Fano Resonances in Plasmonic Ring‐Disc‐Pair Systems

Fano resonances in plasmonic nanostructures, generated by the spectral interference between a broad resonance or continuum and a narrow resonance, have attracted significant interest in recent literature. Herein, by introducing a nanodisc next to a nanoring via electron beam lithography, a set of Fano resonances for such a ring‐disc‐pair (RDP) hybrid is confirmed through coupling between the dipolar disc mode and different multipolar bonding ring modes. Furthermore, the influence of the RDP's geometric dimensions on the dark‐field scattering spectra is experimentally studied, indicating that the contrast ratio of Fano resonances can be improved by optimizing the ring/disc sizes and narrowing the gap in accordance with previous studies. The disc size can also control the spectral locations of these Fano peaks ranging from the visible to the near‐infrared regime. In addition, by comparing the Fano resonances among a series of ring/split‐ring/rod structures with varying curvatures coupled to a neighboring disc in simulations, it is demonstrated that the RDP presents stronger sensitivity for the same gap distance and shows high‐quality Fano resonances compared with more common disc‐inside‐ring cavities in literature.

one for RDCs, which also offers higher FoM and CR for the Fano spectrum. [13] In this article, we adopt a top-down technique to fabricate a series of RDPs on indium tin oxide (ITO)/glass substrates via electron beam lithography (EBL). Then, we experimentally study the tuning of the Fano resonances and quantify their CRs for different geometric dimensions, such as ring/disc sizes and gaps. Numerical simulations also clarify the near-field hybridization, leading to Fano resonances in RDPs. To this end, we perform a systematic simulation study explaining the different Fano resonances observed in RDPs, split-ring/disc, rod/disc, and central RDCs and distinguish spectral behavior from a mere superposition to Fano coupling between the ring, split-ring, or rod and the nearby disc. Figure 1 displays the schematic of a gold RDP nanostructure deposited on an ITO/glass substrate, where the thickness of the ITO layer is 50 nm. The geometric parameters of the RDP are namely the nanoring's center diameter (D ring ) and thickness (T ), the nanodisc's diameter (D disc ), as well as their heights (H) and the edge-to-edge gap (G). Note that during the EBL fabrication, the RDPs' center distance and D ring can be controlled by the EBL pattern design, T and D disc are tailored by the EBL exposure dose, and a constant H of 50 nm controlled by the evaporation is maintained in the current work. All parameters are characterized by scanning electron microscope (SEM) imaging after optical measurements.

Results and Discussion
After fabrication, dark-field scattering spectra of a series of RDP systems are characterized, where unpolarized illumination is introduced to reduce the influence of slight fabrication defects or misalignment. First, by fixing D ring to 450 nm and a center distance of 380 nm, we consider the influence of the exposure dose on the optical properties of a single disc, a single ring, and their hybrids (RDPs), as shown in Figure S1, Supporting Information. The results suggest that the spectral features of both the single disc and ring witness a general redshift as a function of D disc and T over the wavelength range of 695-850 and 575-600 nm, respectively. However, the spectral behavior for their hybrid RDP system changes from a mere superposition to increasing Fano coupling between the structures due to the narrowing gap as the exposure dose increases. The spectral redshift effects for the nanoring and disc are in line with literature and further ensure the reliability of the current experiments. [14] Here, by taking the example of RDP vi from Figure S1, Supporting Information, we perform numerical simulations using Lumerical FDTD solution to study the formation of the Fano resonance (see Experimental Section). In Figure 2a, both experimental and simulated scattering spectra of RDP vi are plotted. The simulation is modeled based on the average sizes extracted from SEM imaging, as