Refractive-index sensor and method

A method for measuring a refractive index of a medium includes exciting a first antisymmetric resonance of a first metasurface, including a first periodic array of resonators formed on a substrate surface, with illumination incident on the first metasurface at a non-normal incidence angle with respect to the substrate surface, the first metasurface including the medium encapsulating the first periodic array of resonators. The method also 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.

BACKGROUND

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.

SUMMARY OF THE EMBODIMENTS

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.

In a second aspect, a refractive-index sensor includes a substrate, a microfluidic chip, a plurality of dielectric resonators, and a light source. The substrate has a top surface. The microfluidic chip is on the top surface and has a non-planar bottom surface that forms a channel bounded between the top surface and the non-planar bottom surface. The channel has a channel depth in a direction perpendicular to the top surface. The plurality of dielectric resonators are arranged as a periodic array on the top surface and extend into the channel to a height above the top surface that is less than the channel depth. The light source is configured to illuminate the periodic array with illumination incident on the top surface at a non-normal incidence angle. The illumination has a center wavelength λ0exceeding the height, a width of each of the plurality of dielectric resonators, and a unit cell size of the periodic array.

In a third aspect, a method for distinguishing a change in refractive index of a medium from a change of a center wavelength of illumination that illuminates the medium is disclosed. The method includes exciting a first resonance of a first metasurface, including a first periodic array of resonators formed on a substrate surface, with illumination incident on the first metasurface, the first metasurface including the medium encapsulating the first periodic array of resonators. The method also 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. The method also includes determining whether a change in a first amplitude, of a first transmitted signal, is caused by a change in the center wavelength of the illumination or a change in the refractive index of the medium by comparing the change in the first amplitude to a change in a second amplitude of a second transmitted signal. The first transmitted signal includes a first portion of the illumination transmitted through the first metasurface. The second transmitted signal includes a second portion of the illumination transmitted through the second metasurface.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1is a cross-sectional view of a refractive-index sensor100in a plane101parallel to the x-z plane of a coordinate system198. Hereinafter, directions and planes described by one or more axes x, y, and z refer to coordinate system198unless otherwise specified.

Refractive-index sensor100includes an optics unit104and a light source150, and, in certain embodiments, a photodetector158. Optics unit104includes a substrate110, a plurality of dielectric resonators121arranged as a periodic array120, and a microfluidic chip140.FIG. 2is a cross-sectional view of optics unit104in a cross-sectional plane102that is parallel to the x-y plane.FIG. 3is a three-dimensional view of optics unit104, with a portion of microfluidic chip140omitted to provide a clear view of dielectric resonators121.FIGS. 1-3are best viewed together in the following description.

Substrate110has a top surface112. Microfluidic chip140is on top surface112and has a non-planar bottom surface141that forms a channel144bounded between top surface112and a portion of non-planar bottom surface141not in contact with top surface112. Channel144has a channel depth146in a direction perpendicular to top surface112.

Each dielectric resonator121is on top surface112and extends into channel144to a height122above top surface112. Height122is less than channel depth146. Each dielectric resonator121has a width124. Periodic array120has a unit cell spacing123, which is a center-to-center distance between nearest-neighbor dielectric resonators121. While resonators121have a circular cross-section in the example depicted inFIGS. 1-3, they may have differently-shaped cross-sections, such as polygonal, without departing from the scope of the embodiments.

Illumination152has a center wavelength λ0exceeding each of height122, width124, and unit cell spacing123. Each dielectric resonator121has a refractive index nr(λ0) and substrate110has a refractive index ns(λ0). In certain embodiments, illumination includes illumination154incident on a region106(FIG. 2) of optics unit104that does not include periodic array120. Optics unit104transmits at least a portion of illumination154as a reference signal154T, which may be used for normalization, e.g., to determine a single-wavelength transmittance or transmittance spectrum of metasurface130.

