Engineering Fano‐Resonant Hybrid Metastructures with Ultra‐High Sensing Performances

Metamaterials‐based sensors are of primary interest in physics, materials science, medicine, and biophysics thanks to their ability to detect very tiny amount of molecules spread into a medium. Here, a metastructure utilizing the epsilon near zero (εNZ) and Fano–Rabi physics is engineered to design a system with ultra‐high sensitivity. So far, a dedicated study of such systems has been missing. In this work, the authors report the results of their efforts to fill the gap by considering a metasurface, designed as a periodical array of rings with a cross in their center, placed on top of a silver (Ag) and zinc oxide (ZnO) epsilon near‐zero optical nanocavity (εNZ‐ONC) metamaterial. The accurate selection of the metasurface parameters allows the design of a sensor exhibiting an extremely high sensitivity of about 16 000 and 21 000 nm RIU−1 depending on incoming polarization. This work paves the way for the development of novel groundbreaking devices for biomedical and environmental application based on plasmonic and photonic design principles.


Introduction
In recent years, the design and realization of bio-sensors based on plasmonic/nanophotonic structures is spurring unprecedented interest as diagnostic protocol for cancer and infectious diseases. [1][2][3] Significant efforts have been devoted to design photonic structures at the nano-scale for probing genes and where ℏω is the photon energy and q = cotδ is the Fano parameter that specifies the ratio of the resonant absorption (due to the metastructure) to the direct absorption amplitude (due to the bare substrate), δ is the phase shift deriving from the interaction of light with metallic slabs, Ω = 2(ℏω − ℏω 0 )/Γ, where Γ and ℏω 0 are respectively width and energy of the given resonance and D 2 = 4sin2δ. [15][16][17] The Fano formula is generally applicable to the considered optical spectral range in a variety of metastructure systems. [18] The FFR spectral location and lineshape are determined by the geometry (periodicity and unit-cell features) of the metasurface placed on top of the considered plasmonic system. [7] The latter can be constituted by optical nano-cavities (ONC) exhibiting epsilon near-zero (ε NZ ) behavior with giant phase shift (δ). [12,13,19,20] The ε NZ system guarantees the existence of two distinct surface plasmon polariton (SPP) modes (at the top or at the bottom of the metal-insulator interfaces [21] ), with different k-vectors at the resonant wavelengths, that can merge into a coupled state also known as gap surface plasmon (GSP) which has its own resonant wavelength ( -ONC NZ λ ε [22] ). If the typical periodicity of the unit metasurface element P (Figure 1a) is such that the related lattice resonance is nearly close to the ε NZ -ONC one, the line-shape can show a narrow feature, which is a consequence of the losses in the metal layers. [23]

Results and Discussions
The intriguing challenge of the proposed work is to study the optical behavior of a polymeric metasurface, designed as a periodical displacement of rings with a cross in their centers, placed on top of an ε NZ -ONC. Figure 1a reports a sketch of the designed system where P = Px = Py is the period of the metasurface, W c the cross arm length, W e and W i represent the outer and inner radii of the ring, respectively. Starting from the glass substrate, the considered ε NZ -ONC comprises of a silver (Ag) layer of 30 nm and a thick zinc oxide (ZnO) cavity of 160 nm followed by other 30 nm layers of Ag and 20 nm of ZnO where the cavity thickness plays a fundamental role to determine the confined modes propagating within the metamaterial. [19,22] As addressed in our previous works, [13,24] for the selected t cav = 160 nm, two confined modes appear, that is, m = 0 and m = 1, centered respectively at λ 0 ≈ 405 nm and λ 1 ≈ 780 nm. The fact that this ONC supports a double plasmonic mode, at lower and higher energies, means that interface interactions with bound and anti-bound modes are allowed. [25] The proposed coupled system is numerically investigated by means of a suitable "Reticolo" script [26] which exploits the rigorous coupled wave analysis (RCWA), details are available in the Experimental Section whereas some sample