shown in Figure 2b, that is, D ring = 450 nm, T = 45 AE 6 nm, D disc = 180 AE 9 nm, and G = 45 nm, respectively. In Figure S4, Supporting Information, we conduct another simulation study to exemplarily compare the ideal geometries with geometries directly extracted from SEM images. The results indicate that fabrication-related irregularities or asymmetries in RDPs will decrease the contrast of Fano resonances without significantly shifting their spectral positions or coupling modes. Therefore, the simulated spectra in Figure 2 performed  with ideal geometries generally reproduce the characteristics and suggest five different peaks for the RDP at the wavelengths of 568, 692, 780, 863, and 1028 nm (where Mode-5 is redshifted by %60 nm compared to the experiment). The dashed red line in Figure 2a plots a superposition of the simulated spectra of the single disc and the ring (R&D) under the same simulation conditions, indicating a plasmonic superposition of an antibonding ring mode at 568 nm and a dipolar disc mode at 840 nm as shown later. Since Fano resonances result from the spectral interference between an overlapping broad spectrum and a narrow discrete resonance, the above results show that in the RDP system the nearby dipolar disc provides the broad continuum for the Fano resonance, indicating four separate Fano peaks of Modes 2, 3, 4, and 5. [2b,8a] These Fano resonances can be also explained by the near-field plasmonic hybridization. Figure 2b shows the surface charge density of these modes at the RDP surface on a logarithmic scale, which directly interprets the charge boundary between the opposite polarities and clarifies the bonding levels for the ring. It can be seen that Mode-2, -3, -4, and -5 exhibit coupling between the dipolar disc mode and multipolar bonding ring modes (bonding level m ≥ 2), that is, bonding level m = 5 for Mode-2 and -3, m = 4 for Mode-4, and m = 3 for Mode-5, respectively. Mode-1 shows a combined mode between a dipolar antibonding ring mode and a hybrid disc mode. The charge distribution for the disc in Mode-1 suggests not only an in-plane dipolar mode (dipolar disc mode) but also an out-of-plane base mode (base disc mode), where opposite charges are distributed on the left/right and top/bottom edges of the disc, respectively. Furthermore, Figure S2 and S3, Supporting Information, show that such RDPs also present Mode-6 of the dipolar bonding ring mode (from now on called dipolar ring mode) and a weak dipolar disc mode in the near-infrared regime at 2348 nm. To confirm these charge distributions, we further plot the electric field distribution, perform additional COMSOL multiphysics simulations, and give a detailed simulation study in Figure S2 and S3, Supporting Information. The above discussion indicates the plasmonic hybridization in the RDP system. To be specific, within the strong dipolar-disc background (e.g., the wavelength λ is between %650 and %1100 nm), the near-field coupling generates various multipolar bonding ring modes which lead to the formation of far-field Fano resonances. In contrast, for wavelengths beyond the dipolar disc mode, such coupling effects from the disc are significantly reduced, and both antibonding (λ = 568 nm) and dipolar ring (λ = 2348 nm) modes remain mostly unchanged in the far-field spectra. At the shorter wavelengths, the high-energy antibonding ring mode will instead excite a weak base mode for the disc.
In the following sections, we experimentally study the influence of the RDPs' geometries, such as the ring/disc sizes (D ring and D disc ) and their edge-to-edge gaps (G), on their spectral behavior. As for the impact of D ring , Figure 3a shows the SEM images of six RDP systems with a similar T, D disc , and G, but an increasing D ring from 250 to 750 nm in steps of 100 nm. Resulting from the geometric parameters given in Table S1,  Table S1, Supporting Information. The scale bar is maintained at 150 nm. b) Experimental scattering spectra for the six RDPs. c) Corresponding simulated spectra of the six RDPs with increasing D ring . d) Simulated electric near-field distribution plots for D ring of 350, 550, and 750 nm, respectively (EF = enhancement factor).
www.advancedsciencenews.com www.adpr-journal.com Supporting Information, the corresponding simulation work considers the constant values of H = 50 nm, D disc = 175 nm, and T = G = 45 nm. Due to the controlled D disc , the experimental and simulated spectra in Figure 3b,c indicate a stable dipolar disc background peak with a maximum at %800 nm. In both plots, the main Fano dips are marked with triangles, indicating the most distinguishable Fano feature within the spectra. Both experimental and simulated spectral evolution suggest a relatively constant but decreasing contrast for the main Fano resonance as the ring size increases. Meanwhile, the electric field distribution at the top surface for these resonances in Figure 3d reveals that the multipolar order of the ring increases from m = 3 at D = 350 to m = 5 at D = 550 and m = 7 at D = 750 nm. The corresponding localized electric near-field enhancement factor (i.e., EF = |E max /E 0 |) gradually decreases with increasing D ring , resulting in a weaker Fano coupling and decreasing contrast. A quantitative analysis of the dip position and CR is shown later. On the other hand, when the near-field coupling effect to the disc is weak (i.e., low spectral overlap with the dipolar-disc background), Lorentzian-shaped peaks are also observed. In line with the literature, [15] experimental and simulated curves display a stable peak at %560/%575 nm that can be attributed to the antibonding ring mode, which depends mainly on ring thickness. In Figure S5a, Supporting Information, the simulated spectra in the near-infrared regime also suggest a significant redshift for the dipolar ring mode from 1500 to 3600 nm as D ring increases, depending on the ring's "effective length" (approximated as the center perimeter). [16] Next, we study the effect of D disc on the RDPs' spectral behavior as shown in Figure 4. These RDPs are of constant D ring = 450 nm, T % G % 45 nm, and increasing D disc from 95.2 AE 19.8 to 239.8 AE 12.8 nm. Since controlling the symmetries of the smaller discs by EBL is challenging, the simulation only models circular discs with their average diameters. In Figure 4b, c, both experimental and simulated curves show a similar constant antibonding ring mode at %575/580 nm. Furthermore, as D disc increases, both spectra outline an increasing intensity and a strong redshift of the peak of the dipolar disc background from %700 to %850 and %650 to %1000 nm, respectively. A general transition from a spectral superposition to final strong Fano interference is observed in both plots as D disc increases from 95.2 to 239.8 nm. By comparing the spectral evolution and the electric field distributions presented in Figure 4d, a similar positive correlation between EF and the CR in Fano resonances is observed. The small disc (D disc = 108.9 nm) exhibits a high curvature, which induces a strong electric field enhancement at the disc surface. However, owing to the lower coupling strength (i.e., EF = 3.42), the RDP ii cannot produce high-contrast Fano resonances in the far field. Furthermore, the corresponding electric field distributions of RDPs v and vii indicate bonding levels of m = 4 and 3 for the respective nanorings. The difference is due to the fact that nanorings present various dark modes in the spectrum at different spectral positions. As the disc size changes, the corresponding dipolar continuum will couple with the most spectrally overlapping discrete dark mode to form Fano resonances.  Table S2, Supporting Information, for geometric parameters. c) Related simulated spectra of the seven RDPs with increasing D disc . d) Simulated electric near-field distribution plots for D disc of 108.9, 176.3, and 239.8 nm, respectively. www.advancedsciencenews.com www.adpr-journal.com Similarly, we also study the influence of RDP gaps from 74.4 nm to the final connection, as shown in Figure 5. To simulate the connected state for RDP vi in Figure 5a, we consider an overlapping RDP system with a gap of À10 nm. In Figure 5b, one can only find the spectral superposition of RDP i and ii due to the signal loss of the weak Fano coupling. However, both simulations and experimental curves indicate a stable Fano dip position independent of the gap variation, as shown in Figure 5b,c. Besides, the electric field distribution plots in Figure 5d also suggest an enhanced coupling strength as EF increases for decreasing G. Here, since the disc and ring size are controlled, the coupling modes (i.e., coupling between the bonding ring mode with m = 4 and dipolar disc mode) in these Fano resonances remain unchanged. In addition, following the plasmonic ruler equation describing the spectral shift in a dimer system with varying gap size, [14a,17] simulation studies in Figure S5b,c, Supporting Information, illustrate that the dipolar ring mode in the near-infrared regime will present a weak redshift as either D disc increases or the gap decreases. Besides, the connected RDP vi presents a set of resonance peaks (e.g., λ 1 = 717.1 nm, λ 2 = 769.4 nm, and λ 3 = 841.6 nm in experiments) due to the redistribution of surface charges by the metal junction instead of coupling between the two parts, [18] and similar trends can be found in simulations which also suggest a broader mode that is redshifted compared to the dipolar ring mode, peaking at %2500 nm as shown in Figure S5c, Supporting Information.
