The invention relates to an optical sensor for sensing a chemical, a method of fabricating an optical sensor for sensing a chemical, a computer-implemented method of determining a target periodic arrangement of nanostructures of an optical sensor, and a computer program.

It is known to fabricate and use optical sensors based on random arrangements of nanoparticles.

According to a first aspect of the invention, there is provided an optical sensor for sensing a chemical, the optical sensor comprising a periodic arrangement of nanostructures configured to support a surface lattice resonance, wherein the optical sensor is configured to sense the chemical via a modification of an optical property of the nanostructures resulting from absorption of the chemical into the nanostructures or from adsorption of the chemical onto surfaces of the nanostructures, wherein a geometry of the nanostructures is configured to balance a spectral linewidth of the surface lattice resonance and field enhancement within the nanostructures so as to configure a limit of detection of the optical sensor with respect to the sensed chemical.

For chemical sensing applications, optical sensors are considered attractive in comparison to electrical sensors because optical sensors have a safer mode of operation by virtue of not requiring the flow of electrical currents in their active transducers. However, electrical sensors tend to have higher sensitivity, typically with limits of detection in the parts-per-bil lion (ppb) range, while optical sensors have lower sensitivity, typically with limits of detection in the parts-per-million (ppm) range.

The inventors have created an optical sensor based on a periodic arrangement of nanostructures with a limit of detection that can be lower than a limit of detection of an optical sensor based on a random arrangement of nanostructures. Contrary to expectations, this was achieved by optimizing the balance between a narrow spectral linewidth of the surface lattice resonance and the strength of the field enhancement within the nanostructures, instead of configuring the geometry of the nanostructures to obtain a spectral linewidth of the surface lattice resonance to be as narrow as possible.

In a preferred embodiment of the invention, a geometry of the nanostructures may be configured to define the spectral linewidth of the surface lattice resonance and the field enhancement within the nanostructures so as to configure the optical sensor to have a limit of detection in the sub-parts-per-million range with respect to the sensed chemical. Using the invention, the inventors have created an optical sensor based on a periodic arrangement of nanostructures with a limit of detection in the sub-parts- per-million range.

The optical sensor may sense the modification of the optical property by detecting transmitted (including refracted) or reflected electromagnetic radiation by the nanostructures. Preferably such electromagnetic radiation is at visible and/or near infrared frequencies.

The invention is applicable to the sensing of any chemical capable of absorption into the nanostructures or adsorption onto the surfaces of the nanostructures, thus having the potential to be used in a wide range of applications requiring the detection of subppm traces of chemicals (such as toxic gases), which include diagnostics, safety, air quality, exhaust analysis, etc.

The optical sensing performance of the optical sensor of the invention may be varied depending on (i) the chemical composition of the nanostructures, which also defines their capability to interact with or bind to the chemical; and/or (ii) the optical properties of the environment surrounding the nanostructures that can affect a spectral shape of the surface lattice resonance.

For the purposes of this specification, the geometry of the nanostructures includes a geometry of the array of nanostructures and an individual geometry of each nanostructure. Such geometries may be configured in accordance with the invention, examples of which are described throughout the specification, including as follows.

In a first example, a pitch and/or a pattern of the periodic arrangement of nanostructures may be configured to balance the spectral linewidth of the surface lattice resonance and the field enhancement within the nanostructures so as to configure a limit of detection of the optical sensor with respect to the sensed chemical. The pitch may be preferably, but not exclusively, in the range of twice the diameter of the nanostructures to 5 times the diameter of the nanostructures. A non-limiting example of the range of the pitch is 300 nm to 800 nm. Non-limiting examples of the pattern include a square pattern (e.g. a square lattice) or a hexagonal pattern (e.g. a hexagonal lattice). In a second example, a shape and/or size and/or aspect ratio of each nanostructure may be configured to balance a spectral linewidth of the surface lattice resonance and the field enhancement within the nanostructures so as to configure a limit of detection of the optical sensor with respect to the sensed chemical. Non-limiting examples of the shape of each nanostructure include nanodisks, nanospheres and nanocubes. The size of each nanostructure may be, for example, in the range of 10 nm to 100 nm (e.g. for isotropic particles). In the case of a nanodisk, the height of the nanodisk may be in the range of 5 nm to 50 nm and the diameter of the nanodisk may be in the range of 50 nm to 300 nm.

The configuration of the nanostructures may vary. In a preferred embodiment, the nanostructures are or include nanoparticles and/or nanoholes. The nanostructures may be formed in or on mirrored surfaces, e.g. nanoparticles-on-mirror.

The material of the nanostructures may vary. In a preferred embodiment, the nanostructures are or include metallic nanostructures.

Preferably the periodic arrangement of nanostructures is configured as a periodic two- dimensional array of nanostructures. However, it will be appreciated that the periodic arrangement of nanostructures may be alternatively configured as a three-dimensional array of nanostructures.

In embodiments of the invention, each of the nanostructures may include a selective functionalised surface, and wherein the optical sensor may be configured to sense the chemical via a modification of an optical property of the nanostructures resulting from adsorption of the chemical onto the selective functionalised surfaces of the nanostructures. The use of selective functionalised surfaces of the nanostructures for the adsorption of the sensed chemical enhances the selectivity of the optical sensor to a certain chemical and/or enable a wider range of chemicals to be sensed. Such selective functionalised surfaces may include functional groups capable of binding selected chemicals (e.g. NOx, CO, etc.).

The optical property modified as a result of the absorption or adsorption of the sensed chemical may vary. The optical property may be, but is not limited to:

* an optical property of electromagnetic radiation transmitted or reflected by the nanostructures; or

• a monochromatic intensity of electromagnetic radiation transmitted or reflected by the nanostructures; or • a wavelength of the surface lattice resonance of the nanostructures; or

* a spectral linewidth of the surface lattice resonance of the nanostructures.

In embodiments of the invention, the optical sensor may include: an electromagnetic radiation source for directing electromagnetic radiation towards the nanostructures; and/or an electromagnetic radiation sensor for detecting electromagnetic radiation transmitted or reflected by the nanostructures.

In further embodiments of the invention, the optical sensor may include a polymer layer arranged over the periodic arrangement of nanostructures. The provision of the polymer layer on top of the nanostructures enables the optical sensor to be provided with an additional functionality.

The optical sensor may include a plurality of polymer layers arranged over the periodic arrangement of nanostructures. The provision of multiple polymer layers on top of the nanostructures enables the optical sensor to be provided with different additional functionalities.

The polymer layer may be configured to act as an oxygen barrier. For example, the polymer layer may be, but is not limited to, poly(vinyl alcohol).

According to a second aspect of the invention, there is provided a method of fabricating an optical sensor for sensing a chemical, the optical sensor comprising a periodic arrangement of nanostructures configured to support a surface lattice resonance, wherein the optical sensor is configured to sense the chemical via a modification of an optical property of the nanostructures resulting from absorption of the chemical into the nanostructures or from adsorption of the chemical onto surfaces of the nanostructures, wherein the method comprises the steps of: defining a target figure of merit (FoM) corresponding to a change in optical property of the nanostructures in response to the absorption or adsorption of the chemical; generating one or more periodic arrangements of nanostructures within one or more predefined geometrical constraints; evaluating a change in optical property of the or each generated periodic arrangement of nanostructures in response to the absorption or adsorption of the chemical against the target figure of merit; iteratively modifying the or each generated periodic arrangement of nanostructures so as to modify the corresponding change in optical property towards the target figure of merit; identifying a generated periodic arrangement of nanostructures with a change in optical property in response to the absorption or adsorption of the chemical that meets the target figure of merit; and fabricating the optical sensor by configuring a geometry of its nanostructures in accordance with the identified generated periodic arrangement of nanostructures with the change in optical property in response to the absorption or adsorption of the chemical that meets the target figure of merit.

