Significantly enhanced coupling effect and gap plasmon resonance in a MIM-cavity based sensing structure

Herein, we design a high sensitivity with a multi-mode plasmonic sensor based on the square ring-shaped resonators containing silver nanorods together with a metal–insulator-metal bus waveguide. The finite element method can analyze the structure's transmittance properties and electromagnetic field distributions in detail. Results show that the coupling effect between the bus waveguide and the side-coupled resonator can enhance by generating gap plasmon resonance among the silver nanorods, increasing the cavity plasmon mode in the resonator. The suggested structure obtained a relatively high sensitivity and acceptable figure of merit and quality factor of about 2473 nm/RIU (refractive index unit), 34.18 1/RIU, and 56.35, respectively. Thus, the plasmonic sensor is ideal for lab-on-chip in gas and biochemical analysis and can significantly enhance the sensitivity by 177% compared to the regular one. Furthermore, the designed structure can apply in nanophotonic devices, and the range of the detected refractive index is suitable for gases and fluids (e.g., gas, isopropanol, optical oil, and glucose solution).


Simulation model and analysis method
displays the top view of the investigated plasmonic sensor, consisting of a MIM bus waveguide coupled with one square ring-shaped cavity containing sixteen nanorods (with radius r) uniformly distributed in the resonance ring. We indicated the structural parameters in Fig. 1,i.e., the gap distance between the bus waveguide and the square ring-shaped cavity is g, the outer and inner lengths of the square resonator are a and a-2w, respectively. In Fig. 1, the cyan-and yellow-colored regions stand for the silver and insulator medium (air with the refractive index of n = 1.00), respectively. The investigated structure in the z-direction is infinite in the simulations, and this simulation system is a 2-D model. We employed a commercially available FEM (COMSOL Multiphysics 59,60 ) www.nature.com/scientificreports/ with perfectly matched layer (PML) absorbing boundary conditions for soaking up the outgoing light. As a result, the investigated structure's subdomains can partition into triangular mesh elements with an "ultra-fine" mesh grid size. This setting permits us to obtain precise simulation results within the available computer resources. A TM-polarized EM wave coupled with the fundamental SPP mode [61][62][63] into the bus waveguide's input port 64 . In Fig. 1, H z is the magnetic field component in the z-direction, E x is the electric field component in the x-direction, and E y is the electric field component in the y-direction. Silver (Ag) was chosen as the plasmonic material to generate an EM wave response within the near-infrared range since its small imaginary part of the relative permittivity and lower power consumption. The relative permittivity (ε m ) of silver can characterize by the Drude model 65 .
The input and output ports are located at the left and right sides of the designed structure with the same length from the center of the bus waveguide to detect the input and output powers. The transmittance (T) can obtain by T = P out (output power)/P in (input power), where the P out and P in can calculate as integral values of energyflux density. The square ring can act as a Fabry-Pérot cavity, and the resonance will happen when the SPPs are coupled into the ring resonator and fit the resonance condition. For a MIM waveguide-cavity system, the SPPs can be excited when the incident EM wave approaches the intrinsic resonance wavelength (λ res ). If Δφ = 2πN (N is an integer), the λ res can be expressed by temporal coupled-mode theory 66,67 . Here, N denotes the order of the standing wave resonance, L eff represents the effective length of the cavity, φ stands for the phase shift, and Re(n eff ) is the real part of the effective refractive index. n eff can describe as: where k = 2π/λ is the wave vector in the waveguide and k 0 is the wave vector in the free space.
The definition of sensitivity (S) is The figure of merit (FOM) and quality factor (Q factor) are S/FWHM and λ res /FWHM, respectively, where FWHM is the full width at half-maximum of the λ res .
