Patent Description:
Biochemical sensors relying on optical resonances have recently drawn attention due to their sensitivity to changes in the bulk refractive index of their surroundings as well as direct interaction with particulates, such as proteins, useful in biomedical applications. In several configurations, these sensors may be re-usable, or capable of real-time detection in a microscale, portable format. <CIT> discloses a method for measuring a refractive index. <NPL>, also discloses method for measuring a refractive index of a medium. <CIT> discloses a biosensor able to measure the refractive index difference between various buffer solutions.

The present invention is directed to a refractive sensor as defined in appended independent claim <NUM> and to a method for sensing refractive index as defined in appended independent claim <NUM>. Embodiments disclosed herein include dielectric metasurface platforms with potential to provide more affordable, highly effective refractive index and biosensing. Transmittance-based single-wavelength amplitude measurements using said embodiments can potentially significantly reduce the cost and physical size of sensing devices without compromising sensitivity, and compatible fabrication processes could allow integration with complementary metal-oxide-semiconductor (CMOS) or other chip-based devices.

In a first aspect, a method for measuring a refractive index of a medium is disclosed. The method includes exciting a first antisymmetric resonance of a metasurface with illumination incident on the metasurface at a non-normal incidence angle with respect to the substrate surface. The metasurface includes a periodic array of resonators formed on the substrate surface. The medium whose refractive index is being measured encapsulates the periodic array of resonators. The method also includes determining a refractive index of the medium from a amplitude of a transmitted signal that includes a portion of the illumination transmitted through the metasurface.

<FIG> is a cross-sectional view of a refractive-index sensor <NUM> in a plane <NUM> parallel to the x-z plane of a coordinate system <NUM>. Hereinafter, directions and planes described by one or more axes x, y, and z refer to coordinate system <NUM> unless otherwise specified.

Refractive-index sensor <NUM> includes an optics unit <NUM> and a light source <NUM>, and, in certain embodiments, a photodetector <NUM>. Optics unit <NUM> includes a substrate <NUM>, a plurality of dielectric resonators <NUM> arranged as a periodic array <NUM>, and a microfluidic chip <NUM>. <FIG> is a cross-sectional view of optics unit <NUM> in a cross-sectional plane <NUM> that is parallel to the x-y plane. <FIG> is a three-dimensional view of optics unit <NUM>, with a portion of microfluidic chip <NUM> omitted to provide a clear view of dielectric resonators <NUM>. <FIG> are best viewed together in the following description.

Substrate <NUM> has a top surface <NUM>. Microfluidic chip <NUM> is on top surface <NUM> and has a non-planar bottom surface <NUM> that forms a channel <NUM> bounded between top surface <NUM> and a portion of non-planar bottom surface <NUM> not in contact with top surface <NUM>. Channel <NUM> has a channel depth <NUM> in a direction perpendicular to top surface <NUM>.

Each dielectric resonator <NUM> is on top surface <NUM> and extends into channel <NUM> to a height <NUM> above top surface <NUM>. Height <NUM> is less than channel depth <NUM>. Each dielectric resonator <NUM> has a width <NUM>. Periodic array <NUM> has a unit cell spacing <NUM>, which is a center-to-center distance between nearest-neighbor dielectric resonators <NUM>. While resonators <NUM> have a circular cross-section in the example depicted in <FIG>, they may have differently-shaped cross-sections, such as polygonal, without departing from the scope of the embodiments.

Light source <NUM> is configured to illuminate periodic array <NUM> with illumination <NUM> incident on top surface <NUM> at a non-normal incident angle <NUM>. Examples of light source <NUM> include light-emitting diodes, fixed-wavelength lasers, and tunable lasers. In certain embodiments, illumination <NUM> is unpolarized.

