Patent Application
20240168358
The present invention generally relates to systems and methods for high quality factor metasurfaces for two-dimensional wavefront manipulation; more sepecifically relates to high quality factor metasurfaces for two-dimensional wavefront manipulation where the metasurfaces act as optical elements and/or optical sensors.
The regulation of electromagnetic waves with traditional optical components, such as lenses and prisms, is realized through the accumulation of phase delay in the process of light propagation, which limits the reduction and integration of optical devices. Control of phase and amplitude plays an important part in wavefront modulation. Traditional optical elements, as well as diffractive elements such as gratings and holograms, can be bulky for optical set-up. Metasurface can modify the amplitude and impart an abrupt phase shift to the incident wave within the sub-wavelength scale through the light-matter interaction, and thus realize the wavefront modulation more efficiently.
In optical metasurfaces, a subwavelength-spaced array of localized resonators can be used to abruptly manipulate the phase, amplitude, polarization, and spectrum of light at an interface. Attaining strong light matter interaction and hence high quality factors in metasurfaces can be desirable. However, the required subwavelength scale wavefront control, imposes a limit on the resonator size, leading to significant radiative loss. As a result, most metasurfaces are broadband and rely on dielectric structures with limited light confinement and hence quality factor (less than about 15). Low quality factor means photon residence times are very short, and hence local electromagnetic fields tend to be small. It is challenging to achieve simultaneous local control over a wavefront with resonance phase and high quality factor.
Many embodiments are directed to systems of high quality factor metasurfaces for two-dimensional wavefront manipulation and methods thereof. In many embodiments, the electromagnetic metasurfaces enable flat optical elements that show a high quality factor, that is a highly resonant behavior with a narrow band response. The metasurfaces, also referred as nanostructures, show strong interaction with light with a large electric field enhancement inside and around the nanostructures and the capability for wavefront manipulation in two dimensions. The nanostructures in accordance with several embodiments can be used to create band-stop filters, beam deflectors, lenses, beam splitters, and/or holograms with high quality factor. In some embodiments, the nanostructures can be used to boost nonlinear optical parametric conversion of light, in harmonic generation or spontaneous parametric down conversion. In a number of embodiments, the nanostructures can operate as a highly sensitive optical sensor for changes in the dielectric environment, such as (but not limited to) refractive index, temperature, and/or concentration of an analyte. In some embodiments, the nanostructures can be adapted for immersion into a liquid environment, where they can be used for sensing the properties of the liquid environment. In certain embodiments, the nanostructures can be adapted for sensing properties in gaseous environments. The nanostructure optical sensors can measure the change in the reflectance and/or transmission spectrum, and/or the change in reflected and/or transmitted light intensity as read-out. Multiple nanostructures configured to sense different analytes or parameters may also be realized on the same substrate in accordance with various embodiments.
The metasurfaces in accordance with many embodiments can be used as compact flat optical elements with a very narrow band response in optical imaging devices, cameras, cell-phones, and/or augmented reality devices. In several embodiments, the metasurfaces can be used for nonlinear generation of light with harmonic generation, and quantum light generation by spontaneous parametric down conversion to generate entangled photon pairs as needed for quantum communication and quantum information processing. In some embodiments, the metasurfaces can be applied as optical sensors for sensing the refractive index of liquids, the temperature of the surrounding, the concentration of biomolecules in liquids, biomedical diagnostics by sensing biomarkers for such as (but not limited to) cancer diagnostics, or sensing environmental toxins. By including a dynamically tunable element into the nanostructures, the nanostructures may also be used for dynamic modulation of the wavefront for applications in light detection and ranging (Lidar) and spatial light modulators. Other applications of the nanostructures include (but are not limited to) hyperspectral imaging and on-chip spectrometry.
Some embodiments include an apparatus comprising: an electromagnetic metasurface comprising a plurality of repeating unit cells with a periodicity conformally disposed on a substrate; wherein the periodicity is less than a wavelength in free space of an operating light; wherein each of the plurality of repeating unit cells comprises at least one nanostructure with a length, a width, and a height; wherein each of the length and the width is less than the periodicity; and wherein at least two different Mie-modes, with one Mie-mode being a higher order, interfere within each of the plurality of repeating unit cells, the interference enables the apparatus to achieve a resonance in transmission or reflection such that the apparatus controls a phase of the operating light in transmission or reflection using a localized mode with a quality factor of at least 200.
In some embodiments, the at least two Mie-modes are selected from the group consisting of: an electric dipole, a magnetic dipole, an electric quadrupole, a magnetic quadrupole, an electric octupole, a magnetic octupole, an electric hexadecapole, a magnetic hexadecapole, electric 32 pole, and a magnetic 32 pole.
In some embodiments, the apparatus controls the phase of the transmitted light or reflected light in two dimensions.
In some embodiments, the wavelength is selected from the group consisting of: an ultraviolet wavelength from 100 nm to 400 nm, a visible wavelength from 380 nm to 800 nm, a near infrared wavelength from 800 nm to 2500 nm, and an infrared wavelength from 780 nm to 1000 μm.
In some embodiments, the plurality of repeating unit cells is arranged in an array.
In some embodiments, the at least one nanostructure has a shape selected from the group consisting of: a cuboid, a cube, a pillar, a cylinder, an elliptical cylinder, a trapezoid, a triangular prism, a polygonal prism, a pyramid, and a combination thereof.
In some embodiments, the at least one nanostructure has a non-symmetric shape.
In some embodiments, the at least one nanostructure comprises a lossless dielectric material with an imaginary refractive index less than or equal to 0.5 at the wavelength of operation.