Since the fast progress in nanophotonics, the manufacturing of the investigated structure is attainable with current fabrication technologies, allowing cost-effective fabrication over a large region 68 . The MIM waveguide with a rectangular ring can realize by using stripping and ion beam lithography processes 69 . The Ag nanorods can be made with high aspect ratios by focus ion beam etching 68 . However, the object of this paper is not to concentrate on the fabrication procedures. As an alternative, several potential articles that investigated in-depth of this topic are advised [70][71][72] . Figure 2 compares the transmittance spectrum of the SPPs mode for two waveguide-cavity types, i.e., a bus waveguide coupled to one square air ring (black, denoted as case 1), and a bus waveguide coupled to one square air ring containing sixteen nanorods (with radius r) uniformly distributed in an air ring (red, denoted as case 2). To ensure only the TM mode can travel in the designed structure, the bus waveguide and square ring's widths are w = 50 nm throughout this paper, otherwise specified. The default structural parameters, a, g, b, and r, signify as 300 nm, 10 nm, 50 nm, and 20 nm, respectively. Besides, the difference between the maximum and minimum transmittance is the dip strength (ΔT) 73 . As shown, an apparent discrepancy of the optical spectrum concerning the different resonance modes can clarify this dissimilarity after the silver nanorods exist in the investigated plasmonic waveguide-cavity system. In case 1, only one available transmittance dip corresponding to an SPP mode at λ res = 1376 nm can be observed. This SPP mode is due to the surface plasmon resonance (SPR) and cavity plasmon resonance (CPR) from the coupling effect between the square air ring and the MIM bus waveguide. When the silver nanorods appear in the square air ring, case 2 can generate more SPPs modes because of the enhanced SPR, CPR and GPR effects among the silver nanorods, leading to four available SPPs modes at λ res = 2188 nm, 1258 nm, 1037 nm, and 820 nm, respectively. The interference of surface, cavity, and gap plasmon resonances cause the multiple SPPs modes among bus waveguides, square air rings, and silver nanorods [74][75][76][77][78][79] . We found that the GPR effect plays a pivotal role in offering more plasmon resonance in the investigated waveguide-cavity system. The resonance dip in case 2 has a muscular dip strength and a narrow FWHM, both beneficial to refractive index sensing performance. This remarkable feature has led to possible applications in IOCs.

Results
To understand the physical nature, Fig. 3 shows the steady-state of the magnetic field (|H|) and electric field (|E|) patterns at corresponding λ res from modes 1 to 4. As seen, the standing wave occurs in the square air ring resonator at λ res , and most input EM wave confines in the resonance cavity. The incident wavelength highly  80 . The light spot number of |H| patterns in square air rings are 2, 4, 4, and 6 when the λ res is varied from 2188 nm, 1258 nm, 1037 nm, and 820 nm, respectively. Thus, the square air ring can behave as a Fabry-Pérot cavity in the investigated plasmonic sensor system. According to the |E| field patterns, the SPPs wave can couple well because of the constructive interference between the bus waveguide and the ring resonator, showing significant GPR among the silver nanorods. The |H| and |E| field enhancement of the SPPs modes in the gap space of silver nanorods exhibit an excellent light-matter coupling in the square ring resonator.

Figure 2.
Comparison of the transmittance spectrum of the SPPs modes of two waveguide-cavity types, i.e., a bus waveguide coupled to one square air ring (black, denoted as case 1), and a bus waveguide coupled to one square air ring containing sixteen nanorods (with radius r) uniformly distributed in an air ring (red, denoted as case 2). The structural parameters w, a, g, b, and r are 50 nm, 300 nm, 10 nm, 50 nm, and 20 nm, respectively. www.nature.com/scientificreports/ The investigated case 2 structure can act as a refractive index sensor and inspect by filling a different detecting medium in a plasmonic waveguide-cavity system. Figure 4 shows the transmittance spectra of the case 2 structure with the filling media, n, are 1.00, 1.05, 1.10, 1.15, and 1.20, respectively. The other parameters keep the same as used in Fig. 2. As observed, the transmission dips show a redshift as the increasing refractive index and a linear relationship between the n eff and the λ res , which reveals a good agreement with Eq. (2). The sensitivity's increment is due to the coupling surface and gap plasmon waves between the bus waveguides and square air ring resonator, which leads to an interaction with the variation in the refractive index 81 .