The method of the invention not only enables sensitivity improvement in optical sensors using a periodic arrangement of nanostructures with a geometry designed by an optimization algorithm based on inverse nanophotonic design, but also widens the scope of the design of the optical sensor by enabling the identification of various periodic arrangements of nanostructures with corresponding changes in optical properties that meet the target figure of merit.

The generation of one or more periodic arrangements of nanostructures within one or more predefined geometrical constraints may be carried out randomly or pseudo- randomly.

The invention is applicable to a wide range of target FoMs and thereby is applicable to a wide range of optical sensors. Such optical sensors may differ in terms of their sensing requirements, for example, their measurement setup, the environment in which they are used and/or chemicals that can be sensed. Accordingly, the invention can be optimized for a particular sensing application and a particular chemical to be sensed.

In embodiments of the method of the invention, a geometry of the nanostructures may be configured to balance a spectral linewidth of the surface lattice resonance and field enhancement within the nanostructures so as to configure a limit of detection of the optical sensor with respect to the sensed chemical. In such embodiments, a geometry of the nanostructures may be configured to define the spectral linewidth of the surface lattice resonance and the field enhancement within the nanostructures so as to configure the optical sensor to have a limit of detection in the sub-parts-per-million range with respect to the sensed chemical. As explained above, the geometry of the nanostructures may include a geometry of the array of nanostructures and an individual geometry of each nanostructure, examples of which are described throughout the specification.

In embodiments of the method of the invention, the target figure of merit may be or may correspond to, but is not limited to:

* a target variation in an optical property of electromagnetic radiation transmitted or reflected by the nanostructures; or

* a target variation in monochromatic intensity of electromagnetic radiation transmitted or reflected by the nanostructures; or

* a target wavelength shift of the surface lattice resonance of the nanostructures; or

* a target narrowing or broadening of a spectral linewidth of the surface lattice resonance of the nanostructures.

In embodiments of the method of the invention, the step of iteratively modifying the or each generated periodic arrangement of nanostructures so as to modify the corresponding change in optical property towards the target figure of merit may include using an evolutionary algorithm to perform the iterative modification. It will be appreciated that different types of evolutionary algorithms may be used. An exemplary evolutionary algorithm is particle swarm optimization.

According to a third aspect of the invention, there is provided a computer-implemented method of determining a target periodic arrangement of nanostructures of an optical sensor, the periodic arrangement of nanostructures configured to support a surface lattice resonance, wherein the optical sensor is configured to sense a chemical via a modification of an optical property of the nanostructures resulting from absorption of the chemical into the nanostructures or from adsorption of the chemical onto surfaces of the nanostructures, the computer-implemented method including the steps of: defining a target figure of merit corresponding to a change in optical property of the nanostructures in response to the absorption or adsorption of the chemical; generating one or more periodic arrangements of nanostructures within one or more predefined geometrical constraints; evaluating a change in optical property of the or each generated periodic arrangement of nanostructures in response to the absorption or adsorption of the chemical against the target figure of merit; iteratively modifying the or each generated periodic arrangement of nanostructures so as to modify the corresponding change in optical property towards the target figure of merit; and identifying a generated periodic arrangement of nanostructures with a change in optical property in response to the absorption or adsorption of the chemical that meets the target figure of merit; and determining the target periodic arrangement of nanostructures of the optical sensor as the identified generated periodic arrangement of nanostructures with the change in optical property in response to the absorption or adsorption of the chemical that meets the target figure of merit.

The features and advantages of the first and second aspects of the invention and their embodiments apply mutatis mutandis to the features and advantages of the computer- implemented method of the third aspect of the invention and its embodiments.

The computer-implemented method may be carried out using an electronic device, a portable electronic device, a portable telecommunications device, a microprocessor, a mobile phone, a personal digital assistant, a tablet, a phablet, a desktop computer, a laptop computer, a server, a cloud computing network, a smartphone, a smartwatch, smart eyewear, and a module for one or more of the same.

In embodiments of the computer-implemented method of the invention, a geometry of the nanostructures may be configured to balance a spectral linewidth of the surface lattice resonance and field enhancement within the nanostructures so as to configure a limit of detection of the optical sensor with respect to the sensed chemical. In such embodiments, a geometry of the nanostructures may be configured to define the spectral linewidth of the surface lattice resonance and the field enhancement within the nanostructures so as to configure the optical sensor to have a limit of detection in the sub-parts-per-million range with respect to the sensed chemical. As explained above, the geometry of the nanostructures may include a geometry of the array of nanostructures and an individual geometry of each nanostructure, examples of which are described throughout the specification.

In embodiments of the computer-implemented method of the invention, the target figure of merit may be or may correspond to, but is not limited to:

• a target variation in an optical property of electromagnetic radiation transmitted or reflected by the nanostructures; or • a target variation in monochromatic intensity of electromagnetic radiation transmitted or reflected by the nanostructures; or

• a target wavelength shift of the surface iattice resonance of the nanostructures; or

• a target narrowing or broadening of a spectral linewidth of the surface lattice resonance of the nanostructures.

In embodiments of the computer-implemented method of the invention, the step of iteratively modifying the or each generated periodic arrangement of nanostructures so as to modify the corresponding change in optical property towards the target figure of merit may include using an evolutionary algorithm to perform the iterative modification. The evolutionary algorithm may be, but is not limited to, particle swarm optimization.

According to a fourth aspect of the invention, there is provided a computer program comprising computer code configured to perform the computer-implemented method of any one of the third aspect of the invention and its embodiments.

The features and advantages of the first, second and third aspects of the invention and their embodiments apply mutatis mutandis to the features and advantages of the computer program of the fourth aspect of the invention and its embodiments.

It will be appreciated that the use of the terms "first" and "second", and the like, in this patent specification is merely intended to help distinguish between similar features, and is not intended to indicate the relative importance of one feature over another feature, unless otherwise specified.

Within the scope of this application it is expressly intended that the various aspects, embodiments, examples and alternatives set out in the preceding paragraphs, and the claims and/or the following description and drawings, and in particular the individual features thereof, may be taken independently or in any combination. That is, all embodiments and all features of any embodiment can be combined in any way and/or combination, unless such features are incompatible. The applicant reserves the right to change any originally filed claim or file any new claim accordingly, including the right to amend any originally filed claim to depend from and/or incorporate any feature of any other claim although not originally claimed in that manner. Preferred embodiments of the invention will now be described, by way of non-limiting examples, with reference to the accompanying drawings in which:

Figure 1 shows scanning electron microscopy (SEM) images of palladium (Pd) square arrays with different diameters and pitch arrays;

Figures 2 to 7 show simulated and experimental optical extinction spectra of Pd nanoparticles in a periodic array;

Figure 8 illustrates the design of the optical sensor of the invention using an inverse optimisation algorithm;

Figures 9 and 10 show simulated optical extinction spectra of Pd nanoparticles in a periodic array;

Figure 11 shows simulated optical extinction spectra of a single Pd nanoparticle;

Figure 12 compares the limit of detection of the optical sensor of the invention and the limit of detection of a control sensor;

Figure 13 shows simulated optical extinction spectra of Pd nanoparticles in a periodic array after 18 generations of optimization;

Figures 14 and 15 show structural, optical and noise characterization of the optical sensor of the invention;

Figures 16 and 17 show structural, optical and noise characterization of a control sensor;

Figure 18 illustrates a particle swarm optimization algorithm; and

Figures 19 to 24 show further structural, optical and noise characterization of the optical sensor of the invention and a control sensor.

The figures are not necessarily to scale, and certain features and certain views of the figures may be shown exaggerated in scale or in schematic form in the interests of clarity and conciseness.

The following embodiments of the invention are described with reference to the exemplary design and use of periodic arrays of Pd-based nanoparticles in optical sensors for sensing hydrogen, where the sensed hydrogen is absorbed into the Pd- based nanoparticles. It will be appreciated that the features of the following embodiments of the invention apply mutatis mutandis to the design and use of periodic arrays of nanostructures in optical sensors for sensing chemicals, where the shape, size and material of each nanostructure may vary, where the chemical to be sensed (e.g. gas, liquid) may vary, and where the sensed chemical may be absorbed into the nanostructures or adsorbed onto the surfaces of the nanostructures. In particular, the sensed chemical may be adsorbed onto selective functionalised surfaces of the nanostructures to enhance the selectivity of the optical sensor to a certain chemical and/or enable a wider range of chemicals to be sensed. In this way, the chemical comes into direct contact with the nanostructures due to absorption of the chemical into the nanostructures or from adsorption of the chemical onto surfaces of the nanostructures.