In some embodiments, the substrate comprises a material with a real part of the refractive index less than the real part of the refractive index at the wavelength of operation of the at least one nanostructure.
In some embodiments, the at least one nanostructure comprises a material selected from the group consisting of: gallium arsenide, gallium phosphide, silicon carbide, titanium oxide, silicon nitride, barium titanate, lithium niobate, tantalum pentoxide, silicon oxide, amorphous silicon, silicon, and a combination thereof.
In some embodiments, the substrate comprises a material selected from the group consisting of: glass, silicon oxide, silicon nitride, gold, silver, aluminum, copper, titanium, platinum, indium tin oxide, aluminum tin oxide, aluminum zinc oxide, magnesium fluoride, tantalum pentoxide, zirconium oxide, vanadium oxide, a germanium-antimony-tellurium alloy, titanium nitride, hafnium oxide, hafnium nitride, molybdenum diselenide, hexagonal boron nitride, black phosphorous, tungsten diselenide, tungsten disulfide, and a combination thereof.
In some embodiments, the quality factor is observed in an area with a diameter of less than or equal to 100 μm due to the localized mode.
In some embodiments, the wavelength is a near infrared wavelength from 800 nm to 2500 nm, the at least two different Mie-modes are an electric dipole mode and an electric octupole mode, and the quality factor is from 202 to 1475.
In some embodiments, the electromagnetic metasurface is configured to be a part of a band-stop filter, a beam deflector, a lens, a beam splitter, or a hologram.
In some embodiments, the lens has a numerical aperture of greater than or equal to 0.8.
In some embodiments, the apparatus is polarization independent.
In some embodiments, the electromagnetic metasurface is configured to be a part of a sensor in a liquid environment or in a gaseous environment.
In some embodiments, a refractive index of each of the plurality of repeating unit cells is dynamically varied using a mechanism selected from the group consisting of: a thermo-optic effect, an electro-optic effect, a magneto optic effect, a nonlinear Kerr effect, and by electrical or optical injection of free charges in to a material of each of the plurality of repeating unit cells.
In some embodiments, the substrate comprises one or more layers; wherein a refractive index of at least one layer of the substrate is varied using a mechanism selected from the group consisting of: a thermo-optic effect, an electro-optic effect, a magneto-optic effect, a nonlinear Kerr effect, and by electrical or optical injection of free charges in to a material of each of the plurality of repeating unit cells.
In some embodiments, the substrate is a deformable substrate, and each of the plurality of repeating unit cells is dynamically displaced from one another by stretching the deformable substrate such that the displacement changes the periodicity.
Some embodiments further comprise a plurality of the electromagnetic metasurfaces, wherein the plurality of electromagnetic metasurfaces are stacked on top of each other to manipulate a monochromatic light in a consecutive manner, or manipulate broadband illuminated light at separate wavelengths.
Some embodiments include an apparatus comprising: an electromagnetic metasurface comprising a plurality of unit cells arranged in an aperiodic manner on a substrate; wherein each of the plurality of cells comprises at least one nanostructure with a length, a width, and a height determined by a phase of a transmitted or reflected light at an operating wavelength; and wherein at least two different Mie-modes, with one Mie-mode being a higher order, interfere within each of the cell, the interference enables the apparatus to achieve a resonance in transmission or reflection such that the apparatus controls the phase of the operating light in transmission or reflection in a localized mode with a quality factor of at least 200.
In some embodiments, the electromagnetic metasurface is configured to be a part of a metalens, wherein the length and the width of the unit cell at a position (x, y) is determined by an equation:
wherein φ is the phase and λ is the wavelength of the operating light, and f is a focal length of the metalens, and wherein an electromagnetic simulation determines a relationship between the length and the width and φ.
In some embodiments, the electromagnetic metasurfaces is configured to be part of an optical element that modulates the phase of the transmitted or reflected light according to a mathematical function:
φ=f(x, y)
that depends on a position (x, y) on the metasurface, and the length , the width, and the height at the position (x, y) are configured to reproduce the phase φ, and are determined from an electromagnetic numerical simulation of the at least one nanostructure and the substrate.
In some embodiments, the at least two Mie-modes are selected from the group consisting of: an electric dipole, a magnetic dipole, an electric quadrupole, a magnetic quadrupole, an electric octupole, a magnetic octupole, an electric hexadecapole, a magnetic hexadecapole, and electric 32 pole, and a magnetic 32 pole.
In some embodiments, the apparatus controls the phase of the operating transmitted light or reflected light in two dimensions.
In some embodiments, the wavelength is selected from the group consisting of: an ultraviolet wavelength from 100 nm to 400 nm, a visible wavelength from 380 nm to 800 nm, a near infrared wavelength from 800 nm to 2500 nm, and an infrared wavelength from 780 nm to 1000 μm.
In some embodiments, the at least one nanostructure has a shape selected from the group consisting of: a cuboid, a cube, a pillar, a cylinder, an elliptical cylinder, a trapezoid, a triangular prism, a polygonal prism, a pyramid, and a combination thereof.
In some embodiments, the at least one nanostructure has a non-symmetric shape.
In some embodiments, the at least one nanostructure comprises a lossless dielectric material with an imaginary refractive index less than or equal to 0.5.
In some embodiments, the substrate comprises a material with a real part of the refractive index less than the real part of the refractive index of the at least one nanostructure.
In some embodiments, the at least one nanostructure comprises a material selected from the group consisting of: gallium arsenide, gallium phosphide, silicon carbide, titanium oxide, silicon nitride, barium titanate, lithium niobate, tantalum pentoxide, silicon oxide, amorphous silicon, and silicon.
