Introduction

Surface plasmon polariton (SPP), the electromagnetic waves trapped on dielectric-metal interfaces, has attracted much research attention due to its unique properties of overcoming the traditional diffraction limit [1,2,3,4,5,6]. In the past few decades, SPPs supported by metal–insulator-metal waveguide (MIMW) have been proposed and investigated widely, a large number of MIMW structures with various resonant resonators have been investigated numerically and theoretically [7,8,9,10,11,12]. For example, Fan et al. studied Fano resonance in MIM waveguide coupled with a Taiji resonator, and a maximal sensitivity of 0.245 nm·L / g is achieved for glucose solution sensing [13]. A vertically racetrack-ring resonator was introduced in MIM waveguide by Volkov et al. [14]. A plasmonic Fano resonance filter with FWHM (full width at half maximum) only 5 nm [15].

Fano resonance, initially realized in an atomic system, was first proposed by Ugo Fano in 1961, has potential application in sensors since its sensitivity to the surrounding environment [16,17,18,19,20,21,22,23]. In the past decade, the independent tunability of Fano resonance has attracted lots of attention since its advantage in plasmonic device design [24,25,26,27,28]. However, it is difficult to develop a multiple Fano resonance with independent tunability. Therefore, there is still a need for developing multiple Fano resonances with a simple structure and independent tunability.

The combination of a connected ring resonator and a defective ring resonator into a MIM waveguide structure has been not investigated before. There is no report on the connected ring resonator and defective ring resonator coupling with MIM waveguide for quintuple Fano resonances, which has great potential for multi-channel plasmonic sensing. In this paper, a novel structure has been proposed to design a RI sensor and glucose solution concentration sensor. The structure is composed of a DRR, a CRR, and a middle-air rectangular resonator. The quintuple Fano resonances are attributed to the interference between the bright modes (supported by DRR and CRR) and the dark modes (supported by the middle air rectangular resonator). The position of the FR peaks can be tuned independently by changing different geometrical parameters. The designed quintuple Fano resonance can work as an excellent sensor, a refractive index sensitivity of about 1085 nm/RIU and a glucose solution sensitivity of about \({0}{\text{.136}}nm \cdot L/g\) are obtained. The results of this paper may have potential applications in on-chip plasmonic nanosensors and slow light [29,30,31,32,33,34,35,36].

Geometry and Simulation Method

The proposed quintuple Fano resonance is schematically depicted in Fig. 1, which consists of a MIM waveguide coupled with a CRR (a central air path is located in the middle to connect the ring resonator), a DRR is located on the other side of the MIM waveguide. The grey and white parts in Fig. 1 represent Ag and air, respectively. Silver is used as metal material in the structure and its refractive index can be calculated by the Drude model [37, 38]:

$$\varepsilon_{{\text{m}}} (\omega ) = \varepsilon_{\infty } - \frac{{\omega_{p}^{2} }}{{\omega^{2} + i\omega \gamma_{p} }}$$
(1)
Fig. 1
figure 1

The schematic diagram of the proposed multiple Fano resonance plasmonic system composed of a (CRR) and a (DRR)

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The parameters in the model are \(\varepsilon_{\infty } = {3}{\text{.7}}\), \(\omega_{p} = {9}{\text{.1}}\;ev\), and \(\gamma_{p} = {0}{\text{.018}}\;ev\). Two power monitors are put in the input and output ports of the bus waveguide, the power can be calculated by:

$$P = \frac{{\int {{\text{Re}} (E \times H^{ * } ) \cdot dS} }}{2}$$
(2)

Then the transmission of the structure can be defined as [39]:

$$T = \frac{{P_{{{\text{out}}}} }}{{P_{{{\text{in}}}} }}$$
(3)

