Multiple-mode bowtie cavities for refractive index and glucose sensors working in visible and near-infrared wavelength range

A multiple-mode metal-insulator-metal plasmonic sensor with four coupled bowtie resonators containing two pair of silver baffles is numerically investigated using the finite element method and verified by the temporal coupled-mode theory. The proposed structure can function as the plasmonic refractive index and glucose sensors working in visible and near-infrared wavelength range. Simulation results show that introducing the silver baffles in bowtie cavities can modify the plasmon resonance modes and give a tunable way to enhance the sensitivity and figure of merit. The highest sensitivity (S) can reach S =1500.00, 1400.00, and 1100.00 nm/RIU and the high figure of merit (FOM) of 50.00, 46.67, and 36.67 RIU -1 from mode 1 to mode 3. The sensitivity obtained from three modes with operating wavelengths in visible and near-infrared simultaneously exceeds 1100.00 nm/RIU along with remarkably high FOM, which are not attainable from other reported literature. The proposed structure can realize multi-mode and shows impressive practical prospects that can be applied for integrated optics circuits (IOCs) and other nanophotonics devices.

In SPPs sensors, the resonance modes generate in the bus waveguide coupled with the cavity under satisfying the Fabry-Pérot resonance condition. The SPPs wave can be reflected back and forth in the cavity, which is highly sensitive to the refractive index's change in the bus waveguide and the cavity's geometrical shape. Resonators (or cavities) with different structural configurations undergo a potential role in generating a better light-matter interaction in the MIM-cavity waveguide system [38][39][40]. Recently, several MIM waveguide with different shape of cavities has been proposed and investigated for the plasmonic sensor, such as rectangular/circular ring cavity [41], tooth-shaped cavity [42], trapezoid cavity [43], ring cavity with metal baffles [44], asymmetric double elliptic cylinders [45], Bragg grating cavity [46], fillet cavity [47], metallic nanorods in hexagonal configuration [48], stub coupled with a square cavity [49] and so forth.
One of the cavity schemes is the bowtie (BT) shaped resonator, which has an excellent light-matter coupling between the incident EM wave and nanostructures. For example, BT nanoantennas [50][51][52][53][54], which possesses the advantagement of hybrid SPR, CPR and GPR modes in a plasmonic nanostructure system, and is less discussed in the plasmonic MIM-cavity system. This paper numerically investigated the optical properties of a multimode waveguide configuration consisting of two MIM bus waveguides connected with the centrally coupled BT cavities containing the silver (Ag) baffles. The finite element method (FEM) systematically simulates BT cavities' resonance modes in the proposed structure. We focus on the flexible optical characteristics of this plasmonic sensor structure for sensing applications. The resonance wavelength-shift features of resonant modes in the BT-shaped cavity inspected by the temporal coupled-mode theory are verified [55]. The calculated transmittance spectra have also been investigated by analyzing the magnetic and electric field's spatial distributions at the resonant wavelengths. The sensitivity analysis of the SPP modes is calculated for two cavity schemes, i.e., the BT cavities excluding and including the Ag baffles. The influence of the geometrical dimension and coupling distance corresponding to the transmittance features was also calculated. The effect of the structural parameters' variation on its sensing characteristics, refractive index sensitivity, figure of merit and quality factor are calculated. The proposed device sensor can achieve multiple modes working in visible and infrared and could be used as practical nanophotonic devices that functionally perform as chemical sensors and biosensors. This study suggests a promising design strategy and improves the plasmonic sensors on the nanoscale and examines their performance before realizing to time-consuming and expensive IOCs construction. A TM-polarized incident EM wave is coupled with the fundamental SPP mode [57] into the bus waveguide's input end. The transmittance (T) can be described as T = (S21) 2 , where S21 is the transmittance. In a real situation, the incident EM wave can be coupled into the bus waveguide by photonic crystal fiber (PCF) [58,59] . Confocal Raman Microscopy can measure the output EM wave. The frequency-dependent complex relative permittivity εm of silver can calculate using the Drude model as [60].