In some embodiments, the substrate comprises a material selected from the group consisting of: glass, silicon oxide, silicon nitride, gold, silver, aluminum, copper, titanium, platinum, indium tin oxide, aluminum tin oxide, aluminum zinc oxide, magnesium fluoride, tantalum pentoxide, zirconium oxide, vanadium oxide, a germanium-antimony-tellurium alloy, titanium nitride, hafnium oxide, hafnium nitride, molybdenum diselenide, hexagonal boron nitride, black phosphorous, tungsten diselenide, tungsten disulfide, and a combination thereof.
In some embodiments, the quality factor is observed in an area with a diameter of less than or equal to 100 μm due to the localized mode.
In some embodiments, the electromagnetic metasurface is configured to be a part of a band-stop filter, a beam deflector, a lens, a beam splitter, or a hologram.
In some embodiments, the apparatus is polarization independent.
In some embodiments, the electromagnetic metasurface is configured to be a part of a sensor in a liquid environment or in a gaseous environment.
In some embodiments, a refractive index of each of the plurality of unit cells is dynamically varied in time using a mechanism selected from the group consisting of: a thermo-optic effect, an electro-optic effect, a magneto optic effect, a nonlinear Kerr effect, and by electrical or optical injection of free charges in to a material of each of the plurality of unit cells.
In some embodiments, the substrate comprises one or more layers; wherein a refractive index of at least one layer of the substrate is varied dynamically in time using a mechanism selected from the group consisting of: a thermo-optic effect, an electro-optic effect, a magneto-optic effect, or a nonlinear Kerr effect, and by electrical or optical injection of free charges in to a material of each of the plurality of unit cells.
In some embodiments, the substrate is a deformable substrate, wherein each of the plurality of unit cells is dynamically displaced dynamically in time from one another by stretching the deformable substrate.
Some embodiments further comprise a plurality of the electromagnetic metasurfaces, wherein the plurality of electromagnetic metasurfaces are stacked on top of each other to manipulate a monochromatic light in a consecutive manner, or manipulate broadband illuminated light at separate wavelengths.
Additional embodiments and features are set forth in part in the description that follows, and in part will become apparent to those skilled in the art upon examination of the specification or may be learned by the practice of the disclosure. A further understanding of the nature and advantages of the present disclosure may be realized by reference to the remaining portions of the specification and the drawings, which forms a part of this disclosure.
The description will be more fully understood with reference to the following figures, which are presented as exemplary embodiments of the invention and should not be construed as a complete recitation of the scope of the invention. It should be noted that the patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.
The recirculation of light in a confined optical mode is a method to amplify the interaction of light and matter. The ability to confine the light to the resonating mode is quantified by the quality factor, Q, as the energy stored per round-trip optical loss in the resonator. With optical micro- and nanostructures including Fabry-Pérot cavities, whispering gallery mode resonators, photonic crystals, guided mode structures, and bound states in the continuum (BIC), quality factors of up to 108 can be achieved. The high level of field enhancement and confinement attained in these structures has led to advances in sensing, active optical devices, light sources, and amplification of photon-matter coupling. However, as the mode volume of an optical resonator decreases and the mode becomes more localized, more radiative decay channels become available and the field enhancement and quality factor may diminish. As a result, there is a tradeoff between spatial mode localization and the attainable quality factor.
In optical metasurfaces, a subwavelength-spaced array of localized resonators can be used to abruptly manipulate the phase, amplitude, polarization, and spectrum of light at an interface. These structures can enable changes in optical imaging, communication, sensing, and display technology. Optical components and phenomena have been realized using metasurfaces such as efficient flat lenses, on-chip holography, and dynamic beam steering. Attaining strong light matter interaction and hence high quality factors in metasurfaces can be desirable, as it enables the realization of ultra-fast spatial light modulators, nonlinear parametric conversion, responsive optical sensing and tailored light emission.
However, the required subwavelength scale wavefront control, imposes a limit on the resonator size, leading to significant radiative loss. As a result, most metasurfaces are broadband and rely on dielectric structures with limited light confinement and hence quality factor (Q less than about 15). Local methods for wavefront manipulation are limited to low quality factors (Q less than about 20). Wavefront manipulation with increased quality factors have been made with structures relying on extended guided mode resonance and nonlocal modes based on bound states in the continuum. Guided mode resonance methods for high quality factor wavefront manipulation are limited to deflection in one dimension, require large illumination apertures, and are highly sensitive to the incident angle. (See, e.g., US Patent Publication No. 2021/0132255 A1; the disclosure of which is incorporated by reference). Non-local methods for high quality factor wavefront manipulation are limited to lower quality factors (Q less than about 150), are unable to operate under oblique incidence illumination, and are not suitable for dynamic wavefront manipulation (See, e.g., Wu, P. C. et al. Nat. Commun. 10, 1-9 (2019); Overvig, A. C., et al., Phys. Rev. Lett. 125, 17402 (2020); Overvig, A. C., et al., Physical Review B, 102(3), p.035434 (2020); Malek, S. C., et al., Light Sci. Appl. 11, 246 (2022); the disclosures of which are herein incorporated by reference.) Achieving simultaneous local control over a wavefront with resonance phase and high quality factor remains challenging.