Hydrogen sensors are used in diverse applications, ranging from safety to medical diagnostics. For example, accurate hydrogen sensing is crucial in the chemical industry, where hydrogen is a heavily used chemical, in the monitoring of structural stability of nuclear power plants, which can be affected by hydrogen embrittlement of metals, and in the detection of leaks in hydrogen vehicles, just to name a few.

Optical plasmonic sensors are advantageous for ultrafast room-temperature operation but due to the broad optical spectra of typically used Pd nanostructures, conventional optical plasmonic sensors lag in terms of their limits of detection, which is in the low ppm range. More specifically, the state-of-the-art of optical hydrogen sensing has reached a limit of detection (LoD), defined as the lowest analyte concentration measurable with a signal larger than 3 times the noise, of 2.5 ppm.

The inventors have surpassed the limits of detection of conventional hydrogen sensors by developing a plasmonic hydrogen sensor based on an optimized periodic array of Pd nanoparticles, which results in the formation of surface lattice resonances characterized by narrow spectral linewidths and small readout noise. Aided by particle swarm optimization, the inventors numerically identified and experimentally demonstrated a sensor with an optimal balance between spectral linewidth and field enhancement in the nanoparticles, with an exemplary measured hydrogen detection limit of 250 ppb. Their work improves current plasmonic hydrogen sensor capabilities and, in a broader context, highlights the potential of optical engineering via inverse nanophotonic design for ultrasensitive optical (gas) detection.

Resonant optical sensors typically rely on wavelength shifts (ZU) of their spectral features, such as peaks in transmission ¹ ' ² and reflection, ³ ' ⁴ induced by analytes. To allow an accurate determination of the peak position and its quantitative dependence on the analyte concentration, one requires sensors with high quality factors (Cofactors), ⁵ - ⁶ defined as the ratios of their resonance frequency by the corresponding linewidth. Since Q-factors are inversely related to the linewidth, which represents the losses of the resonant system, numerous strategies have been proposed to reduce these losses, and therefore sharpen the resonances and decrease the readout noise of optical sensors. ⁵ - ⁷ These approaches include the use of low-loss materials ⁸ - ⁹ and the tailoring of the resonator geometry as in nanoparticles-on-mirror, ¹⁰ whispering-gallery- mode microcavities, ¹¹ and periodic metal nanoparticle arrays. ¹² ' ¹³ In particular, periodic nanoparticle arrays achieve high Q-factors by two processes: first, they reduce the radiative losses of individual nanoparticles by destructive interference of the coherently scattered radiation by the nanoparticles in the array; second, they redistribute the electromagnetic field into the surroundings, thus outside the individual metallic nanoparticles where losses originate. ⁹ ' ¹² ' ¹⁴ This last condition benefits sensors probing phenomena occurring outside the metal nanoparticles, such as changes in the refractive index of the surrounding medium. ¹⁵ On the other hand, the removal of the field from the metallic nanoparticles is unfavorable for other classes of plasmonic sensors that probe changes inside the metal; the so-called direct plasmonic sensors.

Emerging examples of direct plasmonic sensors are plasmonic hydrogen sensors based on Pd nanoparticles and their alloys. ² ' ¹⁶ ' ¹⁷ These devices feature spark-free and roomtemperature operation, efficient remote readout with small footprints, sub-second response time with excellent resistance to cross-contaminating and deactivating gases, and long-term stability. ² ' ¹⁸ ” ²⁰ Mechanistically, these sensors rely on the barrierless dissociation of Hz molecules at the surface of Pd nanoparticles and the subsequent intercalation of H atoms into the metal lattice. The corresponding change in dielectric function between pure Pd and Pd hydride leads to shifts in the localized surface plasmon resonance (LSPR) spectra of Pd nanoparticles, which are linearly proportional to the hydrogen concentration inside the particles. ¹⁷ ' ²¹ Unfortunately, due to the lossy nature of palladium, the LSPR of Pd nanoparticles is broad, ²² ' ²³ with full-widths at half maximum (FWHMs) typically >300 nm for nanostructures with plasmonic spectra at visible or near infrared frequencies. Consequently, these broad peaks introduce inaccuracies in the determination of the sensing readout peak position, ^ _pea k, ¹⁶ leading to higher signal noise, a, and thus higher limits of detection (LoD), defined as the lowest analyte concentration measurable with a signal larger than 3<r. ⁷ ' ²⁴ In fact, the detection limit still remains a significant challenge for conventional plasmonic (and optical) sensors, with the state-of-the-art only at single-digit ppm; a comparably inferior performance than electrical sensors where ppb detection limit has been reported ²⁵ ” ²⁹ (See Table 1). While ppm hydrogen sensitivity is appropriate for some applications, an ultralow detection limit, coupled with the abovementioned advantages of plasmonic sensing, is crucial for various application requiring local and early detection, such as hydrogen embrittlement in engineering structural materials, ³⁰ and intragastric hydrogen production in bacterial infections. ³¹ - ³²

Here, the inventors have overcome the sensitivity bottleneck of optical hydrogen sensors by designing and experimentally demonstrating a sensor capable of detecting hydrogen gas down to the ppb level. The sensing platform is based upon 2D periodic arrays of palladium nanoparticles that support collective surface lattice resonances

(SLRs). These resonances emerge via the hybridization of the LSPRs of the individual nanoparticles and the constructive in-plane diffraction orders of the incoming light, known as Rayleigh anomalies (RAs). ¹² * ³³ ' ³⁴ Since RAs emerge from interference effects outside the metal nanoparticles, they are characterized by narrow spectral features ³⁵ that are therefore inherited by the SLRs. The inventors employed inverse nanophotonic design - an algorithmic technique to find optical structures with set functional targets, ³⁶ to find sensor array configurations with the highest figure-of-merit (FoM), defined as the ratio between the SLR wavelength shift, Δλ _peak , and its FWHM. Critically, the inventors found that the maximum FoM emerging from the inverse optimisation algorithm is not achieved by the array with the narrowest SLR, but rather by the array with an optimal balance between a narrow SLR and sufficiently large field enhancements inside the nanoparticles.

Results and Discussions

Despite their sensing potential, plasmonic SLRs have so far only been extensively studied on prototypical plasmonic metals, such as Au and Ag, with sensing applications limited to refractive index changes outside or at the surface of the metal. ⁷ ' ¹² ' ³⁷ ” ³⁹ The use of SLRs for direct plasmonic sensing of phenomena occurring inside the metals requires the utilization of active plasmonic metals such as Y, ⁴⁰ Mg ⁴¹ and Pd. ²³ Hence, as a crucial step towards the optimized plasmonic sensor, the inventors first demonstrated the existence of SLRs in periodically-arranged Pd nanoparticles and characterized their optical spectra and field distributions. To this end, the inventors fabricated an extensive set of square arrays of 45 nm high Pd nanodisks with varying diameters (d = 70-180 nm, steps of 20/30 nm) and pitch distances (a = 300-600 nm, steps of 50 nm) on fused silica (n _SU b = 1.46). To allow efficient radiative coupling between the nanodisks by the in-plane diffraction orders, an index-matching medium is essential. ³⁴ The inventors thus coated the arrays with a 200 nm thick poly(methylmethacrylate) (PMMA) film (HPMMA = 1.48). Besides having a suitable refractive index, PMMA is also serendipitously beneficial for Pd hydrogen sensors because it accelerates sorption kinetics by lowering the H2 absorption energy into the Pd lattice and rebuffs other interfering and deactivating gases, such as O2, CO, NO2, and volatile hydrocarbons. ² ' ⁴²

Figure 1 shows a collage of SEM images of 42 Pd arrays with different diameters and pitch arrays, but with constant height of 45 nm. Note that for imaging purposes, the overlayer PMMA thin film is etched away. Each panel is 24x24 pm ² .

Figure 2 shows the experimental optical extinction spectra of 42 Pd nanodisks in a periodic array alongside finite-difference time-domain (FDTD) calculations (see "Methods" section) that accurately reproduce all spectral features in the measured data. The figure shows experimental and simulated extinction spectra at normal- incidence from Pd nanodisk square arrays of fixed height, h, of 45 nm and PMMA layer thickness, LPMMA, of 200 nm. The PMMA layer is coated over the Pd nanodisks. The pitch of the array, a, increases from left to right from 300 nm to 600 nm. The nanodisk diameter increases from top to bottom from 70 nm to 180 nm. For comparison, the leftmost panels plot the extinction cross-sections (in m ² ) of the corresponding isolated single particles (a = co). Arranging the nanodisks in arrays results in distinct optical spectra compared to their isolated single particle counterparts. The spectra comprise peaks originating from hybrid RA-LSPR modes. Dashed lines are a guide to the eye to the position of corresponding extinction peaks as function of particle diameter.

Figure 3 shows:

(a) Excerpt of simulated extinction spectra of a Pd square array taken from Figure 1 with different numbers of "peaks" (left: a = 300 nm, middle: a = 450 nm, right: a = 450 nm, all with similar d = 180 nm, h = 45 nm and LPMMA = 200 nm). In each case, Al is consistently assigned to the peak at the longest wavelength, followed by A2 and A3 (the shortest wavelength),

(b) Peak position of Al (left), A2 (middle) and A3 (right) as a function of array pitch distance (h = 45 nm, IPMMA = 200 nm). Clear dependence of the peak position on the pitch distance in all peaks is observed,

(c) Peak position of Al (left), A2 (middle) and A3 (right) as a function of nanodisk diameter. In contrast to (b), here only Al has dependency on the diameter, whereas A2 and A3 are rather constant. This behavior corroborates the dominating contribution of the LSPR in Al, and of the RA in A2 and A3, respectively.

Figure 4 shows:

(a) FWHM of Al (left), A2 (middle) and A3 (right) as a function of array pitch distance (h = 45 nm, LPMMA = 200 nm). Clear dependence of the FWHM on pitch distance in Al is observed, while A2 and A3 exhibit weak dependency,

(b) FWHM of Al (left), A2 (middle) and A3 (right) as a function of nanodisk diameter. Similar to the case in (a), only Al has dependency on the diameter, whereas A2 and A3 are rather constant. This behavior, along with the dependency of the peak position shown in Figure 3, corroborates the dominating contribution of the LSPR in Al, and of the RA in A2 and A3, respectively.

In particular, the inventors observed extinction spectra with one, two, or three peaks, depending on the nanodisk diameter and array pitch. Figure 2 also includes the calculated extinction spectra of the corresponding single-particles, highlighting how arranging the nanodisks in a periodic array results in distinct optical properties compared to their isolated counterparts. Particularly, as the pitch of the array, a, increases, the "main" peaks (as referenced to the array with a = 300 nm) universally redshift and narrow (Figures 3 and 4). For example, for the d = 180 nm sample, its FWHM reduces by one order of magnitude from ~650 to ~65 nm. Furthermore, the inventors observed the appearance of additional redshifting peak(s) at lower wavelength(s) when a reaches 350 and 500 nm. Last, scrutinizing closely these different peaks as a function of diameter reveals contrasting behaviors. While "main" peaks redshift as d increases, the peaks at lower wavelengths are relatively immobile (Figure 3). This observation hints that the "main" peaks are SLRs that are dominated by contributions from the LSPR, and that the peaks at lower wavelengths are dominated by RAs, since their position depends solely on the particle-to-particle distance and not on the nanodisk diameter.

Figure 5 shows:

(a) Extinction spectrum of an array sample with d = 180 nm, h = 45 nm, a = 550 nm, and LPMMA = 200 nm,

(b) 2D maps of the normalized total field amplitude | E| ² of the array at the midheight of the nanoparticles and at different excitation wavelengths, as marked in panel (a). Excitation at wavelengths Ai and A2 generate field maxima far away from the nanodisks - a prominent characteristic in a RA mode. In contrast, excitation at A3 features field maxima surrounding the nanodisks. Dashed lines outline the base of the nanodisks themselves,

(c) Experimental and simulated wavelength-resolved optical dispersion represented as the extinction spectra of the array for different angles of incidence. The dashed lines indicate the different RA orders of the array. The LSPR wavelength of the corresponding single-particle counterpart is also plotted which crosses two lower RA orders.

Figure 6 shows:

(a) Extinction spectra of a array sample with d = 180 nm, h = 45 nm, a = 300 nm and tpMMA = 200 nm,

(b) 2D maps of the normalized total field amplitude | E| ² of the array at wavelength as marked in panel (a) at the mid-height of the nanoparticles. Dashed lines outline the nanodisks,

(c) Experimental and simulated wavelength-resolved angle dispersion extinction spectra of the array with d = 180 nm, h = 45 nm, IPMMA = 200 nm and a = 300 nm, showing the different RA orders (dashed lines) and the LSPR position of the corresponding single-particle counterpart.

Figure 7 shows:

(a) Extinction spectra of a array sample with d = 180 nm, h = 45 nm, a = 400 nm and tpMMA = 200 nm,

(b) 2D maps of the normalized total field amplitude | E| ² of the array at different excitation wavelengths, as marked in panel (a) at the mid-height of the nanoparticles. Dashed lines outline the nanodisks,

(c) Experimental and simulated wavelength-resolved angle dispersion extinction spectra of the array with d = 180 nm, h = 45 nm, IPMMA = 200 nm and a = 400 nm, showing the different RA orders (dashed lines) and the LSPR position of the corresponding single-particle counterpart.

To further characterize the nature of the extinction peaks, the inventors mapped the field distribution and optical dispersion relation of the array with a = 550 nm and d = 180 nm, which pronouncedly features three extinction peaks (Figure 5a; see also a similar analysis for a = 300 and 400 nm in Figures 6 and 7). Figure 5b depicts the FDTD-calculated field distribution map of the array at three different y-polarized excitation wavelengths corresponding to each of the peak wavelengths CAi-^3). At the two shorter wavelengths (^1 and Az), complex field distributions are found, with maxima lying in-between the nanodisks. These features suggest a strong contribution from the RA to the resonance, consistent with the discussion above. The excitation at the longest wavelength (A3) gives rise to field maxima in the vicinity of the nanodisks, suggesting a strong contribution of the LSPR to the resonance. ⁴³ Given such field distribution, these relatively localized but narrow peaks will emerge as the sensing peaks for direct plasmonic sensing of hydrogen in the Pd nanodisk arrays.

After confirming the physical origin of the multiple peaks of the array, the inventors carried out an angle dispersion extinction measurement (see "Methods" section) and plot it alongside data from FDTD simulations (Figure 5c). From the data the inventors determined the different RA orders that give rise to the optical properties of the array. The calculation of Rayleigh Anomalies in a periodic nanoparticle array is carried out as follows:

When light is incident on a 2D square array of subwavelength nanoparticle with pitch distance, a, photons can gain additional momentum in integer multiples of Rayleigh anomaly (RA) is associated with light diffracted parallel to the lattice surface, and it occurs when

The wavelength of the RA occurs at the onset of the (/, j) diffraction order, above which free-space light diffraction is forbidden in the order. Here, 9 is the incident angle.

In more detail, the different orders of RAs are given by equation :

Therefore, when the incident light has polarization of x direction, the wavelengths of (1,0) and (-1,0) orders of RAs are calculated by where n is the refractive index of material at diffracted side and assuming the light is coming from air. Similarly, the wavelength of (0,±l) can be expressed as

For simplicity, the wavelength or wavevector of higher orders of RAs also can be calculated from equation (S3).

The spectral shape is influenced by the higher (± 1,± 1) modes at shorter wavelengths and by the (±1,0) and (0,±l) modes at longer wavelengths. The latter lower order modes overlap with the LSPR deduced from the single-particle extinction peak at certain illumination angles. The coupling of the LSPR to the diffraction orders results in the narrowing of the resonance, while, as shown later below, maintaining its direct plasmonic sensing properties when exposed to Hz gas.

Having established the ability to efficiently engineer the FWHM via SLRs in Pd arrays, the inventors moved on to design the hydrogen sensor of the invention with the aid of FDTD calculation coupled to an inverse design optimization algorithm. As an optimization parameter for the performance of the optical sensor, the inventors used a FoM defined as (Figure 8a): The optimization aims at developing sensors capable of detecting H2 at sub-ppm concentrations. At these concentrations and at room temperature, the Pd-H system will be in the so-called a-phase, characterized by hydrogen concentrations in the metal typically lower than ~1 at.%. To best model the optical properties of the Pd hydride phase, the inventors therefore used the composition PdHo.12, corresponding to the lowest PdHx composition for which an accurate dielectric function is available in the literature. ²¹ From Eq. 1, it is apparent that the highest FoM is obtained by finding an array configuration where the contributions from the LSPR (maximizing AA _pea k upon hydrogenation) and RA (narrowing FWHM) in their hybridized modes are optimized.

Figure 8 shows:

(a) Schematic of the working principle and the associated figure of merit of the plasmonic sensor,

(b) Sketches of the four parameters defining the architecture of the Pd nanodisk array and their range used for the particle swarm optimization (PSO) algorithm. In this four-dimensional searching space, 10 populations are generated at random and allowed to evolve iteratively through the PSO algorithm to find a sensor with the highest FoM, as defined in (a),

(c) Evolution of the FoM for each of the 10 populations through 15 iterative generations. Clearly, in each generation, each population finds structures with higher FoM. At the end, one of the populations reaches the highest FoM of 0.11,

(d) Extinction spectra of the best sensor (d = 124 nm, h = 20 nm, a = 376 nm, tpMMA = 300 nm) calculated for Pd (light grey) and PdHo.12 (dark grey) nanodisk arrays,

(e) Calculated FoM of nanodisk arrays with particle diameters d and array pitches a in close proximity to the ones determined for the best sensor (star symbol). The FoM exhibits ~10% variance from the best sensor, which indicates that a rather constant FoM can be achieved during the fabrication of the sensor.

Typical plasmonic (hydrogen) sensing setups measure transmission or reflection spectra of the nanofabricated samples within the visible and near-infrared range (400- 1000 nm). To have sensors with resonances within this range, the inventors thus limited the array parameter searching space to d = 100-300 nm, h = 20-100 nm and a = 300-500 nm (Figure 8b). For the PMMA layer thickness, ^MMA, the inventors limited the range to 100-300 nm. The lower limit of 100 nm is chosen to ensure robust PMMA deposition when translating the parameters into a real sensor and also to provide sufficient refractive index medium, while the upper limit of 300 nm is to avoid significantly slowing the H2 diffusion kinetics introduced by a thicker layer. ⁴⁴ To efficiently pinpoint the structural parameter combination with the highest FoM within such four-dimensional searching space, the inventors adopted a particle swarm optimization ⁴⁵ (PSO) algorithm combined with the FDTD calculations (Figure 8b). This computational technique comprises populations that together assess the parameter space, and subsequently influence each other to move within this space to maximize the set goal (fitness parameter) that, in this case, is to maximize the FoM. The inventors utilized 10 populations that start with a random set of parameter values and assess their corresponding FoM. In the following generations, each population moves to other parameter values that result in a higher FoM (Figure 8c). Running this process for 15 generations (see "Methods" section), the inventors moved from an average FoM of 0.03 to 0.09, with single-best populations reaching 0.11. The corresponding best sensor architecture is d = 124 nm, h = 20 nm, a = 376 nm and t?MMA = 300 nm (Figure 8d), with AApeak and FWHM of 32 and 296 nm, respectively (see Table 2 and Figure 9).

Figure 10 shows:

(a) Simulated wavelength-resolved angle dispersion extinction spectra of the optimized sensor array, showing the different RA orders (dashed lines) and the LSPR position of the corresponding single-particle counterpart (Figure 11),

(b) Field distribution surrounding the nanoparticle (left) and at the close vicinity and inside of the nanoparticle (right) at three different excitation wavelengths corresponding to the extinction peaks (A1-A3). From the maps it is clear that relative field amplitude inside the nanoparticle excited at Al and A2 are lower than the one at A3. This again corroborates the nature of the peak, in which A3 is dominated by the LSPR and thus is sensitive to the change from Pd to Pd hydride. Dashed lines outline the interfaces between glass/nanodisks/PMMA/air.

Figure 11 shows calculated Pd and PdH0.12 extinction spectra of a single Pd nanodisk with same geometrical parameters to the optimized array sensor obtained by PSO (d

Looking at the best sensor extinction spectrum (Figure 8d), it is observed that only the LSPR-dominated peak responds to hydrogen, whereas the other peaks have lower LSPR contributions and are therefore less sensitive to changes in the refractive index of the nanodisks (Figure 10). This finding further corroborates the interpretation of the origin of the SLR peaks above. Finally, to appreciate the role of SLR excitation in obtaining sensors with high FoM, the inventors also calculated the optical spectra of the best sensor's single-particle counterpart (i.e., similar nanodisk parameters but not in array form). As shown in Figure 11, the isolated nanodisk features comparable AApeak, but suffers from an expansive FWHM of 498 nm, which drops its FoM to 0.07.

Figure 12 shows:

(a) AApeak response to stepwise decreasing H2 concentration (1000 to 0.25 ppm) in Ar carrier gas at room temperature. Inset: zoomed-in version of the sensor response to 250 ppb H2. A stable baseline is observed by the inventors before each hydrogen exposure. Hence, it is unambiguous that any increase in the sensor response is due to hydrogen exposure. In fact, all of the sensor's responses to hydrogen in the time period when any slight baseline drift occurs are significantly larger than the drift. The slight baseline drift likely arises from minor adjustments in the setup over the course of the experiment,

(b) Measured AApeak as a function of H2 concentration derived from (a). Grey dashed line is a guide to the eye and extrapolates the sensor response to the 3a value (0.03 nm, vertical dashed line), indicating a LoD of ^200 ppb (horizontal dashed arrow). Inset: SEM image of the fabricated sensor,

(c) Data from a control quasi-random array sensor analogous to (a),

(d) Data from a control quasi-random array sensor analogous to (b). The control sensor responds comparably to the periodic array sensor but suffers from its higher noise. Hence, its LoD is ~8 times higher at 1.5 ppm.

Figure 13 shows simulated extinction spectra of Pd and PdHo.12 for Population 2 after 18 ^th generation of optimization. Clearly the PSO reaches a configuration where the two SLR peaks are dose to each other and thus indistinguishable. Due to this condition, when the spectra change from Pd to Pd hydride, the program assigns a different peak, which then results in seemingly large peak shift (and thus falsely large FoM). To avoid this problem, we stopped our PSO simulation at the 15 ^th generation.

Figure 14 shows:

(a) SEM image of the sensor array,

(b) Diameter distribution of the particles forming the sensor, showing an average of 130 nm, which is slightly larger than the targeted diameter of 124 nm,

(c) Pitch distance distribution of the sensor array with average of 378 nm, which is very close to the targeted 376 nm,

(d) Experimental extinction spectra of the fabricated array sensor.

Figure 15 shows:

(a) Lorentzian function fitting (dashed line) to the experimental optical spectra to extract Apeak. In this analysis, the fit is only applied within ±60 nm from the peak maximum (grey shaded area, following the method established in Ref. ¹⁸ ), where the peak is symmetric,

(b) Zoomed-in version of (a) within the fit range. Clearly, the Lorentzian represents well the data and thus enables a good fit with R ² > 0.99,

(c) Lorentzian-fitted Δλ _peak response of the best sensor (cf. Figure 12) in the first 30 min of operation used to derive the peak-to-peak readout noise, o, of 0.01 nm. The dashed lines and grey-shaded areas denote the mean of the signal and ±a from the mean, respectively.

Figure 16 shows:

(a) SEM image of the control sensor array with quasi-random particle distribution,

(b) Diameter distribution of the particles forming the sensor, showing an average of 122 nm, which is slightly smaller than the targeted diameter of 124 nm,

(c) Radial distribution function (RDF) of the control sensor. The primary peak in the RDF (i.e., -2.50) indicates the average center-to-center distance between neighboring nanostructures,

(d) Experimental extinction spectra of the quasi-random array.

Figure 17 shows:

(a) Lorentzian function fitting (dashed line) within ±60 nm from the peak maximum (grey shaded area) to extract λ _peak , (b) Zoomed-in version of (a) within the fit range. The Lorentzian represents the data well in the peak-maximum region and thus enables a good fit with R ² > 0.97,

(c) Lorentzian-fitted Δλ _peak response of the quasi-random array control sensor (cf. Figure 12c). The derived peak-to-peak noise, Ocontrai, is 0.08 nm, much higher than that of the optimized regular array sensor. The dashed lines and grey- shaded areas denote the mean of the signal and ±o from the mean, respectively.

Figure 19 shows:

(a) AApeak response to stepwise random H2 concentration (250 to 0.25 ppm) in Ar carrier gas at room temperature. Inset: zoomed-in version of the sensor response to 250 ppb H2,

(b) Measured Δλ _peak as a function of Hz concentration derived from (a). The transparent symbols and gray dashed line are reproduced from Figure 12b.

Figure 20 shows:

(a) a AApeak response to three consecutive cycles of 250 ppb Hz (grey areas). A reversible and reproducible sensor response to such low concentration of H2 is observed,

(b) Average sensor signal to the three cycles of 250 ppb Hz exposure. An uncertainty of ~0.01 nm is recorded, which is in the same order of the sensor's signal noise.

The inventors also numerically assessed the FoM for array parameters in close proximity to the ones of the best sensor architecture. In particular, the inventors varied the pitch of the array, a, and the diameter of the nanodisks, d, within ±6 nm, as these are the parameters that are prone to largest uncertainties in real sample fabrication via electron-beam nanolithography (see "Methods" section). As shown in Figure 8e, the FoM variation within the studied range is relatively small (0.09-0.13, ~10% from 0.11), which enabled the inventors to obtain the expected sensitivity when translating the best sensor parameters into a real sample. Furthermore, it is clear that there are actually a and d combinations that result in slightly higher FoM, which could be identified if the PSO generation iteration were expanded beyond 15 generations. However, there exists a complex relationship between small structural changes in the arrays and peak positions and linewidths in the corresponding extinction spectra. Given the relatively simple definition of the optimization parameter, FoM, extending the algorithm routine to more than ~15 generations typically led to coalescence of peaks and thus spuriously high FoMs originating from inaccurate assignment of peak positions (Figure 13). While beyond the scope of the present work, these issues can be mitigated by a more rigorous definition of the FoM, peak, and the linewidth in the resulting optical spectra, by more stringent boundaries on the structural parameters of the nanodisks, and by using a dielectric function of much smaller hydride concentration relevant to the targeted H2 concentration range of the sensor application.

Guided by the PSO results, the inventors experimentally realized the optimized sensor design using electron beam lithography (Figures 12a-d, Figure 14 and "Methods" section) and assessed its detection limit to hydrogen. To this end, the inventors exposed the sensor to pulses of gradually decreasing H2 concentration in Ar carrier gas (1000 ppm to 250 ppb) at room temperature and plotted its associated Δλ _peak , which is obtained through a Lorentzian fit ² (Figure 15 and "Methods" section). As depicted in Figure 12a, the sensor responds positively to different H2 concentrations, with a signal noise, ffsensor, of 0.01 nm (Figure 15). Due to this small noise, the sensor is able to measure even the lowest 250 ppb pulse (Figure 20), making it the first optical hydrogen sensor to achieve sub-ppm detection (see Table 1 for comparison). As shown in Figure 13, the sensor's responses to random H2 exposures are consistent and thus exemplify the sensing reproducibility of the sensor. Recalling LoD as the lowest hydrogen pressure measurable with a signal larger than 3CT, the inventors extrapolated it to be ~200 ppb (Figure 12b). Such sensitivity is expected to also hold in air, thanks to the excellent O2 sieving provided by PMMA. ² ' ⁴⁶

In particular, the inventors have reached the experimental evidence that the inverse- designed sensor based on a regular (i.e. periodic) two-dimensional array of nanoparticles has a limit of detection 8 times lower than the one of a control sensor in which identical metal nanoparticles are distributed quasi-randomly over the substrate.

With regard to the sensor's speed, the inventors have analyzed quantitatively the corresponding response and recovery times of the sensors, as shown in Figure 21. Both response and recovery times (define as tso and tw, respectively, as defined in panel (a) and (b)) increase with lowering H2 pressures. The recovery and response times of both sensors are comparable and can practically be described with a single trend

Figure 21 shows:

(a) the definition of response time as t90, which correspond to the time it takes to reach 90% of the normalized signal (with respect to signal during the exposure and in the absence of H2), (b) the definition of recovery time as tio, which correspond to the time it takes to reach 10% of the normalized signal (with respect to signal during the exposure and in the absence of H2),

(c) response times of the optimized periodic array sensor and control random array sensor as a function of H2 concentration. Data is extracted from Figure 12a,

(d) recovery times of the optimized periodic array sensor and control random array sensor as a function of H2 concentration. Data is extracted from Figure 12c.

Related to selectivity, the inventors exposed the sensors to H2 mixed with CO and NO2, the gases that typically poison the surface of Pd and render it inactive. From Figure 22, it is clear that the PMMA efficiently filters the poisoning gases and thus the sensor maintains its response within 20% with respect to pure H2 (panel b). The PMMA (or other polymer coating) therefore advantageously increases the sensitivity of the sensors.

Figure 22 shows:

(a) a time-resolved Δλ _peak response of sensor - 1 pulse of 1000 ppm H2 followed by 5 pulses of 1000 ppm H2 + 500 ppm CO, and 1000 ppm H2 + 50 ppm NO2 in Ar,

(b) a normalized sensor signal to the one obtained in 1000 ppm H2. The error bars denote the standard deviation from 5 cycles. The shaded area indicates the ±20% deviation limit from the normalized Δλ _peak in 1000 ppm H2.

As a control, the inventors fabricated an array with similar geometry parameters (d = 124 nm, h = 20 nm, and 4-PMMA = 300 nm), but with the nanodisks dispersed quasi- randomly over the substrate rather than in a periodic lattice (Figures 12c-d and Figure 16). The inventors compared the optical response of this control sensor exposed to H2 pulses under similar experimental conditions as the periodic array of the optical sensor of the invention. Consistent with the FDTD simulations (Figure 11), the control sensor exhibits comparable Δλ _peak with respect to the H2 concentration (Figure 12c). However, due to its larger FWHM, its Apeak determination results in a significantly higher noise, Ocontroi, of 0.08 nm (Figure 17), which ultimately leads to a LoD of 1.5 ppm, nearly an order of magnitude higher than the detection limit of its array sensor counterpart (Figure 12d). This comparison accentuates the critical impact of the narrow FWHM, here engineered through the use of optimized SLRs, for resolving Δλ _peak signals at low concentrations. To demonstrate the applicability of the invention in realistic gas environments, that is, to detect H2 in air, the inventors applied the concept of tandem polymers with different functionalities. Such a concept allowed the utilization of multiple (polymer) layers that independently provide targeted functionalities, such as to block O2 molecules. For this purpose, the inventors used poly(vinyl alcohol), PVOH, known for its very low O2 permeability and thus can be used as an efficient O2 barrier. To maintain an overall polymer thickness of 300 nm in the optimized sensor, the existing PMMA film is etched by 5 nm (which was required to deposit PVOH, see Methods) and subsequently covered by a 5 nm thick PVOH layer (Figure 23b). Due to the similar refractive indices of PMMA and PVOH and the small PVOH layer thickness, the extinction spectra and the corresponding FoM of the tandem sensor are practically identical to the ones of the optimized sensor coated only by PMMA (Figure 24). Consequently, the tandem sensor exposed to decreasing H2 concentration (1000 ppm to 250 ppb) diluted in synthetic air exhibits a very similar response to the optimized sensor in Ar (Figure 23b).

