Broadband achromatic polarization-insensitive metalens with anisotropic nanostructures

Abstract

To provide polarization-insensitive metasurfaces using anisotropic nanostructures.SOLUTION: An anisotropic structures allow for accurate implementation of phase, group delay, and group delay dispersion, while simultaneously making it possible to realize a polarization-insensitive, diffraction-limited and achromatic metalens for wavelength, e.g., λ=about 460 nm to about 700 nm. The inventive approach of polarization-insensitivity can also be applied for other metasurface devices with applications in, e.g., imaging and virtual or augmented reality.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This PCT application claims priority to U.S. Provisional Patent Application No. 62 / 736,420, filed September 25, 2018, entitled "BROADBAND ACHROMATIC POLARIZATION-INSENSITIVE METALENS WITH ANISOTROPIC NANOSTRUCTURES," the entire contents of which are incorporated herein by reference.

[0002] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was made with government support under awards FA9550-14-1-0389 and FA9550-16-1-0156 from the Air Force Office of Scientific Research, and HR00111810001 from the Defense Advanced Research Projects Agency. The U.S. Government has certain rights in this invention. [Background technology]

[0003] background Metasurfaces, which have nanostructures with subwavelength spacing at the interface, offer a way to precisely control the properties of light, including phase, amplitude, and polarization. This opens the door to very compact and efficient devices. Among these devices, metalenses have attracted strong interest due to their potential applications in both consumer products (e.g., phone cameras, virtual or augmented reality headsets) and industrial products (e.g., microscopy, lithography, sensors, and displays). Summary of the Invention

[0004] overview Metasurfaces have attracted widespread attention due to the increasing demand for compact and wearable optical devices. For many applications, polarization-insensitive metasurfaces are highly desirable, but the choice of components seems to be limited to isotropic nanostructures. This severely limits the number of geometric parameter orders that can be utilized in the design of each nanostructure.

[0005] In at least some embodiments of the present disclosure, polarization-insensitive metalens are disclosed, e.g., using anisotropic nanofins (or other types of nanostructures) that provide additional control over the dispersion and phase of the output light. As a result, the metalens can be achromatic and polarization insensitive across nearly the entire visible spectrum, from wavelength λ = 460 nm to 700 nm, while maintaining diffraction-limited performance. Metalenses can be, for example, a single layer of TiO 2 The nanofins may have a numerical aperture of about 0.2 and a diameter of about 26.4 μm. The generality of the polarization-insensitive design of the present invention allows it to be implemented in a large number of other metasurface devices, with applications ranging from imaging to virtual or augmented reality.

[0006] In some embodiments, based on a first aspect of the present disclosure, an optical device includes a metasurface including a plurality of anisotropic nanoscale elements that define an optical profile that focuses an incident broadband light beam into a diffraction-limited spot; where the optical profile is insensitive to the polarization state of the incident broadband light beam and tailorable depending on the wavelength of the incident light.

[0007] In some embodiments according to the first aspect of the present disclosure, each of the anisotropic nanoscale elements comprises a multitude of nanostructures.

[0008] In some embodiments according to the first aspect of the present disclosure, the anisotropic nanoscale elements offer the freedom to impart an additional π phase shift with a 90 degree rotation without a change in dispersion; here, dispersion corresponds to the change in phase retardation with wavelength.

[0009] In some embodiments according to the first aspect of the present disclosure, the length and width of the nanostructures of the anisotropic nanoscale elements are varied to tune the phase terms, group delay terms, and group delay dispersion terms to provide an adaptive optical profile with wavelength.

[0010] In some embodiments according to the first aspect of the present disclosure, the anisotropic nanoscale elements are TiO 2 , GaN, Si 3 N 4 , SiO 2 , Al 2 O 3 , or other optical glass that is lossless in the visible spectrum.

[0011] In some embodiments according to the first aspect of the present disclosure, each anisotropic nanoscale element is aligned either substantially parallel or substantially perpendicular to an adjacent anisotropic nanoscale element.

