effects clearly depend on the polarization of the fundamental field, directly indicating the importance of multipole effects in the nonlinear response. We estimate that higher multipoles contribute up to 20% of the total emitted SH field amplitude for certain polarization configurations.

title: Metamaterials with tailored nonlinear optical response.
abstract: We demonstrate that the second-order nonlinear optical response of noncentrosymmetric metal nanoparticles (metamolecules) can be efficiently controlled by their mutual ordering in an array. Two samples with minor change in ordering have nonlinear responses differing by a factor of up to 50. The results arise from polarization-dependent plasmonic resonances modified by long-range coupling associated with metamolecular ordering. The approach opens new ways for tailoring the nonlinear responses of metamaterials and their tensorial properties.

title: Polarization-controlled circular second-harmonic generation from metal hole arrays with threefold rotational symmetry.
abstract: The discrete rotational symmetry of nanostructures provides a powerful and simple guiding principle for designing the second-harmonic generation process in nonlinear metamaterials. We demonstrate that, in achiral nanostructures with threefold rotational symmetries, a circularly polarized fundamental beam produces a countercircularly polarized second-harmonic beam. In this case, the polarization state of the second harmonic is determined in a very simple manner. We also demonstrate how rotational symmetries in nonlinear metamaterials manifest themselves in SHG selection rules.

title: Enhancement of second-harmonic generation from metal nanoparticles by passive elements.
abstract: We prepare arrays of gold nanoparticles that include both noncentrosymmetric particles with a second-order nonlinear optical response (active particles) and centrosymmetric particles with no second-order response (passive particles). The plasmon resonances of the active and passive particles are at distinct wavelengths, yet the passive particles modify the electromagnetic modes of the structure in such a way that second-harmonic generation from the active particles is enhanced. Our results provide a completely new concept for optimizing the nonlinear responses of metamaterials.

title: Nonlinear Electroreflectance in Silicon and Silver
abstract: The intensity of second harmonic light produced in reflection by a laser beam incident on silver and silicon surfaces shows a significant variation when a dc electric field is applied normal to the surface. Experimental data on the intensity, polarization, and dispersive properties of the induced surface harmonic polarization are presented and discussed.

title: PHASE‐MATCHED NONLINEAR INTERACTION BETWEEN CIRCULARLY POLARIZED WAVES
abstract: This paper reports the first observation of phase‐matched nonlinear interaction between three circularly polarized waves.

title: Quasi-phase-matched second harmonic generation: tuning and tolerances
abstract: The theory of quasi-phase-matched second-harmonic generation is presented in both the space domain and the wave vector mismatch domain. Departures from ideal quasi-phase matching in periodicity, wavelength, angle of propagation, and temperature are examined to determine the tuning properties and acceptance bandwidths for second-harmonic generation in periodic structures. Numerical examples are tabulated for periodically poled lithium niobate. Various types of errors in the periodicity of these structures are then analyzed to find their effects on the conversion efficiency and on the shape of the tuning curve. This analysis is useful for establishing fabrication tolerances for practical quasi-phase-matched devices. A method of designing structures having desired phase-matching tuning curve shapes is also described. The method makes use of varying domain lengths to establish a varying effective nonlinear coefficient along the interaction length.

title: Gradient Nonlinear Pancharatnam-Berry Metasurfaces.
abstract: We apply the Pancharatnam-Berry phase approach to plasmonic metasurfaces loaded by highly nonlinear multiquantum-well substrates, establishing a platform to control the nonlinear wave front at will based on giant localized nonlinear effects. We apply this approach to design flat nonlinear metasurfaces for efficient second-harmonic radiation, including beam steering, focusing, and polarization manipulation. Our findings open a new direction for nonlinear optics, in which phase matching issues are relaxed, and an unprecedented level of local wave front control is achieved over thin devices with giant nonlinear responses.

title: Spin and wavelength multiplexed nonlinear metasurface holography
abstract: Metasurfaces, as the ultrathin version of metamaterials, have caught growing attention due to their superior capability in controlling the phase, amplitude and polarization states of light. Among various types of metasurfaces, geometric metasurface that encodes a geometric or Pancharatnam–Berry phase into the orientation angle of the constituent meta-atoms has shown great potential in controlling light in both linear and nonlinear optical regimes. The robust and dispersionless nature of the geometric phase simplifies the wave manipulation tremendously. Benefitting from the continuous phase control, metasurface holography has exhibited advantages over conventional depth controlled holography with discretized phase levels. Here we report on spin and wavelength multiplexed nonlinear metasurface holography, which allows construction of multiple target holographic images carried independently by the fundamental and harmonic generation waves of different spins. The nonlinear holograms provide independent, nondispersive and crosstalk-free post-selective channels for holographic multiplexing and multidimensional optical data storages, anti-counterfeiting, and optical encryption.