An excellent refractive index sensor should possess a high sensitivity (S) and acceptable FOM and Q-factor. Figure 5 plots the calculated λ res versus the refractive index of the proposed structure. We summarize the S, FOM, and Q factor and dip strength (ΔT) of case 1 for mode 1 and case 2 from mode 1 to mode 4 in Table 1. Note that the sensitivity values obtained from case 2 from mode 1 to mode 3 can simultaneously achieve above 1000 nm/ RIU, which shows excellent sensitivity and acceptable FOM and Q factor. Compared to its typical structure (case  www.nature.com/scientificreports/ 1), the case 2 structure remarkably enhanced the sensitivity by 157%. These values are more noticeable than the previous literature (e.g., [82][83][84] ) and show multiple modes that can fit the requirement of refractive index sensors in the wavelength of visible and near-infrared. The SPPs modes arising from the case 2 structure are due to the coupling effect between bus waveguide and square ring resonator, significantly influenced by the structural size. In case 2 frame, w is fixed at 50 nm to promise that the TM mode can propagate in the bus waveguide. Therefore, in our simulations, we further inspect the other four parameters, i.e., g, b, a, and r. First, Fig. 6a,b depict the influence of g and b of the case 2 structure on the transmittance spectrum. Figure 7a,b also illustrate the dip strength (∆T) and FWHM of the proposed case 2 structure in mode 1 and 2 for varying g and b, respectively. We numbered the available resonance modes in the inset of the figures and listed the structural parameters at the top of the figures. As observed, the transmittance dips blueshifts with the increasing g and b. The transmittance profiles have different behaviors to the change of g and b since their different physical nature. In Fig. 6a, the coupling effect between bus waveguide and sidecoupled resonator becomes weaker because of the increase of g. Note that the transmittance dips show a strong oscillation since the more substantial coupling effect when g = 0 nm. Besides, the transmittance dip strength (∆T) and FWHM can significantly reduce with the increase of g due to the more negligible coupling effect of a  Successively, we show the variation influence of a and r on the transmittance spectrum in Fig. 8a,b, respectively. As shown, the λres redshifts with increasing of a and r. Specifically, the shift of λ res by varying a and r is more sensitive than that of g and b, e.g., λ res changes from 992 to 3200 nm for mode 1 when a varies from 150 to 400 nm, and λ res varies from 1046 to 2948 nm for mode 1 when r varies from 0 to 23 nm, correspondingly. It is evident from Fig. 8a, a more significant a can provide a longer optical path and results in a more GPR effect among silver nanorods in the square air ring cavity. However, a strong coupling effect causes a shortcoming of broad FWHM since the more indirect coupling strategy could give rise to a more ohmic loss in the resonator influenced by the silver nanorods. Accordingly, it is a bargain between a slender FWHM strength and a more muscular dip strength. When a ≥ 300 nm, FWHM increases and declines the FOM. Therefore, we selected a = 300 nm as the starting pointing of the further study. The air gap among adjacent silver nanorods can alter the resonance condition and offer a different optical path in the square air ring cavity. In Fig. 8b, the GPR in the resonator gets more substantial with the increasing of r. This phenomenon is that the balance of strength of the discrete state in the resonator and the continuum state in the bus waveguide can change by varying r, the resonance modes are changed. The FWHM can significantly enlarge with the increasing r since the GPR mode is enhanced by increasing r in the resonator. As a result, the optimum coupling effect is achieved at r = 20 nm based on FWHM and ∆T, as shown in Fig. 8b.
Based on the case 2 structure analysis, we found the coupling effect between the bus waveguide and the side-coupled resonator will enhance by generating more GPR effect inside the coupled resonator. To increase the coupling effect and gap plasmon resonance, we proposed a case 3 structure, i.e., the second air ring is added in the case 2 structure. Figure 9 shows the top view of the proposed case 3 structure, containing a MIM bus waveguide coupled with two square ring-shaped cavities with sixteen and eight silver nanorods (with radius r) uniformly distributed and second rings, respectively. The structural perimeters are signified in Fig. 9, i.e., the space between the first and second rings is c, the gap between the bus waveguide and the first square ring cavity is g, the outer lengths of the first and second square rings are a and a-2b-2c, while the inner lengths of first and second square rings are a-2b and a-4b-2c, respectively. For simplicity, we do not discuss the influence of the c value on the plasmonic responses but directly give the optimized value, which is c = 10 nm for the case 3 structure. The rest structural parameters, w, g, r, a, b, are set as 50 nm, 10 nm, 20 nm, 300 nm, and 50 nm. Figure 10 shows the transmittance spectra of case 3 structure at different ambient medium, i.e., air (n = 1.00), water (n = 1.33), isopropanol (n = 1.37) and optical oil (n = 1.63), respectively. This range of detecting fluids is associated with the biological sample analytes. The fluids are located on the entire structure's upper surface in the refractive index sensing process and consider the infinite thickness. It is evident in Fig. 10a that a remarkable redshift of transmittance dip with the increase of the ambient refractive index. Figure 10b illustrates the λ res versus the refractive index value (n) from 1.00 to 1.63 of case 3 structure from mode 1 to mode 4. We found a redshift of λ res with increases n in the refractive index range of gas and liquid. Figure 10c depicts the S and FOM of case 3 structure from mode 1 to mode 4 and shows a more massive shift in mode 1 than the other modes.
We summarized the calculated S, FOM, and Q factor of case 3 structure from modes 1 to 4 in Table 2. The sensitivity obtained from modes 1 to 3 of case 3 configuration simultaneously exceeds 1160 nm/RIU, revealing more excellent sensitivity, acceptable FOM, and Q factor than cases 1 and 2 frames. The proposed case 3 structure www.nature.com/scientificreports/ can significantly improve 177% and 112% sensitivity compared to cases 1 and 2. Furthermore, the combination of the first and second square air rings, including the silver nanorods in case 3 structure, offers a better sensing performance, as shown in Fig. 10b,c and Table 2. In addition, a more quantity of detecting medium can participate in the case 3 structure due to the longer optical path, resulting in more GPR and SPR effects and enhancing the cavity plasmon resonance in the resonator. Therefore, it will significantly benefit the interaction between the testing sample and the proposed plasmonic sensing system. When the fluid is resonant with the case 3 structure, the transmittance spectrum varies with the refractive index increase, showing an excellent exciton-plasmon coupling and generating a deep bonding mode based on GPR in the resonator. This phenomenon can interpret by the magnetic field intensity (|H|) (including the surface electric force lines (green lines), Fig. 11), electric field intensity (|E|, Fig. 12), and time-average power flow (green lines) with arrows (red arrows) (Fig. 13), respectively. Figures 11, 12, 13 show the occurrence of resonant fluids (e.g., n = 1.33 as an example) around the case 3 structure from modes 1 to 4. The cavity resonance in case 3 structure is highly sensitive to the changes in the refractive index. The presence of fluids affects the fluid-field interaction and the spatial distribution of the E-field intensity and the power flows (time average, W/m 2 ) across the interface between bus waveguide and resonator of the case 3 structure. Concerning the electric force lines and the power flow arrows, as shown in Figs. 11 and 13, it raises a robust EM Feld localization and enhancement (see Fig. 12) and the power flows in the first and second square air rings. As a result, the effect of the accumulated GPR at λ res meets the Fabry-Pérot resonance condition and forms a strong cavity resonance in the side-coupled resonator. Besides, the EM waves and energy flows show that the enhanced surface plasmon among the gaps of silver nanorods, revealing a broad range of interactions with analytes, thereby demonstrating the potential of the case 3 structure for sensing applications.
The recorded sensitivity and FOM in the case 3 structure are superior to those of previous MIM-cavity systems. We summarize S and FOM comparing this work and other reported similar SPR sensors in Table 3. where c g is the glucose concentration (g/L). Equation (5) elucidates the linear relationship between the n g and λ res . Figure 14a reveals the transmittance spectrum of the glucose solution in case 3 structure from modes 1 to 4 when the glucose concentration, c g , varies from 0 g/L, 100 g/L, 200 g/L to 300 g/L, respectively. The structural parameters are the same as Fig. 10a. As observed, the λ res of the transmittance dips exhibits a redshift and all curves show the linear relations with c g , which is good agreement with Eq. (5). Figure 14b shows the approximately linear relationships between the c g and the λ res . Thus, the sensitivity of glucose solution sensing is S g = ∆λ/∆c g . In these cases, the obtained sensitivity from modes 1 to mode 4 can reach 0.19 nm·L/g, 0.16 nm·L/g, 0.14 nm·L/g and 0.14 nm·L/g from modes 1 to mode 4, respectively.

Conclusion
This study proposed a plasmonic sensor based on a side-coupled resonator in a MIM-cavity waveguide system for refractive index and biomedical sensor applications. We scrutinized and compared three patterns of resonators, i.e., case 1 (one square ring), case 2 (one square ring with silver nanorods), and case 3 (double square rings with silver nanorods), respectively. The designed structure's EM field distributions and transmittance spectra are studied using 2-D FEM for resonance mode analysis and sensing capability characterization. Results show that the suggested case 3 structure greatly contributes to gap plasmon resonance modes for improving sensing performance. The case 3 structure can significantly improve the sensitivity by 177% compared to its traditional design (i.e., case 1). The best sensitivity and FOM of the sensing devices in mode 1 are 1400 nm/ RIU and 14.00 1/RIU for case 1, 2200 nm/ RIU and 40.00 for case 2, and 2473 nm/ RIU and 34.18 for case 3, respectively, while the maximum recorded Q factor are 13.76, 41.48 and 56.35 for case 1, 2, and 3, respectively. This sensor can widely use in gas and biochemistry since its ease of preparation, excellent sensing performance, and broad working wavelengths with multiple modes.
(5) n g = 0.00011889 × c g + 1.33230545 Figure 9. Top view of the proposed case 3 structure, consisting of a MIM bus waveguide side-coupled with two square ring-shaped cavities with sixteen and eight silver nanorods (with radius r) uniformly distributed in the first and second rings, respectively. The structural perimeters are in the figure, i.e., the space between the first and second rings is c, the gap between the bus waveguide and the first square ring-shaped cavity is g, the outer length of the first and second square rings are a and c, while the internal size of first and second square rings are a-2b and a-2b-2c, respectively.     Table 3. Comparison of the best sensitivity and FOM between this work and some selected published articles. P. S. FOM* = max(|dT(λ)/dn(λ)/T(λ) |), where T (λ) is the transmittance, and dT(λ)∕dn(λ) is the transmittance change at a fixed wavelength induced by a refractive index change. Reference