[0012] In some embodiments according to the first aspect of the present disclosure, the broadband incident light beam comprises a plurality of wave packets, and the optical profile comprises phase terms that specify parameters of the anisotropic nanoscale elements such that the wave packets are transmitted toward a diffraction-limited spot.

[0013] In some embodiments according to the first aspect of the present disclosure, the broadband incident light beam comprises multiple wave packets, and the optical profile includes a group delay term that specifies parameters of the anisotropic nanoscale elements such that the wave packets arrive at the diffraction-limited spot simultaneously.

[0014] In some embodiments according to the first aspect of the present disclosure, the group delay term is a first derivative term of the optical profile.

[0015] In some embodiments according to the first aspect of the present disclosure, the broadband incident light beam includes multiple wave packets, and the optical profile includes a group delay dispersion term that specifies parameters of the anisotropic nanoscale elements such that the wave packets reaching the diffraction-limited spot have identical widths in the time domain.

[0016] In some embodiments according to the first aspect of the present disclosure, the group delay dispersion term is a second derivative term of the optical profile.

[0017] In some embodiments according to the first aspect of the present disclosure, the wavelength of the incident light is in the visible spectrum.

[0018] In some embodiments, according to a second aspect of the present disclosure, an optical device comprises a metasurface comprising a plurality of anisotropic nanoscale elements that impart an optical profile that efficiently disperses light into different diffraction angles; where the optical profile is insensitive to the polarization state of an incident broadband light beam and remains unchanged with wavelength.

[0019] In some embodiments according to the second aspect of the present disclosure, the optical profile is an optical profile of a lens, a grating, or an axicon.

[0020] In some embodiments according to the second aspect of the present disclosure, the optical efficiency of the optical device is greater than 60% compared to the power of the incident light. [Brief description of the drawings]

[0021] For a better understanding of the nature and objectives of several aspects of the present disclosure, reference should be made to the following detailed description taken in conjunction with the accompanying drawings.