codes are reported in Section S2, Supporting Information. The refractive indices of the materials used for the simulation are reported in Figure S1, Supporting Information. In order to design optimized metastructures, we have to consider at least two main aspects: first, we span the entire visible range and second, the metasurface has to interact with the plasmonic resonances of the ε NZ -ONC. To this end, the presented metasurface is a periodic structure whose unit cell is chosen as a cross centered into a ring (Figure 1a) with thickness fixed at 300 nm, thus ensuring a subwavelength behavior for almost the whole considered spectral range. A general perspective of the metastructure optical response can be caught by performing a parametric sweep study in which the period P of the unit cell is varied from 100 to 1000 nm with 4 nm steps and the fill fraction is fixed at 67%. The structure parameters are accordingly calculated as a function of P following the formulas The obtained reflectance (R) and absorbance (A) maps, reported in Figure 1b,c, suggest that a dip in reflectance corresponds to a peak in absorbance in agreement with the Fano description. An insight of these results is reported in Figure 2a,b where the stacked plots (with 50 nm steps) clearly evidence the presence of FFR and Rabi-analogue splits [27] which strongly depend on the geometrical parameters of the metasurface; numbers (1-8) identify the different spectral behaviors shown in the maps and explained hereafter. Three Rabi-analogue splits (anti-crossing modes) are observed for periods spanning from ≈100 nm to ≈600 nm. In this range, when R goes to zero, A increases (up to case # 5). The opposite situation occurs when the period changes from 700 nm to 1000 nm (case # 6 # 8 − ), which is the case for shorter wavelengths. This  is due to the presence of the FFR which is a consequence of the high wave vector (k) mode coupling induced by the metasurface placed on top of the ε NZ -ONC. The stacked plots also allow an eye-catching identification of the cavity modes: indeed, the modes where R goes to zero and A is maximized, and viceversa, the modes where R is maximized and A goes to zero. An in-depth investigation of the above-mentioned two peculiar behaviors is presented as well. For this, two sets of metasurface parameters are selected. In the first case, a period P x = P y = 400 nm is chosen that corresponds to W e = 290 nm, W i = 170 nm, and W c = 100 nm. When the metasurface is placed on top of the ε NZ -ONC, the light-matter interaction produces p-polarized R dips and A peaks at the wavelengths λ = 422, 557, 626, 689, and 781 nm, as shown in Figure 3a. The electric field behavior of the p-polarized coupled resonant mode at λ = 626 nm is studied by considering the refractive index modulation of the metasurface (Figure 3b(1)). As expected by the interaction of the metasurface with the ε NZ -ONC, the electric field along X is highly confined between neighbor rings and in-plane coupled modes also arise between the metasurface and the cavity, as shown in Figure 3b(2). On the other hand, a highly confined electric field in the Y direction is present within the ONC, as shown in Figure 3b(3). [13] The electric field along Z presents a weak interaction among the lower Ag layer and the ZnO cavity and a strong interaction between the upper ZnO layer and the polymer structures (Figure 3b(4)). In Figure 3c, the top view of the electric field evidences the interaction of the neighboring rings. By considering the second metastructure with period increased to P x = P y = 900 nm (and W e = 652 nm, W i = 382 nm, and W c = 225 nm) p-polarized R peaks and A dips show up at λ = 463, 506, 591, and 669 nm, or the opposite behavior with R dips and A peaks at λ = 470, 509, 600, and 683 nm, see Figure 4a. The electric field simulation using p-polarized incoming radiation are now performed at λ = 463 nm. The refractive index modulation of the studied metastructure is reported in Figure 4b(1). The electric field along X is confined both inside and outside the metastructure (Figure 4b(2)), while along Y and Z it is vertically coupled with the ε NZ -ONC demonstrating the presence of Fano resonances [28] (Figure 4b   field highlights the confined field in the diagonal direction of neighboring unit cells.