title: Imaging through Nonlinear Metalens Using Second Harmonic Generation.
abstract: The abrupt phase change of light at metasurfaces provides high flexibility in wave manipulation without the need for accumulation of propagating phase through dispersive materials. In the linear optical regime, one important application field of metasurfaces is imaging by planar metalenses, which enables device miniaturization and aberration correction compared to conventional optical microlens systems. With the incorporation of nonlinear responses into passive metasurfaces, optical functionalities of metalenses are anticipated to be further enriched, leading to completely new application areas. Here, imaging with nonlinear metalenses that combine the function of an ultrathin planar lens with simultaneous frequency conversion is demonstrated. With such nonlinear metalenses, imaging of objects with near infrared light while the image appears in the second harmonic signal of visible frequency range is experimentally demonstrated. Furthermore, the functionality of these nonlinear metalenses can be modified by switching the handedness of the circularly polarized fundamental wave, leading to either real or virtual nonlinear image formation. Nonlinear metalenses not only enable infrared light imaging through a visible detector but also have the ability to modulate nonlinear optical responses through an ultrathin metasurface device while the fundamental wave remains unaffected, which offers the capability of nonlinear information processing with novel optoelectronic devices.

title: Ultrathin Nonlinear Metasurface for Optical Image Encoding.
abstract: Security of optical information is of great importance in modern society. Many cryptography techniques based on classical and quantum optics have been widely explored in the linear optical regime. Nonlinear optical encryption in which encoding and decoding involve nonlinear frequency conversions represents a new strategy for securing optical information. Here, we demonstrate that an ultrathin nonlinear photonic metasurface, consisting of meta-atoms with 3-fold rotational symmetry, can be used to hide optical images under illumination with a fundamental wave. However, the hidden image can be read out from second harmonic generation (SHG) waves. This is achieved by controlling the destructive and constructive interferences of SHG waves from two neighboring meta-atoms. In addition, we apply this concept to obtain gray scale SHG imaging. Nonlinear metasurfaces based on space variant optical interference open new avenues for multilevel image encryption, anticounterfeiting, and background free image reconstruction.

title: Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes.
abstract: Laser light with a Laguerre-Gaussian amplitude distribution is found to have a well-defined orbital angular momentum. An astigmatic optical system may be used to transform a high-order Laguerre-Gaussian mode into a high-order Hermite-Gaussian mode reversibly. An experiment is proposed to measure the mechanical torque induced by the transfer of orbital angular momentum associated with such a transformation.

title: Quantum teleportation of multiple degrees of freedom of a single photon
abstract: Quantum teleportation provides a ‘disembodied’ way to transfer quantum states from one object to another at a distant location, assisted by previously shared entangled states and a classical communication channel. As well as being of fundamental interest, teleportation has been recognized as an important element in long-distance quantum communication, distributed quantum networks and measurement-based quantum computation. There have been numerous demonstrations of teleportation in different physical systems such as photons, atoms, ions, electrons and superconducting circuits. All the previous experiments were limited to the teleportation of one degree of freedom only. However, a single quantum particle can naturally possess various degrees of freedom—internal and external—and with coherent coupling among them. A fundamental open challenge is to teleport multiple degrees of freedom simultaneously, which is necessary to describe a quantum particle fully and, therefore, to teleport it intact. Here we demonstrate quantum teleportation of the composite quantum states of a single photon encoded in both spin and orbital angular momentum. We use photon pairs entangled in both degrees of freedom (that is, hyper-entangled) as the quantum channel for teleportation, and develop a method to project and discriminate hyper-entangled Bell states by exploiting probabilistic quantum non-demolition measurement, which can be extended to more degrees of freedom. We verify the teleportation for both spin–orbit product states and hybrid entangled states, and achieve a teleportation fidelity ranging from 0.57 to 0.68, above the classical limit. Our work is a step towards the teleportation of more complex quantum systems, and demonstrates an increase in our technical control of scalable quantum technologies.

title: Terabit free-space data transmission employing orbital angular momentum multiplexing
abstract: Researchers demonstrate the ability to multiplex and transfer data between twisted beams of light with different amounts of orbital angular momentum — a development that provides new opportunities for increasing the data capacity of free-space optical communications links.