[0022] (Figure 1) Illustrates an example of a polarization-insensitive and achromatic metalens. Figure 1A shows the quadrant layout of the metalens. The metalens has a numerical aperture (NA) of about 0.2 and a diameter of about 26.4 μm. The inset shows a schematic diagram of its components. Each element is a TiO2 The metalens elements include nanofins. The metalens elements are equally spaced along the x and y directions with a lattice constant of 400 nm. Figure 1B shows a scanning electron microscope image of a portion of the fabricated metalens; the scale bar is approximately 1 μm. The inset shows a close-up perspective view of the nanofin; the scale bar is approximately 500 nm. Figure 1C shows a simulation of the phase shift of the components of the transmitted electric field with polarization orthogonal to the circularly polarized incident light. The legend indicates, for example, T LCP→RCP represents the phase of light transmitted through the RCP under LCP incidence. The upper and lower curves show the same element containing three nanofins oriented along the horizontal and vertical directions, respectively. The nanofin parameters, in nanometers, are approximately (w 1 , l 1 w 2 , l 2 , w 3 , l 3 , g) = (50, 50, 170, 370, 50, 90, 60). The element exhibits identical phase under both RCP and LCP illumination. Note that for a given circular polarization, a rotation of approximately 90 degrees can introduce a π phase shift without affecting the group delay (tilt) and group delay dispersion (curvature). (FIG. 2) Plots a comparison of specified and realized phase, group delay, and group delay dispersion for the metalens shown in FIG. 1A. FIG. 2A shows the phase, group delay, and group delay dispersion for all elements in the simulation library, as well as the specified values. Each element is represented by two associated points in this plot, since a 90 degree rotation can impart a phase change of π without changing the group delay and group delay dispersion. FIGs. 2B, 2C, and 2D show the realized (circles) and specified (curves) phase, group delay, and group delay dispersion at each radial coordinate across the polarization-insensitive, achromatic metalens. FIG. 3 illustrates the measured focal spot profile and efficiency for an achromatic metalens and a diffractive metalens. The measured metalens have an NA = approx. 0.2 and a focal length of approx. 67 μm at λ = approx. 560 nm. FIG. 3A shows the measured intensity distribution in the yz plane corresponding to each wavelength in the visible range (labeled in nanometers to the left of the plot). The left and right panels correspond to an achromatic metalens and a diffractive metalens, respectively. The latter, as a control sample, may be realized without dispersion engineering and has a focal length shift similar to a Fresnel lens. The incident light moves along the positive z-axis. FIG. 3B shows the normalized intensity profile along the white dashed line in FIG. 3A for the achromatic metalens (top) and the diffractive metalens (bottom). The position of the dashed line corresponds to the focal length at λ = approx. 460 nm. Figure 3C shows the efficiency of the achromatic metalens as a function of the angle of linearly polarized incident light in steps of about 4°. The illumination source alternates between a single-wavelength diode laser at about 532 nm and a tunable broadband laser with a bandwidth of about 200 nm centered at about 570 nm. The efficiency measured with the monochromatic and broadband sources is represented by the top and bottom symbols, respectively. The inset shows the focal spot profiles, with the top and bottom rows corresponding to the diode (monochromatic) laser and tunable broadband laser illumination, respectively. The polarization of the input light is labeled at the top, and the scale bar is about 2 μm. (FIG. 4) Simulation of efficiency for polarization-insensitive phase gradient metasurface is illustrated. FIG. 4A shows the layout of the designed metasurface. The metasurface contains parallel and perpendicular nanofins whose geometry and orientation are selected to deflect a normal incident beam at an angle of about 15 degrees at a design wavelength of about 530 nm. The bottom panel shows the target and realized phases as lines and circles, respectively. FIG. 4B shows the normalized far-field power under x-polarized light incidence as a function of incident wavelength and diffraction angle. FIG. 4C shows the diffraction efficiency for the metasurface of the present invention across the visible spectrum under linear and circular polarization. The polarization angle is labeled on the y-axis, while the last two columns show the right-handed and left-handed polarization cases. At each wavelength, the efficiency remains relatively constant, thus indicating polarization insensitivity. (FIG. 5) Illustrates the Strehl ratio and focal spot size of an achromatic and polarization insensitive metalens. FIG. 5A shows the Strehl ratio as a function of incident wavelength. The Strehl ratio can be calculated by dividing the measured focal spot peak intensity by the theoretical Airy disk peak intensity, assuming equal power in the second main lobe. FIG. 5B shows the measured focal spot full width at half maximum (FWHM). The dashed lines indicate the FIG. 9128 shows the theoretical focal spot size given by TIFF2025061193000002.tif9128; in which λ is the incident wavelength and NA is the numerical aperture, whose value is approximately 0.2. (Figure 6) The polarization conversion efficiency of each library element at the design wavelength λ d = 560 nm. The polarization conversion efficiency (%) of each library element is shown. The polarization conversion efficiency may be normalized to the power transmitted through the glass-to-air interface. (Figure 7) Illustrates the absolute efficiency of the chromatic metasurface beam deflector. The absolute efficiency of the chromatic metasurface beam deflector is shown across the visible spectrum for all incident linear polarizations and both incident circular polarizations. The absolute efficiency may be defined as the power diffracted to approximately 15° divided by the total incident power. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] Detailed Description There have been various efforts focused on developing broadband achromatic focusing performance of metalenses in the visible spectrum. However, these metalenses suffer from polarization sensitivity, e.g., they can focus light with a specific circular polarization. This challenge can be overcome by using symmetric cylindrical or square nanopillars. However, doing so loses a degree of freedom in the design space due to the symmetry.