Figure 23 illustrates detection in air using a tandem polymer concept, showing :

(a) AApeak response to stepwise decreasing H2 concentration (1000 to 0.25 ppm) diluted in synthetic air at room temperature. Inset: zoomed-in version of the sensor response to 250 ppb H2,

(b) Measured AA _pea k as a function of H2 concentration derived from (a). The curved dashed line is a guide to the eye. Light gray symbols are the response of the optimized sensor (i.e. without PVOH) in Ar (cf. Figure 12b). The horizontal dashed line marks the 3a value (0.03 nm). Inset: To-scale schematic of the tandem sensor comprising a 5 nm PVOH film on top, acting as an O2 barrier, on a 295 nm PMMA layer. The tandem sensor shows a similar response to the optimized sensor measured in Ar.

Figure 24 shows:

(a) Experimental refractive indices of PMMA and PVOH,

(b) FDTD-calculated extinction spectra of the tandem sensor (see the schematic in Figure 23b for Pd (light gray) and PdHo 12 (dark grey) nanodisk arrays. The spectra are basically identical to the ones of the sensor coated with 300 nm PMMA (cf. Figure 12d).

Conclusions

In summary, the inventors have used an inverse nanophotonic design approach to identify and experimentally demonstrate an ultrasensitive plasmonic hydrogen detector based on collective resonances in periodic arrays of palladium nanoparticles. The optimized sensor displays a non-trivial balance between a large optical response upon hydrogenation and narrow spectral features. The measured ppb limit of detection is an order of magnitude lower than any previous optical hydrogen sensor and becomes competitive with the more mature electrical sensors (see Table 1). The genericity of the strategy allows it to be combined with other optimization approaches, including the use of more sensitive transduction materials such as PdAu, ² ' ¹⁷ ' ⁴⁷ ' ⁴⁸ (eightfold more sensitive than Pd at low Hz concentrations) or PdTa ⁴⁹ alloys, and advanced data fittings capable of producing lower signal noise ⁵⁰ and with sensor designs aimed at increasing detection speed such as the use of nanoparticles with faster Hz sorption kinetics (e.g. PdAu, PdCo, PdTa) and of coating layers with higher kinetic-enhancement effects (e.g. PTFE, twice as high as PMMA). The inverse design approach also permits the optimization of nanoparticle arrays for sensing platforms using different configurations, such as perfect absorbers and nanoparticles-on-mirror, and using different readouts such as single-wavelength mode devices, ⁵¹ ' ⁵² opening the door to low-cost, practical, ultrasensitive platforms. Beyond hydrogen sensing, the approach of the invention can be extended to arrays of surface-functionalized nanoparticles with resonances that are sensitive to the adsorption of specific gasses via refractive index effects or chemical interface damping, ⁵³ with the potential to address a wider range of societal needs, from home safety to urban air pollution monitoring. ⁵⁴

Methods

Sensor fabrication and characterization. The samples of Pd periodic array were fabricated from a 4-inch fused silica wafer with electron-beam lithography, thermal evaporation, electron-beam evaporation, wet-chemical etching, reactive-ion etching, lift-off, and dicing. The steps involved included: i) Using a 4-inch fused silica substrate (Siegert Wafer), a lift-off layer of 80 nm MCC NANO Copolymer EL4 (Microlithography Chemicals Corp.) was first spin coated and baked on a contact hotplate for 5 min at 180 °C. Following that, an imaging layer of 70 nm MCC NANO 950k PMMA A2 (Microlithography Chemicals Corp.) was spin coated and baked on a contact hotplate for 5 min at 180 °C, ii) A 20 nm thick Cr layer was deposited with thermal evaporation (Lesker Nano 36) to enable electrical discharge during electron-beam exposure, ill) The nanodisks were defined in the double resist layer on areas of 10x 10 mm ² with electron-beam lithography (Raith EBPG 5200) by exposing circles of 35 nm radius. Each circle was filled with 19 shots at a beam current of 50 nA and at a base frequency of 5.19 MHz, iv) The 20 nm Cr discharge layer was removed by immersing the substrate for 60 s in Nickel/Chromium etchant (SunChem), followed by water rinsing and blow drying, v) The exposed resist was developed for 60 s in MIBK 1 :3 IPA solution, dried in Nz-stream, and descummed in oxygen plasma for 5 s at 50 W RF-power, 250 mTorr chamber pressure, and 40 seem gas flow in a BatchTop Reactive Ion Etcher (PlasmTherm), vi) To form the nanostructures, Pd were deposited through the resist mask with electron-beam evaporation at a deposition rate of 1 Â/s in a PVD 225 system (Lesker), lifted off in acetone for 24 h, rinsed in IPA and blow dried in Nz-stream, vii) Finally, the wafer was diced (DAD3350, Disco) into individual chips of 10x 10 mm ² . For the control quasi-random array sample, the fabrication procedures (steps, materials, and tools used) followed exactly the protocol reported in ref. 2. The only difference was the polystyrene beads used, that is, 120 nm sulfate latex, Interfacial Dynamics Corporation, 0.2 wt.% in Milli-Q water (Millipore). To deposit PMMA on top of the samples, a spin coat of 950k PMMA A4 (Microlithography Chemicals Corp.) was conducted, followed by soft baking on a hotplate for 5 min at 170 °C. To produce the tandem sample, the sensor with PMMA was first etched in oxygen plasma for 2 s (50 W RF-power, 250 mTorr chamber pressure, and 40 seem gas flow in a BatchTop Reactive Ion Etcher, PlasmTherm), to introduce hydrophilicity to the surface so that the PVOH solution can be dropcasted on it, which also resulted in the reduction of the PMMA thickness by ~5 nm according to the etch rate determined before. Following that, a PVOH solution (0.1 wt.% in water) was spin coated (5000 rpm, 60 s) and then baked at 80 °C for 5 min. The obtained thicknesses were confirmed by ellipsometry (J. A. Woollam M2000, Figure 24). The SEM images were collected from glass samples coated with 5 nm Cr layer (Zeiss Supra 60 VP with secondary electron detector, working distance 4 mm, and an electron beam acceleration voltage of 7-15 kV).

Finite-Difference Time-Domain simulations. Commercial Lumerical FDTD software was used to calculate the optical properties of both single and array of Pd nanodisks. The inventors modelled the nanodisks as cylinders with a taper angle (the angle between the base and the side wall) of 65° to be close with the fabricated samples. ⁵⁵ The permittivity values of Pd and Pd hydride (PdHo.12) were taken from the literature. ²¹ The nanodisks were placed directly on top of a fused silica substrate (n = 1.46). On top of the substrate and embedding the particles, a PMMA layer was added, whose permittivity was obtained from an ellipsometry measurement. ⁵⁶ Finally, on top of this layer, there was air (n = 1). The simulations of the scattering efficiencies were done using a total-field scattered-field (TFSF) source with a broadband (400-1100 nm) beam incident from air and along the normal direction. The TFSF source divides the simulation region into two concentric volumes: one centered around the particle with the total fields, and another external where only the scattered fields propagate. Power transmission monitors were positioned around the TFSF source to calculate the scattering cross sections. The efficiency was calculated by dividing the former quantities by the geometrical cross section, i.e., the area of the cylinder perpendicular to the propagation vector k of the incident field. Perfectly matched layer (PML) boundaries were implemented in every direction. The simulations of the periodic arrays were performed using periodic boundary conditions in the x- and /-directions, and PML boundaries in the z-direction. The illumination consisted of a broadband (400-1100 nm) beam, approximated by a plane wave, which was incident normal to the array plane (the xy-plane) from air. To extract the transmission, an xy monitor was placed at the substrate side. Another xy monitor was placed at the center of the particles to extract the fields. The polarization of the incident electric field was set along the y- axis. To extract the extinction (i.e. 1 - transmission) dispersion data, several simulations with different incident angles were performed.

