Patent Description:
Measuring intraocular pressure can be challenging. Current techniques require expensive, cumbersome sensors. These sensors may require the eye to be still and for sensors to be placed at a fixed angle of incidence on the eye. Metamaterials, which may include plasmonic materials, on the other hand, hold potential for a variety of improvements to current methods, including decreased size and decreased angle dependence. Metamaterials currently are not angle-independent and cannot be embedded in the eye. There exists a need for a metamaterial that is angle-independence or has reduced angle dependence.

<NPL>a flexible PSM device with an active high-efficiency tunability, large tuning range, and ultrahigh Q_-factor. The PSM device exhibits a tunable single and dual-resonance with ultranarrow bandwidth. These resonances can be tuned by using mechanical force to deform the geometrical period of the PSM. The resonant tuning range can span from <NUM> to <NUM> THz. ie PSM device can be used to not only realize an ultranarrowband filter but also a polarization switch in the THz-frequency range. Furthermore, the PSM device exhibits the multifunctionalities of singJe/duaJ-band switching and polarization switching. The integration of the PSM device on a mechanically flexible PDM S substrate offers a new route toward optoelectronics applications and provides potential possibilities for the next generation of programmable and digital metamaterials with multi-channel data processing. The PSM device possesses high flexibility, applicability, and cost-effectiveness for widespread THz-wave applications.

<NPL> that it is possible to nano-tailor the shape and dimensions of the pores in an aluminum template by applying a multistep anodization and etching method.

<NPL> a broad subclass of metasurfaces, viz. gradient metasurfaces, which are devised to exhibit spatially varying optical responses resulting in spatially varying amplitudes, phases and polarizations of scattered fields.

The invention is defined in the appended independent claim. Further developments of the invention are specified in the dependent claims. An example embodiment provides a metamaterial structure, comprising a substrate, and nanostructures located in a pattern on or within the substrate, wherein the nanostructures are paraboloid shaped and periodic. A further example embodiment provides a method to fabricate a metamaterial surface, comprising depositing a nanostructure metal on a substrate, and forming paraboloids from the nanostructure metal.

Metamaterials are capable of interacting with light in unconventional ways. A metamaterial may comprise of an array of nanostructures distributed across a surface. A spectrum, such as the visible spectrum, may interact with the nanostructures. A plasmonic material may be a type of metamaterial. There may be a surface plasmon (SP) mode, where the spectrum may cause a charge distribution on the metamaterial's nanostructured surface that may oscillate between a positive and negative charge periodically.

A surface plasmon mode may occur when the nanostructures have a certain shape and distribution. In some embodiments, the nanostructures may be shaped like paraboloids and the distribution may comprise overlapping tiles that may be hexagonal in shape. The surface plasmon mode, also known as normal-to-plane mode, together with the distribution of the nanostructures, may interact together to reflect one wavelength from the spectrum at a much greater intensity than other wavelengths, which may be known as a "peak wavelength reflected" or a "target wavelength. " The nanostructures may be capable of operating in normal-to-plane mode. For many metamaterials, the angle of incidence may change the peak wavelength reflected. However, with paraboloid-shaped nanostructures and the overlapping tile distribution, a change in angle of incidence may result in a markedly lower change of peak wavelength reflect compared to other shapes and distributions of nanostructures.

This greatly reduced dependence of the peak wavelength on the angle of incidence may lead to the term "angle independence" being used herein to describe this phenomenon.

Furthermore, when the nanostructure is stretched or compressed, the peak wavelength reflected may change. This property of changing the peak wavelength reflected may be used to measure pressure changes when the nanostructure is part of a pressure sensing device. Lastly, a change in peak wavelength may also occur if the nanostructure is exposed to a liquid on its surface. The liquid may interact with the nanostructures surface to change the peak wavelength shift. This property of changing peak wavelength shift may be used to identify chemicals in a chemical analysis sensor.

While previous processing techniques may allow for shapes including disks and pillars, none may allow for paraboloid or other rounded shapes that may be manufactured at the nanometer scale. As will be described, these processing techniques may enable a normal-to-plane mode nanostructure.

<FIG> depicts an example embodiment of a structure <NUM>. Structure <NUM> may comprise nanostructures <NUM>. Nanostructures <NUM> may be embedded within a substrate <NUM>, or may be on top of a substrate <NUM>. Nanostructures <NUM> may be organized in a pattern <NUM>.

In some embodiments, nanostructures <NUM> may be gold, aluminum, silver, copper, aluminum-doped zinc oxide, Indium tin oxide, titanium nitride, indium gallium arsenide, tungsten oxide, titanium-tungsten or any other metals or metal alloys, however, they may be made of other materials as well, not listed. Nanostructures <NUM> may be distributed or located in a pattern <NUM> on or within substrate <NUM>. Pattern <NUM> may be periodic, which may be a repeatable distribution of nanostructures. Pattern <NUM> may have equidistant nanostructures <NUM>, such as a hexagonal pattern. Pattern <NUM> may have both equidistant and non-equidistant structures (i.e. are partially equidistant), such as a square pattern where some neighboring nanostructures may be equidistant while other neighboring nanostructures have a different distance (EG, diagonal neighbors). Pattern <NUM> may be periodic or it may be semi-periodic, where there may be a repeatable pattern for some of the nanostructures while there is a non-repeatable pattern for other parts of the nanostructure.

In some embodiments, pattern <NUM> may form a tessellation, which may be a tile. The tessellation may be overlapping or may be non-overlapping. Pattern <NUM> may be a periodic pattern that may provide an equidistant spacing of nanostructures <NUM>. Equidistant may be an approximation where the distances between nanostructures are approximately equal but may have variations due to the accuracy limitations of fabrication techniques, which will be described later in more detail.