[0024] At least some embodiments of the present disclosure differ from approaches related to spatial multiplexing and symmetry, e.g., TiO 2 We describe the use of anisotropic nanofins such as , to simultaneously realize metalenses that are achromatic and polarization insensitive in the visible spectrum. These anisotropic nanofins allow for the simultaneous accurate implementation of phase versus frequency as well as its higher order derivative terms (e.g., group delay and group delay dispersion). The disclosed techniques describe the design and fabrication of a metalense with a numerical aperture (NA) of about 0.2. The metalense has a measured focal length shift of about 9% at wavelengths λ = about 460 to about 700 nm and a diffraction-limited focal spot. The focusing efficiency of the metalense varies by about 4% under various incident polarizations. To demonstrate the generality of the principles of the invention, we also present a polarization-insensitive metasurface with a diffraction efficiency of about 92% at wavelengths λ = about 530 nm.

[0025] principle To achromatically focus a broadband incident beam into a diffraction-limited spot, the metalens imparts a spatially and frequency-dependent phase profile given by the following equation: TIFF2025061193000003.tif11128In the above equation, r, ω, and F are the radial coordinate, angular frequency, and constant focal length of the lens, respectively. The Taylor expansion of Eq. TIFF2025061193000004.tif16128 is the desired phase φ(r,ω d ) and group delay TIFF2025061193000005.tif12128 and group delay dispersion TIFF2025061193000006.tif13128. One way to intuitively understand each term in Equation 2 is to treat the incident light as a wave packet. The desired phase profile sends the incident wave packet towards the focal point, while the first and higher derivative terms ensure that the incident wave packets arrive at the focal point simultaneously and identically in the time domain, respectively. The challenge here is that the nanostructures chosen satisfy each derivative term in Equation 2 at every lens coordinate. In some embodiments, some designs use a phase φ(r,ω d To decouple the polarization dependence of the polarization (polarization) from the dispersion (group delay and group delay dispersion), they exploited the principle of geometric phase (or Pancharatnam-Berry phase). However, this approach also entails undesirable polarization sensitivity; in other words, these metalenses may focus incident light with a specific circular polarization.

[0026] Some embodiments of the present disclosure involve a Pancharatnam-Berry phase; however, by specifying the rotation angle of each anisotropic element to be aligned either substantially parallel or substantially perpendicular to a neighboring anisotropic element (e.g., to have a rotation of about 0 or about 90 degrees, or about +45 degrees or about -45 degrees), the aforementioned drawbacks are avoided. Each element includes one or many nanofins to provide additional degrees of freedom for engineering dispersion (FIG. 1A, inset). A layout of a small portion of an achromatic and polarization insensitive metalens of the present invention is shown in FIG. 1A, and a scanning electron microscope image of a region of a fabricated metalens is shown in FIG. 1B. To tune the phase and dispersion, the length and width of each nanofin may be varied, and the gap g between the nanofins may be set, such as, for example, to either about 60 nm or about 90 nm. By using anisotropic elements instead of symmetrical circular or square pillars, additional geometric parameters can be altered to better control the dispersion. In addition, the anisotropic element provides the freedom to impart an additional π phase shift without changing its dispersion properties, which can be used to satisfy both the desired phase and dispersion given by Eq. 2 and described by the Pancharatnam-Berry phase.

[0027] When light passes through a nanofin, the transmitted electric field can be described by the Jones vector: TIFF2025061193000007.tif13128TIFF2025061193000008.tif5128 represent the complex transmission coefficient when the normalized electric field of the incident light is polarized along the long and short axes of the nanofin, respectively. The α term is defined as the counterclockwise rotation angle of the nanofin about the x-axis. The first term in Equation 3 can cause unwanted scattering, but it can be minimized if the nanofin is designed as a tiny half-wave plate. In this case, the amplitude of the second term TIFF2025061193000009.tif10128 increases, which corresponds to the maximum polarization conversion efficiency.±i2α contains a polarization-transformed term, which indicates the origin of the Pancharatnam-Berry phase. For left-handed circularly polarized light, the rotation of α is This imparts a frequency-independent phase of 2α to the right-handed circularly polarized output light without affecting the dispersion determined by TIFF2025061193000010.tif10128. This can lead to polarization sensitivity; since the exp i2α and exp -i2α α = 0° α = 90° α = ...