Optics unit104transmits at least a portion of incident illumination152as transmitted illumination152T that, in embodiments, is detected by photodetector158. In operation, spectral properties of transmitted illumination152T are used to measure the refractive index of an encapsulating medium132in channel144, as described herein. Encapsulating medium132may be a gas or a fluid. Encapsulating medium132and periodic array120form a metasurface130within channel144. InFIG. 1, the callout referring to metasurface130touches a dashed box adjacent to surfaces112and141. In embodiments, the spectral bandwidth of illumination152is narrower than a stopband of metasurface130. Illumination152may have a center wavelength within the stopband. Light source150may include a bandpass filter to achieve said spectral bandwidth relationship.

In certain embodiments, metasurface130is a Huygens metasurface, that is, a metasurface with spectrally overlapping electric and magnetic dipole resonances. In certain other embodiments, metasurface130is 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 may be 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 illumination152and (b) greater than ½(δE+δB), where δEand δBare respective spectral widths of the electric dipole resonance and the magnetic dipole resonance.

Herein, the refractive index of encapsulating medium132is referred to as the encapsulant refractive index. In embodiments, ns(λ0)<αnr(λ0)−β for sufficient refractive index contrast of dielectric resonators121to the encapsulant refractive index to yield a stopband. In embodiments, coefficient α is between 0.6 and 0.7 and offset β is between 0.08 and 1.2. Coefficient α may equal the encapsulant refractive index divided by nr. The encapsulant refractive index may differ from substrate refractive index nsby less than offset β.

FIG. 4illustrates electric field amplitudes of illumination452incident upon, and propagating through, one of a plurality of dielectric resonators421of a metasurface430at a four-degree incidence angle. Metasurface430is on substrate110and has an electric dipole resonance that spectrally overlaps its magnetic dipole resonance at a center wavelength of illumination452. As a result, metasurface430transmits nearly one-hundred percent of illumination452as transmitted illumination453. Metasurface430is an example of metasurface130.

FIG. 5illustrates electric field amplitudes of illumination552incident upon one of a plurality of dielectric resonators421of metasurface430at a wavelength that excites an antisymmetric mode432of metasurface430. In dielectric resonators421, the electric field amplitude of illumination552is antisymmetric about a plane592. As a result of a symmetry mismatch between incident illumination552and the excited an antisymmetric mode, metasurface430transmits only an evanescent field into substrate110, rather than a propagating electromagnetic field in which energy flows into substrate110.

FIG. 6illustrates electric field amplitudes of illumination652normally-incident upon, and reflected by, one of a plurality of dielectric resonators521of a metasurface630. Metasurface630is on substrate110and has an electric dipole resonance that is spectrally adjacent to, and not overlapping with its magnetic dipole resonance. The center wavelength of illumination652is between the respective electric and magnetic dipole resonance wavelengths of metasurface630, which results in metasurface630reflecting nearly one-hundred percent of illumination652as reflected illumination653. Metasurface630is an example of metasurface130.

Transmittance plot700includes numerically-simulated transmittance spectra700and704, which correspond to illumination152incident on optics unit104at incidence angle156equal to zero degrees and four degrees, respectively. Transmittance spectrum704has a stopband710, which corresponds to an excitation of an antisymmetric resonance excited by illumination152incident at four-degrees. Stopband710has a center wavelength712and a linewidth714. Center wavelength712is approximately 1237 nm. In one embodiment, illumination152has a spectral linewidth that is less than linewidth714. In another embodiment, illumination152has a spectral linewidth that is exceeds linewidth714.

FIG. 8is a transmittance plot890for embodiment A of metasurface130corresponding toFIG. 7for two refractive index values of encapsulant material filling channel144. Transmittance plot890includes numerically-simulated transmittance spectra833and838, which correspond to respective encapsulant refractive indices n=1.333 and n=1.338. Transmittance spectra833and838have respective stopbands803and808centered at respective wavelengths2\, =1210 nm a, =1212 nm. The difference in center wavelengths is caused by the difference in refractive indices of the respective encapsulating media132, Δn=0.005. In certain embodiments, illumination152has a spectral linewidth that is less than a linewidth of either stopband803and808.