In some embodiments, pattern <NUM> may be six-sided, which may be a hexagonal tile pattern, which may also be known as a hexagonal lattice. Nanostructures <NUM> may form a hexagonal tile pattern, where six nanostructures can form the six vertices of a hexagon. In some embodiments, nanostructures 102a-f may form pattern <NUM> for the example case of a hexagonal pattern. There may be an additional nanostructure embedded within pattern <NUM>, such as at the center of pattern <NUM> which may be nanostructure <NUM>. Nanostructure <NUM> may form a vertex of another pattern <NUM> of nanostructures.

Nanostructure 102a may be a first distance <NUM> away from nanostructure 102b. First distance <NUM> may be known as a lattice constant, and may be the distance between the center of nanostructure 102a and the center of nanostructure 102b. Furthermore, nanostructure 102b may be a first distance <NUM> away from nanostructure 102c. First distance <NUM> may be based on a target wavelength of structure <NUM> and the structure <NUM> may be designed for peak wavelength reflection, which will be described in more detail in <FIG>. In some embodiments, first distance <NUM> may be between <NUM> and <NUM>. In other embodiments, first distance <NUM> may be greater for longer target wavelengths and may be less for shorter target wavelengths.

The angle between the edge formed by nanostructure 102a to nanostructure 102b and nanostructure 102b to nanostructure 102c may be a first angle <NUM>. In some embodiments, if pattern <NUM> is hexagonal, first angle <NUM> may be about <NUM> degrees. The first distance <NUM> and first angle <NUM> may be approximately the same for all edges and angles of pattern <NUM> for all subsequent nanostructures 102a-f.

In alternate embodiments, the shape of pattern <NUM> may be any shape that can be tessellated. In some embodiments, pattern <NUM> may maintain the equidistant and equal-angle properties for all nanostructures as described previously. In another embodiment, pattern <NUM> may not be have fully equidistance and equal-angled nanostructures. In another embodiment, pattern <NUM> may not be periodic, that is, there may be a fixed pattern where nanostructures <NUM> may not be equidistant from each other. As may be readily appreciated, pattern <NUM> may alternatively be expressed as a tiling of the triangles (e.g., equilateral triangles or isosceles triangles) that make up a hexagonal or square pattern.

In some embodiments, substrate <NUM> may be a flexible or stretchable material that may allow for flexing of the substrate, such as polydimethylsiloxane (PDMS), but may be other materials as well. In another embodiment, substrate <NUM> may be rigid, such as nickel, but may be other materials as well. In some embodiments, substrate <NUM> may be between <NUM> to <NUM> thick.

<FIG> depicts a side view <NUM> of structure <NUM> of <FIG>. A spectrum <NUM> may travel onto structure <NUM> at a first angle of incidence 203a, which may also be known as a first angle 203a. First angle 203a may be any angle between <NUM> degrees (parallel to the plane of structure <NUM>) and <NUM> degrees (perpendicular to the plane of structure <NUM>). In some embodiments, spectrum <NUM> may comprise any wavelength or range of wavelengths, which may be known as broadband light, in the visible and near-infrared spectrum. In another embodiment, spectrum <NUM> may be in a different spectrum range, such as near-infrared, ultraviolet, microwave, or other wavelength range. There may be a second angle of incidence 203b and a third angle incidence 203c, which may also be any angle between <NUM> degrees and <NUM> degrees.

Spectrum <NUM> may interact with structure <NUM> and produce a reflected spectrum <NUM>, which may be reflected from structure <NUM> at a first angle of reflection 204a. First angle of reflection 204a may be any angle between <NUM> degrees (perpendicular to the plane of structure <NUM>) and <NUM> degrees (parallel to the plane of structure <NUM>). Reflected spectrum <NUM> may have a peak wavelength, which may also be known as the target wavelength, that is reflected and all other wavelengths may have little to no reflection, which will be described in more detail below. There may also be a second angle of reflection 204b and a third angle of reflection 204c, which may be any angle between <NUM> degrees and <NUM> degrees. The first angle of reflection 204a may depend on the first angle of incidence 203a. The second angle of reflection 204b may depend on the second angle of incidence 203b, and so on.

In some embodiments, reflected spectrum <NUM> may be approximately the same for all angles of angles of incidence 203a-c. That is, the response of structure <NUM> to spectrum <NUM> may be angle-independent. Angle-independence may not be truly independent, that is, there may be some variations in the exact peak wavelength reflected in reflected spectrum <NUM> based on the angles of incidence 203a-c, but such angle dependence is greatly reduced compared to other metamaterials.

The peak wavelength reflected may vary slightly based on the angle of incidence 203a-c. For example, spectrum <NUM> may be broadband light spanning <NUM> - <NUM>. First angle of incidence 203a may be <NUM> degrees, second angle 203b may be <NUM> degrees, and third angle 203c may be <NUM> degrees. In response, reflected spectrum <NUM> may have a first peak wavelength of about <NUM> for first angle 203a, a second peak wavelength of about <NUM> for second angle 203b, and a third peak wavelength of about <NUM> for a third angle 203c. The first, second, and third peak wavelengths may be substantially similar so as to apply the term "angle-independent," however, there may still be small wavelength variations in reflected spectrum <NUM> based on the angles of incidence 203a-c.

In another embodiment, the peak wavelength for any given angle may change when structure <NUM> is stretched or compressed. If structure <NUM> is stretched or compressed, reflected spectrum <NUM> may have a new peak wavelength that is different than the first peak wavelength. The difference between the new peak wavelength and the first peak wavelength may be used to infer a change in pressure, as described further below.