[0028] Design of achromatic and polarization-insensitive metalens The design of a polarization insensitive and achromatic metalens may begin by building a library with a parameter sweep of the elements shown in the inset of FIG. 1A. The process may employ a finite-difference time-domain (FDTD) solver to obtain the phase of each element at λ = ≈530 nm, as well as its group delay and group delay dispersion. FIG. 2A shows three quantities of interest for each element at a design wavelength of ≈530 nm: phase, group delay, and group delay dispersion. There may be over 10,000 geometric combinations, which results in a dense dot scatter plot for fine tuning the dispersion. Note that, due to the principles outlined in FIG. 1C, an element rotated 90 degrees may experience a π phase shift for all frequencies without a change in the value of its dispersion. The library can then be expanded, which allows for better implementation of the desired phase and dispersion calculated based on Equation 1 for an achromatic metalens with a diameter of ≈26.4 μm and NA = ≈0.2.

[0029] To realize the metalens of the present invention, each element selected may be the element closest to a specified point in the three-dimensional space of phase, group delay, and group delay dispersion shown in FIG. 2A. Because the relative values ​​of these parameters are utilized, the library may be shifted within this three-dimensional space to better fit the specific values. To find the optimal shifts for phase, group delay, and group delay dispersion, a particle swarm optimization method may be used that minimizes the distance between each point and the values ​​provided by the elements in the library. The final result can be better viewed in FIGS. 2B, 2C, and 2D. The phase, group delay, and group delay dispersion of the selected metalens elements are shown along with the corresponding desired values ​​(curves). In some embodiments, only terms up to the group delay dispersion are considered; since the higher order values ​​for the selected elements decrease with order.

[0030] Preparation and Results Achromatic and polarization-insensitive metalens can be fabricated, for example, by electron beam lithography followed by the deposition of TiO 2 The diffractive metalens may be fabricated using atomic layer deposition of 100 nm ZnO, followed by resist removal. The performance of the fabricated device is compared to a diffractive metalens of the same diameter and NA. The comparative diffractive metalens may be designed with nanofins of the same length and width but with varying rotation angles. The diffractive metalens represents the case without dispersive engineering and may have a focal length shift similar to a Fresnel lens.

[0031] The fabricated metalens may achieve a perfect metalens with smaller lens diameters, higher NA, e.g., about 0.6, and achromatic and polarization insensitive focusing behavior. The focal length shift of the fabricated achromatic and diffractive metalens may be determined by measuring the point spread function at each wavelength along the propagation direction (z-axis) with a resolution of about 1 μm ( FIG. 3A ). The left panel of FIG. 3A shows that the focal length variation of the achromatic metalens is about 6 μm, compared to about 30 μm for the diffractive metalens (right panel).

[0032] The normalized intensity profile along the white dashed line can be seen in Figure 3B, where the top panel corresponds to the achromatic metalens and the bottom panel corresponds to the chromatic metalens. The achromatic metalens is diffraction limited, and its focal size and Strehl ratio as a function of wavelength are shown in Figure 5.

[0033] The achromatic metalens is also shown to be polarization insensitive by measuring the efficiency of the focal spot as the polarization of the incident light changes. This measurement may be performed by varying the angle of the linearly polarized incident light from about 0° to about 90° in steps of about 4°. As shown in FIG. 3C, the measured efficiency varies slightly with polarization, proving that the focusing is polarization insensitive. The symbols in the figure represent the efficiency measured at a single wavelength of about 532 nm and at a broadband wavelength of about 470 to about 670 nm, respectively. It should be noted that the polarization state of the focal spot of the metalens may differ from the polarization state of the incident light due to the phase of the polarization-converted term (the second term in Equation 3).