title: Nonlinear Beam Shaping with Plasmonic Metasurfaces
abstract: We present here a method for generating second-harmonic beams with tailored beam profiles using nonlinear metasurfaces based on split ring resonators. By manipulating both the phase and the amplitude of the quadratic nonlinear coefficient locally, at the single inclusion level, the emitted second-harmonic wavefront is perfectly controlled. These concepts are demonstrated experimentally by the far-field generation of second-harmonic Airy and vortex beams from nonlinear binary phase computer-generated holograms and the perfect near-field generation of a Hermite–Gauss beam by precise amplitude and phase construction. We believe that these demonstrations open the door to use nonlinear metasurfaces for a variety of integrated nonlinear beam shaping devices.

title: Nonlinear Metasurface for Simultaneous Control of Spin and Orbital Angular Momentum in Second Harmonic Generation.
abstract: The spin and orbital angular momentum (SAM and OAM) of light is providing a new gateway toward high capacity and robust optical communications. While the generation of light with angular momentum is well studied in linear optics, its further integration into nonlinear optical devices will open new avenues for increasing the capacity of optical communications through additional information channels at new frequencies. However, it has been challenging to manipulate the both SAM and OAM of nonlinear signals in harmonic generation processes with conventional nonlinear materials. Here, we report the generation of spin-controlled OAM of light in harmonic generations by using ultrathin photonic metasurfaces. The spin manipulation of OAM mode of harmonic waves is experimentally verified by using second harmonic generation (SHG) from gold meta-atom with 3-fold rotational symmetry. By introducing nonlinear phase singularity into the metasurface devices, we successfully generate and measure the topological charges of spin-controlled OAM mode of SHG through an on-chip metasurface interferometer. The nonlinear photonic metasurface proposed in this work not only opens new avenues for manipulating the OAM of nonlinear optical signals but also benefits the understanding of the nonlinear spin-orbit interaction of light in nanoscale devices.

title: Photonic spin-controlled multifunctional shared-aperture antenna array
abstract: Multifunction planar optics Specially designed two-dimensional (2D) arrays of nanometer-scale metallic antennas, or metasurfaces, may allow bulky optical components to be shrunk down to a planar device structure. Khorasaninejad et al. show that arrays of nanoscale fins of TiO can function as high-end optical lenses. At just a fraction of the size of optical objectives, such planar devices could turn your phone camera or your contact lens into a compound microscope. Maguid et al. interleaved sparse 2D arrays of metal antennas to get multifunctional behavior from the one planar device structure (see the Perspective by Litchinitser). The enhanced functionality of such designed metasurfaces could be used in sensing applications or to increase the communication capacity of nanophotonic networks. Science, this issue pp. 1190 and 1202; see also p. 1177 A 2D nanophotonic system can be designed with multifunctional optical capability. The shared-aperture phased antenna array developed in the field of radar applications is a promising approach for increased functionality in photonics. The alliance between the shared-aperture concepts and the geometric phase phenomenon arising from spin-orbit interaction provides a route to implement photonic spin-control multifunctional metasurfaces. We adopted a thinning technique within the shared-aperture synthesis and investigated interleaved sparse nanoantenna matrices and the spin-enabled asymmetric harmonic response to achieve helicity-controlled multiple structured wavefronts such as vortex beams carrying orbital angular momentum. We used multiplexed geometric phase profiles to simultaneously measure spectrum characteristics and the polarization state of light, enabling integrated on-chip spectropolarimetric analysis. The shared-aperture metasurface platform opens a pathway to novel types of nanophotonic functionality.

title: Third harmonic generation of optical vortices using holography based gold-fork microstructure
abstract: Light with orbital angular momentum has found novel applications in macro-manipulation, quantum optics, and optical communication, etc. The generation of orbital angular momentum in nonlinear media, such as second harmonic generation and high harmonic generation, is demonstrated using an optical superlattice and a gas medium. Here, by combining a gold-fork microstructure with a conjugated polymer thin film with strong nonlinearity, both second- and third-order harmonic generation of vortex beams with orbital angular momentum are created. Compared to the previously reported medium to generate nonlinear optical vortex, this approach brings great advantages in device miniaturization and provides a promising strategy for realizing on-chip nonlinear optical vortex devices.

title: The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light
abstract: When a shaft of circular section is revolving uniformly, and is transmitting power uniformly, a row of particles originally in a line parallel to the axis will lie in a spiral of constant pitch, and the position of the shaft at any instant may be described by the position of this spiral. Let us suppose that the power is transmitted from left to right, and that as viewed from the left the revolution is clockwise. Then the spiral is a left-handed screw. Let it be on the surface, and there make an angle є with the axis. Let the radius of the shaft be a , and let one turn of the spiral have length λ along the axis. We may term λ the wave-length of the spiral. We have tan є = 2 πa / λ . If the orientation of the section at the origin at time t is given by θ = 2 π N t , where N is the number of revolutions per second, the orientation of the section at x .