In another embodiment, the peak wavelength may change when structure <NUM> is exposed to and/or in contact with a liquid or other material. The composition of the liquid or other material may be determined based on the change in peak wavelength. If structure <NUM> exposes nanostructures <NUM> and a liquid or new material is in contact with nanostructures <NUM>, such as a fluid, reflected spectrum <NUM> may have a different peak wavelength relative to the peak wavelength in absence of the material. The difference between the first and different peak wavelengths may be used to infer information such as the presence of a certain material in contact with structure <NUM>, and may be discussed in more detail later in the description.

Structure <NUM> may also be polarization-independent. That is, the reflected spectrum <NUM> may be polarization independent. For example, spectrum <NUM> may have different transverse electric (TE) or transverse magnetic (TM) polarizations. That is, for any polarization of spectrum <NUM>, reflected spectrum <NUM> may be approximately the same.

<FIG> depicts a side view <NUM> of nanostructure 102a. There may be a z-axis and an x-axis shown, with a y-axis going into the plane of side view <NUM>. The z-axis may depict the height of nanostructure 102a and the x-axis may depict the width of nanostructure 102a. At the bottom of the z-axis, nanostructure 102a may be at its widest point, which may be its diameter. The diameter of the nanostructure 102a is defined as the intersection of the nanostructure 102a and the base substrate on which the nanostructure 102a is formed. The cross section of nanostructure 102a may be shown along the Z-X plane. In some embodiments, the diameter of nanostructure 102a at its base may be <NUM>, but may be other diameters between <NUM> and <NUM>. The height of nanostructure 102a may be <NUM>, but may be other heights, for example, between <NUM> and <NUM>.

The dimensions of nanostructure 102a may change based on the target wavelength and the material used. Resolving the height and the diameter of the nanostructures for a target wavelength requires solving for two variables (height and diameter), and as one varies within an acceptable range, the other will vary accordingly. In some embodiments, the height of nanostructure 102a may be between <NUM>% and <NUM>% of the first distance <NUM>. In some embodiments, the diameter of nanostructure 102a may be between <NUM>% and <NUM>% of the first distance <NUM>.

The height and diameter of nanostructure 102a may be determined by checking for normal-to-plane mode for a fixed lattice constant and varying the diameter and height of nanostructure 102a. There may be parameters f and r, which may be used in conjunction with experimental testing to confirm a normal-to-plane mode and to determine a range of acceptable height and diameter values. The experiment may compare variables f to r, defined as::
f = diameter of nanostructure 102a / the lattice constant (i.e. first distance <NUM>) and
r = height of nanostructure 102a / diameter of nanostructure 102a.

Referring to <FIG>, there may be an experimental test <NUM> based on experimentally varied height and diameter values, and which may compare the variables f and r for a fixed lattice constant value. A lattice constant value may be determined based on a target wavelength, and the final height and diameter of nanostructure 102a may be determined based on the results of test <NUM>. Test <NUM> may reveal regions <NUM> and <NUM> and there may be a border line <NUM>. Region <NUM>, which may include border line <NUM>, may be a region in which normal-to-plane mode exists and may allow for the angle independent behavior. Region <NUM> may be a region in which normal-to-plane mode does not exist.

For height and diameter values of nanostructure 102a in region <NUM>, the angle of incidence of spectrum <NUM> may result in a large change in peak wavelength shift of reflected spectrum <NUM>, which will be described in more detail later in <FIG> and <FIG>. For height and diameter values of nanostructure 102a in region <NUM>, however, the angle of incidence of spectrum <NUM> may result in a small change in peak wavelength shift of reflected spectrum <NUM>, relative to region <NUM>. That is, region <NUM>, including border line <NUM>, may result in an angle independent or less angle dependent peak wavelength shift of reflected spectrum <NUM>.

Furthermore, when performing measurements of peak wavelength shift of spectrum <NUM> for a normal-to-plane (i.e. angle independent) mode structure <NUM> of <FIG>, it may be desirable to have a larger peak wavelength shift to more clearly read results from a sensor <NUM> which may be described in <FIG>/B and <FIG>. The further away from the border line <NUM> into the normal-to-plane mode region, the less of a change in shift in peak wavelength that may occur. The less of a change in shift in peak wavelength that may occur, the more difficult it may be to perform measurements. The angle independent nature of structure <NUM> may not change, however, reading measurements may be more difficult when the change in peak wavelength is smaller.

The physical parameters of height, diameter, and lattice constant of nanostructure 102a may impact the peak wavelength shift of the reflected spectrum <NUM>. However, as long as the parameters enable a normal-to-plane mode, there may be little to no differences in the measured peak wavelength shift due to angle the angle of incidence (unlike values found in region <NUM>). Therefore, it may be advantageous to select a height and diameter value that may be on border line <NUM>.

The lattice constant, first distance <NUM>, may be determined based on a target wavelength, which may be the peak wavelength reflected for reflected spectrum <NUM> and may be approximately ½ the target wavelength. For example, if a target wavelength is <NUM>, the lattice constant may be about <NUM>. For a range of diameter, height, and lattice constant values, a normal-to-plane mode may exist to allow reflected spectrum <NUM> to have a peak wavelength shift. In some ranges of f and r, the peak wavelength shift for reflected spectrum <NUM> may be greater than for other ranges of f and r.