[0034] In some embodiments, the efficiency of the metalens relies on the fact that several elements with small polarization conversion can be selected to cover a wide range of dispersion values ​​for achromaticity (see FIG. 6 for efficiency and dispersion plots). However, the polarization-insensitive design approach of the present invention does not preclude the design of highly efficient metasurfaces. For example, FIG. 4A shows the layout of a conventional chromatic metasurface beam deflector designed for a wavelength λ = 530 nm with an output diffraction angle of approximately θ = 15°. FIG. 4B shows the normalized far-field power over the visible range as a function of wavelength under x-polarized light incidence. The metasurface has mainly a single diffracted beam over a bandwidth of about 50 nm centered at about 530 nm, resulting in a high diffraction efficiency of about 92%. The diffraction efficiency is defined as the power of the first order (+1) diffraction divided by the transmitted power. Such high diffraction efficiency can be numerically verified in FIG. 4C to be maintained under a variety of linearly and circularly polarized incident beams. At a given wavelength, the efficiency remains relatively constant across all polarizations, demonstrating remarkable polarization insensitivity. The absolute efficiency at λ = ≈530 nm, e.g., the power diffracted into 15 degrees divided by the total incident power, can be about 70% (see Figure 7 for a plot of the absolute efficiency of the metasurface).

[0035] In some embodiments, the metasurface comprises a substrate and a plurality of nanoscale elements on the substrate. The substrate can be, for example, glass (e.g., silica (SiO 2 )) may be a substrate. In some embodiments, the nanoscale elements are TiO 2 Additionally or alternatively, other suitable dielectric materials may be included, including those that have an optical transmittance of at least about 40%, at least about 50%, at least about 60%, at least about 70%, at least about 80%, at least about 85%, at least about 90%, or at least about 95% over the design wavelength or range of design wavelengths. For example, other suitable dielectric materials include oxides (oxides of aluminum (e.g., Al 2 O 3 ), oxides of silicon (e.g., SiO 2 ), hafnium oxide (e.g. HfO 2 ), zinc oxide (e.g. ZnO), magnesium oxide (e.g. MgO), or titanium oxide (e.g. TiO 2 ), nitrides (silicon nitrides (e.g., Si 3 N 4 ), nitrides of boron (e.g., BN), or nitrides of tungsten (e.g., WN), sulfides, and pure elements. In some embodiments, each nanoscale element comprises a number of nanostructures. In some embodiments, the cross-section of each nanostructure has twofold rotational symmetry, such as rectangular or elliptical.

[0036] As used herein, the singular terms "a," "an," and "the" can include plural referents unless the context clearly indicates otherwise.

[0037] Spatial descriptions such as "above," "below," "up," "left," "right," "down," "top," "bottom," "vertical," "horizontal," "side," "higher," "lower," "upper," "over," "under," and the like, are shown with respect to the orientation shown in the drawings, unless otherwise specified. It should be understood that the spatial descriptions used herein are for illustrative purposes only, and that practical embodiments of the structures described herein may be spatially arranged in any orientation or manner so long as the advantages of the aspects of the present disclosure are not departed from by such arrangement.

[0038] As used herein, the terms "approximately," "substantially," "substantial," and "about" are used to describe and account for small variations. When used in connection with an event or circumstance, they can refer to the exact instance where that event or circumstance occurs, as well as instances where the event or circumstance occurs in close approximation. For example, when used in connection with a numerical value, they can refer to a range of variation of ±10% or less of that numerical value, such as ±5% or less, ±4% or less, ±3% or less, ±2% or less, ±1% or less, ±0.5% or less, ±0.1% or less, or ±0.05% or less. For example, two numerical values ​​may be considered to be "substantially" the same if the difference between the values ​​is ±10% or less, such as ±5% or less, ±4% or less, ±3% or less, ±2% or less, ±1% or less, ±0.5% or less, ±0.1% or less, or ±0.05% or less of the mean of the values.

[0039] In addition, quantities, ratios, and other numerical values ​​may be presented herein in a range format, with the understanding that such range format is used for convenience and brevity and should be understood flexibly to include not only the numerical values ​​expressly recited as the limits of the range, but also all individual numerical values ​​or subranges subsumed within the range, as if each numerical value and subrange were expressly recited.

[0040] Although the present disclosure has been described and illustrated with reference to specific embodiments thereof, these descriptions and illustrations are not intended to limit the present disclosure. It should be understood by those skilled in the art that various modifications may be made and equivalents may be substituted without departing from the true spirit and scope of the present disclosure as defined by the appended claims. The drawings are not necessarily to scale. Due to manufacturing processes and tolerances, there may be differences between the artistic depictions in the present disclosure and the actual devices. There may be other aspects of the present disclosure that are not specifically illustrated. The specification and drawings should be regarded as illustrative rather than restrictive. Modifications may be made to the objective, spirit, and scope of the present disclosure to suit particular situations, materials, compositions of matter, methods, or processes. All such modifications are intended to be within the scope of the appended claims. Although the methods disclosed herein have been described with reference to certain operations performed in a particular order, it should be understood that these operations may be combined, sub-divided, or reordered to form equivalent methods without departing from the teachings of the present disclosure. Thus, unless specifically indicated herein, the order and grouping of operations is not intended to be limiting of the disclosure.

Claims

1. A metasurface comprising a plurality of anisotropic nanoscale elements defining an optical profile that focuses a broadband incident light beam into a diffraction-limited spot. Equipped with The optical profile is insensitive to the polarization state of the broadband incident light beam and is tailorable according to the wavelength of the incident light. Optical devices.

2. The optical device of claim 1 , wherein each of the anisotropic nanoscale elements comprises a multitude of nanostructures.

3. 3. The optical device of claim 2, wherein the anisotropic nanoscale elements provide the freedom to impart an additional π phase shift with a 90 degree rotation without a change in dispersion, the dispersion corresponding to a change in phase retardation with wavelength.

4. The optical device of claim 2, wherein the nanostructures of the anisotropic nanoscale elements vary in length and width to tune the phase terms, group delay terms, and group delay dispersion terms to provide an optical profile that is adaptive with wavelength.

5. The anisotropic nanoscale elements are TiO 2 , GaN, Si 3 N 4 , SiO 2 , Al 2 O 3 3. The optical device of claim 2, made of .alpha., .alpha., or other optical glass that is lossless in the visible spectrum.

6. 10. The optical device of claim 1, wherein each anisotropic nanoscale element is aligned either substantially parallel or substantially perpendicular to an adjacent anisotropic nanoscale element.

7. the broadband incident light beam comprises a plurality of wave packets; the optical profile includes a phase term that specifies parameters of the anisotropic nanoscale elements such that the wave packet is transmitted toward a diffraction-limited spot; 13. The optical device of claim 1.

8. the broadband incident light beam comprises a plurality of wave packets; the optical profile includes a group delay term that specifies parameters of the anisotropic nanoscale elements such that the wave packets arrive simultaneously at the diffraction-limited spot; 13. The optical device of claim 1.

9. 9. The optical device of claim 8, wherein the group delay term is a first derivative term of the optical profile.

10. the broadband incident light beam comprises a plurality of wave packets; the optical profile includes a group delay dispersion term that specifies parameters of the anisotropic nanoscale elements such that the wave packets arriving at the diffraction-limited spot have the same width in the time domain; 13. The optical device of claim 1.

11. 11. The optical device of claim 10, wherein the group delay dispersion term is a second derivative term of the optical profile.

12. 10. The optical device of claim 1, wherein the wavelength of the incident light is in the visible spectrum.

13. A metasurface that includes a plurality of anisotropic nanoscale elements that impart an optical profile that efficiently disperses light into different diffraction angles. Equipped with The optical profile is insensitive to the polarization state of the broadband incident light beam and remains unchanged with wavelength. Optical devices.

14. 14. The optical device of claim 13, wherein the optical profile is the optical profile of a lens, a grating, or an axicon.

15. 14. The optical device of claim 13, wherein the optical efficiency of the optical device is higher than 60% compared to the power of the incident light.

Images