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AIETA: \"Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces\", NANO LETT., vol. 12, 21 August 2012 (2012-08-21), pages 4932 - 4936, XP055206638, DOI: doi:10.1021/nl302516v","npl_type":"s","xp_number":"055206638","external_id":["10.1021/nl302516v","22894542"],"record_lens_id":"005-411-623-496-187","lens_id":["065-062-130-497-994","080-223-571-805-911","194-207-115-753-226","005-411-623-496-187"],"sequence":6,"category":[],"us_category":[],"cited_phase":"APP","cited_date":"2016-07-12","rel_claims":[]}},{"npl":{"num":6,"text":"D. E. 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for invention","granted":false,"earliest_filing_date":"2015-12-10","has_disclaimer":false,"patent_status":"PENDING","publication_count":2,"has_spc":false,"has_grant_event":false,"has_entry_into_national_phase":false},"abstract":{"en":[{"text":"Multi-wavelength light is directed to an optic including a substrate and achromatic metasurface optical components deposited on a surface of the substrate. The achromatic metasurface optical components comprise a pattern of dielectric resonators. The dielectric resonators have nonperiodic gap distances between adjacent dielectric resonators; and each dielectric resonator has a width, w, that is distinct from the width of other dielectric resonators. A plurality of wavelengths of interest selected from the wavelengths of the multi-wavelength light are deflected with the achromatic metasurface optical components at a shared angle or to or from a focal point at a shared focal length.","lang":"en","source":"WIPO_FULLTEXT","data_format":"ORIGINAL"}],"fr":[{"text":"Une lumière à multiples longueurs d'onde est dirigée vers une optique comprenant un substrat et des composants optiques à métasurface achromatique placés sur une surface du substrat. Les composants optiques à métasurface achromatique comprennent un motif de résonateurs diélectriques. Les résonateurs diélectriques ont des distances d'écart non périodique entre des résonateurs diélectriques adjacents, et chaque résonateur diélectrique a une largeur, w, qui est distincte de la largeur d'autres résonateurs diélectriques. Une pluralité de longueurs d'onde d'intérêt sélectionnées parmi les longueurs d'onde de la lumière à multiples longueurs d'ondes sont déviées avec les composants optiques à métasurface achromatique, à un angle partagé, ou vers/depuis un point focal à une longueur focale partagée.","lang":"fr","source":"WIPO_FULLTEXT","data_format":"ORIGINAL"}]},"abstract_lang":["en","fr"],"has_abstract":true,"claim":{"en":[{"text":"CLAIMS What is claimed is: 1. A method for dispersive phase compensation using achromatic metasurface optical components, comprising: directing multi-wavelength light to an optic including a substrate and achromatic metasurface optical components deposited on a surface of the substrate, wherein the achromatic metasurface optical components comprise a pattern of dielectric resonators, the dielectric resonators having nonperiodic gap distances between adjacent dielectric resonators; and each dielectric resonator having a width, w, that is distinct from the width of other dielectric resonators; and deflecting a plurality of wavelengths of interest selected from the wavelengths of the multi-wavelength light with the achromatic metasurface optical components at a shared angle or to or from a focal point at a shared focal length. 2. The method of claim 1, wherein the wavelengths of interest span a range of more than 100 nm. 3. The method of claim 1, wherein the substrate comprises silica, and wherein the dielectric resonators comprise silicon. 4. The method of claim 1, wherein each of the dielectric resonators have a width and thickness that are smaller than the wavelengths of interest. 5. The method of claim 4, wherein widths of different dielectric resonators differ by at least 25 nm. 6. The method of claim 5, wherein each of the dielectric resonators have a width of at least 100 nm. 7. The method of claim 1, wherein the dielectric resonators have multiple electric and magnetic resonances that overlap at the wavelengths of interest. 8. The method of claim 1, wherein the surface of the substrate on which the achromatic metasurface optical components are deposited and a surface on an opposite side of the substrate are both flat. 9. The method of claim 1, wherein light at wavelengths other than the wavelengths of interest (a) is not deflected or (b) is deflected at angles other than the shared angle or is deflected at angles other than to/ from the focal point at the shared focal length. 