The geometric centers of the CRR, the DRR, and the bus waveguide are on the same line. The geometrical parameters are as follows: The width of the central air path is \(d\), the length of the middle air rectangular resonator is \(t\), the coupling distance between the middle air rectangular resonator and the bus waveguide is \(s_{1}\) and \(s_{{2}}\). The outer radius of CRR and DRR is set as \(R_{1}\) and \(R_{{2}}\), the notch of the DRR is set as \(\theta\), and the coupling distance between the CRR, DRR, and the bus waveguide is \(g_{1}\) and \(g_{{2}}\). The width of the bus waveguide, CRR and DRR is \(w = 50\;nm\). We use 2D simulation instead of 3D for saving computation time and memory, for actual 3D structure in laboratory, this assumption is acceptable for the thickness larger than 1 um. The grid sizes in the FDTD solution are set to be \({3}\;nm \times {3}\;nm,\) \(\Delta t = \frac{\Delta x}{{2c}}\), where c is the free space speed of light. The simulation area is \({1800}\;nm \times {1200}\;nm\), and the distance between the two power monitors is 1250 nm. The calculated size in the coupling region is \({2}\;nm \times {2}\;nm\). Perfectly matched layers (PMLs) are applied in the \(X\) direction and metal boundary condition was selected in the Y direction.The proposed MIM waveguide with the middle air rectangular resonator can be made by physical vapor deposition and focused ion beam method. And the CRR and DRR resonators can be made by beam lithography process [40,41,42,43].

Based on the standing wave theory, for the DRR, the \(TM_{0}\) model of the MIM waveguide and the resonance wavelength can be determined by the equations [44]:

$$\tan (kw) = \frac{{ - 2k\varepsilon_{{\text{n}}} \alpha }}{{\varepsilon_{{\text{m}}} (k^{2} + \varepsilon_{n}^{2} /\varepsilon_{m}^{2} + \alpha^{2} )}}$$
(4)
$$\alpha = \sqrt {k_{0}^{2} (\varepsilon_{n} - \varepsilon_{m} ) + k^{2} }$$
(5)
$$\lambda = \frac{{{2}{\text{Re}} (neff)L_{eff} }}{n - \varphi /2\pi },\;n = 1,2,3...$$
(6)

where \(k\) and \(k_{{0}}\) are the wave vector in the waveguide and in the free space. \(\varphi\) is the phase shift induced by the reflection,\(R{\text{e(}}n_{eff} )\) is the real part of the effective refractive index, and \(n\) is the order of the resonance mode. \(n_{eff}\) can be described as:

$$n_{eff} (\omega ) = \sqrt {\varepsilon_{Ag} (\omega ) + (\frac{k}{{k_{0} }})^{2} }$$
(7)

where the wave vector in the MIM waveguide can be calculated by:

$${\text{k}} = \sqrt {\beta^{{2}} { - }\varepsilon_{{A{\text{g}}}} (\omega )k_{0}^{2} }$$
(8)

\(k_{0} = 2\pi /\lambda\) and \(\beta\) is the wave vector in the free space and the propagation constant. \(L_{{{\text{eff}}}}\) is the effective length of the DRR which can be determined by:

$$L_{{{\text{eff}}}} = {2}\pi R\frac{360 - \theta }{{360}}$$
(9)

\(R\) is the effective radius of the DRR which can be calculated by:

$$R = \frac{{R_{2} + R_{2} - 50}}{2} = R_{2} - 25$$
(10)

In the proposed plasmonic MIM resonator system, the CRR can be seen as a Fabry–Perot cavity. The resonance wavelength is determined by the equation [45]:

$$\lambda^{^{\prime}} = \frac{{{2}{\text{Re}} (neff)L^{^{\prime}}_{eff} }}{{m - \varphi^{^{\prime}} /2\pi }},\;m = 1,2,3...$$
(11)

According to Eqs. (6) and (11), the resonant wavelength redshifts when \(L_{{{\text{eff}}}}\) increases. Therefore, the effective length of the DRR and CRR can be adjusted to tune the resonant wavelength.

To analyze the Fano resonance mechanism of the proposed structure, the Multimode interference coupled-mode theory (MICMT) is used to calculate the transmission spectrum. The time evolution amplitude \(a_{n}\) of the CRR and DRR resonators can be described as follows [46]:

$$\frac{{da_{n} }}{dt} = ( - j\omega_{n} - \frac{1}{{\tau_{n0} }} - \frac{1}{{\tau_{n1} }} - \frac{1}{{\tau_{n2} }})a_{n} + k_{n1} S_{n,1 + } + k_{n2} S_{n,2 + }$$
(12)
$$S_{{1 - }} = { - }S_{{{1} + }} + \sum\limits_{n} {k_{n1}^{*} } a_{n}$$
(13)
$$S_{{2 - }} = { - }S_{{{2} + }} + \sum\limits_{n} {k_{{n{2}}}^{*} } a_{n}$$
(14)
$$S_{n,1 + } = e^{{j\phi_{n1} }} S_{1, + }$$
(15)
$$S_{{n,{2} + }} = e^{{j\phi_{{n{2}}} }} S_{{{2}, + }}$$
(16)

where \(\omega_{n}\) are the resonant frequency of the \(n_{th}\) resonant mode, \(\tau_{n,i} (i = 1,2)\) are the decay time of the coupling between the resonant cavity and the input and output waveguide, \(k_{n,i} (i = 1,2)\) are the coupling coefficient of the \(n_{th}\) mode, \(\varphi_{n,i}\) are the phase change from input to output part of the \(n_{th}\) resonant mode.