The earlier sections illustrate that the Fano resonances of RDPs can be manipulated by their geometries, for example, the Fano CRs can be increased by optimizing the D ring /D disc ratio or narrowing the gap, and the general spectral positions of Fano resonances can be adjusted from the visible to the infrared regime by increasing D disc . Figure 6 presents a quantitative analysis of the spectral evolution for these Fano resonances, where the Fano dip positions and their CRs are plotted as a function of D ring , D disc , and G, based on both experimental (solid lines) and simulation results (dashed lines), respectively. Here, CR is defined as the ratio of the intensity difference between two adjacent peaks and their intermediate Fano dip to the intensity of the two peaks (i.e., CR 1 = (I left-peak À I dip )/I left-peak and CR 2 = (I right-peak À I dip )/I right-peak ), and the average value (CR avg = (CR 1 þ CR 2 )/2) and error bars (indicating CR 1 and CR 2 ) are then introduced. Despite the deviations between experimental and simulated plots, the overall trend for the dip positions and CRs remains consistent in Figure 6a,b,c. Notably, the simulated Fano behavior as a function of G, shown in Figure 6c, indicates a constant Fano dip position under gap variation at λ = 828 nm. Here the CRs also follow an exponential decay with respect to G, fit as CR= À0.017 þ 0.357 Â e (À0.020⋅G/nm) , as depicted in the blue dotted line. Since CRs refer to the intensity difference in Fano resonances, the exponential growth in Fano coupling versus decreasing G implies that RDPs, due to their unique structure compared with RDCs, can serve as sensors for nanoemitters, such as in surface-enhanced Raman scattering  Table S3, Supporting Information, for geometric parameters. c) Related simulated spectra of the six RDPs with decreasing edge-to-edge gap. d) Simulated electric near-field distribution plots for G of 74.4, 46.3, and 20.0 nm, respectively.
www.advancedsciencenews.com www.adpr-journal.com (SERS). [19] Preliminary results (not shown here) predict potential applications for RDPs in active flexible plasmonics in future work, where the appearance/enhancement of Fano resonances and SERS signals can be monitored by altering the gap with applied strains once these RDPs are transferred onto stretchable polydimethylsiloxane (PDMS). [120] While in literature, [5b,21] conventional RDCs exhibit Fano responses under extreme conditions such as thinner widths and smaller gaps, the present studies show that RDPs offer higher geometry tunability and CR quality for the Fano resonances than RDCs. To explain such a difference, we perform a detailed simulation work to study the influence of the "bending level" on the Fano line shape by introducing 27 hybrid systems combining the same disc and a nearby ring, split-ring, or rod. Their dimensions include D disc = 200 nm, G = T = H = 50 nm, and a controlled perimeter of 2π Â 225 nm for the rings/split rings/rod to maintain a similar effective length. The "bending level" of the rings/split rings/rod is quantified as a uniform curvature K ranging from À1/225 to 1/225 nm À1 , where the negative and positive values for K refer to the relative position of the disc outside or inside the split ring. Table S4 and Figure S6, Supporting Information, give the parameters and schematic for these systems, and Figure 7 shows the simulated scattering spectra. Here, we separate these spectra into four regions, namely antibonding (A), bonding/Fano coupling (B/F), quadrupolar (Q ), and dipolar (D). The regions A, Q, and D are generally outside the strong dipolar disc background (%650 nm < λ < %1200 nm), where the spectra follow a superposition between the ring/split ring/ rod modes and a weak dipolar disc mode due to weak coupling. In region A, all the spectra show a constant antibonding ring mode at %560 nm due to the fixed T, and in region D, the spectra except for the rod-disc system present a dipolar ring mode located at 2400-2500 nm due to the controlled perimeters, but its intensity significantly increases with increasing |K|. (The nomenclature for the split-ring modes here follows that of a ring if the ends were connected.) Furthermore, in region Q, there are some additional "isolated" peaks that only occur for the split-ring-disc systems. The surface charge distributions of the two half-ring-disc systems (K8 and K20) suggest these peaks to consist of combined modes between the dipolar disc mode and inherent quadrupolar splitring modes (see Figure S7-S10, Supporting Information). Finally, region B/F indicates the potential coupling of the ring/ split-ring/rod modes with the dipolar disc mode. Due to a stronger plasmonic hotspot/tip effect (see Figure S9, Supporting Information for the near-field enhancement of K8 and K20), pronounced Fano resonances with higher CRs can be found when the disc is outside the ring/split ring (K < 0). Figure S10, Supporting Information, indicates that due to symmetry breaking split rings show some additional orders (e.g., corresponding to m = 1 to 5 for the half ring) in their scattering spectra compared to rings (antibonding or dipolar) or a rod (dipolar), [11a] which contributes to the Fano coupling and leads to the best CR for the halfring-disc-pair structure in Figure 7. Therefore, only ring-disc or rod-disc systems show Fano peaks in the region B/F that are contributed merely by the near-field coupling effect to modes that do not appear in the initial scattering spectra, where the RDP presents the highest CRs. On the other hand, when the disc is positioned in the interior of the ring/split rings (K > 0), all Fano resonances continue to weaken and present a merging trend as K increases. Ultimately, the RDC system shows only negligible fluctuations or weak hybridization. These results show that RDPs especially compared with RDCs exhibit distinct Fano resonances in terms of contrast ratio and quality factor, indicating advantageous properties for chemical and biological sensing applications. [5b] In addition, by comparing the spectra between single structures and their corresponding hybrid structures ( Figure S10, Supporting Information vs Figure 7), the current study proves www.advancedsciencenews.com www.adpr-journal.com that the RDP system offers strong spectral sensitivities to the approaching disc, which can not only relax such tight fabrication requirements but also offer a variety of prospects, for example, in active flexible plasmonics and nanoemitter sensing applications in future work.

Conclusion
In conclusion, coupled RDP systems enable plasmonic hybridization between the multipolar bonding ring modes and dipolar disc modes in the near field, forming a set of Fano peaks within the dipolar disc mode background as observed in the far field. The quality of these Fano resonances (e.g., contrast ratios) can be improved by tailoring the RDPs' geometric dimensions, such as optimizing the ring/disc sizes and minimizing the gaps. In addition, the number of Fano resonances can be increased by larger rings, and the general positions of the Fano peaks can be redshifted by defining larger discs. Finally, comparing the spectra of RDPs, split-ring-disc or rod-disc pairs, and RDCs, the numerical studies illustrate that RDPs and split-RDPs with the disc facing the outer wall of the split ring show more pronounced Fano effects than cavity systems with the disc facing the inner wall due to a more intense hotspot. Considering the spectral behavior between a single disc or ring/split ring/rod and their hybrid structures, we demonstrate that RDPs have higher Fano sensitivity from initial spectral superposition to final Fano coupling with respect to the disc in a narrowing gap than all the other systems. Structures with such properties are of strong interest for future work, for example, on nanoemitters/quantum dots sensing, or far-field spectra respectively SERS in gapaltering flexible plasmonics once the RDPs are transferred onto a stretchable substrate.

Experimental Section
RDP Fabrication: A set of Au RDP arrays (period of 5 μm and array size of 50 μm) were fabricated on ITO/glass substrate via the traditional EBL processes, consisting of substrate preparation, photoresist spin coating, lithography, development, Au deposition, and lift-off. 1) %50 nm ITO adhesion layer was sputtered onto a cleaned glass substrate to avoid charging effects. 2) 2.5 wt% solution of poly(methylmethacrylate) (PMMA)/methyl isobutyl ketone (MIBK) was spin coated at 5000 rpm for 60 s on the above substrate. 3) After soft baking at 150°C overnight, %150 nm thickness of PMMA resist was formed. 4) The lithography work was carried out by a JEOL JSM-6500 F SEM and a XENOS pattern generator, with an accelerating voltage of 30 kV and an adjusted beam current of 26 pA. 5) The exposed samples were developed for optimized %75 s through 2propanol/MIBK (vol. 3:1). 6) 50 nm of Au was then thermally evaporated onto the developed sample by a Pfeiffer Vacuum evaporator PLS 570 at a pressure below 4 Â 10 À7 Torr. Finally, 7) the lift-off process included overnight acetone immersion at room temperature. More details can be found in our previous publications. [20c,22] The structures showed some inherent fabrication-related irregularities. Note that such asymmetries could enable coupling to higher-order modes even in the absence of a second particle. However, no such effects were observed in the investigated range.
Dark-Field Scattering: Dark-field scattering spectra of RDPs were characterized on a Nikon Eclipse Ti inverted microscope with an external Nikon dark-field condenser (dry 0.95-0.80). The samples were illuminated by a 100 W halogen lamp, where no polarizer was introduced. The resolving power was improved by oil immersion (n = 1.518) and a Nikon Plan Fluor 100Â/0.5-1.3 oil objective. A grating spectrometer LOT SR-303i-B analyzed the scattered light. The effectively detected spectra ranged from %480 to 1020 nm. The detection area was %1 μm 2 , and thus grating effects of the RDPs (spaced at 5 μm) were negligible. In all cases, the raw spectra (I raw ) were normalized by the lamp (I lamp ), dark current (I dc ), and background (I bg ) spectra by Equation (1) as follows: Numerical Simulations: The scattering spectra of RDPs shown in the main text were performed by the commercial software Lumerical FDTD Figure 7. Simulation study on the scattering intensity for a set of ring/split-ring/rod-disc hybrids with an increasing K over a) the full range of 400 to 3500 nm and b) a zoomed-in range of 400-1500 nm. The curvature values for the RDP, half-ring-disc pair, rod disc, half-ring-disc-cavity, and RDC are namely, K1 = À1/225, K8 = À1/450, K14 = 0, K20 = 1/450, and K27 = 1/225 nm À1 .
www.advancedsciencenews.com www.adpr-journal.com solutions. The geometric parameters of each RDP were taken from the average sizes in the SEM characterization as shown in Table S1-S3, Supporting Information. The total-field scattered-field (TFSF) source, together with 3D perfectly matched layer (PML) boundary conditions, was used to study the scattering cross sections of each RDP. A set of gradient meshes was introduced, with the minimum fine size of 2 Â 2 Â 2 nm 3 . The charge density distributions were studied by the predefined script of divergence current, which assumed the material was pure plasma. The refractive indexes of Au and glass came from Johnson-Christy and Palik. [23] Based on our previous simulation work, we considered an approximated and constant refractive index of 1.9 for the sputtered ITO layer (strictly speaking n ITO is wavelength dependent and depends on the exact composition of the ITO) [24] and introduced superimposed orthogonally polarized incidences (i.e., two polarizations along and perpendicular to the gap direction) to simulate the unpolarized illumination from experiments. [20] For the corresponding charge distribution analysis, we only showed the plots under the gap-direction polarization. See Supporting Information for a simulation study on the polarization dependence of the RDPs' scattering spectra, which suggests that unpolarized plots show very similar features but lower CR compared with gap-polarized curves. In the Figure S3, Supporting Information, an additional simulation by COMSOL Multiphysics was used to visualize the 3D charge densities of RDPs. The structure's boundary conditions, dimensions, and complex refractive indexes were maintained. The mesh was systematically created, and the scattering field was simulated by calculating the total and background field separately. The charge density (ρ a.u. ) was evaluated by the following equation: where n i and E i are the normal vector and E-field components in each direction at the structure surface.

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