Illumination <NUM> has a center wavelength λ<NUM> exceeding each of height <NUM>, width <NUM>, and unit cell spacing <NUM>. Each dielectric resonator <NUM> has a refractive index nr(λ<NUM>) and substrate <NUM> has a refractive index ns(λo). In certain embodiments, illumination includes illumination <NUM> incident on a region <NUM> (<FIG>) of optics unit <NUM> that does not include periodic array <NUM>. Optics unit <NUM> transmits at least a portion of illumination <NUM> as a reference signal 154T, which may be used for normalization, e.g., to determine a single-wavelength transmittance or transmittance spectrum of metasurface <NUM>.

Optics unit <NUM> transmits at least a portion of incident illumination <NUM> as transmitted illumination 152T that, in embodiments, is detected by photodetector <NUM>. In operation, spectral properties of transmitted illumination 152T are used to measure the refractive index of an encapsulating medium <NUM> in channel <NUM>, as described herein. Encapsulating medium <NUM> may be a gas or a fluid. Encapsulating medium <NUM> and periodic array <NUM> form a metasurface <NUM> within channel <NUM>. In <FIG>, the callout referring to metasurface <NUM> touches a dashed box adjacent to surfaces <NUM> and <NUM>. In embodiments, the spectral bandwidth of illumination <NUM> is narrower than a stopband of metasurface <NUM>. Illumination <NUM> may have a center wavelength within the stopband. Light source <NUM> may include a bandpass filter to achieve said spectral bandwidth relationship.

In embodiments in accordance with the present invention, metasurface <NUM> is a Huygens metasurface, that is, a metasurface with spectrally overlapping electric and magnetic dipole resonances. In certain other embodiments, metasurface <NUM> is not a Huygens metasurface, such that any overlap of electric dipole resonance and magnetic dipole resonance is insufficient for the metasurface to qualify as a Huygens metasurface. In such other embodiments, the electric dipole resonance is spectrally adjacent to the magnetic dipole resonance. For example, a spectral separation between the electric dipole resonance and an adjacent magnetic dipole resonance is at least one of (a) less than a linewidth of illumination <NUM> and (b) greater than ½(δE + δB), where δE and δB are respective spectral widths of the electric dipole resonance and the magnetic dipole resonance.

Herein, the refractive index of encapsulating medium <NUM> is referred to as the encapsulant refractive index. In embodiments, ns(λ<NUM>) < αnr(λ<NUM>) - β for sufficient refractive index contrast of dielectric resonators <NUM> to the encapsulant refractive index to yield a stopband. In embodiments, coefficient α is between <NUM> and <NUM> and offset β is between <NUM> and <NUM>. Coefficient α may equal the encapsulant refractive index divided by nr. The encapsulant refractive index may differ from substrate refractive index ns by less than offset β.

<FIG> illustrates electric field amplitudes of illumination <NUM> incident upon, and propagating through, one of a plurality of dielectric resonators <NUM> of a metasurface <NUM> at a four-degree incidence angle. Metasurface <NUM> is on substrate <NUM> and has an electric dipole resonance that spectrally overlaps its magnetic dipole resonance at a center wavelength of illumination <NUM>. As a result, metasurface <NUM> transmits nearly one-hundred percent of illumination <NUM> as transmitted illumination <NUM>. Metasurface <NUM> is an example of metasurface <NUM>.

<FIG> illustrates electric field amplitudes of illumination <NUM> incident upon one of a plurality of dielectric resonators <NUM> of metasurface <NUM> at a wavelength that excites an antisymmetric mode <NUM> of metasurface <NUM>. In dielectric resonators <NUM>, the electric field amplitude of illumination <NUM> is antisymmetric about a plane <NUM>. As a result of a symmetry mismatch between incident illumination <NUM> and the excited an antisymmetric mode, metasurface <NUM> transmits only an evanescent field into substrate <NUM>, rather than a propagating electromagnetic field in which energy flows into substrate <NUM>.

<FIG> illustrates electric field amplitudes of illumination <NUM> normally-incident upon, and reflected by, one of a plurality of dielectric resonators <NUM> of a metasurface <NUM>. Metasurface <NUM> is on substrate <NUM> and has an electric dipole resonance that is spectrally adjacent to, and not overlapping with its magnetic dipole resonance. The center wavelength of illumination <NUM> is between the respective electric and magnetic dipole resonance wavelengths of metasurface <NUM>, which results in metasurface <NUM> reflecting nearly one-hundred percent of illumination <NUM> as reflected illumination <NUM>. Metasurface <NUM> is an example of metasurface <NUM>.

<FIG> is a simulated transmittance plot <NUM> for an embodiment of metasurface <NUM> that has spectrally overlapping electric and magnetic dipole resonances. In this embodiment, hereinafter embodiment A, substrate <NUM> is formed of SiO<NUM>, polydimethylsiloxane (PDMS) fills channel <NUM>, and height <NUM>, unit cell spacing <NUM>, and width <NUM> are, respectively, <NUM>, <NUM>, and <NUM>.

Transmittance plot <NUM> includes numerically-simulated transmittance spectra <NUM> and <NUM>, which correspond to illumination <NUM> incident on optics unit <NUM> at incidence angle <NUM> equal to zero degrees and four degrees, respectively. Transmittance spectrum <NUM> has a stopband <NUM>, which corresponds to an excitation of both the electric dipole resonance and the magnetic dipole resonance of metasurface <NUM> excited by illumination <NUM> incident at four-degrees. Stopband <NUM> has a center wavelength <NUM> and a linewidth <NUM>. Center wavelength <NUM> is approximately <NUM>. In one embodiment, illumination <NUM> has a spectral linewidth that is less than linewidth <NUM>. In another embodiment, illumination <NUM> has a spectral linewidth that is exceeds linewidth <NUM>.

<FIG> is a transmittance plot <NUM> for embodiment A of metasurface <NUM> corresponding to <FIG> for two refractive index values of encapsulant material filling channel <NUM>. Transmittance plot <NUM> includes numerically-simulated transmittance spectra <NUM> and <NUM>, which correspond to respective encapsulant refractive indices n = <NUM> and n = <NUM>. Transmittance spectra <NUM> and <NUM> have respective stopbands <NUM> and <NUM> centered at respective wavelengths λ = <NUM> λ = <NUM>. The difference in center wavelengths is caused by the difference in refractive indices of the respective encapsulating media <NUM>, Δn = <NUM>. In certain embodiments, illumination <NUM> has a spectral linewidth that is less than a linewidth of either stopband <NUM> and <NUM>.

<FIG> is a transmittance plot <NUM> for embodiment A of metasurface <NUM> at λ = <NUM> where the PDMS in channel <NUM> has an encapsulant refractive index ranging from <NUM> to <NUM>. Transmittance plot <NUM> includes numerically-simulated transmittance <NUM>, and its derivative <NUM> (dT/dn) with respect to cavity refractive index.

<FIG> is a schematic illustrating a cross-section of a refractive-index sensor <NUM>, which is an example of refractive-index sensor <NUM>. Refractive-index sensor <NUM> includes an optics unit <NUM> and a light source <NUM>, which are examples of optics unit <NUM> and light source <NUM> respectively. Optics unit <NUM> includes microfluidic chip <NUM> on substrate <NUM>, periodic array <NUM>, and a second periodic array <NUM>. Periodic arrays <NUM> and <NUM> are in channel <NUM> between surfaces <NUM> and <NUM>, and are part of respective metasurfaces <NUM> and <NUM>. Light source <NUM> is configured to simultaneously illuminate each of periodic array <NUM> and <NUM> with respective illumination <NUM>(<NUM>) and <NUM>(<NUM>).

Second periodic array <NUM> is an example of periodic array <NUM>, and includes a plurality of second dielectric resonators arranged as second periodic array <NUM> on top surface <NUM>. In embodiments, at least one of (i) a second width of each of the plurality of second dielectric resonators differs from width <NUM> of resonators <NUM> and (ii) a second unit cell size of the second periodic array differs from the unit cell size <NUM> of resonators <NUM>. In embodiments, periodic array <NUM> is identical to periodic array <NUM>.

In certain embodiments, refractive-index sensor <NUM> includes at least one of photodetector <NUM> and a photodetector <NUM>. Photodetector <NUM> is configured to detect illumination <NUM>(<NUM>) transmitted by metasurface <NUM>.

<FIG> is a schematic transmittance plot <NUM> that includes a stopband <NUM> of metasurface <NUM> and a stopband <NUM> of metasurface <NUM>. In one embodiment, stopbands <NUM> and <NUM> result from excitation of a respective antisymmetric resonances (either electric dipole or magnetic dipole) of respective metasurfaces <NUM> and <NUM> by illumination <NUM>, where angle <NUM> is between two degrees and ten degrees. In another embodiment, stopbands <NUM> and <NUM> result from excitation of non-antisymmetric (e.g., symmetric) resonances of respective metasurfaces <NUM> and <NUM> by illumination <NUM>, where angle <NUM> is between negative two degrees and positive two degrees such that illumination <NUM> is at normal or near-normal incidence.

Stopband <NUM> has a center wavelength <NUM> (λ<NUM>) and a stopband linewidth <NUM> (δλ<NUM>). Stopband <NUM> has a center wavelength <NUM> (λ<NUM>) and a stopband linewidth <NUM> (δλ<NUM>). In embodiments, illumination <NUM> has an illumination center wavelength <NUM> (λ<NUM>), that is between stopband center wavelengths <NUM> and <NUM>: λ<NUM> < λ<NUM> < λ<NUM>. Also, in certain embodiments, stopband linewidth δλ<NUM> is greater than two times the spectral separation (λ<NUM> - λ<NUM>) such that the stopband <NUM> includes illumination center wavelength <NUM> (λ<NUM>): (λ<NUM> - λ<NUM>) < <NUM>δλ<NUM>. Similarly, in embodiments, (λ<NUM> - λ<NUM>) < <NUM>. 5δλ<NUM>, such that the stopband <NUM> also includes illumination center wavelength <NUM> (λ<NUM>).

<FIG> is a transmittance plot <NUM> of embodiment A of metasurface <NUM> for two refractive index values of encapsulating medium <NUM>. Transmittance plot <NUM> includes numerically-simulated stopbands <NUM> and <NUM>, which correspond to respective encapsulant refractive indices n = <NUM> and n = <NUM>. Stopbands <NUM> and <NUM> have respective center wavelengths <NUM> and <NUM>. The difference in refractive indices may result from the introduction, or change in concentration of, of an analyte in a fluid comprising the encapsulant material.

Stopbands <NUM> and <NUM> are examples of stopbands <NUM> and <NUM>, respectively, where illumination <NUM> excites non-antisymmetric resonances (e.g., symmetric resonances) of metasurfaces <NUM> and <NUM>. Since transmittance plot <NUM> is of embodiment A with two different encapsulant materials, periodic arrays <NUM> and <NUM> are identical, such that differences between stopbands <NUM> and <NUM> are due to differences in the encapsulant refractive index.

Stopband <NUM> results from metasurface <NUM> having an electric dipole resonance, center wavelength λE<NUM> thereof being less than center wavelength <NUM>, and a magnetic dipole resonance, center wavelength λB<NUM> thereof being greater than center wavelength <NUM>. Similarly, stopband <NUM> results from metasurface <NUM> having an electric dipole resonance, center wavelength λE<NUM> thereof being less than center wavelength <NUM>, and a magnetic dipole resonance, center wavelength λB<NUM> thereof being greater than center wavelength <NUM>. Hence, each of stopbands <NUM> and <NUM> have an "electric side" less than their respective center wavelengths and a "magnetic side" greater than their respective center wavelengths.

Respective magnetic sides of stopbands <NUM> and <NUM> more closely overlap (λ<NUM> ≈ <NUM>-<NUM>) than do their respective electric sides (λ<NUM> ≈ <NUM>-<NUM>). For example, in transmittance plot <NUM>, wavelength range <NUM> is smaller than wavelength range <NUM>. This occurs because the electric dipole resonance of metasurface <NUM> is more sensitive to encapsulant refractive index than is the magnetic dipole resonance. This asymmetry of stopbands <NUM> and <NUM> enables distinguishing between (i) a drift in a stopband center wavelength that results from drift in illumination center wavelength <NUM> and (ii) a change in refractive index of encapsulating medium <NUM>.

In certain embodiments, metasurfaces <NUM> and <NUM> have respective stop bands less than and greater than center wavelength <NUM>. For example, stopbands <NUM> and <NUM> are stop bands of metasurfaces <NUM> and <NUM>, respectively. Such positioning of stop bands enables distinguishing between wavelength drift (of center wavelength <NUM>) and the encapsulant refractive index of encapsulating medium <NUM>, which may be common to both metasurfaces <NUM> and <NUM>. For example, encapsulating medium <NUM> is a fluid that flows through and surrounds both resonator arrays <NUM> and <NUM>.

When the encapsulant refractive index increases, both stopbands <NUM> and <NUM> shift to a greater wavelength (as in <FIG>), such that the detected transmittance of metasurface <NUM> decreases while the detected transmittance of metasurface <NUM> increases. However, if center wavelength <NUM> decreases, the detected transmittance of metasurface <NUM> decreases while the detected transmittance of metasurface <NUM> increases. Hence, merely evaluating a whether transmittance increases or decreases is insufficient for distinguishing between center-wavelength drift and change in encapsulant refractive index.

Yet, if center wavelength <NUM> correspond to the "electric" side of stopband <NUM> and the "magnetic" side of stopband <NUM>, then, in response to a change in encapsulant refractive index, the transmittance of metasurface <NUM> (stopband <NUM>) will change more than that of metasurface <NUM> (stopband <NUM>) because the electric dipole resonance is more sensitive to change in encapsulant refractive index. A drift in center wavelength <NUM> would cause a significantly smaller transmittance-change difference between metasurface <NUM> and <NUM>.

Other relationships between illumination center wavelengths and electric/magnetic dipole resonances result in the above-mentioned asymmetric wavelength shift that enables distinguishing between illumination wavelength drift and change in encapsulant refractive index. Examples of such relationships are described in the following. In an embodiment B, center wavelength <NUM> of stopband <NUM> is determined by an electric dipole resonance and a magnetic dipole resonance of metasurface <NUM> having respective center wavelengths λE<NUM> and λB<NUM>. In embodiment B, center wavelength <NUM> of stopband <NUM> is determined by an electric dipole resonance and a magnetic dipole resonance of the second metasurface having respective center wavelengths λE<NUM> and λB<NUM>. When illumination <NUM> has an illumination center wavelength <NUM> between center wavelengths <NUM> and <NUM>, either (i) λE<NUM> > λB<NUM> and λE<NUM> > λB<NUM> or (ii) λE<NUM> < λB<NUM> and λE<NUM> < λB<NUM>. When both λ<NUM> and λ<NUM> are either less than illumination center wavelength <NUM> or greater than illumination center wavelength <NUM>, either (iii) λE<NUM> > λB<NUM> and λE<NUM> < λB<NUM> or (iv) λE<NUM> < λB<NUM> and λE<NUM> > λB<NUM>.

<FIG> is a schematic of a refractive-index sensor <NUM>, which is an example of refractive-index sensor <NUM>. Refractive-index sensor <NUM> includes a light source <NUM>, an optics unit <NUM>, a detector <NUM>, and a post-processor <NUM>. Light sources <NUM> and <NUM> are examples of light source <NUM>. Light source <NUM> emits illumination <NUM>, of which illumination <NUM> and <NUM> are examples. Optics units <NUM> and <NUM> are examples of optics unit <NUM> and transmits at least a portion of illumination <NUM> as transmitted illumination 1352T. Detector <NUM> includes at least one detector <NUM>, such as photodetector <NUM>, <FIG>. Post-processor <NUM> includes a processor <NUM> and a memory <NUM>. Detector <NUM> is communicatively coupled to post-processor <NUM>, for example to one or both of processor <NUM> and memory <NUM>.

Memory <NUM> may be transitory and/or non-transitory and may include one or both of volatile memory (e.g., SRAM, DRAM, computational RAM, other volatile memory, or any combination thereof) and non-volatile memory (e.g., FLASH, ROM, magnetic media, optical media, other non-volatile memory, or any combination thereof). Part or all of memory <NUM> may be integrated into processor <NUM>.

Memory <NUM> stores at least one of a reference optical signal <NUM>, a metasurface optical signal <NUM>, a wavelength lookup table <NUM>, a transmittance lookup table <NUM>, software <NUM>, a center wavelength <NUM>, and a measured refractive index <NUM>. An example of reference optical signal <NUM> is output of photodetector <NUM> in response to transmitted illumination 154T. An example of metasurface optical signal <NUM> is output of photodetector <NUM> in response to transmitted illumination 152T.

Transmittance lookup table <NUM> includes a plurality of transmittance values, such as simulated transmittance <NUM> (<FIG>), paired with a respective one of a plurality of candidate refractive indices (such as the abscissa of plot <NUM>) of encapsulating medium <NUM>. In certain embodiments, a full-wave electromagnetic simulation of metasurface <NUM> generates entries of at least one of lookup tables <NUM> and <NUM>.

Software <NUM> includes at least one of a stopband analyzer <NUM>, a wavelength interpolator <NUM>, and a transmittance interpolator <NUM>. In embodiments, stopband analyzer <NUM> determines center wavelength <NUM> from transmittance spectra <NUM>. Examples of center wavelengths <NUM> includes center wavelength <NUM> (<FIG>), respective center wavelengths λ = <NUM> and λ = <NUM> of stopbands <NUM> and <NUM> (<FIG>), center wavelengths <NUM> and <NUM> (<FIG>), and center wavelengths <NUM> and <NUM> (<FIG>). In embodiments, wavelength interpolator <NUM> determines a measured refractive index <NUM> from center wavelength <NUM> and wavelength lookup table <NUM>.

<FIG> is a flowchart illustrating a method <NUM> for measuring a refractive index of a medium. Method <NUM> may be implemented within one or more embodiments of refractive-index sensor <NUM> to determine the encapsulant refractive index of encapsulating medium <NUM>. In certain embodiments, software <NUM> encodes method <NUM> as computer-readable instructions, and method <NUM> is implemented by processor <NUM> executing the computer-readable instructions of software <NUM>. Method <NUM> includes at least one of steps <NUM>, <NUM>, and <NUM>.

Step <NUM> includes exciting a first antisymmetric resonance of a first metasurface with illumination incident on the first metasurface at a non-normal incidence angle with respect to a substrate surface. The first metasurface includes a first periodic array of resonators formed on the substrate surface. The medium, whose refractive index is being measured, encapsulates the first periodic array of resonators. In an example of step <NUM>, optics unit <NUM> of refractive-index sensor <NUM> is optics unit <NUM>, and light source <NUM> excites an antisymmetric resonance of metasurface <NUM> with illumination <NUM>. The medium is encapsulating medium <NUM>.

In certain embodiments, step <NUM> includes step <NUM>. Step <NUM> includes exciting, with the illumination, a second antisymmetric resonance of a second metasurface including a second periodic array of resonators formed on a substrate surface, the second periodic array geometrically differing from the first periodic array. In certain embodiments, the incidence angle of the illumination on the second metasurface equals the incidence angle of step <NUM>. In an example of step <NUM>, light source <NUM> excites an antisymmetric resonance of metasurface <NUM> with illumination <NUM>(<NUM>), <FIG>.

Step <NUM> includes determining a refractive index of the medium from a first amplitude of a first transmitted signal that includes a portion of the illumination transmitted through the first metasurface. In an example of step <NUM>, refractive-index sensor <NUM> determines measured refractive index <NUM> of encapsulating medium <NUM>.

In certain embodiments, step <NUM> includes steps <NUM> and <NUM>, which are applicable when a spectrum of the first transmitted signal has a stopband at a center wavelength λ<NUM> with a linewidth δλ<NUM>, and the illumination has a spectral bandwidth exceeding linewidth δλ<NUM> and including center wavelength λ<NUM>.

Step <NUM> includes determining center wavelength λ<NUM> from the first transmitted signal. In an example of step <NUM>, stopband analyzer <NUM> determines center wavelength <NUM> from metasurface optical signal <NUM>, where metasurface optical signal <NUM> includes transmittance spectrum and detector <NUM> includes a spectrum analyzer.

Step <NUM> includes determining the refractive index at center wavelength λ<NUM> according to a lookup table that maps each of a plurality of stopband center-wavelengths to a respective one of a plurality of candidate refractive indices of the medium. In an example of step <NUM>, wavelength interpolator <NUM> determines measured refractive index <NUM> at center wavelength <NUM> according to wavelength lookup table <NUM>. In this example, wavelength lookup table <NUM> maps each of a plurality of stopband center-wavelengths to a respective one of a plurality of candidate refractive indices of medium <NUM>.

In certain embodiments, step <NUM> includes step <NUM>, which is applicable when a spectrum of the first transmitted signal has a stopband with a linewidth δλ<NUM> and the illumination has a center wavelength λ<NUM> and a spectral bandwidth less than linewidth δλ<NUM>. In such embodiments, light source <NUM> may be a fixed-wavelength source, which is more economical and space-efficient than a tunable source, and optical signals <NUM> and <NUM> corresponding to optical power measured by detector <NUM> may be single-wavelength measurements.

Step <NUM> includes determining the refractive index from the first transmitted signal according to a lookup table that maps each of a plurality of numerically-simulated transmittances of the medium, at center wavelength λ<NUM>, to a respective one of a plurality of refractive indices of the medium. In an example of step <NUM>, transmittance interpolator <NUM> determines measured refractive index <NUM> from metasurface optical signal <NUM>, reference optical signal <NUM>, and transmittance lookup table <NUM>.

In certain embodiments, step <NUM> includes step <NUM>, for example, when step <NUM> includes step <NUM>. Step <NUM> includes determining the refractive index of the medium from a second amplitude of a second transmitted signal and the first amplitude, the second transmitted signal including a portion of the illumination transmitted through the second metasurface. In an example of step <NUM>, metasurface optical signal <NUM> includes a second optical signal <NUM>, which may be a transmitted-power spectrum or a single-wavelength transmitted power value of metasurface <NUM>. Software <NUM> determines a second measured refractive index <NUM> of metasurface <NUM> via either steps <NUM> and <NUM>, or via step <NUM>. Post-processor <NUM> may generate an error message when measured refractive index and second measured refractive index differ by more than a predetermined value.

In certain embodiments, method <NUM> includes both steps <NUM> and a subsequent step <NUM>. Step <NUM> includes determining whether a change in the first amplitude is caused by a change in center wavelength of the illumination or the change in the refractive index of the medium by comparing the change in the first amplitude to a change in the second amplitude. Step <NUM> may apply when (a) the first metasurface has spectrally adjacent electric dipole and magnetic dipole resonances and (b) the second metasurface has spectrally adjacent electric dipole and magnetic dipole resonances.

In an example of step <NUM>, metasurfaces <NUM> and <NUM> of refractive index sensor <NUM> have respective stop bands <NUM> and <NUM> relative to center wavelength <NUM>, <FIG>, and software <NUM> compares changes in transmittance of metasurfaces <NUM> and <NUM>. In this example of step <NUM>, metasurfaces <NUM> and <NUM> have respective electric and magnetic dipole resonances per embodiment B described above. Also in this example of step <NUM>, when illumination <NUM> has an illumination center wavelength <NUM> between center wavelengths <NUM> and <NUM>, either (i) λE<NUM> > λB<NUM> and λE<NUM> > λB<NUM> or (ii) λE<NUM> < λB<NUM> and λE<NUM> < λB<NUM>. When both λ<NUM> and λ<NUM> are either less than illumination center wavelength <NUM> or greater than illumination center wavelength <NUM>, either (iii) λE<NUM> > λB<NUM> and λE<NUM> < λB<NUM> or (iv) λE<NUM> < λB<NUM> and λE<NUM> > λB<NUM>.

<FIG> is a flowchart illustrating a method <NUM> for distinguishing a change in refractive index of a medium from a change of a center wavelength of illumination that illuminates the medium. Method <NUM> may be implemented within one or more embodiments of refractive-index sensor <NUM> to determine the encapsulant refractive index of encapsulating medium <NUM>. In certain embodiments, software <NUM> encodes method <NUM> as computer-readable instructions, and method <NUM> is implemented by processor <NUM> executing the computer-readable instructions of software <NUM>.

Method <NUM> includes steps <NUM> and <NUM>, which are similar to respective steps <NUM> and <NUM> of method <NUM>. In steps <NUM> and <NUM>, unlike steps <NUM> and <NUM>, the resonances need not be antisymmetric and the incidence angle may correspond to normal incidence. Steps <NUM> and <NUM> involve a first metasurface and a second metasurface respectively. In certain embodiments, (a) the first metasurface has spectrally adjacent electric dipole and magnetic dipole resonances and (b) the second metasurface has spectrally adjacent electric dipole and magnetic dipole resonances, for example, as in the example of step <NUM> above. Method <NUM> also includes step <NUM>, which is similar to step <NUM> of method <NUM>.

Step <NUM> includes exciting a first resonance of a first metasurface with illumination incident on the first metasurface an incidence angle with respect to a substrate surface. The incidence angle may be zero degrees (normal incidence), near-normal incidence (between ±<NUM> degrees) or between two degrees and ten degrees. The first resonance may be symmetric, antisymmetric, or non-antisymmetric. The first metasurface includes a first periodic array of resonators formed on the substrate surface. The medium, whose refractive index is being measured, encapsulates the first periodic array of resonators. In an example of step <NUM>, optics unit <NUM> of refractive-index sensor <NUM> is optics unit <NUM>, and light source <NUM> excites a resonance of metasurface <NUM> with illumination <NUM>. The medium is encapsulating medium <NUM>.

Step <NUM> includes exciting, with the illumination, a second resonance of a second metasurface including a second periodic array of resonators formed on a substrate surface, the second periodic array geometrically differing from the first periodic array. In certain embodiments, the incidence angle of the illumination on the second metasurface equals the incidence angle of step <NUM>. In an example of step <NUM>, light source <NUM> excites a resonance of metasurface <NUM> with illumination <NUM>(<NUM>), <FIG>.

Claim 1:
A refractive-index sensor (<NUM>), comprising:
a substrate (<NUM>) having a top surface (<NUM>);
a microfluidic chip (<NUM>) on the top surface and having a non-planar bottom surface (<NUM>) that forms a channel (<NUM>) between the top surface and the non-planar bottom surface, the channel having a channel depth (<NUM>) in a direction perpendicular to the top surface;
characterized in that the refractive-index sensor includes:
a plurality of dielectric resonators (<NUM>) forming a metasurface (<NUM>,<NUM>,<NUM>) on the top surface, each of the plurality of dielectric resonators extending into the channel to a height (<NUM>) above the top surface that is less than the channel depth, the metasurface having an electric dipole resonance and a magnetic dipole resonance that are either (i) spectrally overlapping or (ii) spectrally adjacent; and
a light source (<NUM>) configured to illuminate the metasurface with illumination (<NUM>) incident on the top surface at an incidence angle (<NUM>), the illumination (<NUM>) having a center wavelength λ<NUM> exceeding the height (<NUM>), a width (<NUM>) of each of the plurality of dielectric resonators, and a unit cell size (<NUM>) of the metasurface.