In some embodiments, nanostructure 102a may comprise gold, f may be in the range of <NUM> to <NUM>, and r may be in the range of <NUM> to <NUM>. Therefore, f*r may be in range of <NUM>*<NUM>, <NUM> to <NUM>*<NUM>, <NUM>, providing the ratio to be <NUM>% to <NUM>% of height of nanostructure 102a to first distance <NUM>. In other embodiments, other ratios may exist. This embodiment may be for the visible spectrum for spectrum <NUM>. In another embodiment, spectrum <NUM> may be near infrared (NIR), and other metals may be used, which may include gold, silver, or aluminum.

In another embodiment, nanostructure 102a may have a cross section in the Z-X plane that may be based on a paraboloid in shape, however, other shapes may be used, including square, rectangular, spherical, trapezoidal, hemi-ellipsoid, or other shape. A paraboloid may be a quadric surface with one axis of symmetry (Z axis for <FIG>), however, nanostructure 102a may not be exactly paraboloid in shape. It may have natural variations due to physical constraints of fabrication techniques, or it may be purposefully not fully paraboloid by design.

Nanostructure 102a may have a surface <NUM>. Surface <NUM> may have a charge distribution <NUM>. Surface <NUM> may have a surface plasmon (SP) mode, where the charge distribution <NUM> on the surface may oscillate between a positive and negative charge periodically, which may be known as periodicity. This may be known as a normal-to-plane mode which may be a resonant oscillation of conduction electrons that may occur along surface <NUM> of nanostructure 102a and may be according to a refractive index (RI) perceived by a wave at surface <NUM>. The gradual increase of the RI along the Z axis may enable the normal-to-plane mode.

Without being bound by theory, it is believed that there may be an electric field polarized along the z-axis, as shown in <FIG>, which may be denoted as Ez. Similarly, there may be an electric field polarized along the x-axis, which may be denoted as Ex. There may be a dipole moment obtained from the Ez or the Ex electric field profiles. Ez may be oriented perpendicular and Ex may be oriented parallel to the plane of periodicity of pattern <NUM> on structure <NUM>. That is, Ez may be along the z-axis and Ex may be along the x-axis. The dipole moment may be substantially less dependent on the first angle of incidence 203a of spectrum <NUM> due to the surface plasmon mode.

A normal-to-plane mode may be along the z-axis, which may be a SP mode where the dipole moment of nanostructure 102a may be oriented normal to the plane of periodicity irrespective of the angle and polarization of spectrum <NUM>. As described previously, this may result in angle-independence and polarization-independence, however, there may be some variations in response based on angle and polarization. The variations may be much less than for other (Non-paraboloid) nanostructure 102a shapes and patterns <NUM>, which will be described further in <FIG>.

Nanostructure 102a may have an effective plasmonic refractive index (RI) that varies based on the depth (z-axis) between the top and the bottom of nanostructure 102a. From the top of a nanostructure 102a and to the bottom of nanostructure 102a along the z-axis, there may be a gradual increase in the effective plasmonic RI. The effective plasmonic RI may be affected by neighboring nanostructures 102a-f of <FIG>. As the first distance <NUM> increases between two nanostructures, the refractive index may decrease. As the first distance <NUM> decreases between two nanostructures, the refractive index may increase. Similarly, for two nanostructures, the bases of the nanostructures are closer together than the tops of the nanostructures, along the z-axis. These differences in distance between the bottom and the top of two nanostructures may create an effective plasmonic RI gradient <NUM>. An effective plasmonic RI gradient <NUM> may show a relationship between the depths from the top of nanostructure 102a to the base of nanostructure 102a. The effective plasmonic RI, neff, may be lower at the top of nanostructure 102a and may increase linearly along the surface <NUM> of nanostructure 102a.

<FIG> depicts an example comparison of two differently-shaped nanostructures <NUM> of <FIG>. There may be an array of paraboloid-shaped nanostructures <NUM> and an array of disk-shaped nanostructures <NUM>, which will be described in more detail below. The shape of nanostructures <NUM> may impact the change in wavelength dependence over a range of angles of incidence for input angles 203a to 203c. A paraboloid array may comprise paraboloid-shaped nanostructures <NUM> of <FIG> and may exhibit a normal-to-plane mode. A disk array may comprise disk-shaped nanostructures <NUM> of <FIG> and may exhibit an out-of-plane mode.

Spectrum <NUM> of <FIG> may have an input angle range 203a-c, which may be shown as between <NUM> degrees to <NUM> degrees on the X- axis in the presently illustrated example. Spectrum <NUM> may interact with nanostructures <NUM> on structure <NUM>, and may result in a reflected spectrum <NUM> with a peak wavelength for each output angle 204a-c. The difference between the peak wavelength of reflected spectrum <NUM> at <NUM> degree and angles higher than <NUM> degree spectrum <NUM> may be measured and denoted as Δλ on the Y-axis of <FIG>, with units that may be in nanometers.

In some embodiments, a first nanostructure type <NUM>, which may be a non-paraboloid shape, has a difference between peak reflected spectrum <NUM> at <NUM> degree and angles higher than <NUM> degrees, and peak spectrum <NUM> may change linearly with input angle range 203a-c. For each five degree change in an input angle, there may be a <NUM>% or greater change in Δλ. That is, there may be a change in Δλ that may be known as an angle-dependent response. For example, for a fixed spectrum <NUM>, an input angle 203a may be <NUM> degrees and Δλ may be about <NUM>. An input angle 203b may be <NUM> degrees and Δλ may be about <NUM>. Input angle 203c may be <NUM> degrees and Δλ may be about <NUM>.

In another embodiment, second nanostructure type <NUM> may have a paraboloid shape and there may be a much more angle-independent response than for a disk shape structure in first nanostructure type <NUM>. There may still be an angle-dependent response for second nanostructure type <NUM>, however, relative to first nanostructure type <NUM>, the response may be far less and the term angle-independence may be used. For example, for a fixed spectrum <NUM>, an input angle 203a may be <NUM> degrees and Δλ may be about <NUM>. An input angle 203b may be <NUM> degrees and Δλ may be about <NUM>. An input angle 203c may be <NUM> degrees and Δλ may be <NUM>.

<FIG> depicts a fabrication process <NUM> for fabrication of structure <NUM>. <FIG> depicts a process <NUM> of fabrication process <NUM> of <FIG>. Fabrication of structure <NUM> may begin on a substrate <NUM>.

Substrate <NUM> may be any material upon which fabrication of structure <NUM> may take place. In some embodiments, substrate <NUM> may be made from silicon. Substrate <NUM> may be a silicon wafer.

A photoresist <NUM> may be deposited onto substrate <NUM>. This may be process <NUM> of <FIG>: depositing photoresist <NUM> onto a substrate <NUM>. In some embodiments, photoresist <NUM> may be about <NUM> micrometer (µm ) thick. In another embodiment, photoresist <NUM> may be between <NUM> and <NUM> thick. In some embodiments, photoresist <NUM> may be level and approximately equal in thickness across substrate <NUM>.

Photoresist <NUM> may comprise a light-sensitive polymer material that may be used in a process to form a patterned coating on a surface, where patterning may also include removing all non-patterned photoresist <NUM> from a surface.

Photoresist <NUM> may have an associated sensitizer and solvent. In some embodiments, photoresist <NUM> may be used in a positive or a negative photoresist process. The chemical structures of photoresist <NUM> may be photopolymeric, photodecomposing, photocrosslinking, or any other photoresist structure. In another embodiment, the photoresist <NUM> may be exposed by electron beams.

In some embodiments, photoresist <NUM> may be spin coated onto substrate <NUM> to form a uniformly thick layer. In some embodiments, photoresist <NUM> may then be heated to between <NUM> C and <NUM> C for <NUM> seconds to <NUM> seconds.

Process <NUM> of <FIG> may comprise depositing a first metal <NUM> onto photoresist <NUM>. First metal <NUM> may also be referred to as a substrate metal. In some embodiments, some of first metal <NUM> may also be deposited on substrate <NUM> in addition to photoresist <NUM>. This may include a region between an edge of substrate <NUM> and an edge of photoresist <NUM>. In another embodiment, all of first metal <NUM> may be deposited on photoresist <NUM>.

In some embodiments, first metal layer <NUM> may be nickel. In another embodiment, first metal <NUM> may be any other metal in the periodic table, or a mixture or alloy of metals. In some embodiments, first metal layer <NUM> may be between <NUM> and <NUM> thick and may be used as a sacrificial layer. In some embodiments, first metal layer <NUM> may be deposited using electron beam (e-beam) evaporation. In some embodiments, the speed of evaporation of first metal <NUM> may be <NUM>/s to <NUM>/s.

Process <NUM> of <FIG> may comprise depositing resist <NUM> onto first metal layer <NUM>. In some embodiments, resist <NUM> may be a synthetic resin, such as polymethyl methacrylate (PMMA). In another embodiment, resist <NUM> may be a ZEON electron beam positive-tone (ZEP) resist, as marketed and sold by ZEON SPECIALTY MATERIALS, INC. In another embodiment, resist <NUM> may be any kind of electron-beam resist.

In some embodiments, resist <NUM> may be spin coated onto first metal <NUM>. In some embodiments, the time to bake resist <NUM> may be between <NUM> seconds and <NUM> seconds. In some embodiments, resist <NUM> may be baked at between <NUM> C and <NUM> C.

In some embodiments, resist <NUM> may be between <NUM> and <NUM> in thickness, however, the thickness of resist <NUM> may be larger or smaller and may depend on the target aspect ratio of holes <NUM>. The thickness of resist <NUM> may depend on fabrication requirements, such as an aspect ratio of patterns formed on resist <NUM>.

In some embodiments, electron beam (e-beam) lithography may be applied to resist <NUM> to form a pattern of holes, for forming the pattern <NUM> of <FIG>. Process <NUM> of <FIG> may comprise forming pattern <NUM> on resist <NUM>. The beam of the e-beam lithography may be between a <NUM> to <NUM> nano-Amp beam with a power intensity of <NUM> - <NUM> micro-coloumbs per cubic centimeter, and may be other values beyond this range.

The e-beam lithography applied to resist <NUM> may form holes <NUM> with a pattern <NUM>. Holes <NUM> may expose first metal <NUM> at the location of holes <NUM>. Pattern <NUM> of holes <NUM> may be used to aid in the formation of nanostructures <NUM>. A hole of the holes <NUM> may have an aspect ratio, which may be the ratio of the height of the hole to the diameter of the hole. In some embodiments, the aspect ratio may be between <NUM> and <NUM>.

In some embodiments, the diameter of a hole of the holes <NUM> may be between <NUM> and <NUM>, however, the diameter of the hole may be greater or smaller depending on the target wavelength application. In some embodiments, the diameter of a hole in holes <NUM> may be within an order of magnitude of the target wavelength application. In another embodiment, there may be multiple diameters of holes used in holes <NUM>.

In some embodiments, a layer <NUM> may be deposited onto first metal <NUM> at the location of holes <NUM>. Process <NUM> of <FIG> may comprise optionally depositing layer <NUM> onto first metal <NUM>. Layer <NUM> may be an adhesion layer and may be used to aid in the deposition process of metals. Layer <NUM> may be a metal, such as chromium, and may be between <NUM> and <NUM> in thickness. Layer <NUM> may also be known as an adhesion layer. Layer <NUM> may allow for better adhesion between first metal <NUM> and a second metal <NUM>.

A second metal <NUM> may be deposited onto part of or all of layer <NUM> at the location of holes <NUM>, which may be the same location as pattern <NUM> and may form pattern <NUM>. Second metal <NUM> may also be referred to as a nanostructure metal. In another embodiment, where first metal <NUM> is not used, second metal <NUM> may be deposited onto any substrate at the location of holes <NUM>. Process <NUM> of <FIG> comprises depositing second metal <NUM> at the location of holes <NUM>. In another embodiment, second metal <NUM> may be deposited onto first metal <NUM> at the location of holes <NUM> when layer <NUM> is not present. In some embodiments, second metal <NUM> may be gold, however, it may be other metals, including aluminum, silver, copper, aluminum-doped zinc oxide, Indium tin oxide, titanium nitride, indium gallium arsenide, tungsten oxide, titanium-tungsten or any other metals or metal alloys. In some embodiments, second metal <NUM> is between <NUM> and <NUM> thick, but may be other thicknesses depending on the target wavelength application, as described previously. A target wavelength application may be the wavelength at which nanostructures <NUM> interact with the target wavelength and may be the peak wavelength reflected in reflected spectrum <NUM> of <FIG>. In some embodiments, the second metal <NUM> chosen may depend on the target wavelength. For visible spectrum, second metal <NUM> may be gold, but it may be other metals. For NIR spectrum, second metal <NUM> may be aluminum or silver, but it may be other metals. The spectrum range a metal reflects at may be used to determine the metal to select for the target wavelength. Gold may be able to reflect visible spectrum, whereas aluminum and silver may be able to reflect NIR spectrum.

In some embodiments, second metal <NUM> may be deposited using e-beam deposition, however, other deposition methods may be used.

Second metal <NUM>, once deposited, may be initially in a shape <NUM>. In some embodiments, shape <NUM> may be a cone shape. The top of the cone may be flat or level, and may not finish at a singular point. The cone shape may be formed as a result of the aspect ratio of holes <NUM>. If the aspect ratio is low, shape <NUM> may look more like a disk. If the aspect ratio is high, shape <NUM> may look more like a cone with a sharp, singular point as its tip. As will be described below, the shaping of second metal <NUM> from shape <NUM> into a shape <NUM> may occur after resist <NUM> is removed.

In some embodiments, resist <NUM> may be removed. Process <NUM> of <FIG> comprises removing resist <NUM>. Resist <NUM> may be removed with a lift-off bath method using a solvent stripper such as REMOVER PG, as marketed and sold by KAYUKA ADVANCED MATERIALS. REMOVER PG may be used and resist <NUM> may be in a lift-off bath for <NUM> to <NUM> hours. In another embodiment, a different method may be used to remove resist <NUM>.

Second metal <NUM> may be in shape <NUM> and may be transformed to shape <NUM> without resist <NUM>. Process <NUM> of <FIG> may comprise transforming second metal <NUM> from shape <NUM> to shape <NUM>. In some embodiments, shape <NUM> may be paraboloid in shape. In another embodiment, shape <NUM> may be a disk, cone, or hemi-sphere. In some embodiments, exposure to an ion beam may be used to shape second metal <NUM> from shape <NUM> to shape <NUM>.

Focused-ion beam exposure may be used to form second metal <NUM> into shape <NUM>, with a <NUM> to <NUM> nano-Amp beam which may have a <NUM> to <NUM> millisecond dwell time. Dwell time may be the exposure time of the ion beam to second metal <NUM>. The focused-ion beam may be a directional beam, which may allow the edges of the second metal <NUM> in shape <NUM> to wear off. That is, the focused-ion beam may be directional, which may be perpendicular to the substrate <NUM> in some embodiments. The sharp features facing the focused-ion beam directions, such as edges, points, or flat surfaces, may be removed. In some embodiments, the direction of the ion beam may be at an angle between <NUM> degrees (parallel) and <NUM> degrees (perpendicular) to substrate <NUM>. In some embodiments, the direction may not change during the dwell time where the ion beam is being exposed. In another embodiment, the direction may change during the dwell time where the ion beam is being exposed.

Process <NUM> of <FIG> may comprise optionally depositing surface <NUM> onto second metal <NUM>. In some embodiments, surface <NUM> may be PDMS and may be deposited via spin coating, however, surface <NUM> may be other materials, such as materials that are elastic or that may allow waves to travel through it and may be deposited by another technique. In some embodiments, surface <NUM> may be between <NUM> and <NUM> times the height of second metal <NUM>. Surface <NUM> may be an optional surface and may not be deposited onto second metal <NUM> in some embodiments.

In some embodiments, first metal <NUM> may extend beyond the base of photoresist <NUM>. This extended area may be cut away and the structure of photoresist <NUM>, first metal <NUM>, layer <NUM> (if included in the deposition process), second metal <NUM>, and surface <NUM> may be removed from substrate <NUM>. Photoresist <NUM> may then be removed by using a solvent, such as acetone. In some embodiments, acetone solvent may be used for between <NUM> and <NUM> minutes to remove photoresist <NUM>.

In some embodiments, when structure <NUM> comprises nanostructures <NUM> of <FIG> embedded in surface <NUM>, first metal <NUM> may be removed with an acid bath. Process <NUM> of <FIG> may comprise removing first metal <NUM>. In some embodiments, there may be a cut on the sides of first metal <NUM> that exposes photoresist <NUM> and layer <NUM> (when present), and an acid bath may be used to remove layers from the bottom up. That is, photoresist layer <NUM> may be removed, followed by layer <NUM>, and followed by layer <NUM> when present. Hydrochloric acid may be used and the structure may be in an acid bath for between <NUM> and <NUM> hours. In another embodiment, first metal <NUM> may be removed with alternate methods. The resulting structure may be structure <NUM> which may comprise layer <NUM>, second metal <NUM>, and surface <NUM>. In another embodiment, layer <NUM> may also be removed using the hydrochloric acid bath.

In another embodiment, first metal <NUM> and layer <NUM> may not be needed and the resulting structure may be directly fabricated on substrate <NUM>. Subsequently, process <NUM> and process <NUM> may not occur. This embodiment may be for a structure <NUM> where nanostructures <NUM> are exposed and are on the surface of substrate <NUM> with no surface <NUM> present. In this embodiment, process <NUM> may not occur and no acid bath may be used. Instead, substrate <NUM> may be cut to form structure <NUM>.

The resulting structure may be structure <NUM> which may comprise second metal <NUM>, and surface <NUM>.

In another embodiment, structure <NUM> may comprise second metal <NUM> and surface <NUM> when layer <NUM> is not used.

<FIG> depicts a perspective view of an example embodiment of a sensor <NUM> and <FIG> depicts a top view of the same. Sensor <NUM> may use structure <NUM> to measure a change in pressure. Sensor <NUM> may comprise a cavity <NUM>. A membrane <NUM> may be on the top side of cavity <NUM>. Structure <NUM> may be on membrane <NUM>.

Cavity <NUM> may be an elastomeric material, such as PDMS. Cavity <NUM> may be filled with a compressible fluid at a known pressure, such as air, and sealed so that if immersed in a fluid, no fluid may penetrate cavity <NUM>. In some embodiments, cavity <NUM> may be a cylinder with a height of between <NUM> to <NUM> and diameter of between <NUM> and <NUM>. Structure <NUM> may be attached to cavity <NUM> on the surface of membrane <NUM>, or it may be embedded in membrane <NUM>.

In some embodiments, membrane <NUM> may deflect based on a pressure differential of the outside relative to the inside. A spectrum <NUM> may be transmitted to structure <NUM>, which may be reflected as a reflected spectrum <NUM>, which may have an associated peak wavelength that is reflected. The peak wavelength reflected in reflected spectrum <NUM> at an unknown pressure may be compared to the peak wavelength observed when the pressure differential is known to determine a pressure change in membrane <NUM>.

Specifically, Cavity <NUM> may experience a pressure differential between its internal cavity <NUM> fluid and the external environment, which may deflect membrane <NUM>. The deflection of membrane <NUM> may result in radial strain on structure <NUM>, which may cause the nanostructures <NUM> embedded within structure <NUM> to become more or less tightly spaced. This in turn causes a change in peak wavelength, which may be used to estimate the pressure differential, as will be described in <FIG>. In some embodiments, cavity <NUM> may be placed in the anterior chamber of an eye, in a position that may be outside of the field of view. An eye pressure change may lead to a pressure change in cavity <NUM>, which may in turn cause membrane <NUM> to deflect and structure <NUM> to deflect.

While the previously described embodiment focuses on a pressure sensor using structure <NUM> and cavity <NUM>, structure <NUM> may also be used without cavity <NUM>. In another embodiment, membrane <NUM> and structure <NUM> may form a sensor without cavity <NUM>. Structure <NUM> may be embedded in membrane <NUM>, or may be placed on top of membrane <NUM>. With structure <NUM> embedded in membrane <NUM>, the resulting configuration may be used as a sensor for measuring the stretch or compression of the material when placed on a surface. With structure <NUM> placed on top of membrane <NUM>, the resulting structure may be used to detect the composition of a material or liquid placed on top of or in direct contact with structure <NUM>.

<FIG> depicts a pressure measurement <NUM> of sensor <NUM> of <FIG> with structure <NUM>. <FIG> may compare the change in peak wavelength of reflected spectrum <NUM> at varying pressures for structures <NUM> with a first nanostructure type <NUM> and a second nanostructure type <NUM> of <FIG>. <FIG> may illustrate an advantage of using paraboloid shaped nanostructures. The x-axis may show a change in wavelength |Δλ| in nm. The y-axis may show a reflectivity of reflected spectrum <NUM> in arbitrary units (a. Reflection may be measured in photon counts that may be measured by a spectrometer. They photon count may vary depending on the physical environment, light source power, and other variables. Therefore, a. may be used for analyzing the reflectivity and to compare a peak wavelength shift.

A change in peak wavelength of reflected spectrum <NUM> for a first nanostructure type <NUM> at varying pressure levels and varying angles of incidence 203a-c of <FIG> may be depicted in responses <NUM>. A change in peak wavelength of reflected spectrum <NUM> for a second nanostructure type <NUM> at varying pressure levels and varying angles of incidence 203a-c of <FIG> may be depicted in responses <NUM>. As described in <FIG>, first nanostructure type <NUM> may comprise disk or other non-paraboloid shapes. Second nanostructure type <NUM> may comprise paraboloid-shaped nanostructures.

<FIG> may show three angles of incidences for spectrum <NUM> of <FIG> in scenarios <NUM>, <NUM>, and <NUM>. In scenario <NUM>, the angle of incidence may be <NUM> degrees. In scenario <NUM>, the angle of incidence may be <NUM> degrees, and in scenario <NUM>, the angle of incidence may be <NUM> degrees. Scenarios <NUM>, <NUM>, and <NUM> may correspond to input angles 203a-c of <FIG>, respectively.

For each scenario <NUM>, <NUM>, and <NUM>, and for both responses <NUM> and <NUM>, there may be three sets of peak wavelength changes that may correspond to pressures in sensor <NUM> of <NUM> mmHg (i.e. no pressure change), <NUM> mmHg, and <NUM> mmHg. For each set of three graph lines, the topmost graph line may correspond to <NUM> mmHg pressure change, the middle graph line may represent a <NUM> mmHg pressure change, and the lowest graph line may represent <NUM> mmHg pressure change. For example, measurement 702a may show a peak wavelength shift for second nanostructure type <NUM> when sensor <NUM> is calibrated to <NUM> mmHg pressure change.

Referring to scenario <NUM>, there are responses <NUM> and <NUM> for an angle of incidence of <NUM> degrees. In response <NUM>, which may correspond to second nanostructure type <NUM>, within scenario <NUM>, there may be three profiles of corresponding peak wavelength shifts, shown as measurements 702a-c. Measurement 701a may correspond to a pressure change of <NUM> mmHg. Measurement 702b may correspond to a pressure change of <NUM> mmHg, and measurement 702c may correspond to a pressure change of <NUM> mmHg.

Similarly, for response <NUM>, referring to scenario <NUM>, measurement 701a may have a pressure change of <NUM> mmHg, measurement 701b may have a pressure change of <NUM> mmHg, and measurement 701c may have a pressure change of <NUM> mmHg.

Referring to the <NUM> mmHg pressure change of response <NUM> across multiple angles of incidences, corresponding to scenarios <NUM>, <NUM>, and <NUM>, there may be peak wavelength shift 702a in scenario <NUM>, peak wavelength shift <NUM> in scenario <NUM>, and peak wavelength shift <NUM> in scenario <NUM>. Peak wavelength shift 702a may be approximately <NUM>, peak wavelength shift <NUM> may be approximately <NUM>, and peak wavelength shift <NUM> may be approximately <NUM>.

Referring to the <NUM> mmHg pressure change of response <NUM>, there may be a peak wavelength shift 701a in scenario <NUM>, <NUM> in scenario <NUM>, and <NUM> in scenario <NUM>. Peak wavelength shift 701a may be approximately <NUM>, peak wavelength shift <NUM> may be approximately <NUM>, and peak wavelength shift <NUM> may be approximately <NUM>. Reviewing the other pressure change responses <NUM> and <NUM>, one may find that response <NUM> may have an angle-independent response (EG, very little peak wavelength shift) to a change in peak wavelength of spectrum <NUM>. As described previously, angle independent may be less angle-dependent than other solutions. Response <NUM>, which may use paraboloid-shaped nanostructures of second nanostructure shape <NUM>, may have a peak wavelength shift at <NUM> mmHg of between <NUM> and <NUM> for angle of incidence ranges from <NUM> degrees of scenario <NUM> to <NUM> degrees of scenario <NUM> respectively. The difference in peak wavelength shift between a <NUM> degree and <NUM> degree angle of incidence may be approximately <NUM>. In the visible spectrum, a difference in peak wavelength shift of <NUM> may not result in a color change. Therefore, if a paraboloid-shaped nanostructure is used in sensor <NUM>, there may be an "angle independent" range where measurements may provide approximately the same readings across a range of angles of incidence.

Meanwhile, response <NUM>, which may use first nanostructure type <NUM>, which use disc-shaped nanostructures, may show an angle-dependent response to peak wavelength shifts 701a, <NUM>, and <NUM>. Response <NUM> may have a peak wavelength shift at <NUM> mmHg of between <NUM> and <NUM> for angle of incidence ranges from <NUM> degrees of scenario <NUM> to <NUM> degrees of scenario <NUM>. The difference in peak wavelength shift between a <NUM> degree and <NUM> degree angle of incidence may be approximately <NUM>. In the visible spectrum, a difference in peak wavelength shift of <NUM> may result in a color change. Therefore, if a disc-shaped nanostructure is used in sensor <NUM>, there may be an "angle dependent" range where measurements may provide different readings across a range of angles of incidence.

As described previously, paraboloid-shaped nanostructures may allow for a useful sensor <NUM> because it may be angle independent or less dependent on angles of incidence. The angle of incidence of spectrum <NUM> may not need to be exact and it may be a range of angles, such as from <NUM> degrees to <NUM> degrees. This may be shown in responses <NUM>. Unlike responses <NUM>, in responses <NUM>, there may be an angle dependent response which may not be useful for a sensor <NUM> because measurements may require an exact angle of incidence to provide repeatable measurements.

Pressure measurement readings may be calibrated for sensor <NUM> by using the data of pressure measurement <NUM>, specifically responses <NUM>.

Claim 1:
A metamaterial structure (<NUM>), comprising:
a substrate (<NUM>), and
nanostructures (<NUM>) located in a pattern (<NUM>) on the substrate,
wherein the nanostructures (<NUM>) are paraboloid in shape and arranged in a periodic pattern,
characterized in that the distance (<NUM>) between closest nanostructures (<NUM>) is between <NUM> and <NUM>,
wherein the nanostructures (<NUM>) are capable of operating in normal-to-plane mode, wherein the normal-to-plane mode further comprises an angle-independent surface plasmon mode and polarization-independent surface plasmon mode, and
wherein the nanostructures (<NUM>) are comprised of one or more of the following: gold, aluminum, silver, copper, aluminum-doped zinc oxide, indium tin oxide, titanium nitride, indium gallium arsenide, tungsten oxide, or titanium-tungsten, or a combination thereof.