When the proposed structure is symmetrically distributed, \(\tau_{n1} = \tau_{n2} = \tau_{n}\), and \(\phi_{n} = \phi_{n1} + \varphi_{n}\), according to MICMT formula, when \(S_{{{2} + }} = {0}\), the transmission coefficient is obtained as follows:

$$T = \left| {\frac{{S_{2 - } }}{{S_{1 + } }}} \right|^{2} = \left| {\sum\limits_{n} {\frac{{2e^{{j\phi_{n} }} }}{{ - j(\omega - \omega_{n} )\tau_{n} + 2 + \frac{{\tau_{n} }}{{\tau_{n0} }}}}} } \right|^{2}$$
(17)

Figure 2 shows the transmission spectra of the coupled plasmonic system calculated by FDTD. It can be noticed that quintuple Fano resonances (labeled by FR1, FR2, FR3, FR4, FR5) at the resonant wavelength of \(\lambda_{{1}} = {6}96\;nm\), \(\lambda_{{2}} = {830}\;nm\), \(\lambda_{{3}} = {9}52\;nm\), \(\lambda_{4} = 1019\;nm\), \(\lambda_{{5}} = 1178\;nm\). The transmittances of the Fano resonance peaks are 0.41, 0.42, 0.12, 0.24, 0.48, respectively. For further investigation, we can define the asymmetry degree factor \(p\) of the Fano line shape as:

$$p = (\lambda_{peak} - \lambda_{left\;dip} )/(\lambda_{right\;dip} - \lambda_{peak} )$$
(18)
Fig. 2
figure 2

The transmission spectra of the coupled plasmonic system calculated by FDTD. (The geometrical parameters were set as \(w = 50\;nm\), \(s_{{1}} = s_{2} { = 5}\;nm\), \(R_{{1}} = {16}0\;nm\), \(R_{{2}} = {17}0\;nm\) and \(t = 60\;nm\), \(g_{1} = g_{2} { = 1}0\;nm\), \(\theta = {90}^{{0}}\), \(d = {5}0\;nm\))

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Finally, the asymmetry degree factor \(p\) of the five Fano resonances were obtained:

$$p_{FR1} = \frac{{6{96} - 6{53}}}{{{70}2 - 6{96}}} = {7}{\text{.16}}$$
(19)
$$p_{FR2} = \frac{{{831} - {784}}}{{{842} - {831}}} = {4}{\text{.27}}$$
(20)
$$p_{FR3} = \frac{{{953} - {847}}}{{{965} - {853}}} = {0}{\text{.5}}$$
(21)
$$p_{FR4} = \frac{{{1020} - {975}}}{{1{034} - 1{020}}} = 3.{21}$$
(22)
$$p_{FR5} = \frac{{1{178} - 1{034}}}{{1{218} - 1{178}}} = {3}{\text{.60}}$$
(23)

here, \(p = {1}\) means a symmetric line shape, therefore, the asymmetry degree factor of FR1 is the best. To investigate the mechanism of the Fano resonance, we examined the magnetic-field patterns. Figure 3a and d show the field intensity distribution at resonant wavelength 696 nm (FR1 peak) and 1019 nm (FR 4 peak), it can be noticed that almost all the magnetic-field confined in the DRR, indicating that FR1 and FR4 are caused by the interference of the narrow discrete state (DRR resonant mode) and the broad continuum state (middle air rectangular resonator). According to Eq. (2), the orders of resonance mode of FR 1 and FR 4 are 3 and 2 respectively. Figure 3b, c, and e show the field intensity distribution at resonant wavelengths 830 nm (FR2 peak), 952 nm (FR 3 peak), and 1178 nm (FR 5 peak), one can see that almost all the magnetic-field confined in the CRR, indicating that FR2, FR3, and FR5 are caused by the interference of the narrow discrete state (CRR resonant mode) and the broad continuum state (middle air rectangular resonator). The gap plasmonic resonance and cavity plasmonic resonance in CRR offers more flexible control than a popular ring resonator. As can be seen from Fig. 3b, the central air path in the CRR plays an important role in providing more resonance modes since dipolar or quadrupole effects can be induced. Figure 3f shows the incident light is at off-resonance mode 1400 nm, the input SPPs can hardly oscillate in the CRR and DRR, and almost no energy can pass through the outport. These above characteristics indicate that FR 1 and FR4 are more sensitive to the dimension of DRR, while FR 2, FR 3, and FR5 are more sensitive to the dimension of CRR.

Fig. 3
figure 3

Magnetic field patterns of a FR1 at 696 nm b FR2 at 830 nm c FR3 952 nm d FR4 1019 nm e FR5 1178 nm f 1400 nm

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The influence of the dimensions of the CRR \(R_{1}\) on the transmittance of the proposed structure is then investigated. As shown in Fig. 4a, when the radius of CRR increases from \(R_{1} = 140\;nm\;\) to 165 nm with a step of 5 nm, it can be seen that the resonant wavelengths of FR2, FR 3 and FR5 are red-shifted, but the positions of FR 1 and FR 4 keep unchanged. Figure 4b shows the linear relationships between the radius of CRR and the resonant wavelength of FR1, FR 2, FR3, FR4, and FR5. As the radius of CRR increases, FR 2 makes a red-shift from 740 to 860 nm, FR 3 and FR 5 make a red-shift from 845 to 990 nm and from 1049 to 1220 nm, respectively. The transmittance spectra with different air path widths \(d\) are shown in Fig. 5a, it can be seen that when the width of the air path increases from \(d = 40\;nm\;\) to 90 nm with a step of 10 nm, it can be noticed that the resonant wavelengths of FR2, FR 3, FR 5 are red-shifted, but the positions of FR 1, FR 4 keep fixed. Figure 5b shows the linear relationships between the width of the air path and the resonant wavelength of FR1, FR 2, FR3, FR 4, and FR5. As the width of the air path increases, FR 2 makes a blue shift from 849 to 786 nm, FR 3 and FR 5 make a blue shift from 986 to 844 nm and from 1191 to 1104 nm, respectively. Therefore, the results indicate that FR 2, FR3, and FR5 can be tuned by the radius of the CRR and the width of the air path.

Fig. 4
figure 4

a The transmission spectra of the plasmonic Fano system with different \(R_{1}\) b Relationships between the radius of the CRR and the resonance wavelengths

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Fig. 5
figure 5

a The transmission spectra of the plasmonic Fano system with different \(d\) b Relationships between the air path width and the resonance wavelengths of FR1 (black), FR2 (green), FR3 (blue), FR4 (red), FR5 (pink)

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The effect of the dimensions of the DRR \(R_{2}\) on the transmittance of the proposed structure is studied in detail. As shown in Fig. 6a, when the radius of DRR increases from \(R_{2} = 165\;nm\;\) to 185 nm with a step of 5 nm, it can be seen that the resonant wavelengths of FR1, FR4 are red-shifted, but the positions of FR 2, FR 3 and FR 5 keep fixed. Figure 6b shows the linear relationships between the radius of DRR and the resonant wavelengths. As the radius of DRR increases, FR 1 and FR 4 make a red shift from 673 to 757 nm and from 986 to 1115 nm, respectively. Figure 7a shows the transmission spectra of the plasmonic Fano system with different notch degrees \(\theta\), when the \(\theta\) increases from \(\theta = {60}^{{0}}\) to \({100}^{{0}}\) with a step of \({10}^{{0}}\), it can be seen that the resonant wavelengths of FR1, FR4 are blue-shifted, but the positions of FR 2, FR 3, and FR 5 keep fixed. Figure 7b shows the linear relationships between the notch degree of DRR and the resonant wavelengths. As \(\theta\) increases, FR 1 and FR 4 makes a blue shift from 763 to 675 nm and from 1121 to 986 nm, respectively. Therefore, the results indicate that FR 1, and FR4 can be tuned by the radius and the notch degree of the DRR.

Fig. 6
figure 6

a The transmission spectra of the plasmonic Fano system with different \(R_{2}\) b Relationships between the radius of the DRR and the resonance wavelengths of FR1 (black), FR2 (green), FR3 (blue), FR4 (red), FR5 (pink)

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Fig. 7
figure 7

a The transmission spectra of the plasmonic Fano system with different \(\theta\) b Relationships between the angle of the defective-ring resonator and the resonance wavelengths of FR1 (black), FR2 (green), FR3 (blue), FR4 (red), FR5 (pink)

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To gain insight into the sensing application, we investigate the refractive index sensing characteristics of the proposed structure, the refractive index of the medium filled in the CRR and DRR is increased from 1.29 to 1.37 with a step of 0.02. With \(w = 50\;nm\), \(s_{{1}} = s_{2} { = 5}\;nm\), \(R_{{1}} = {16}0\;nm\), \(R_{{2}} = {17}0\;nm\) and \(t = 60\;nm\), \(g_{1} = g_{2} { = 1}0\;nm\), \(\theta = {90}^{{0}}\), \(d = 90\;nm\), the corresponding transmission spectra are shown in Fig. 8a, it can be seen that the resonant wavelength of the quintuple Fano resonances all have a considerable red shift. Figure 8b shows the linear relationships between the refractive index and the resonant wavelengths. The refractive index sensitivity is defined as the shift of the transmittance dip with respect to the change in the refractive index [47]:

$$S = d\lambda /dn(nm/RIU)$$
(24)
Fig. 8
figure 8

a The transmission spectra of the proposed plasmonic Fano system with different refractive indexes of the CRR and DRR (\(\theta = {90}^{{0}}\), \(d = 90\;nm\)). b Relationships between the refractive index and the resonant wavelengths. c FOM of the designed structure

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And the figure of merit (FOM) can be defined as:

$$FOM = \frac{\Delta T}{{T\Delta {\text{n}}}}$$
(25)

The resonant wavelengths of FR to the refractive index were linearly fitted, the relationships are given by:

$$\lambda_{{FR{1}}} = {660}n + 37.4$$
(26)
$$\lambda_{{FR{2}}} = {790}n{ - 11}{\text{.9}}$$
(27)
$$\lambda_{{FR{3}}} = {850}n{ - 11}{\text{.9}}$$
(28)
$$\lambda_{{FR{4}}} = {1020}n{ - 6}{\text{.2}}$$
(29)
$$\lambda_{{FR{5}}} = {1085}n + {19}{\text{.95}}$$
(30)

Therefore, the sensitivity are approximately 660 nm/RIU, 790 nm/RIU, 850 nm/RIU, 1020 nm/RIU, and 1085 nm/RIU at FR1, FR2, FR3, FR4, and FR5, respectively. The value of maximum FOM reaches 7667.

The proposed plasmonic waveguide structure can be used for biosensing. When the proposed structure is used for glucose concentration sensing, the refractive index of the glucose solution can be calculated by [48]:

$$n = 1.33230545 + 0.00011889C$$
(31)

where \(C\) is the concentration of glucose solution. As shown in Fig. 9a, when the concentration of glucose solution increases from \(C = 0\;g/L\) to \(200\;g/L\) with a step of \(50\;g/L\), it can be seen that the resonant wavelengths of the quintuple Fano resonances all have a considerable red shift. Figure 9b shows the linear relationships between the glucose solution concentration and the resonant wavelengths. The glucose solution sensitivity is defined as the shift of the transmittance dip with respect to the change in the concentration:

$$S = d\lambda /dC(nm \cdot L/g)$$
(32)
Fig. 9
figure 9

a The transmission spectra of the plasmonic Fano system with different glucose solution concentrations. b Relationship between the glucose solution concentrations and the resonance wavelengths. c The phase shift spectrum of the proposed structure. d The group delay of the proposed structure

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The resonant wavelengths of FR to the glucose solution concentration were linearly fitted, the relationships are given by:

$$\lambda_{{FR{1}}} = {0}{\text{.07c}} + {917}{\text{.8}}$$
(33)
$$\lambda_{{FR{2}}} = {0}{\text{.086c}} + {1040}$$
(34)
$$\lambda_{{FR{3}}} = {0}{\text{.102c}} + {1120}$$
(35)
$$\lambda_{{FR{4}}} = {0}{\text{.118c}} + {1120}$$
(36)
$$\lambda_{{FR{5}}} = {0}{\text{.136c}} + {1465}{\text{.6}}$$
(37)

Therefore, the sensitivity are approximately \({0}{\text{.07}}nm \cdot L/g\) for FR1, \({0}{\text{.086}}nm \cdot L/g\) for FR2,\({0}{\text{.102}}nm \cdot L/g\) for FR3, \({0}{\text{.118}}nm \cdot L/g\) for FR4, and \({0}{\text{.136}}nm \cdot L/g\) for FR5. The sensing performance of other related structures are compared and the results are shown in Table 1. The sensitivity of the present quintuple FR structure is relatively good compared to previous work [49,50,51,52,53,54]. Another potential application of Fano resonance is slow light. The slow light can be described by the optical delay time \(\tau_{{\text{g}}} (\lambda )\), which can be expressed by [55]:

$$\tau_{g} (\lambda ) = - \frac{{\lambda^{2} }}{2\pi c}\frac{d\phi (\lambda )}{{d\lambda }}$$
(38)
$$n_{g} = \frac{c}{{v_{g} }} = \frac{c}{D}\tau_{g}$$
(39)

where, c is the speed of light, \(\phi (\lambda )\) is the transmission phase shift, \(v_{g}\) and D are the group velocity and the length of the proposed system. Figure 9c shows the phase shift spectrum of the proposed structure.The group delay of the proposed structure is shown in Fig. 9d, the maximum optical delay time is about 0.08 ps and the maximum negative group delay is about -0.185 ps.

Table 1 Comparison of sensing performance to other related plasmonic structures
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When the proposed structure is used as water-soluble B vitamins concentration sensing, the molecular structures of vitamins can be found from [56,57,58]. At 25 °C, the refractive index of water-soluble B vitamins can be measured by Abbe refractometer, and the average refractive index of water-soluble B vitamins is: \(n(Vita\min B1) = 1.3366\), \(n(Vita\min B5) = 1.3360\), and \(n(Vita\min B{6}) = 1.33{71}\). When 1–2 drops of the water-soluble B vitamins dripping into the CRR and DRR resonator. As shown in Fig. 10, FR5 has a larger spectral sensitivity for RI sensing, so FR5 is used to detect water-soluble B vitamins. For FR5, the peak wavelengths of FR5 for B5, B1, and B6 are 1469.1 nm, 1470 nm, and 1470.8 nm, respectively, Recently, an employable detection system can identify wavelength variation as small as 0.1 nm, so the detection of B5, B1, and B6 can be separated from each other. In practice sensing, the device manufacturing accuracy should be considered, from Figs. 4–7, we can see the Fano sensing of the proposed structure is depend on the geometrical sizes, therefore, low manufacturing accuracy will reduce the sensitivity and destroy the linearity. Taking the DRR resonator as an example, Fig. 11 shows the DRR resonator mismatch case. If the DRR resonator rotate by an angle of \(\beta=5^\circ\), The five Fano resonance peaks attain new sensitivity of 670 nm/RIU, 765 nm/RIU, 820 nm/RIU, 1005 nm/RIU, and 1095 nm/RIU, respectively. For \(\beta = { - 5}^\circ\), the sensitivities are about 675 nm/RIU, 780 nm/RIU, 830 nm/RIU, 1005 nm/RIU, and 1100 nm/RIU, respectively. Table 2 show the comparison of sensing performance for DRR resonator rotation mismatch. The result shows the most suitable Fano peak for sensing, FR 5, suffers a minimum and maximum sensitivity increment of 0.92%, and 1.38%, respectively. Compared with the result of work [59], out proposed sensor has a high level of tolerance. Another difficulty in operation is filling the resonator with sensing materials such as glucose concentration and water-soluble vitamins, the non-uniformity filling of the sensing materials will cause a larger sensitivity error. Although the present paper is mainly theoretical simulation, several important experimental work can be found [60, 61].

Fig. 10
figure 10

The transmission spectra of the plasmonic Fano system with different types of water-soluble B vitamins

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Fig. 11
figure 11

DRR resonator mismatch by \(\beta\) (in degrees)

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Table 2 Comparison of sensing performance for DRR resonator rotation mismatch
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Conclusion

In conclusion, we present a quintuple Fano resonance based on a DRR, a CRR coupled to a MIM waveguide. Results show that five Fano resonances can be independently tuned by the geometrical parameters, such as the radius of DRR, CRR, the width of the air path, and the notch degree of the DRR. Based on the ultra-sharp Fano line shape, a refractive index sensitivity of about 1085 nm/RIU and a glucose solution sensitivity of about \({0}{\text{.136}}nm \cdot L/g\) were obtained. And the proposed sensor can be used to identify water-soluble vitamins B1, B5, and B6. The designed quintuple Fano resonance structure can be applied to the areas of on-chip plasmonic nanosensors, and slow light.