FIG. 9is a transmittance plot990for embodiment A of metasurface130at λ=1212.02 nm where the PDMS in channel144has an encapsulant refractive index ranging from 1.333 to 1.338. Transmittance plot990includes numerically-simulated transmittance910, and its derivative912(dT/dn) with respect to cavity refractive index.

FIG. 10is a schematic illustrating a cross-section of a refractive-index sensor1000, which is an example of refractive-index sensor100. Refractive-index sensor1000includes an optics unit1004and a light source1050, which are examples of optics unit104and light source150respectively. Optics unit1004includes microfluidic chip140on substrate110, periodic array120, and a second periodic array1020. Periodic arrays120and1020are in channel144between surfaces112and141, and are part of respective metasurfaces130and1030. Light source1050is configured to simultaneously illuminate each of periodic array120and1020with respective illumination1052(1) and1052(2).

Second periodic array1020is an example of periodic array120, and includes a plurality of second dielectric resonators arranged as second periodic array1020on top surface112. In embodiments, at least one of (i) a second width of each of the plurality of second dielectric resonators differs from width124of resonators121and (ii) a second unit cell size of the second periodic array differs from the unit cell size123of resonators121. In embodiments, periodic array1020is identical to periodic array120.

In certain embodiments, refractive-index sensor1000includes at least one of photodetector158and a photodetector1058. Photodetector1058is configured to detect illumination1052(2) transmitted by metasurface1030.

FIG. 11is a schematic transmittance plot1190that includes a stopband1110of metasurface130and a stopband1120of metasurface1030. In one embodiment, stopbands1110and1120result from excitation of a respective antisymmetric resonances of respective metasurfaces130and1030by illumination1052, where angle156is between two degrees and ten degrees. In another embodiment, stopbands1110and1120result from excitation of non-antisymmetric resonances (e.g., symmetric electric dipole or magnetic dipole resonances) of respective metasurfaces130and1030by illumination1052, where angle156is between negative two degrees and positive two degrees such that illumination1052is at normal or near-normal incidence.

FIG. 12is a transmittance plot1290of embodiment A of metasurface130for two refractive index values of encapsulating medium132. Transmittance plot1290includes numerically-simulated stopbands1210and1220, which correspond to respective encapsulant refractive indices n=1.333 and n=1.383. Stopbands1210and1220have respective center wavelengths1212and1222. 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.

Stopbands1210and1220are examples of stopbands1110and1120, respectively, where illumination1052excites non-antisymmetric resonances (e.g., symmetric resonances) of metasurfaces130and1030. Since transmittance plot1290is of embodiment A with two different encapsulant materials, periodic arrays120and1020are identical, such that differences between stopbands1210and1220are due to differences in the encapsulant refractive index.

Stopband1210results from metasurface130having an electric dipole resonance, center wavelength λE1210thereof being less than center wavelength1212, and a magnetic dipole resonance, center wavelength λB1210thereof being greater than center wavelength1212. Similarly, stopband1220results from metasurface130having an electric dipole resonance, center wavelength λE1220thereof being less than center wavelength1222, and a magnetic dipole resonance, center wavelength λB1220thereof being greater than center wavelength1222. Hence, each of stopbands1210and1220have an “electric side” less than their respective center wavelengths and a “magnetic side” greater than their respective center wavelengths.

Respective magnetic sides of stopbands1210and1220more closely overlap (λ0≈1425-1450 nm) than do their respective electric sides (λ0≈1325-1350 nm). For example, in transmittance plot1290, wavelength range1231is smaller than wavelength range1232. This occurs because the electric dipole resonance of metasurface130is more sensitive to encapsulant refractive index than is the magnetic dipole resonance. This asymmetry of stopbands1210and1220enables distinguishing between (i) a drift in a stopband center wavelength that results from drift in illumination center wavelength1151and (ii) a change in refractive index of encapsulating medium132.