Metasensor
Taking into account the observed plasmonic and Fano-Feshbach resonances, the simulated metastructure can be designed to work as a metasensor. In fact, a system able to excite FFR modes presents high performances in terms of spectral sensitivity and specificity for low molecular weight compounds such as nucleic acids, viruses, lipids, and proteins. When a particular species is dissolved in another medium like water + is modified according with the well known procedure reported in literature. [29,30] As illustrated in Figure 5a, the metasensor is designed to be completely covered by the analyte through the realization of a microfluidic channel. In the corresponding simulation, we assumed that the layer of air has been replaced by a infinitely thick layer of analyte, hence, it allows retrieving the bulk sensitivity. The results obtained are therefore intended as very likely of what might be the actual experimental situation when a microfluidic channel is placed on the metastructure. The main parameters that establish the metasensor performance are the sensitivity S, calculated as the wavelength shift induced by a very small change of refractive index and measured in nm RIU −1 , and the spectral sensitivity S Δλ , that is calculated as the ratio of the refractive index variation to the Δλ, and is measured in RIU nm −1 . [31] In order to evaluate the performance of the proposed metasensor, the structures constituting the metasurface are considered separately, namely first only crosses, then rings, and finally their combination. The first numerical study has been performed considering a cross unit cell and a refractive index variation from 1.3330 H O 2 n = to = n 1.343. The variation of refractive index of the metastructure overlayer from air to water has a tremendous influence on the optical response of the metastructure. In terms of p-and s-reflectance, the calculated values pass from the solid black and red lines of Figure 5 to the corresponding dashed ones. When the refractive for R s is observed with a spectral shift of Δλ = 1.6 nm for both cases. This refractive index variation (Δn = 0.01), matches a sensitivity of the system S = 160 nm RIU −1 and a spectral sensitivity S Δλ = 1.00 × 10 −2 RIU nm −1 , see Figure 5b. The second study considers a metasurface including only a ring as a unit cell. This time, a refractive index variation of only 0.0006 determines a wavelength shift from λ = 541.8 nm to 543.3 nm λ′ = and a spectral variation of Δλ = 1.5 nm. This turns out into one order sensitivity increase to S = 2500 nm RIU −1 and spectral sensitivity S Δλ = 4.00 × 10 −4 RIU nm −1 , see Figure 5c. Finally, in the last study, the unit cell of the metasurface comprises both ring and cross, as depicted in Figure 5a. In this case, when the system is completely covered by water, a strong modification of the p-and s-pol reflectance peaks occurs which are now very sharp (black and red dashed lines in Figure 5d). In this condition, the proposed metasensor is able to resolve a refractive index variation as low as 0.0001 by producing spectral red-shifts for both light polarizations In order to benchmark the bulk sensitivity of the proposed metasensor with that of other sensors reported in literature, relevant data has been gathered in Table 1. Our sensor working in the visible range shows excellent performance when compared with state-of-the-art solutions. Moreover, thanks to the presence of an ε NZ metamaterial, a noticeable advantage of our metasensor is that it is operated at normal incidence, for both p-and s-polarized light, and in free space thus not requiring complex optical coupling elements.
Furthermore, an in-depth numerical analysis of the robustness of the sensitivity performance has been conducted by taking into account common fabrication errors that can occur  during the metasurface fabrication process. Detailed information are reported in Section S3, Supporting Information.
In the first case, we considered a period fluctuation of ±20 nm in the X and Y directions in the range of 380-420 nm. As previously discussed, when the period is varied, the other parameters change accordingly (Equations (2)-(4)), as depicted in Figure S2a, Supporting Information. The results demonstrate that when the period is varied and the metastructure is covered by air, both dips in p-and s-polarization are shifted, as shown in Figure S2b, Supporting Information. By considering pure water and water with a 0.0001 refractive index variation (as shown in Figure S2c,d, Supporting Information, respectively), the sensitivity remains consistent with our previously reported results, particularly for the dips in R s which change in the range of ±1000 nm RIU −1 .
In the second case, it has been analyzed the impact of variations in the cross length (W c ). We applied a 15% ± variation on W c , that results in a length change in the range of 85-115 nm, see Figure S3a, Supporting Information. Based on our previous experience in nano-fabrication, [39] we have chosen a fabrication error of 15% ± for the geometrical dimensions under consideration. In this scenario, interestingly, small variations in the cross length do not significantly affect the positions of the reflectance dips in both polarizations, as depicted in Figure S3b, Supporting Information. Also in this case, the sensing performance is only slightly affected, see Figure S3c,d, Supporting Information, for both polarizations with a largest variation ±1500 nm RIU −1 (p-polarization).
In the third case, a 15% ± variation on W e and W i is applied, resulting in a length range of 249-333 nm for W e and 144-195 nm for W i , see Figure S4a  dips in p-polarization while they do not affect the dips at all in s-polarization ( Figure S4b, Supporting Information). When the same system is instead tested in environments with different refractive indices, such as water and water with a 0.0001 refractive index variation ( Figure S4c,d, Supporting Information, respectively), the sensitivity increases by 1000 nm RIU −1 for both polarizations with a negative length variation (−15%) while decreases with a positive length variation (+15%).
In the fourth case, the impact of variations in the ring section has been tested. To perform this simulation, we kept fixed the inner ring radius W i and applied a 15% ± variation on the outer radius W e , resulting in a length range of 249-333 nm, as shown in Figure S5a, Supporting Information. This scenario reveals characteristics similar to the previous cases where variations in the ring radii significantly affect the positions of the reflectance dips in p-polarization while in s-polarization they remain fixed when the metastructure is covered by air, as shown in Figure S5b, Supporting Information. The variation of sensitivity shows the same trend as in the case when both ring radii change. For all the considered fabrication errors, the Tables S1-S4, Supporting Information, report the resonance wavelengths and the corresponding values of sensitivity for the extreme variations. In all tested cases, even taking into account the worst scenario, the sensitivity remains at very high values of at least 12 000 nm RIU −1 , while in some situations it also increase a bit. We confidently conclude that the proposed design is very robust to fabrication error.

Conclusions
In conclusion, we numerically investigated the interaction of plasmonic ε NZ -ONCs with an optimized polymer metasurface resulting into Fano-Feshbach resonances (FFRs) and Rabi-analogue split. These phenomenona pave the way for the realization of metasensors with extremely high performance, namely sensitivity S that can assume values from few hundreds to many thousands (21 000 nm RIU −1 ). Furthermore, the proposed system presents the advantage to be excited using normally incident light thus allowing the realization of compact and portable devices, including also disposable parts that offer a quick and simple solution especially in medical applications.

Experimental Section
The numerical simulations were performed using a Matlab script that was based on the "Reticolo" algorithm. In the first step, the focus was on designing a metasurface coupled with an ε NZ metamaterial. To find the optimal size, a code that was realized, through a "for" loop, varied the period, internal and external radius of a ring, and the length of a cross, see Example 1 in Section S1, Supporting Information. This loop returned a map of reflectance, transmittance, and absorbance (1-T-R). In the second step, once an appropriate structure was designed, the electric and magnetic fields were evaluated. For this, a part of the previous code was used and the suggested method by "Reticolo" was included to evaluate both fields. Finally, using the first code but fixing the period and structural size, tests were performed on bulk sensing by changing the medium surrounding the entire metasurface and altering the refractive index.
Materials: Silver (Ag), zinc oxide (ZnO), and soda lime glass were used as materials, with the latter serving as a substrate. Along with them, a polymeric material was also used. The refractive index of the polymer was fixed at 1.56, which is typical for a general photo-polymer, while the imaginary part is negligible. [40,41] However, the refractive indices of the other materials, which have both real and imaginary parts, were considered as a function of wavelength, as shown in Figure S1, Supporting Information.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.