Optical dispersion measurements. An unpolarized broadband light source was used to illuminate the samples and investigate their optical dispersion. The light was focused onto the sample and collected with a Nikon L Plan 20x/0.45NA and a Nikon S Plan Fluor 40x/0.6NA objectives, respectively. Using a dedicated lens system, the back focal plane of the objective was imaged with an imaging spectrometer connected to a multiplying CCD camera (ProEM : 512B). The back focal plane contained the Fourier transform of the optical field transmitted by the sample upon illumination, i.e. the angular dispersion of the transmitted light. The image on the CCD contained 2D angular information for all the wavelengths illuminating the sample. Closing the slit that controlled the light entering the imaging spectrometer allowed selection of one angular component and its spectral decomposition into the CCD. To get accurate wavelength resolution, a grating of 150 g/mm was used. This allowed ±150 nm range to be imaged for a selected wavelength center. To image the full spectrum of the sample (400-1000 nm), the inventors measured spectra at several wavelength centers (i.e. 470, 620, 770, and 900 nm, respectively). Using a polarizer before the illumination objective allowed us to select between TM and TE polarizations. Particle Swarm Optimization calculation. To design the most sensitive hydrogen sensors, the FDTD method associated with the particle swarm optimization (PSO) algorithm was adopted. PSO is a robust population-based stochastic evolutionary computation technique, which is inspired by the natural social behavior and dynamic movements with communications of animal species (called particles) and looking for their requirements in a search space. ⁴⁵ It is envisaged that a different evolutionary algorithm may be used in place of the PSO.

Here PSO was employed to optimize the structural parameters of the plasmonic hydrogen sensor to yield the highest FoM defined by Eq. 1. To this end, the inventors chose to use PdHo nfor the calculation of the hydride phase for the following reasons: i) This is the lowest Pd hydride concentration whose dielectric function is available in the literature ²¹ , ii) At this concentration, the Pd hydride is still at the diluted o-phase, with negligible lattice expansion. This condition prevents inaccurate calculation during FDTD simulation where the expansion of the nanodisk has to be included ⁵⁷ , iii) The chosen hydride concentration is also in line with the targeted range of the hydrogen concentration, iv) Lastly, the accompanied spectral change of the sensor at this hydride concentration was expected to be small enough so that it would be the same SLR peak that was considered, thus avoiding false AApeak determination when calculating the FoM, as detailed later below.

To begin the optimization, the algorithm was initialized with 10 Pd/PdHo.12 nanodisk arrays of random locations of parameters in their own spaces, which then were sent to the Lumerical FDTD platform, where the transmission was numerically evaluated. After that, FDTD sent the computed optical values back to the algorithm where the FoM was calculated, and produced the parameters for the next generation. A technical description of the PSO used here is provided as follows, with reference to Figure 18 which shows the PSO algorithm for a nanoparticle array in the PSO terminology updating during one generation: a) If the position of the Pd/PdHo.12 in the parameter space is assumed as a function of four variables, Xi(n) = f(d(d),h(n),a(n),t _PMMA (n)), where d(n), h(n), a(n) and tpMMA(n) are the particle diameter, height and the pitch distance of the array, tpMMA is the thickness of PMMA, and n is the generation counter. During the optimizing process, the particle is subjected to three forces as it moves through the parameter spaces: (i) a frictional force that is proportional to the velocity, avj(n), where a is the inertial weight; (ii) a spring force towards the individual best value of this particle, where c _x is the cognitive factor and rL is a random number between 0 and 1; and (iii) a spring force towards the global best value of all the particles, where c ₂ is the social factor and r ₂ is a random number between 0 and 1, b) The velocity in the next generation can be obtained from the sum of these three forces, In the Lumerical solver, we used the default values of c and linearly spaced values of a between minimum 0.4 and maximum 0.9 for PSO simulations that have been verified to converge well in many test optimization for photonic design problems. The position of the particle in the next generation is then given by

Ideally, the PSO should keep iterating until all particles converge to the global optimal solution instead of stopping at the 15 ^th generation as detailed above. However, the inventors found that a number of populations updated their FoM through very large peak shifts and very broad FWHM that included two SLR different peaks. In Figure 13, an example for a population at the 18 ^th generation is shown. In this case there are two dose SLR peaks in both Pd and PdHo.12 arrays at around 530 nm and 650 nm, respectively. In this case, the algorithm wrongly considered the lower wavelength peak for the case of Pd, and the longer wavelength peak for the case of PdHo.12, causing a wrong evaluation of Δλ _peak . Furthermore, the FWHM was also calculated for two close SLRs. Consequently, in such cases, the FoM could not be correctly calculated since the parameters originated from two different peaks. Because this similar array began to appear in the 16 ^th generation, the PSO was stopped after the 15 ^th generation for this particular case. However, it is anticipated that other numbers of generations are possible for other conditions.

Hydrogen sensing measurements. Prior to measurements, all sensors were exposed to multiple cycles (>20) of pure H ₂ (1 bar) and vacuum at room temperature to stabilize hydrogen-induced microstructural changes in the nanoparticles. The sensors' LoD determination was performed in a custom-made reactor chamber (effective volume ca. 1.5 mL) equipped with two fused silica viewports (1.33" CF Flange, Accu-Glass) that enabled transmission-mode optical monitoring. The detail of the chamber is reported in ref. ⁵⁸ . The transmission measurements were carried out through fiber-coupled, unpolarized halogen light source (AvaLight-HAL-S-Mini) and a high-resolution visible range spectrophotometer (Avantes Sensline Avaspec-HS-TEC). The H2 gas concentration was controlled by adjusting the flow rate (v [mL/min]) ratio of 1000 ppm Hz (diluted in Ar) and 100% Ar using mass flow controllers (MFCs, Bronkhorst El-Flow Select series), see Table 3.

Table 3. Set Flow of Hydrogen and Argon Gas to Achieve the Targeted Hydrogen Concentrations.

All experiments were carried out at constant 30°C, regulated via a PID controller (Eurotherm 3216) in a feedback loop manner, where the sample surface temperature inside the chamber was continuously used as input. For the selectivity tests, the measurements were carried out in a quartz tube flow reactor with optical access for transmittance measurements (XI, Insplorion AB). Gas flow rate of 350 ml min ^-1 and gas composition were regulated by mass flow controllers (Bronkhorst AP). The sample was illuminated by unpolarized white light (AvaLight-Hal, Avantes) with a coupled optical fibre with collimating lens. The transmitted light was recorded using a spectrometer (AvaSpec-1024, Avantes). The measurement temperature was maintained at 30 °C and the chamber was kept at atmospheric pressure. As readout, the LSPR peak descriptors λ _peak ) were obtained following the method established earlier. ² In detail, a Lorentzian fit was applied to the wavelength range at ±60 nm around the LSPR peak in the measured optical extinction spectra. Despite the asymmetry of the global LSPR peak, a good fit (R ² > 0.97) was obtained, and thus the fit is appropriate to determine the λ _peak (Figures 15 and 17). References

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The listing or discussion of an apparently prior-published document or apparently prior- published information in this specification should not necessarily be taken as an acknowledgement that the document or information is part of the state of the art or is common general knowledge.

Preferences and options for a given aspect, feature or parameter of the invention should, unless the context indicates otherwise, be regarded as having been disclosed in combination with any and all preferences and options for all other aspects, features and parameters of the invention.