In certain embodiments, metasurfaces130and1030have respective stop bands less than and greater than center wavelength1151. For example, stopbands1110and1120are stop bands of metasurfaces130and1030, respectively. Such positioning of stop bands enables distinguishing between wavelength drift (of center wavelength1151) and the encapsulant refractive index of encapsulating medium130, which may be common to both metasurfaces130and1030. For example, encapsulating medium130is a fluid that flows through and surrounds both resonator arrays120and1020.

When the encapsulant refractive index increases, both stopbands1110and1120shift to a greater wavelength (as inFIG. 12), such that the detected transmittance of metasurface130decreases while the detected transmittance of metasurface1030increases. However, if center wavelength1151decreases, the detected transmittance of metasurface130decreases while the detected transmittance of metasurface1030increases. 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 wavelength1151correspond to the “electric” side of stopband1110and the “magnetic” side of stopband1120, then, in response to a change in encapsulant refractive index, the transmittance of metasurface130(stopband1110) will change more than that of metasurface1030(stopband1120) because the electric dipole resonance is more sensitive to change in encapsulant refractive index. A drift in center wavelength1151would cause a significantly smaller transmittance-change difference between metasurface130and1030.

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 wavelength1112of stopband1110is determined by an electric dipole resonance and a magnetic dipole resonance of metasurface130having respective center wavelengths λE1and λB1. In embodiment B, center wavelength1122of stopband1120is determined by an electric dipole resonance and a magnetic dipole resonance of the second metasurface having respective center wavelengths λE2and λB2. When illumination1052has an illumination center wavelength1151between center wavelengths1112and1122, either (i) λE1>λB1and λE2>λB2or (ii) λE1<λB1and λE2<λB2. When both λ1and λ2are either less than illumination center wavelength1151or greater than illumination center wavelength1151, either (iii) λE1>λB1and λE2<λB2or (iv) λE1<λB1and λE2>λB2.

FIG. 13is a schematic of a refractive-index sensor1300, which is an example of refractive-index sensor100. Refractive-index sensor1300includes a light source1350, an optics unit1304, a detector1358, and a post-processor1310. Light sources150and1050are examples of light source1350. Light source1350emits illumination1352, of which illumination152and1052are examples. Optics units104and1004are examples of optics unit1304and transmits at least a portion of illumination1352as transmitted illumination1352T. Detector1358includes at least one detector158, such as photodetector1058,FIG. 10. Post-processor1310includes a processor1302and a memory1320. Detector1358is communicatively coupled to post-processor1310, for example to one or both of processor1302and memory1320.

Memory1320may 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 memory1320may be integrated into processor1302.

Memory1320stores at least one of a reference optical signal1321, a metasurface optical signal1322, a wavelength lookup table1324, a transmittance lookup table1326, software1330, a center wavelength1342, and a measured refractive index1348. An example of reference optical signal1321is output of photodetector158in response to transmitted illumination154T.

An example of metasurface optical signal1322is output of photodetector158in response to transmitted illumination152T.

Transmittance lookup table1326includes a plurality of transmittance values, such as simulated transmittance910(FIG. 9), paired with a respective one of a plurality of candidate refractive indices (such as the abscissa of plot990) of encapsulating medium130. In certain embodiments, a full-wave electromagnetic simulation of metasurface130generates entries of at least one of lookup tables1324and1326.

Software1330includes at least one of a stopband analyzer1332, a wavelength interpolator1334, and a transmittance interpolator1336. In embodiments, stopband analyzer1332determines center wavelength1342from transmittance spectra1325. Examples of center wavelengths1342includes center wavelength712(FIG. 7), respective center wavelengths λ=1210 nm and λ=1212 nm of stopbands803and808(FIG. 8), center wavelengths1112and1122(FIG. 11), and center wavelengths1212and1222(FIG. 12). In embodiments, wavelength interpolator1334determines a measured refractive index1348from center wavelength1342and wavelength lookup table1324.