Many embodiments provide high quality factor metasurfaces by leveraging higher-order Mie resonances to locally manipulate the wavefront of light in two dimensions based on resonance phase. In many embodiments, a metasurface comprises a plurality of optical nanostructure unit cells. The optical metasurface uses the interference of two or more higher order Mie modes in a single nanostructure unit cell to impart a local phase shift on a wavefront with high quality factor. Some embodiments superimpose higher Mie modes with lower Mie modes in order to create optical resonance within the unit cell. Examples of Mie modes that can be used in the nanostructures include (but are not limited to) electric dipoles, magnetic dipoles, electric quadrupoles, magnetic quadrupoles, electric octupoles, magnetic octupoles, electric hexadecapoles, magnetic hexadecapoles, electric 32 poles, magnetic 32 poles, and any higher modes. Specific combination of Mie modes in accordance with certain embodiments can locally manipulate the phase of the wavefront of the light. Several embodiments interfere the electric dipole mode and an electric octupole mode in optical metasurfaces at near infrared wavelengths (from about 800 nm to about 2500 nm). The metasurfaces in accordance with many embodiments enable two dimensional wavefront manipulation with high quality factor, finite illumination apertures and oblique incidence illumination. In various embodiments, the metasurfaces can achieve quality factor of at least about 200; or at least about 300; or at least about 400; or at least about 500; or at least about 600; or at least about 700; or at least about 800; or at least about 900; or at least about 1000; or at least about 1100; or at least about 1200; or at least about 1300; or at least about 1400; or at least about 1500; or at least about 1600; or at least about 1700; or at least about 1800; or less than or equal to about 1500; or from about 200 to about 1500; or from about 200 to about 1400; or from about 200 to about 1300; or from about 200 to about 1200; or from about 200 to about 1100; or from about 200 to about 1000.
The metasurfaces in accordance with many embodiments can manipulate the wavefront of light of various wavelengths with high quality factors. The light can have wavelengths ranging from ultraviolet wavelengths from about 100 nm to about 400 nm; from visible wavelengths from about 380 nm to about 800 nm; near infrared wavelengths from about 800 nm to about 2500 nm; infrared wavelengths from about 780 nm to about 1000 μm. The light being manipulated by the metasurfaces can have a single wavelength or a range of wavelengths such as broadband illumination. In order to manipulate different wavelengths of incoming light, the metasurfaces can be made of different dimensions and/or be made of different materials. In certain embodiments, the desired dimensions and/or materials of the nanostructures on the metasurfaces can be selected for the light wavelength(s). The metasurfaces can be designed to exhibit multiple high quality optical resonances that appear at different wavelengths, and show selective wavefront manipulation capabilities at different wavelengths.
The nanostructures on the metasurface can be made of various shapes and/or dimensions. The nanostructures on the metasurface can be arranged in an array; or in parallel lines; or in straight lines; or in curved lines; or in an aperiodic manner. A repeating unit of the nanostructures can be referred as a unit cell. A unit cell can include at least one nanostructure; or at least two nanostructures; or at least three nanostructures; or at least four nanostructures; or at least five nanostructures. The repeating unit cells can have a periodicity P. The nanostructure has dimensions including a length L, a width W, and a height H. In several embodiments, the periodicity P of the metasurfaces is less than the wavelength of the light. In some embodiments, the length L, the width W, and the height H of the nanostructure are less than the periodicity P. The length L, the width W, and the height H of the nanostructure can be the same or can be different. In various embodiments, the length L, the width W, and the height H scale linearly with the operating wavelength of the light. In several embodiments, the nanostructure can have a symmetrical shape. In some embodiments, the nanostructure can have a non-symmetrical shape to induce a polarization selective response or a chiral response. The nanostructure can have various shapes such as (but not limited to) cuboids, cubes, pillars, cylinders, elliptical cylinders, trapezoids, triangular prisms, polygonal prisms, pyramids, and any combinations thereof. As can readily be appreciated, any of a variety of shapes of the nanostructures can be utilized as appropriate to the requirements of specific applications in accordance with various embodiments of the invention. In some embodiments, the nanostructure can comprise a plurality layers of the same or different materials. The geometrical dimensions of the nanostructures, such as length of the L and width W, or height H, can vary arbitrarily in a non-uniform manner over the aperture of the metasurface device according to the optical function of the metasurface.
The nanostructures of the metasurfaces can be made of various materials. Suitable materials for nanostructures include materials with a large nonlinear optical susceptibility to enhance nonlinear optical parametric conversion processes and/or lossless dielectric materials. The lossless dielectric materials can have an imaginary refractive index (also known as extinction coefficient) of less than or equal to about 0.5; or less than or equal to about 0.1; or less than or equal to about 0.05 at the wavelength of operation. Examples of materials for nanostructures include (but are not limited to) gallium arsenide, gallium phosphide, silicon carbide, titanium oxide, silicon nitride, barium titanate, lithium niobate, tantalum pentoxide, silicon oxide, amorphous silicon, and silicon parallelpipeds. As can readily be appreciated, any of a variety of materials can be utilized as appropriate to the requirements of specific applications in accordance with various embodiments of the invention. In several embodiments, the refractive index of each of the unit cells can be dynamically varied in time using a mechanism such as (but not limited to): a thermo-optic effect, an electro-optic effect, a magneto optic effect, a nonlinear Kerr effect, and/or by electrical or optical injection of free charges in to the unit cell materials.