Structure and basics
Where ε∞ (the dielectric constant at the infinite angular frequency)=3.7, ω is the angular frequency of incident light, ωp (bulk plasma frequency)=9.10 eV=1.38×10 16 rad/s, and γ (the electron collision frequency concerning loss)=18 meV =2.7×10 13 rad/s. The resonance wavelength (λres) can obtain from the temporal coupled-mode theory [61]. When the SPPs propagate through the proposed structure, they will be confined in the cavity to produce an oscillation. The cavity including Ag baffles can play as a Fabry-Pérot cavities. The gathered phase change per cycle in the cavities can be expressed as Δφ=4πneffℓeff/λ+φ, where neff is the effective refractive index of the SPPs, ℓeff is the effective lengths of cavity, φ is the phase shift generated from the reflection at the metal-dielectric interface in the cavity, respectively. If Δφ = 2πj (j is an integer), the resonance wavelength λres of the cavity can be described by temporal coupled-mode theory.
Re(neff) represents the real part of the effective refractive index obtained from the dispersion equation [62].

Simulation results and discussions
First, we compare the transmittance spectrum of the SPPs mode for two cavities configurations, i.e., the BT cavities excluding and including the Ag baffles as shown in propagating specific incident EM wave wavelengths. An apparent discrepancy after the Ag baffles are included in the plasmonic BT-cavity waveguide system, and the different resonance modes formed in the BT cavities can explain this difference. In Fig. 2  sharp tips, as shown in Fig. 3 and Fig. 4. In Fig. 3, the |H| field intensities show strong field confinement inside the BT cavities, a magnetic dipole resonance feature. In contrast, the |E| field intensities can enhance at the edge and sharp surface of the Ag nanometals, showing a signature of electric field dipole resonance (see Fig. 4). It is worth noting that the |H| and |E|field profiles offer different distribution patterns in the BT cavities depending on the different incident wavelengths at λres. It is evident from Fig. 3 and Fig.   4 that the SPPs wave is coupled to the BT cavities well at λres, which can form the standing-      correspondingly. Note that a very sharp transmittance peak (i.e., high resolution or narrow FWHM) can be seen in Fig. 4( The transmittance features of the proposed plasmonic sensor system can be affected by its structural parameters by changing the size of structural parameters, leading to a variation of ℓeff and neff. The resonance wavelength will be changed to keep the phase match condition if the resonant cavity's environment is varied [70]. Next, we will inspect the impact of structural parameters on sensitivity and figure of merit from mode 1 to mode 3, summarized in Tables 2, 3, 4, and 5, respectively. As observed in Table 2, 3, and 4, the influence of coupling distance between bus waveguides and BT cavities (g), bottom length of the BT cavity (L), and coupling distance among each BT cavity (d) appears to have little influence on sensitivity performance. At the same time, the FOM exhibits a different value because of the different FWHM. It is worth noting that the variation of Ag baffle's size (i.e., x-direction width of pair 1 and y-direction width of pair 2) can significantly improve the sensitivity when their size increases from 20 nm to 100 nm. The Ag baffles's size plays a potential role in enhancing EM waves in the narrow region of the BT cavities. Simulation results (not shown) reveal that λres redshifts with the increased baffle's size, which results in a higher sensitivity to the variation of baffle's size than the other structural parameters (i.e., g, L and d). In Table 5, The highest sensitivity can achieve S=1500.00, 1400.00, and 1100.00 nm/RIU along with the high FOM= 50.00, 46.67, and 36.67 RIU -1 from mode 1 to mode 3, respectively. These results offer the highest mode sensitivity since the large shift of λres when exposed to a little variation in the medium refractive index. The sensitivity obtained from mode 1 to mode 3 can simultaneously reach above 1100.00 nm/RIU in the wavelength range of visible and near-infrared that is considerably greater than that of previously reported sensor designs. Note that a suitable modifying of the Ag baffle's size in the BT cavities can dramatically increase the sensitivity and FOM of the proposed structure excluding increasing the BT cavity size. Table 6 summarizes the comparisons among several published sensitivity and FOM values for diverse MIM-based sensor designs. The high quantity of sensitivity attained in the proposed structure gives a path toward optical on-chip sensors. Table 2 The influence of coupling distance between bus waveguides and BT cavities (g) on sensitivity and figure of merit from mode 1 to mode 3. The other structural parameters referred to Fig. 1 are set as w=50 nm and d=10 nm, respectively.  Table 3 The influence of bottom length (L) of the BT cavity on sensitivity and figure of merit from mode 1 to mode 3. The other structural parameters referred to Fig. 1 Table 5 The influence of each baffle's size (i.e.,x-direction size of pair 1 and y-direction size of pair 2) on sensitivity and figure of merit from mode 1 to mode 3. The other structural parameters referred to Fig. 1 are w=50

Application as a glucose sensor
Comprehensing optical features of liquid (e.g., water or glucose) is considerable for solving problems in medical optics and biosensors. As a result of the SPPs could resonant at varied wavelengths due to their changing of refractive index. For nano-medicine applications, it is crucial to develop a sensor structure to monitor the glucose concentrations. With the capability to detect the refractive index's little changes, plasmonic sensors can serve as various biomedical analytes sensing [76,77]. The SPPs modes in the proposed plasmonic MIM BT cavity sensor system are a promising candidate for efficiently inspecting the glucose value [78]. In the simulations, we can describe the refractive index of the glucose solution as [46,79]: cg denotes the glucose concentration (g/L), and ng represents the glucose concentration's refractive index. Eq. (3) describes the linear relationship between the cg and ng. A relationship can be built between ng and λres through FEM simulations since the variation of λres also varies the ng. Figure 7 depicts the transmittance spectrum of the solution of mode 1 to mode 4 when the glucose concentration, cg, varies from 0 g/L, 120 g/L to 240 g/L, respectively. When the cg increases, the ng increases from 1.33230545 to 1.36083905 based on Eq. (3). As seen, all curves reveal the linear relations with cg. For comparison, the structural parameters are the same as those used in Fig. 5(b). As shown in Fig. 7, the λres are red-shifted with the increasing cg. In these cases, the calculated density for mode 1 to mode 4 can reach S=1100, 900, 600, and 500 nm/RIU, respectively, which are in good agreement with the results obtained from Fig. 6. Fig. 7 Transmittance spectrum of the solution of mode 1 to mode 4 when the glucose concentration, cg, varies from 0 g/L, 120 g/L to 240 g/L, respectively. For comparison, the structural parameters are the same as those used in Fig. 5(b).

Conclusion
This study proposes a new design strategy of a plasmonic sensor with multi-mode based on MIM-BT cavity configuration working in visible and infrared for refractive index and glucose sensing applications. Finite element method was used to simulate the influence of the BT cavities' geometrical parameters on the fine structure of transmittance spectra and sensor performance. Ag baffles in BT cavities can effectively adjust multiple resonant modes, which considerably raises the sensitivity by 57.14% for mode 1 compared to its counterpart excluding Ag baffles. Variation of the baffle's width (see Table 5) results in the appearance of remarkably resonances wavelength shift towards longer wavelength, which provides the highest mode sensitivity since the large change of resonance wavelength when exposed to a little variation in the medium refractive index. This research offers the theoretical foundation for comparing designs for guided nanostructures that enable the measurement of a wide variety of refractive index medium and analytes. The high sensitivity of 1500 nm/RIU and FOM of 50.00 RIU -1 can be achieved.
We believe that the proposed structure can find significant applications in the future optical sensing domain.

Conflicts of interest/Competing interests:
The author declares that has no conflict of interest.
Availability of data and material: All the data and material are in the manuscript.