FIG. 14is a flowchart illustrating a method1400for measuring a refractive index of a medium. Method1400may be implemented within one or more aspects of refractive-index sensor1300to determine the encapsulant refractive index of encapsulating medium132. In certain embodiments, software1330encodes method1400as computer-readable instructions, and method1400is implemented by processor1302executing the computer-readable instructions of software1330. Method1400includes at least one of steps1410,1420, and1430.

Step1410includes 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 step1410, optics unit1304of refractive-index sensor1300is optics unit1004, and light source1350excites an antisymmetric resonance of metasurface130with illumination1352. The medium is encapsulating medium132.

In certain embodiments, step1410includes step1412. Step1412includes 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 step1410. In an example of step1412, light source1050excites an antisymmetric resonance of metasurface1030with illumination1052(2),FIG. 10.

Step1420includes 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 step1420, refractive-index sensor1300determines measured refractive index1348of encapsulating medium132.

In certain embodiments, step1420includes steps1422and1424, which are applicable when a spectrum of the first transmitted signal has a stopband at a center wavelength λ1with a linewidth δλ1, and the illumination has a spectral bandwidth exceeding linewidth δλ1and including center wavelength λ1.

Step1422includes determining center wavelength from the first transmitted signal. In an example of step1422, stopband analyzer1332determines center wavelength1342from metasurface optical signal1322, where metasurface optical signal1322includes transmittance spectrum and detector1358includes a spectrum analyzer.

Step1424includes determining the refractive index at center wavelength λ1according 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 step1424, wavelength interpolator1334determines measured refractive index1348at center wavelength1342according to wavelength lookup table1324. In this example, wavelength lookup table1324maps each of a plurality of stopband center-wavelengths to a respective one of a plurality of candidate refractive indices of medium132.

In certain embodiments, step1420includes step1426, which is applicable when a spectrum of the first transmitted signal has a stopband with a linewidth δλ1and the illumination has a center wavelength λ0and a spectral bandwidth less than linewidth δλ1. In such embodiments, light source1350may be a fixed-wavelength source, which is more economical and space-efficient than a tunable source, and optical signals1321and1322corresponding to optical power measured by detector1358may be single-wavelength measurements.

Step1426includes 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 λ0, to a respective one of a plurality of refractive indices of the medium. In an example of step1426, transmittance interpolator1336determines measured refractive index1348from metasurface optical signal1322, reference optical signal1321, and transmittance lookup table1326.

In certain embodiments, step1420includes step1428, for example, when step1410includes step1412. Step1428includes 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 step1428, metasurface optical signal1322includes a second optical signal1323, which may be a transmitted-power spectrum or a single-wavelength transmitted power value of metasurface1030. Software1330determines a second measured refractive index1349of metasurface1030via either steps1422and1424, or via step1426. Post-processor1310may generate an error message when measured refractive index and second measured refractive index differ by more than a predetermined value.

In certain embodiments, method1400includes both steps1412and a subsequent step1430. Step1430includes 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. Step1430may 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 step1430, metasurfaces130and1030of refractive index sensor1000have respective stop bands1110and1120relative to center wavelength1151,FIG. 11, and software1330compares changes in transmittance of metasurfaces130and1030. In this example of step1430, metasurfaces130and1030have respective electric and magnetic dipole resonances per embodiment B described above. Also in this example of step1430, when illumination1052has an illumination center wavelength1151between center wavelengths1112and1122, either (i) λE1>λB1and λE2>λB2or (ii) λE1<λB1and λE2<λB2. When both λ1and λ2are either less than illumination center wavelength1151or greater than illumination center wavelength1151, either (iii) λE1>λB1and λE2<λB2or (iv) λE1<λB1and λE2>λB2.

