Introduction

Surface plasmon polaritons (SPPs) are electromagnetic (EM) wave coupled to the collective oscillations of free electrons on the metal surface and propagate between the metal-dielectric interface [1–8]. Plasmonic metal-insulator-metal (MIM) waveguide, one of the SPP waveguide schemes, has received fascinated attentions because of its attractive features, such as bonding strongly localized surface plasmon resonance (SPR), overcoming diffraction limit in conventional optics, low propagation loss, simple manufacturing steps, and compatible integration optics circuits (IOCs) [5, 9–15]. Therefore, a variety of functional plasmonic components utilizing MIM waveguides have been designed experimentally and demonstrated theoretically, such as sensors [16], all-optical switches [17], splitters [18], modulators [19], demultiplexers [20], filters [21], interferometers [22], etc. A plasmonic MIM waveguide consists of the cavities (i.e., resonators) and the bus waveguides [7, 11, 17, 20, 23–31]. The MIM waveguides’ cavities greatly impact the SPP modes and resonance conditions because they can support an excellent mechanism for achieving wavelength and sensing selective. In other words, the SPR, cavity plasmon resonance (CPR), and gap surface plasmon resonance (GPR) properties of the plasmonic cavity-waveguide system pick out the specific operating wavelength which required exactly [1, 9, 32–37].

In SPP sensors, the resonance modes generate in the bus waveguide coupled with the cavity under satisfying the Fabry–Pérot resonance condition. The SPP 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 [38–40]. Recently, several MIM waveguides with different shape of cavities have 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 [50–53] possess the advantage of hybrid SPR, CPR, and GPR modes in a plasmonic nanostructure system and are less discussed in the plasmonic MIM-cavity system. This paper numerically investigated the optical properties of a multi-mode 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 (e.g., a glucose sensor). The resonance wavelength-shift features of resonant modes in the BT-shaped cavity inspected by the temporal coupled-mode theory are verified [54]. 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 effects 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 IOC construction.

Structure and Basics

Figure 1 shows the schematic two-dimensional (2D) plot of the proposed plasmonic refractive index sensor that consists of two bus waveguides (width w) and four coupled BT cavities (bottom length L = 6w and height H = 5w) containing two pairs of silver baffles in the BT cavities. We termed the Ag baffles as pair 1 in x-direction and pair 2 in the y-direction. The length and width of the bigger Ag baffles in pair 1 and pair 2 are 3w and 2w, while the length and width of the smaller Ag baffles in pair 1 and pair 2 are set the same value of w. The center to center distance of bigger and smaller Ag baffles is fixed as 2w. The gap distance between the coupled cavities and the bus waveguides is set as g, while the gap distance among four BT cavities is d. Simulations were performed by a 2D FEM using COMSOL Multiphysics [34, 55] with perfectly matched layer absorbing boundary conditions for absorbing outgoing EM waves surrounding the input and output ends. Besides, scattering boundary conditions (SBC) are used at the FEM simulation window’s outer edges. It should be noted that a 3D simulation model is simplified to a 2D one because the similar results will be obtained from both models in simulations [40, 56] and experiments [37, 57]. Besides, the 2D simulation can shorten the working time and reduce the required computer resources, without losing the precision [58, 59]. In COMSOL simulations, the proposed structure’s subdomains are divided into triangular mesh elements with a fine mesh grid size for the MIM-cavity waveguide geometries. This setting permits us to achieve accurate calculation results within the available computer resources.

Fig. 1
figure 1

Schematic 2D diagram of the proposed plasmonic refractive index sensor consisting of two bus waveguides (width w), four coupled BT cavities, including two pairs of Ag baffles in the BT cavities

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A TM-polarized incident EM wave is coupled with the fundamental SPP mode [60] 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) [61, 62]. 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 [63]

$${\varepsilon }_{\mathrm{m}}\left(\upomega \right)={\varepsilon }_{\infty }-\frac{{\omega }_{\mathrm{p}}^{2}}{{\omega }^{2}+i\omega \gamma }$$
(1)

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 × 1016 rad/s, and γ (the electron collision frequency concerning loss) = 18 meV = 2.7 × 1013 rad/s. The resonance wavelength (λres) can be obtained from the temporal coupled mode theory [64]. 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.

$${{\lambda }_{\mathrm{res}}=\frac{{2\ell}_{\mathrm{eff}}{Re(n}_{\mathrm{eff}})}{j-\frac{\varphi }{2\pi }} (j=\mathrm{1,2},3\dots )}$$
(2)

Re(neff) represents the real part of the effective refractive index obtained from the dispersion equation [65].

Furthermore, sensitivity (S) and figure of merit (FOM) are potential characteristics extensively used to evaluate the sensor performance. The definition of sensitivity is S = Δλ/Δn nanometer per refractive index (nm/RIU), where Δλ is the shift of the resonant wavelength of transmittance, λres is the resonant wavelength at transmittance peak, and Δn is the change in the refractive index of the medium in the space of bus waveguides and BT cavities. The figure of merit (FOM) and quality factor (Q factor) can be defined as S/FWHM and λres/FWHM, respectively, where FWHM is the full width at half-maximum of the transmittance peak.

The fabrication of the proposed plasmonic structure is attainable with prevalent nanotechnologies, such as e-beam lithography, electron-beam deposition, thermal evaporation, and chemical etching. It is well known that the e-beam lithography will enable to create the BT and the baffles and then deposit the silver. The other feasible method can deposit Ag’s thin layer on a silica substrate utilizing E-beam deposition or thermal evaporation, which can inscribe desired patterns [66, 67]. To fabricate MIM bus waveguides, we can remove Ag metal’s unwanted parts using chemical etching [27, 68-70].

Simulation Results and Discussions

First, we compare the transmittance spectrum of the SPP mode for two cavity configurations, i.e., the BT cavities excluding and including the Ag baffles as shown in Fig. 2. The structural parameters and the related sizes are denoted in Fig. 1. The initial values w, g, and d are 50 nm, 10 nm, and 10 nm, and air (n = 1) is used as a medium in the bus waveguides and BT cavities. Note that the bus waveguide width (w) is set as 50 nm to ensure that the fundamental mode can be excited in the bus waveguide. The proposed plasmonic sensor can function as band-pass and band-stop filters, limiting and prohibiting propagating specific incident EM wave wavelengths. An apparent discrepancy after the Ag baffles is 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, the two cases’ transmittance spectrum shows discrete peaks and behaves as a multiple-mode plasmonic filter, leading to the EM wave that can be transmitted at the resonance wavelength (λres). The transmittance reached a peak value when the SPP modes satisfied the resonance condition in the BT cavities. There are four transmittance peaks found at λres = 823 nm, 731 nm, 609 nm, and 494 nm (denoted by mode 1 to mode 4, hereafter) for the case excluding Ag baffles and four modes at λres = 1121 nm, 888 nm, 654 nm, and 525 nm for the case including Ag baffles, respectively. It is evident that the transmittance peaks of the case excluding Ag baffle are weaker than the case including Ag baffles, i.e., the case including Ag baffles reveals better light-matter interaction than the case excluding Ag baffle. Besides, the working wavelengths of the case excluding Ag baffle exist in the visible wavelength range.

Fig. 2
figure 2

Transmittance spectra of the proposed plasmonic sensor excluding (black color) and including (red color) Ag baffles in the BT cavities

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In contrast, the Ag baffle case’s working wavelengths can be reshifted to visible and infrared. These results can be ascribed to the different degree of resonant modes that occurred in the BT cavities. It can be interpreted from Eq. (2) that λres is closely related to neff and ℓeff of the BT cavities. Ag baffles in the BT cavities can generate a larger neff and increase λres (i.e., redshift).

To explain the physical mechanism, Figs. 3 and 4 show the steady state of the magnetic field (|H|) and electric field (|E|) distributions of the case excluding Ag baffles (Figs. 3a–d and 4a–d) and including Ag baffles (Fig. 3e–h and 4e–h) in the BT cavities at corresponding λres from mode 1 to mode 4, respectively. The BT cavities can regard as the Fabry-Pérot cavities, i.e., optical waves can pass through the optical cavities only when resonating with it. The inclusion of Ag baffles in BT cavities allows the strong confinement of SPPs formed among the gaps of Ag baffles and BT’s sharp tips, as shown in Figs. 3 and 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 Figs. 3 and 4 that the SPP wave is coupled to the BT cavities well at λres, which can form the standing-wave patterns between the bus waveguide and the BT cavities. The |E| profiles as shown in Fig. 4a–h exhibit standing wave-like EM wave patterns on the surface of Ag baffles and Ag wall of BT cavities with a remarkable field enhancement since the hybridization of SPR, GPR, and CPR [71, 72]. Ag baffles’ case facilitates the stronger SPP mode confinement on the metal surface than the case excluding Ag baffles due to the GPR. The gap regions formed in BT cavities are among the Ag baffles and the wall of BT cavities. High sensitive SPP modes can confine among the gap. As shown in Fig. 4a–h, the electric field intensity can reach its maximum value at the gap regions and sharp edges. SPPs modes in the BT cavities have substantial field enhancements and can constrain the EM waves to the nanometer scale. This critical observation implies that the gap and cavity plasmon resonances can significantly contribute to the field enhancement in the proposed plasmonic BT cavity system including the Ag baffles.

Fig. 3
figure 3

Truncate views of magnetic field intensity (|H|) of (a–d) the case excluding Ag baffles and (e–h) including Ag baffles in the BT cavities at corresponding resonance wavelengths from mode 1 to mode 4, respectively

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Fig. 4
figure 4

Truncate views of electric field intensity (|E|) of (a–d) the case excluding Ag baffles and (e–h) including Ag baffles in the BT cavities at corresponding resonance wavelengths from mode 1 to mode 4, respectively

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Figures 3 and 4 provide high confinement of |H| and |E| field distributions of SPP mode in the narrow region between BT cavities and Ag baffles. Consequently, the neff of the mode increases and is highly responsive to the surrounding medium. When the proposal plasmonic sensor system includes the testing medium, the neff of the bus waveguide and BT cavities is changed. Therefore, λres experiences a redshift. SPP modes are highly sensitive to the variation of the surrounding refractive index, which will change λres, intensity, or phase. Based on Fig. 2, we can use the proposed structure as a refractive index sensor. We can fill the testing medium in the bus waveguides and BT cavities with the different refractive index. Figures 5a, b compare the proposed plasmonic sensors’ transmittance spectra excluding and including Ag baffles in the BT cavities. The refractive index of the test medium, n, is set to be 1.01, 1.03, 1.13, and 1.15, respectively, and other ranges of refractive index values have the same trend of transmittance spectrum. The other structural parameters, w, and g are 50 nm and 10 nm, respectively. As seen in Fig. 5, both cases’ transmission peaks redshift with the increasing refractive index due to the rising neff in the BT cavities, giving a linear relationship between wavelength shift with n of the medium being tested. This result is in good agreement with Eq. (2). The increasing redshift is because of the enhancing EM wave in a BT cavity, mostly interacting with the refractive index change. Since there is a hybridization of the SPR, GPR, and CPR modes in the BT-cavity waveguide system, a little refractive index change (∆n) leads to a remarkable λres shift.

Fig. 5
figure 5

Transmittance spectra of the proposed plasmonic sensors (a) excluding and (b) including Ag baffles in the BT cavities. The test medium’s refractive index, n, is set as 1.01, 1.03, 1.13, and 1.15, respectively. The other structural parameters, w and g, are 50 nm and 10 nm, respectively

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Figure 6 shows the calculated resonance wavelength (λres) versus the refractive index (n) of the cases including Ag baffles in the BT cavities. As seen, there is a linear relationship between λres and n. The λres increases linearly by varying the refractive index, and we can see an apparent redshift. A small variation of n can lead to an enormous shift in λres. A redshift of λres with the increase in the value of n is most significant for mode 1 compared with other modes. Consequently, the value of n can obtain from λres based on its linear relationship obtained from Eq. (2). This result demonstrates the characteristics of the sensing function of our proposed structure as a refractive index sensor. We can summarize the S and FOM of the case excluding and including Ag baffles from modes 1 to 4 in Table 1.

Fig. 6
figure 6

Calculated resonance wavelength (λres) from mode 1 to mode 4 for the cases including Ag baffles versus refractive index (n)

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Table 1 The S and FOM of the case excluding Ag baffle and the case including Ag baffles in BT cavities from mode 1 to mode 4
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Compared with the case excluding Ag baffle, Ag baffles’ existence in the BT cavities generates an increase of device’s sensitivity by 57.14% for mode 1 and 28.57% for mode 2, correspondingly. Note that a very sharp transmittance peak (i.e., high resolution or narrow FWHM) can be seen in Fig. 4b, yielding a high Q factor. The calculated average Q factors are 28.02, 98.67, 109.00, and 105.00 in modes 1 to 4 of the case including Ag baffles. The proposed structure with the features of high sensitivity, FOM, and Q factors can transfer the desirable wavelength-noise-limited performance, which is attributed to the sharp transmittance peaks and results in acceptable spectral resolution.

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 [73]. Next, we will inspect the impact of structural parameters on sensitivity and figure of merit from mode 1 to mode 3, summarized in Tables S1, S2, and S3 in supplementary information and Table 2, respectively. As observed in Tables S1, S2, and S3, 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 to 100 nm. The Ag baffles’ 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 2, 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 3 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 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 nm, g = 10 nm, and d = 10 nm, respectively
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Table 3 Comparison of the sensitivity and FOM between this work and some other published works
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Application as a Glucose Sensor

Comprehending optical features of liquid (e.g., water or glucose) is considerable for solving problems in medical optics and biosensors. As a result, the SPPs could be 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 analyte sensing [79, 80]. The SPP modes in the proposed plasmonic MIM BT cavity sensor system are a promising candidate for efficiently inspecting the glucose value [81]. In the simulations, we can describe the refractive index of the glucose solution as [46, 82]:

$${n}_{\mathrm{g}}= 0.00011889\times {c}_{\mathrm{g}}+ 1.33230545$$
(3)

cg denotes the glucose concentration (g/L) and ng represents the glucose concentration's refractive index. Equation (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. 5b. As shown in Fig. 7, the λres are red-shifted with the increasing cg. In these cases, the calculated sensitivity from 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 Figs. 6 and 8.

Fig. 7
figure 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. 5b

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Fig. 8
figure 8

Calculated resonance wavelength (λres) from mode 1 to mode 4 versus the glucose concentration (cg) in the range from 0 to 240 g/L

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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 raise the sensitivity by 57.14% for mode 1 compared with its counterpart excluding Ag baffles. Variation of the baffle’s width (see Table 2) results in the appearance of remarkable resonance 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.