The nanostructures can be deposited on a substrate. In many embodiments, the nanostructures are deposited conformally onto the substrate. The substrate can be made of various materials. Suitable materials for nanostructures include materials with a large nonlinear optical susceptibility to enhance nonlinear optical parametric conversion processes and/or lossless dielectric materials. At the wavelength of operation, the real part of refractive index of the substrate material should be less than the real part of the refractive index of the nanostructure material in accordance with several embodiments. In several embodiments, the substrate comprises a plurality of layers of different materials. For the plurality of layers of the substrate, the first layer that is in immediate contact with the nanostructure should have a real part of the refractive index less than the real part of the refractive index of the nanostructure material at the wavelength of operation in accordance with some embodiments. Examples of materials for the substrate include (but are not limited to) glass, silicon oxide, silicon nitride, gold, silver, aluminum, copper, titanium, platinum, indium tin oxide, aluminum tin oxide, aluminum zinc oxide, magnesium fluoride, tantalum pentoxide, zirconium oxide, vanadium oxide, germanium-antimony-tellurium alloys, titanium nitride, hafnium oxide, hafnium nitride, molybdenum diselenide, hexagonal boron nitride, black phosphorous, tungsten diselenide, tungsten disulfide and any combinations thereof. In certain embodiments, the substrate can be made with elastic materials including (but not limited to) elastic polymers, silicone, polydimethylsiloxane (PDMS), poly(methyl methacrylate) (PMMA), and any combinations thereof. As can readily be appreciated, any of a variety of substrate materials can be utilized as appropriate to the requirements of specific applications in accordance with various embodiments of the invention.
In many embodiments, the substrates can be made with deformable materials. The nanostructures can be deposited conformably on the substrate. The deformable substrate can be stretched in any of a direction such that the nanostructures can be dynamically displaced and the periodicity of the unit cells can be changed. In several embodiments, the deformable substrates can be stretched in x direction, or in y direction, or in z direction, or in any diagonal direction, or in any concentric direction, in order to achieve the desired periodicity of the unit cells.
In several embodiments, the substrates can comprise one or more layers. The refractive index of at least one layer of the substrate can be varied dynamically in time using a mechanism such as (but not limited to): a thermo-optic effect, an electro-optic effect, a magneto-optic effect, or a nonlinear Kerr effect, and/or by electrical or optical injection of free charges in to the unit cell materials.
In some embodiments, the in-plane dimension of the substrates can have various sizes ranging from microns to millimeters or larger. Examples of one dimension of the substrate include (but are not limited to) greater than or equal to about 1 μm; greater than or equal to about 5 μm; greater than or equal to about 10 μm; greater than or equal to about 50 μm; greater than or equal to about 100 μm; greater than or equal to about 150 μm; greater than or equal to about 200 μm; greater than or equal to about 300 μm; greater than or equal to about 400 μm; greater than or equal to about 500 μm; greater than or equal to about 1 mm; greater than or equal to about 2 mm; greater than or equal to about 3 mm; greater than or equal to about 4 mm; greater than or equal to about 5 mm; greater than or equal to about 10 mm. The layer thickness of the substrate (i.e. in the z direction) can have a thickness ranging from 0.1 nm to several millimeters or larger.
The nanostructures 101 of the metasurface can be made of different materials. Suitable materials for nanostructures include materials with a large nonlinear optical susceptibility to enhance nonlinear optical parametric conversion processes and/or lossless dielectric materials. The nanostructures 101 can comprise at least one suitable material. Multiple materials can be used for a nanostructure as appropriate to the requirements of specific applications in accordance with various embodiments of the invention.
The nanostructures 101 of the metasurface can have different dimensions for light manipulation.
The nanostructures 101 of the metasurface can have different shapes for light manipulation.
A repeating unit of the nanostructures can be referred as a unit cell. In
In some embodiments, higher order Mie modes such as the electric dipole mode and an electric octupole mode can be interposed in the optical nanostructures on the metasurface at near infrared wavelengths. In certain embodiments, the electric dipole mode and an electric octupole mode in nanostructures comprising silicon parallelepipeds on a substrate comprising silicon oxide interfere at near infrared wavelengths. The nanostructures can be made of an array of silicon parallelpipeds with varying geometrical dimensions on a glass substrate. Several embodiments implement the metasurfaces as band stop filters, beam deflectors and radial lenses with quality factor in the range from about 200 to about 1500; or from about 202 to about 1475. The control over the wavefront in accordance with various embodiments is local and allows for operation with finite illumination apertures and angled illumination.
The higher-order Mie-resonant metasurface in accordance with many embodiments enable high quality factor two-dimensional wavefront manipulation. By spectrally overlapping an electric dipole and electric octupole mode, a sharp resonance in transmission can be obtained that enables local control of the wavefront of light. Using local phase control, several embodiments achieve beam deflectors with high directivity and quality factors Q from about 288 to about 1475. In some embodiments, radial lensing with near-diffraction-limited focusing and quality factors Q from about 314 to about 880 can be achieved. Due to the local nature of these modes, high quality factors can be observed with small illumination areas, for example less than or equal to about 100 μm; or less than or equal to about 50 μm; or less than or equal to about 30 μm, in diameter. Several embodiments provide consistent fabrication processes of the metasurface structures with high yield and high reproducibility. The quality factors can be limited by fabrication imperfections and coupling between neighboring structures. Higher quality factors may be realized by using structures supporting different higher-order Mie modes in accordance with embodiments. The amplitude variation across the resonant mode can be reduced by modifying the device design, for example by operating in reflection, or by using other types of higher order modes such as magnetic octupole, hexapoles or toroidal modes.
The high level of wavefront control and strong light interactions with the metasurface in accordance with various embodiments, as evidenced by the high quality factor, make the higher-order Mie-resonant metasurfaces suitable for optical sensing, nonlinear optics, directional lasing, and active wavefront manipulation. Compared to non-local metasurfaces, the metasurfaces in several embodiments are polarization independent, robust against incidence angle variations and show higher quality factor, efficiency, and numerical aperture. Furthermore, in non-local metasurfaces the quality factor for a given numerical aperture is limited by the bandstructure, and a single layer surface shows an upper bound of about 25% efficiency. The locally controlled metasurfaces in accordance with some embodiments do not show these limitations. In certain embodiments, the metasurfaces may not need additional polarization optics and are advantageous for implementation of active optical devices that dynamically modulate the dielectric environment of a metasurface unit cell. For example, by introducing a refractive index change in the nanoblocks using either the thermo-optic or electro-optic effect, the metasurface may be used to dynamically steer light. The high-Q metasurfaces may also be realized at visible wavelengths, where the narrow spectral response is advantageous for display and coloring applications.