FIG. 15is a flowchart illustrating a method1500for distinguishing a change in refractive index of a medium from a change of a center wavelength of illumination that illuminates the medium. Method1500may be implemented within one or more aspects of refractive-index sensor1300to determine the encapsulant refractive index of encapsulating medium132. In certain embodiments, software1330encodes method1400as computer-readable instructions, and method1500is implemented by processor1302executing the computer-readable instructions of software1330.

Method1500includes steps1510and1512, which are similar to respective steps1410and1412of method1400. In steps1510and1512, unlike steps1410and1412, the resonances need not be antisymmetric and the incidence angle may correspond to normal incidence. Steps1510and1512involve 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 step1430above. Method1500also includes step1530, which is similar to step1430of method1400.

Step1510includes 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 ±2 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 step1410, optics unit1304of refractive-index sensor1300is optics unit1004, and light source1350excites a resonance of metasurface130with illumination1352. The medium is encapsulating medium132.

Step1512includes 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 step1510. In an example of step1412, light source1050excites a resonance of metasurface1030with illumination1052(2),FIG. 10.

Step1530includes determining whether a change in a first amplitude, of a first transmitted signal, is caused by a change in the center wavelength of the illumination or a change in the refractive index of the medium by comparing the change in the first amplitude to a change in a second amplitude of a second transmitted signal. The first transmitted signal includes a first portion of the illumination transmitted through the first metasurface. The second transmitted signal includes a second portion of the illumination transmitted through the second metasurface. An example of step1530is the same as the example of step1430provided above.

Combinations of Features

Features described above as well as those claimed below may be combined in various ways without departing from the scope hereof. The following enumerated examples illustrate some possible, non-limiting combinations:

(A1) A method for measuring a refractive index of a medium includes exciting a first antisymmetric resonance of a first metasurface, including a first periodic array of resonators formed on a substrate surface, with illumination incident on the first metasurface at a non-normal incidence angle with respect to the substrate surface, the first metasurface including the medium encapsulating the first periodic array of resonators. The method also 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.

(A2) In method (A1), a spectrum of the first transmitted signal has a stopband at a center wavelength λ1with a linewidth δλ1, wherein, when the illumination has a spectral bandwidth exceeding linewidth δλ1and including center wavelength λ1, determining the refractive index may include: (i) determining center wavelength λ1from the first transmitted signal, and (ii) determining the refractive index at center wavelength λ1according 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. Center wavelength λ1may exceed both a maximum spatial dimension of each resonator of the first periodic array of resonators and a unit cell size of the first periodic array

(A3) In method (A1) a spectrum of the first transmitted signal has a stopband with a linewidth λδ1, wherein, when the illumination has a center wavelength λ0and a spectral bandwidth less than linewidth δλ1, determining the refractive index may include: 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 λ0, to a respective one of a plurality of refractive indices of the medium.

(A4) In any of methods (A1) through (A3), when exciting the first antisymmetric resonance, the non-normal incidence angle may be between two degrees and ten degrees

(A5) Any of methods (A1) through (A4) may further include (i) 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; and (ii) 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.

(A6) Any of methods (A1) through (A5) may further include (i) 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, and (ii) determining whether a change in the first amplitude is caused by a change in center wavelength of the illumination or a change in the refractive index of the medium by comparing the change in the first amplitude to a change in a second amplitude of a second transmitted signal, the second transmitted signal including a portion of the illumination transmitted through the second metasurface.

(B1) A method for distinguishing a change in refractive index of a medium from a change of a center wavelength of illumination that illuminates the medium includes exciting a first resonance of a first metasurface, including a first periodic array of resonators formed on a substrate surface, with illumination incident on the first metasurface, the first metasurface including the medium encapsulating the first periodic array of resonators. The method also 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. The method also includes determining whether a change in a first amplitude, of a first transmitted signal, is caused by a change in the center wavelength of the illumination or a change in the refractive index of the medium by comparing the change in the first amplitude to a change in a second amplitude of a second transmitted signal. The first transmitted signal includes a first portion of the illumination transmitted through the first metasurface. The second transmitted signal includes a second portion of the illumination transmitted through the second metasurface.