10. The method of claim 1, wherein a majority of the light at wavelengths other than the wavelengths of interest is removed by the optic to provide multiband optical filtering of the light. 11. The method of claim 1, wherein each dielectric resonator has a rectangular cross-section in a plane perpendicular to the substrate surface 12. An achromatic metasurface optical device, comprising; a substrate including a surface; and a pattern of dielectric resonators on the surface of the substrate, wherein the dielectric resonators have nonperiodic gap distances between adjacent dielectric resonators; and each dielectric resonator has a width, w, that is distinct from the width of other dielectric resonators. 13. The achromatic metasurface optical device of claim 12, wherein the widths and the gaps of the dielectric resonators are configured to deflect a plurality of wavelengths of interest to or from a focal point at a shared focal length. 14. The achromatic metasurface optical device of claim 12, wherein the widths and the gaps of the dielectric resonators are configured to deflect a plurality of wavelengths of interest at a shared angle. 15. The achromatic metasurface optical device of claim 12, wherein the widths and gaps of the dielectric resonators are configured to form a same complex wave-front for a plurality of wavelengths of interest. The achromatic metasurface optical device of claim 15, wherein the compL wave-front is selected from a vortex beam and a Bessel beam. 17. The achromatic metasurface optical device of claim 12, wherein the substrate comprises silica. 18. The achromatic metasurface optical device of claim 17, wherein the dielectric resonators comprise silicon. 19. The achromatic metasurface optical device of claim 12, wherein widths of different dielectric resonators differ by at least 25 nm. 20. The achromatic metasurface optical device of claim 12, wherein each of the dielectric resonators have a width of at least 100 nm. 21. The achromatic metasurface optical device of claim 12, wherein the surface of the substrate on which the achromatic metasurface optical components are deposited and a surface on an opposite side of the substrate are both flat. 22. The achromatic metasurface optical device of claim 12, wherein each dielectric resonator has a rectangular cross-section in a plane perpendicular to the substrate surface.","lang":"en","source":"WIPO_FULLTEXT","data_format":"ORIGINAL"}]},"claim_lang":["en"],"has_claim":true,"description":{"en":{"text":"ACHROMATIC METASURFACE OPTICAL COMPONENTS BY DISPERSIVE PHASE COMPENSATION GOVERNMENT SUPPORT This invention was made with government support under Grant No. FA9550-12-1-0289 awarded by the Air Force Office of Scientific Research. The Government has certain rights in the invention. BACKGROUND Refractive and diffractive optical components share many similarities when they are used with monochromatic light. If we illuminate a prism and a grating with a laser beam, they will both bend the incoming light. In a similar fashion, a spherical lens and a diffractive lens (zone plate) both focus light. However, the behavior of refractive optics and diffractive optics is very different when they are used to manipulate broadband light. A prism with normal dispersion will deflect the longer wavelengths to a smaller angle compared to the shorter wavelengths; a diffraction grating, instead, does the opposite. Likewise, the focal distance for a refractive lens in the visible wavelengths will be larger for red light than for blue, while the contrary occurs for a diffractive lens. This contrasting behavior arises because two different principles are used to shape the light. Wavefront control in refractive optics is obtained by gradual phase accumulation as the light propagates through a material of a given refractive index, η=η(λ), on account of material dispersion. In most transparent materials, the refractive index decreases with increasing wavelength (\"normal dispersion\") over the visible region. Since the deflection angle, Θ, of a prism increases with the index, a lens focal length, f, is inversely proportional to n(A), the resulting effect of refractive optics 11 is the one shown in images A and B of FIG. 1. A diffractive optical element (DOE) 13, instead, operates by means of interference of light transmitted through an amplitude or phase mask. The beam deflection angle and the focal length, respectively, are directly and inversely proportional to A (images C and D of FIG. 1), generating a dispersion opposite to that of standard refractive devices. Although for many applications a spatial separation of different wavelengths is desirable (spectrometers, monochromators, wavelength division multiplexing (WDM)), in many others this spatial separation represents a problem. For example, the dependence of the focal distance on A produces chromatic aberrations and is responsible for the degradation of the quality of an imaging system. We note that the wavelength dependence is typically much more pronounced in diffractive optics than in refractive optics. Materials used to make high-quality refractive optics can have very low dispersion; and in some cases, materials with opposite dispersion are used to cancel out the effect {e.g., achromatic doublets). Another difference between these technologies is represented by the efficiency with which a desired function is achieved. In refractive optics, the efficiency can be very high and is limited only by material losses, fabrication imperfections, and interface reflections. In diffractive optics, instead, the presence of higher diffraction orders imposes severe limitations on performance. On the other hand, diffractive optical elements have the advantage of being relatively flat, light and often low cost. Blazed gratings and Fresnel lenses are diffractive optical devices with an analog phase profile, and thus they are simultaneously refractive and diffractive. As such, they integrate some benefits of both technologies {e.g., small footprint and high efficiency); but they still suffer from strong chromatic aberrations. Multi-order diffractive (MOD) lenses overcome this limitation by using thicker phase profiles optimized such that the phase difference corresponds to an integer number of 2π for each wavelength. With this approach, one can in principle obtain a set of wavelengths that are chromatically corrected (_/). The realization of thick, analog phase profiles, however, is challenging for conventional technologies, such as greyscale lithography or diamond turning. Metasurfaces are thin optical components that rely on a different approach for light control; a dense arrangement of subwavelength resonators is designed to modify the optical response of the interface. As shown previously [N. Yu, etal., \"Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,\" 334 Science 333-37 (2011), and PCT Patent Application Publication No. WO 2013/033591 Al], the resonant nature of the scatterers introduces a local abrupt phase shift in the incident wavefront making it possible to mold the scattered light at will and enabling a new class of planar photonics components {i.e., flat optics) [see N. Yu, et a!, \"Flat optics: Controlling wavefronts with optical antenna metasurfaces,\" IEEE J. Sel. Top. Quantum Electron. 19(3), 4700423 (2013), and N. Yu, F. Capasso, \"Flat optics with designer metasurfaces,\" 13 Nat. Materials 139-150 (2014). Different types of resonators (metallic or dielectric antennas, apertures in metallic films, etc.) have been used to demonstrate various flat optical devices, including blazed gratings, lenses, holograms, polarizers, and wave plates. The metasurface approach is unique in that it provides continuous control of the phase profile {i.e., from 0 to 2π) with a binary structure (only two levels of thickness). Metasurfaces also circumvent the fundamental limitation of multiple diffraction orders typical of binary diffractive optics while simultaneously maintaining the size, weight, and ease-of-fabrication advantages compared to refractive optics. Metasurface -based optical devices demonstrated so far, however, are affected by large chromatic aberrations {i.e., strong wavelength-dependence). Research efforts have recently shown that relatively \"broadband\" optical metasurfaces can be achieved. The claim of large bandwidth usually refers to the broadband response of the resonators, which is the result of the high radiation losses necessary for high scattering efficiency and, to a lesser extent, of the absorption losses. As a consequence, the phase function implemented by the metasurface can be relatively constant over a range of wavelengths. This constant phase function, however, is not sufficient to obtain an achromatic behavior. SUMMARY Achromatic metasurface optical devices and methods for dispersive phase compensation using achromatic metasurface optical components are described herein, where various embodiments of the apparatus and methods for their fabrication and use may include some or all of the elements, features and steps described below. An embodiment of an achromatic metasurface optical device includes a substrate including a surface and a pattern of dielectric resonators on the surface of the substrate, wherein the dielectric resonators have nonperiodic gap distances between adjacent dielectric resonators; and each dielectric resonator having a width, w, that is distinct from the width of other dielectric resonators. The widths and the gaps of the dielectric resonators can be configured to deflect a plurality of wavelengths of interest to or from a focal point at a shared focal length. In other embodiments, the widths and the gaps of the dielectric resonators can be configured to deflect a plurality of wavelengths of interest at a shared angle. In additional embodiments, the widths and gaps of the dielectric resonators can be configured to form a same complex wave-front (such as a vortex beam or a Bessel beam for a plurality of wavelengths of interest). In particular embodiments, the resonators can have a rectangular cross-section in a plane perpendicular to the substrate surface. In a method for dispersive phase compensation using achromatic metasurface optical components, multi-wavelength light is directed to an optic including a substrate and achromatic metasurface optical components deposited on a surface of the substrate, wherein the achromatic metasurface optical components comprise a pattern of dielectric resonators, the dielectric resonators having nonperiodic gap distances between adjacent dielectric resonators; and each dielectric resonator having a width, w, that is distinct from the width of other dielectric resonators. A plurality of wavelengths of interest selected from the wavelengths of the multi- wavelength light are deflected with the achromatic metasurface optical components at a shared angle or to or from a focal point at a shared focal length. The wavelengths of interest can span a range of more than 100 nm. In particularly embodiments, the substrate comprises silica. In additional embodiments, the dielectric resonators comprise silicon. Each of the dielectric resonators can have a width and thickness that are smaller than the wavelengths of light. Widths of different dielectric resonators can differ by at least 25 nm. Additionally, each of the dielectric resonators can have a width of at least 100 nm. The dielectric resonators can have multiple electric and magnetic resonances that overlap at the wavelengths of interest. In particular embodiments, the surface of the substrate on which the achromatic metasurface optical components are deposited and a surface on an opposite side of the substrate are both flat. In additional embodiments, light at wavelengths other than the wavelengths of interest (a) is not deflected or (b) is deflected at angles other than the shared angle or is deflected at angles other than to/ from the focal point at the shared focal length. In still further embodiments, a majority of the light at wavelengths other than the wavelengths of interest is removed by the optic to provide multiband optical filtering of the light. The replacement of bulk refractive elements with flat ones enables the miniaturization of optical components required for integrated optical systems. This process comes with the limitation that planar optics suffer from large chromatic aberrations due to the dispersion of the phase accumulated by light (in the visible or non-visible spectrum) during propagation. We show that this limitation can be overcome by compensating the dispersion of the propagation phase with the wavelength-dependent phase shift imparted by a metasurface. We demonstrate dispersion-free, multi-wavelength dielectric metasurface deflectors in the near- infrared and design an achromatic flat lens in the same spectral region. This design is based on low-loss coupled dielectric resonators that introduce a dense spectrum of modes to enable dispersive phase compensation. Achromatic metasurfaces can be used in applications, such as multi-band-pass filters, lightweight collimators, and chromatically-corrected imaging lenses. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 includes a series of images providing a comparison between refractive optics 11 (assuming a material with normal dispersion) in A and B, diffr active optics 13 (C and D), and achromatic metasurfaces 15 (E and F), where the deflection or focusing of different wavelengths of light 22, 24, and 26 are shown in each image. In the first two cases (A-D), the angle of deflection, Θ, and the focal length, f, change as a function of wavelength. The achromatic metasurface (E) and (F), consisting of subwavelength spaced resonators, is designed to preserve its operation {i.e., same Θ and f) for multiple wavelengths. In order to achieve this result, the phase shifts, ψηι,ί and (pm , imparted by the metasurface at points, r and / ; of the interface, are designed so that the paths, J- = J(r-) and l j = are optically equivalent at different wavelengths. FIG. 2 illustrates the scattering properties of an isolated silicon rectangular dielectric resonator 18 with dimensions, w— t— 350 nm (with infinite length along the y-axis), excited by a plane wave traveling at normal incidence along the ^-axis. Chart A plots the scattering efficiency, Qscat, which is defined as the ratio of the two- dimensional scattering cross-section, which has the dimension of a length, and the geometric length, w, for transverse-magnetic (TM) excitation 12, electric dipole excitation 14 and magnetic dipole excitation 16. The grey arrows indicate the resonant frequencies calculated with the analytical model for the first two modes (TMn and TM 2 i). Images B and C show the electric field intensity distribution at the two resonant frequencies obtained with plane wave excitation. The white lines give a schematic representation of the instantaneous electric field lines around the resonator. FIG. 3 includes a side view of the metasurface 15 designed for beam deflection, wherein a 240-μηι long array of silicon rectangular dielectric resonators 18 is patterned on a fused silica substrate 20. The effect of the phase profile, ψηι, is to deflect normally incident transverse-electric (TE) polarized light to an angle, θο = - 17° for A\\ = 1300 nm, λι = 1550 nm, and A3 = 1800 nm. The metasurface 15 is divided into 240 unit cells similar to the one shown in the inset. FIG. 4 plots the scattering efficiency for one unit cell of the metasurface of FIG. 3 with geometry, 6 = 1 μηι, t- 400 nm, w\\ = 300 nm, w∑ =100 nm, and g- 175 nm. The spectrum shows resonances due to the individual elements and to the coupling between the resonators, as shown by the electric field intensity distributions. FIG. 5 is a vector representation of the interference between the electric fields scattered by the slot and by the two resonators, proportional to a and b, respectively. The phase of b associated with the resonant response can span the range (π/2, 3π/2), as indicated by the double-line. The vector sum of a (in green) and b is represented by the phasor, E (orange), for two different wavelengths (solid and dashed lines). FIG. 6 plots the normalized intensity (solid line) 22 and phase (dashed line) 24 calculated at a distance of 10 cm away on the vertical axis to the interface for the same unit cell. The crosses represent the required phase values calculated from Equation 2 for Ai, λι, and A3. The circles correspond to the scattered intensities for the same wavelengths. FIG. 7 is an SEM image of the cross section of the metasurface. FIG. 8 is a photographic image of a 240 μηι x 240 μηι section of the fabricated metasurface of FIG. 7 taken with an optical microscope. FIG. 9 is a schematic illustration of the experimental setup, including a tunable laser source 26 (that produces the incident light 28) and an InGasAs detector 30. FIG. 10 plots the simulated far-field intensity as a function of the angle, Θ, from the normal to the interface for A\\— 1300 nm 32, Az = 1550 nm 34, and A3 = 1800 nm 36. FIG. 11 plots the measured far-field intensity as a function of the angle, Θ, from the normal to the interface. The intensity is normalized to the maximum value for the three wavelengths. The inset plot in FIG. 11 is close-up around the angle, θο. FIG. 12 plots experimentally measured deflection angles (circles) and simulated deflection angles (squares) for wavelengths from 1100 nm to 1950 nm. The curves correspond to the predicted deflection angle calculated from Equation 2 for fixed phase gradients designed for θο = -17° and A = 1300 nm 32, 1550 nm 34, and 1800 nm 36, respectively. FIG. 13 plots the intensity measured by the detector at θο; the three peaks at the wavelengths, Ai, A2 and A3, have similar intensities and a high suppression ratio (50:1) with respect to other wavelengths. FIG. 14 shows the results of a simulation of an achromatic flat lens 38 based on rectangular dielectric resonators. Illustration A shows a broadband plane wave 28 illuminating the backside of the cylindrical lens 38 with side, D = 600 μηι, and focal distance, f= 7.5 mm. Images B-H show the far-field intensity distribution for different wavelengths. The dashed lines correspond to the desired focal planes. FIG. 15 plots the cross section across the focal plane of the intensity distribution for λ , and A3 for the achromatic flat lens 38 of FIG. 14 with rectangular dielectric resonators. FIG. 16 plots the focal lengths as a function of wavelength, calculated as the distance between the lens center and highest intensity point on the optical axis, for the achromatic flat lens of FIG. 14 with rectangular dielectric resonators. The three larger markers 40 correspond to the wavelengths of interest. FIG. 17 plots an ellipsometric characterization of the 400-nm-thin a-Si film deposited with PECVD. The thinner curve 42 is obtained by fitting the experimental data 44 with the analytical model. The imaginary part of the refractive index is negligible at the wavelengths of interest (1100 nm - 2000 nm). FIG. 18 shows the geometry and field distribution of a rectangular dielectric resonator 18. FIG. 19 charts the scattering cross section for a silicon rectangular dielectric resonator in vacuum with geometry, w— 400 nm and t— 500 nm, excited with TM polarization. FIG. 20 charts a comparison between the theoretical model 46 and a FDTD simulation 48 of the resonant wavelengths for the first three modes (TMn, TM1 2 , FIGS. 21 and 22 provide a comparison between the theoretical model and FDTD simulations of the resonant wavelengths for TE excitation for different widths, w, and for t = 300 nm (FIG. 21) and t = 500 nm (FIG. 22). FIGS. 23 and 24 provide a comparison between the theoretical model and FDTD simulations of the resonant wavelengths for TM excitation for different widths, w, and for t = 300 nm (FIG. 23) and t = 500 nm (FIG. 24). FIG. 25 plots the far-field measurement of the beam deflector for Ai and A3. Since the structure does not present any periodicity, there is no peak in correspondence of the -1 order (θ = 17°). FIGS. 26-29 plot a FDTD simulation of the beam deflector performance for non-normal incidence, where the incoming beam forms an angle of -1° (FIG. 26), +1° (FIG. 27), -3° (FIG. 28) and +8° (FIG. 29) with respect to the normal. The orange arrows indicate the expected deflection angles for an achromatic metasurface. FIG. 30 plots the performance of the beam deflector as a multi-band filter, where a FDTD simulation confirms the uniformity and suppression ratio of the experimental data. The inset shows a close up of the peak corresponding to λι from which we can estimate the FWHM bandwidth of the filter. In the accompanying drawings, like reference characters refer to the same or similar parts throughout the different views. The drawings are not necessarily to scale; instead, emphasis is placed upon illustrating particular principles in the exemplifications discussed below. DETAILED DESCRIPTION The foregoing and other features and advantages of various aspects of the invention(s) will be apparent from the following, more-particular description of various concepts and specific embodiments within the broader bounds of the invention(s). Various aspects of the subject matter introduced above and discussed in greater detail below may be implemented in any of numerous ways, as the subject matter is not limited to any particular manner of implementation. Examples of specific implementations and applications are provided primarily for illustrative purposes. Unless otherwise herein defined, used or characterized, terms that are used herein (including technical and scientific terms) are to be interpreted as having a meaning that is consistent with their accepted meaning in the context of the relevant art and are not to be interpreted in an idealized or overly formal sense unless expressly so defined herein. For example, if a particular composition is referenced, the composition may be substantially, though not perfectly pure, as practical and imperfect realities may apply; e.g., the potential presence of at least trace impurities {e.g., at less than 1 or 2%) can be understood as being within the scope of the description; likewise, if a particular shape is referenced, the shape is intended to include imperfect variations from ideal shapes, e.g., due to manufacturing tolerances. Percentages or concentrations expressed herein can represent either by weight or by volume. Processes, procedures and phenomena described below can occur at ambient pressure {e.g., about 50-120 kPa— for example, about 90-110 kPa) and temperature {e.g., -20 to 50°C— for example, about 10-35°C) unless otherwise specified. Although the terms, first, second, third, etc., may be used herein to describe various elements, these elements are not to be limited by these terms. These terms are simply used to distinguish one element from another. Thus, a first element, discussed below, could be termed a second element without departing from the teachings of the exemplary embodiments. Spatially relative terms, such as \"above,\" \"below,\" \"left,\" \"right,\" \"in front,\" \"behind,\" and the like, may be used herein for ease of description to describe the relationship of one element to another element, as illustrated in the figures. It will be understood that the spatially relative terms, as well as the illustrated configurations, are intended to encompass different orientations of the apparatus in use or operation in addition to the orientations described herein and depicted in the figures. For example, if the apparatus in the figures is turned over, elements described as \"below\" or \"beneath\" other elements or features would then be oriented \"above\" the other elements or features. Thus, the exemplary term, \"above,\" may encompass both an orientation of above and below. The apparatus may be otherwise oriented {e.g., rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. Further still, in this disclosure, when an element is referred to as being \"on,\" \"connected to,\" \"coupled to,\" \"in contact with,\" etc., another element, it may be directly on, connected to, coupled to, or in contact with the other element or intervening elements may be present unless otherwise specified. The terminology used herein is for the purpose of describing particular embodiments and is not intended to be limiting of exemplary embodiments. As used herein, singular forms, such as \"a\" and \"an,\" are intended to include the plural forms as well, unless the context indicates otherwise. Additionally, the terms, \"includes,\" \"including,\" \"comprises\" and \"comprising,\" specify the presence of the stated elements or steps but do not preclude the presence or addition of one or more other elements or steps. Additionally, the various components identified herein can be provided in an assembled and finished form; or some or all of the components can be packaged together and marketed as a kit with instructions {e.g., in written, video or audio form) for assembly and/ or modification by a customer to produce a finished product. Dispersive phase compensation A desired optical functionality {e.g., focusing, beaming, etc.) requires constructive interference between multiple light paths separating the interface and the desired wavefront {i.e., the same total accumulated phase, (fitot, modulo 2π for all light paths, as shown in images E and F of FIG. 1). The total accumulated phase is the sum of the following two contributions: (p tot {r, Λ) = φ η (r, λ) + φ ρ (r, λ) , where ψηι is the phase imparted at point, r, by the metasurface 15, where φ ρ is the phase accumulated via propagation through free space, and where λ is the wavelength of light. The first term is related to the scattering of the individual metasurface elements and is characterized by a significant variation across the resonance. The second term 2π is given by φ {r,X) =— l{r,X) , where I^r) is the physical distance between the λ interface at position, r, and the desired wavefront (as shown in images E and F of FIG. 1). To ensure achromatic behavior of the device {e.g., with deflection angle or focal length independent of wavelength), the condition of constructive interference should be preserved at different wavelengths by keeping q) to t constant. The dispersion of ψηι is designed to compensate for the wavelength-dependence of φ ρ via the following equation: 9m {r, ) = -^-l{r) , (1) where ^r) contains information on the device function {i.e., beam deflector [N. Yu, et al, \"Flat optics: Controlling wavefronts with optical antenna metasurfaces,\" IEEE J. Sel. Top. Quantum Electron. 19(3), 4700423 (May 2013) and F. Aieta, etal, \"Out-of- plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,\" 12 Nano Lett. 1702-1706 (27 Feb. 2012)], lens, axicon [F. Aieta, \"Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,\" 12 Nano Lett. 4932-36 (21 Aug. 2012)], etc.}. Equation 1 is the cornerstone for the design of an achromatic metasurface 15. This approach to flat optics features the advantages of diffractive optics 13, such as flatness and small footprint, while achieving achromatic operation. As an example of an achromatic metasurface 15, we demonstrate a dispersion-free beam deflector based on dielectric resonators 18. While the typical function of a diffractive grating is the angular separation of different wavelengths, we show beam deflection with a wavelength-independent angle of deflection, Θ, for a discrete set of wavelengths (Ai = 1300 nm, A 2 = 1550 nm, and A 3 = 1800 nm). The basic unit of the achromatic metasurface 15 is a resonator 18 that can be designed to adjust the scattered phase at different wavelengths, (pm(r, A), in order to satisfy Equation 1. In particular embodiments, the resonators 18 are dielectric antennas (i.e., resonant elements that interact with electromagnetic waves via a displacement current and that can have both electric and magnetic resonances). Primarily used in the microwave frequency range, dielectric antennas have recently been proposed in the optical regime as an alternative to metallic antennas because of their low losses at shorter wavelengths. Nanostructures made of a material with a large refractive index exhibit resonances while remaining small compared to the wavelength of light in free-space, similar to what occurs in plasmonic antennas. Design of dielectric achromatic metasurfaces To design an achromatic metasurface 15, the scattering properties of a rectangular dielectric resonator (RDR), which is a resonator 18 with rectangular cross-section in the x-z plane and infinite extent along the y axis, were studied, as shown in the inset of FIG. 2. Despite the simple geometry, an analytical closed-form for the electromagnetic fields does not exist for rectangular dielectric resonators; therefore, designs described herein are optimized using finite-difference time- domain (FDTD) simulations. However, in order to estimate the spectral position of the resonant modes, an approximated solution based on the dielectric waveguide model is derived. The model predicts the existence of a transverse magnetic (TM mn ) mode 12 and a transverse electric (TE mn ) mode inside the resonator. TM modes 12 are excited by an electric field with a polarization parallel to the side, w, of the rectangular dielectric resonator, while TE modes are activated by an excitation polarized along the 7-axis. The subscripts, m and n, denote the number of field extrema in the x- and ^-directions. The derivation of the model and a detailed comparison with FDTD simulations are reported in the Exemplification section, below. Plot A of FIG. 2 shows scattering efficiencies calculated from FDTD simulations for an isolated silicon rectangular dielectric resonator in vacuum with geometry, w= t = 350 nm, and excited with TM-polarized light (black line). Analogous to the scattering of dielectric spheres rigorously described by Mie theory, the first two peaks correspond to the electric and magnetic dipole resonances of the electric dipole excitation 14 and the magnetic dipole excitation 16, respectively. This correspondence is confirmed by showing the scattering spectra of the same rectangular dielectric resonator independently excited with an electric and a magnetic dipole placed at the center of the resonator and oriented along the x and y axis, respectively. The grey arrows indicate the resonant frequencies calculated with the analytical model for the first two modes (TMn and TM 2 1). The electric field intensity distributions at the two resonances (images B and C of FIG. 2) confirm the electric and magnetic dipole-like scattering. At shorter wavelengths, many higher orders exist with multi-pole-like scattering. By placing two rectangular dielectric resonators in close proximity such that their near fields overlap, a system of coupled resonators 18 is created that significantly changes the spectral positions and widths of the resonances. We can thus utilize the gap size and position as additional degrees of freedom to engineer the scattering amplitude and phase. Because of the lack of an analytical solution for coupled rectangular dielectric resonators, we rely on FDTD simulations to predict their optical response. An achromatic metasurface 15 can be designed by judiciously selecting an appropriate distribution of rectangular dielectric resonators. FIG. 3 shows the side view of the metasurface, wherein a 240 μηι-long collection of silicon (Si) resonators patterned on a fused silica (S1O 2 ) substrate is designed to deflect normally incident light at an angle, θ = -17°, for three different wavelengths {i.e., λ\\ = 1300 nm, λχ = 1550 nm, and A3 = 1800 nm). The target wavelengths and spatially varying phase functions, represented by the three lines 32, 34, and 36, respectively for A\\, A 2 , and A3 in FIG. 3 are defined by the following equations:
w I 2), right (x< - w I 2), up (z> 112) and down (z< -t I 2) are as follows: -wl 2