Due to the near-field coupling of the ED and EO among neighboring elements, the resonance is dependent on the array size, i.e., number of repetitions of the unit cell, which can be a signature of a partially delocalized mode. This array size dependence is similar to low-order Mie-resonant metasurfaces or asymmetry-induced quasi-BIC structures. The calculations suggest that for an array size beyond 10×10 unit cells, there may be no further significant change in the modal properties. For the ED/EO mode, the increase in quality factor can be attributed with increasing array size to an enhancement of the ED through multipole coupling of the ED and EO in the array through neighboring particles. To further provide insight into the ED/EO mode, several embodiments provide analysis of its degree of localization. Exciting the mode in a single nanoblock of the array shows that it localized within the nanoblock but extends primarily to its nearest neighbors along the direction of polarization. From this calculation, a mode volume of about 3.6 times the volume of a unit cell, or 0.86 I3 can be determined, where I is the wavelength in free space. The mode localization can also be inferred from its dependence on the incidence-angle of the illumination (see
In many embodiments, the local response of the higher-order Mie-resonant metasurface enables local wavefront manipulation by controlling the phase of the transmitted light. Varying the length L of the nanoblocks can spectrally shift the ED and EO modes, and hence the resonance wavelength. The spectral shift accompanying the change in length L allows employing the resonance phase to impose a phase shift on the transmitted light.
Several embodiments fabricate the high-Q metasurfaces by single-step electron beam lithography and dry etching. Some embodiments implement single-step electron beam lithography and dry etching of plasma-deposited amorphous silicon on a glass substrate (see Examples for details).
To experimentally characterize the surfaces, linearly polarized, normally incident light can be employed through the substrate from a wavelength-tunable diode laser, collected the transmitted light with an objective lens and imaged it onto an InGaAs IR-camera, or focused it onto a power meter.
To selectively deflect light over a narrow wavelength range, several embodiments imprint a linear phase gradient on the transmitted light by varying the nanoblock side lengths along one of the metasurface in-plane directions. The nanoblock size lengths are set based on the phase look up table determined from numerical simulations in
The operating wavelength for beam deflection can be adjusted by shifting the average length of nanoblocks.
To demonstrate the wavefront shaping capabilities of the metasurfaces, several embodiments realize high quality factor radial metalenses that focus light along two dimensions over a narrow wavelength range. The metalenses are designed by imposing a paraboloidal phase profile on the transmitted light by setting the nanoblock size lengths according to the look up table in
In wavefront shaping with high quality factors there is an inherent tradeoff between quality factor and accurate phase sampling due to fabrication limitations. This can be due to the rapid variation of the phase on resonance. For example, in the nanostructures, the phase of the transmitted light varies with 9.4 rad/nm within the range of π/2 to 3π/2 (see
Although specific embodiments of systems and apparatuses are discussed in the following sections, it will be understood that these embodiments are provided as exemplary and are not intended to be limiting.
The fabricated metasurfaces are characterized on a custom-built optical transmission microscope (
The transmission of the metasurfaces, T=PT/PI, is calculated by recording the power transmitted though the metasurface, PT, normalized by the power incident on the metasurface, PI. For the beam deflectors, the diffraction efficiency is defined as the fraction of transmitted power coupled into a specific diffraction order. To this end the intensity around each diffraction order is integrated within a square with a side length of 4 FWHM of the intensity of the diffraction order. For the metalenses the diffraction efficiency is defined as the fraction of transmitted power coupled into a circle around the focal spot with a radius of 2 times the airy disk radius.
Scanning electron micrographs are acquired on an FEI Nova 200 NanoLab system to measure the sizes of the fabricated structures. For imaging, the surfaces are covered with a 2 nm thick gold layer by sputter deposition.
The metasurfaces are fabricated on borosilicate glass substrates (n=1.503) with a thickness of 220 μm. To remove organic residues from the surface, the substrates are cleaned in an ultrasonic bath in acetone, isopropyl alcohol, and deionized water each for 15 min, dried using a N2 gun and subsequently cleaned using oxygen plasma. Amorphous silicon is deposited onto the glass using plasma-enhanced chemical vapor deposition. In a subsequent step, the nanoblocks are written in a spin coated MaN-2403 resist layer by standard electron beam lithography. The nanoblocks are then transferred to the amorphous silicon using an SiO2 hard mask with chlorine-based inductively coupled reactive ion etching. As a last step, the residual mask is removed by immersing the samples in buffered hydrofluoric acid (1:7) for 5 s, and subsequent rinsing in deionized water. The uniform and beam deflector metasurfaces are fabricated on an area of 150 μm×150 μm. The metalenses are fabricated with a diameter of 100 um and a parabolic phase profile according to the equation
where λ is the design wavelength and f the focal length. All metalenses are designed for a wavelength of λ about 1280 nm. The variation of the nanorod side length is set according to
The numerical modelling of the nanostructures is carried out using an FDTD method. Simulations are performed with a commercially available FDTD software. A constant refractive index of n=1.503 is used for the borosilicate glass and a constant value of n=3.45 for amorphous silicon, as experimentally determined by ellipsometry. The simulations are carried out with a spatially coherent plane wave illumination and periodic boundary conditions are applied on all sides of the computational domain unless otherwise noted. A smallest mesh-refinement of 5 nm is used. For the oblique illumination simulations, the broadband fixed angle technique (BFAST) is used.
To gain an understanding of the optical modes supported by the metasurface unit cells, finite difference time domain simulations can be performed.
To understand the origin of the resonance mode and the high quality factor, a multipole expansion can be performed.
To account for the neighboring effect between different nanoblocks, some embodiments calculate the reflected field amplitude and phase of a periodic array of nanoblocks from the multipoles.
For comparison with the field profiles of the nanoblocks,
Several embodiments analyze the properties of the ED/EO mode and the light scattering of the structures in the context of local supercavity modes reported in isolated nanoparticles nanoparticles. Some embodiments record the total light scattered by a metasurface with uniformly sized nanoblocks using finite difference time domain simulations. Some embodiments employ a total field scattered field light source with periodic boundary conditions.
To investigate the localization of the ED/EO mode, several embodiments perform FDTD simulations where the mode is excited in a single resonator within a finite sized array (11×11 repetitions). The mode is resonantly excited with an electric dipole source at the center of the resonator polarized along the x direction. The electric field components around the excited resonator over an area of 5×5 repetitions are recorded. The electric field is recorded using an apodization time to suppress the initial field components of the dipole excitation.
where E denotes the electric field at position r. In the calculation, a mode volume is of 1.8 μm3. The volume of a unit cell is estimated to 0.736 μm×0.736□μm×0.895 μm≈0.5 μm3, with an added 0.2 μm to the height as an approximate extent of the evanescent component in z. Comparing this volume to the mode volume, suggests that the mode is localized around a single resonator and its nearest neighbors. This can also be observed in
In a separate analysis, the reflection of a finite-sized array of uniformly sized nanoblocks is studied. The reflection of a uniform N×N array of nanoblocks is as a summation of the backward scattering σu,L of each nanoblock with length L
where γ is a lumped parameter accounting for the finite size and light coupling to each nanoblock. Next, a perturbation is added in the array, by modifying the length of one nanoblock in the array to L+dL. Assuming the hypothesis that the scattering of each nanoblock is independent. For this case, the total reflection of the perturbed array can be obtained by
where σp,L+dL represents the backward scattering of a single nanoblock with length L+dL in a perturbed array. Following this logic, by combining Eq. (2) and (3), the difference in backward scattering between an individual nanoblock of length L and one of length L+dL can be retrieved as
This difference can then be determined from FDTD simulations. Two simulations are preformed, one simulation with an identical array of nanoblocks with L=555 nm, and another simulation of a perturbed array, where the central nanoblock has a length of L+dL=558 nm and the remaining nanoblocks L=555 nm.
Some embodiments investigate mode localization and resonance-based beam steering. The high-quality factor resonance observed in a q-BIC structure can also be used for modulating the phase of the transmitted light. To illustrate this, we simulate the structure in Campione et al. with geometric parameters adapted to shift the resonance to the near infrared spectral range. (See, e.g., Campione, S .; et al., ACS Photonics 2016, 3 (12), 2362-2367; the disclosure of which is incorporated by reference.)
The variation of geometric parameters has a large effect on the optical properties of high quality factor metasurfaces. To analyze this effect, a uniform nanoblock array with the geometrical parameters from
In experiment, a non-uniformity of the geometric parameters over the metasurface aperture results in a superposition of many of high-Q scatterers with varying resonant wavelength. Consequently, a variation of L, H, α or du, is expected to result in a wider resonance peak of the surface, hence a reduced quality factor and an increase in the transmission minimum of the surface. To further understand this effect, some embodiments numerically model the non-uniformity of the structure by limiting the variation only to the nanoblock side length, since the side length has the largest effect on the spectral resonance shift. Some embodiments model the non-uniformity by considering a 4×4 array of nanoblocks that is periodically repeated and impose a normal distribution of the side length on the 16 nanoblocks in the array.
σtot2=σL2+σH2+σα2+σdu2. (6)
The simulated case in
To avoid a strong variation of the scattered electric field amplitude from the metasurface unit cell, a gold reflector can be added to the metasurface with an SiO2 gap between the nanoblocks and the reflector.
The metasurfaces shaping wavefront in two dimensions with high quality factor in accordance with many embodiments are based on geometric phase and the rotation of high quality factor birefringent unit cells, also known as non-local metasurfaces. The response of these non-local metasurfaces can be described by a bandstructure, with their resonance frequency for an incidence angle θ given by
ωres=ω0+bk2, (7)
where b is the band curvature, k=k0 sin θ, k0 the free space wave vector, and ω0 is the resonant angular frequency of at k=0.
Quality factor: In non-local metasurfaces with uniform phase (i.e. no wavefront manipulation) the quality factor can be tuned to very large number following the relation Q˜1/δ, where δ represents a geometrical perturbation of the unicell. However, when imprinting a phase profile on the metasurface the quality factor is largely reduced due to the bandstructure dispersion. For this reason, the quality factors that have been demonstrated for wavefront manipulation are limited, i.e. for 1D beam deflection/focusing up to Q≤300, and for 2D wavefront manipulation Q≤86 for a radial lens. The higher-order Mie-resonant metasurfaces in accordance with some embodiments have quality factor of less than or equal to about 880 for 2D manipulation, and quality factor of less than or equal to about 1492 for 1D manipulation. In higher-order Mie-resonant metasurfaces, the quality factor is limited by the specific Mie-modes employed. The ED/EO shows Q less than or equal to about 668. With other higher-order modes an increased Q can be attained. Furthermore, the high Q-factor is also preserved for wavefront manipulation. Higher wavefront-shaping quality factors can be attained for beam deflection or focusing, as these depended on the specific alignment of the phase different resonators.
Numerical aperture: In non-local metasurfaces, the maximum attainable numerical aperture of an optical element is limited by the dispersion of the resonance wavelength by
This can limit the numerical aperture to less than 0.26 with a quality factor of 86. For higher quality factors the attainable numerical aperture further decreases. Higher-order Mie-resonant metasurfaces in accordance with embodiments do not show a limit on numerical aperture for wavefront shaping, enabling the present demonstration of high-Q metalenses with numerical apertures of greater than or equal to about 0.8.
Limitation of efficiency: The overall efficiency of wavefront shaping with non-local metasurfaces is limited to less than 25% due to their use of geometric phase and the resulting polarization conversion. Higher efficiencies can be attained with multilayer metasurfaces, but these are difficult to realize experimentally at optical wavelengths, due to demanding overlay fabrication accuracies. In higher-order Mie-resonant metasurfaces in accordance with some embodiments, there is no limit on the overall efficiency, and high efficiencies can be attained with simple single layer designs.
Incident angle dependence/dispersion: The bandstructure of non-local metasurfaces shows a dispersion that depends on the orientation of the incidence angle with respect to the perturbation in the structure. Along the direction of the perturbation (TM) the dispersion amounts to a resonance wavelength shift of about 70 nm/10° change in incidence angle. Along the orthogonal direction (TE), the dispersion amounts to a resonance wavelength shift of 9 nm/10° change in incidence angle. Higher-order Mie-resonant metasurfaces in accordance with embodiments show a dispersion with resonance wavelength shift of less than 2 nm /10° change in incidence angle in both directions. This shows that higher-order Mie-resonant metasurfaces are much less sensitive to illumination conditions and can operate with focused/diverging and oblique illumination.
Polarization dependence: Non-local metasurfaces require illumination with circularly polarized light of the correct handedness. This requires additional polarization optics for interfacing these surfaces with a light source. Furthermore, to reject unconverted light, a second polarizer is required in the detection. Higher-order Mie-resonant metasurfaces in accordance with embodiments show a polarization-independent response and hence do not require additional polarization optics for integration.
Fabrication requirements: The fabrication requirements of high quality factor optical elements are generally demanding. Small changes in geometrical parameters of the unit cell can spectrally shift the optical resonance and hence affect the optical device performance, by resulting in errors in the scattered electric field amplitude and/or phase. In non-local metasurfaces this resonance shift can be 1.6 nm wavelength per nanometer change in unit cell dimensions. In higher-order Mie resonant metasurfaces in accordance with embodiments this shift is about 1.3 nm wavelength per nanometer change of the unit cell dimensions (
Potential for active spatial light modulation: Non-local metasurfaces employ Pancharatnam-Berry phase (also known as geometric phase) for wavefront manipulation, whereas higher-order Mie-resonant metasurfaces in accordance with embodiments use resonance phase. For metasurfaces relying on geometric phase, the phase profile is permanently imprinted on the surface based on the fabricated geometry and cannot be arbitrarily reconfigured with an external input (e.g. by applying electrical voltage). While simple reconfiguration such as on-off switching or deformation of the phase profile has been demonstrated with non-local metasurfaces, an arbitrary reconfiguration of the phase is difficult for non-local metasurfaces, since it would require the in-plane re-orientation of the fabricated unit cells. Resonance-phase based metasurfaces may allow for such an arbitrary reconfiguration of the phase profile (e.g. continuous beam steering) at up to microsecond time scales. For higher-order Mie-resonant metasurfaces in accordance with embodiments such a realization is straightforward, for example by using the materials with a thermo-optic, or electro-optic effect to spectrally shift the resonance and perform active phase modulation.
Table 1 lists design parameters of beam deflector metasurfaces. Parameters are given for all the beam deflector metasurfaces in
Table 2 lists design parameters of metalenses. Design parameters are given for the metalenses in
As can be inferred from the above discussion, the above-mentioned concepts can be implemented in a variety of arrangements in accordance with embodiments of the invention. Accordingly, although the present invention has been described in certain specific aspects, many additional modifications and variations would be apparent to those skilled in the art. It is therefore to be understood that the present invention may be practiced otherwise than specifically described. Thus, embodiments of the present invention should be considered in all respects as illustrative and not restrictive.
As used herein, the singular terms “a,” “an,” and “the” may include plural referents unless the context clearly dictates otherwise. Reference to an object in the singular is not intended to mean “one and only one” unless explicitly so stated, but rather “one or more.”
As used herein, the terms “approximately,” and “about” are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. When used in conjunction with a numerical value, the terms can refer to a range of variation of less than or equal to ±10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%.
Additionally, amounts, ratios, and other numerical values may sometimes be presented herein in a range format. It is to be understood that such range format is used for convenience and brevity and should be understood flexibly to include numerical values explicitly specified as limits of a range, but also to include all individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly specified. For example, a ratio in the range of about 1 to about 200 should be understood to include the explicitly recited limits of about 1 and about 200, but also to include individual ratios such as about 2, about 3, and about 4, and sub-ranges such as about 10 to about 50, about 20 to about 100, and so forth.
The current application claims the benefit of and priority under 35 U.S.C. § 119 (e) to U.S. Provisional Patent Application No. 63/427,038 entitled “High Quality Factor Metasurfaces For Two-Dimensional Wavefront Manipulation” filed Nov. 21, 2022. The disclosure of U.S. Provisional Patent Application No. 63/427,038 is hereby incorporated by reference in its entirety for all purposes.
This invention was made with government support under Grant No. FA9550-21-1-0312 awarded by the Air Force. The government has certain rights in the invention.
| Number | Date | Country | |
|---|---|---|---|
| 63427038 | Nov 2022 | US |