(C1) A refractive-index sensor includes a substrate, a microfluidic chip, a plurality of first dielectric resonators, and a light source. The substrate has a top surface. A microfluidic chip on the top surface and has a non-planar bottom surface that forms a channel bounded between the top surface and the non-planar bottom surface. The channel has a channel depth in a direction perpendicular to the top surface. The plurality of first dielectric resonators are arranged as a first periodic array on the top surface and extend into the channel to a height above the top surface that is less than the channel depth. The light source is configured to illuminate the first periodic array with illumination incident on the top surface at a non-normal incidence angle. The illumination has a center wavelength λ0exceeding the height, a first width of each of the plurality of first dielectric resonators, and a first unit cell size of the first periodic array.

(C2) In refractive-index sensor (C1), each resonator may have a refractive index nr(λ0), the substrate having a refractive index ns(λ0)<αnr(λ0)−β, α being 0.6 and 0.7 and β being between 0.08 and 1.2.

(C3) In any of refractive-index sensors (C1) and (C2), the plurality of first dielectric resonators and an encapsulating medium in the channel form a metasurface, the illumination may have a spectral linewidth that is less than a linewidth of a stopband resulting from excitation of an antisymmetric resonance of the metasurface excited by the illumination.

(C4) Any of refractive-index sensors (C1) through (C2) may further include a plurality of second dielectric resonators arranged as a second periodic array on the top surface, at least one of (i) a second width of each of the plurality of second dielectric resonators differing from the first width and (ii) a second unit cell size of the second periodic array differing from the first unit cell size, and the light source may be further configured to simultaneously illuminate the first periodic array and the second periodic array with the illumination.

(C5) In any refractive-index sensors (C4), the plurality of first dielectric resonators and an encapsulating medium in the channel may form a first metasurface; the plurality of second dielectric resonators and the encapsulating medium in the channel may form a second metasurface; and the illumination may have a spectral linewidth δλ0that is less than (i) a linewidth δλ1of a first stopband resulting from excitation of a first resonance of the first metasurface excited by the illumination and (ii) a linewidth δλ2of a second stopband resulting from excitation of a second resonance of the second metasurface excited by the illumination.

(C6) In any refractive-index sensor (C5), the first stopband and the second stopband may have respective center wavelengths λ1, and λ2, wherein λ1<λ0<λ2, (λ0−λ1)<0.5δλ1, and (λ2−λ0)<0.5δλ2.

(C7) In any refractive-index sensor (C5) and (C6), the first stopband may have a center wavelength λ1determined by an electric dipole resonance and a magnetic dipole resonance of the first metasurface having respective center wavelengths λE1and λB1. The second stopband may have a center wavelength λ2determined by an electric dipole resonance and a magnetic dipole resonance of the second metasurface having respective center wavelengths λE2and λB2. When center wavelength λ0of the illumination is between λ1and λ2, either of the following pairs of inequalities, denoted (i) and (ii), may apply: (i) λE1>λB1and λE2>λB2, and (ii) λE1<λB1and λE2<λB2.

(C8) Any refractive-index sensor (C4) through (C7) may further include: a first photodetector configured to detect a first portion of the illumination transmitted through the first periodic array; and a second photodetector configured to detect a first portion of the illumination transmitted through the second periodic array.

(C9) Any refractive-index sensor (C1) through (C8) may further include a photodetector, a processor, and a memory. The photodetector is configured to detect a transmitted signal that includes a portion of the illumination transmitted through the substrate and the first periodic array. The processor is communicatively coupled to the photodetector. The memory stores non-transitory computer-readable instructions that, when executed by the processor, control the processor to execute any of the methods (A1) through (A5) and (B1).

Changes may be made in the above methods and systems without departing from the scope hereof. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. Herein, and unless otherwise indicated, the phrase “in embodiments” is equivalent to the phrase “in certain embodiments,” and does not refer to all embodiments. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween.