Introduction

Surface plasmon polaritons (SPPs) are electromagnetic (EM) waves excited through the interaction of incident photons and the free electrons in metals, which propagate along the metal-insulator interface [1]. In addition, their amplitudes decrease exponentially along perpendicular to the metal-insulator surface [2]. The EM energy is strongly localized near the boundary, which enables to break through the conventional optical diffraction limit and to manipulate light in sub-wavelength scales [3]. Therefore, SPPs have received attentions from many researchers, and numerous photonic devices with different functions have been designed and examined, such as plasmonic sensors, absorbers, filters, switches, and slow light devices [4,5,6,7,8]. Among them, plasmonic sensing has become an important area of biosensing research due to its label-free detection, fast response, and strong resistance to EM interference [9]. So far, most of the plasmonic sensors are usually realized based on metal-insulator-metal (MIM) waveguide coupled cavity resonators [10]. The main advantages of MIM waveguide structures are low fabrication cost, high ability to confine light, simple structure, easy integration, and low bending loss [11]. Hence, MIM waveguide structures are considered to be one of the most desirable methods for realizing nano-integrated photonic devices.

MIM waveguide structures based on SPPs can arise many unique optical phenomena, such as Fano resonance and plasma-induced transparency (PIT) [12, 13]. Fano resonance, possessing a sharp and asymmetric line shape in the transmission spectrum, is widely used in the field of plasmonic sensing because of its highly sensitive properties to structural parameters and ambient environment [14]. It can be achieved through the mutual interference of a wide continuous state and a narrow discrete state. In recent years, many works have been published with respect to plasmonic sensors based on MIM waveguide by utilizing multiple Fano resonances. Qi et al. designed a stub MIM straight waveguide coupled to an elliptical ring resonator. The structure can excite triple Fano resonances and obtain a refractive index (RI) sensitivity of 1400 nm/RIU [15]. Yadav et al. proposed a plasmonic sensor based on a MIM straight waveguide coupled tapered waveguide cavity resonator. It was able to excite dual Fano resonances and obtain the highest RI sensitivity up to 2544.3 RIU/nm [16]. Figuigue et al. studied an MIM waveguide system consisting of a semi‑elliptical ring and a MIM straight waveguide with baffle. The system can generate triple Fano resonances and achieve a RI sensitivity 1783 RIU/nm and a figure of merit (FOM) of 27 [17]. Multiple Fano resonances often originate from the common resonator, which restricts the flexibility of plasmonic sensor. Therefore, Liu et al. reported the independent tunability of multiple Fano resonances using a MIM straight waveguide with baffle coupling two resonators (a rectangular resonator and a semicircular ring resonator) [18]. However, for MIM straight waveguide coupling multiple resonators, this approach reduces the usage efficiency for the integration space. To further enhance the integration of photonic devices, MIM S-shaped waveguides exhibit higher practical value. At present, there are fewer studies based on MIM S-shaped waveguide coupling to achieve the independent tunability of plasmonic sensors. Moreover, the sensing performances of plasmonic structures should be also further improved.

In this work, a compact plasmonic sensor consisting of a MIM S-shaped waveguide with baffle, an analogous C-shaped resonator (ACR), and a T-shaped resonator with an annular cavity (TRAC) is proposed. The transmission spectrum and magnetic field distribution are numerically simulated through the finite element method (FEM). The impacts of structural parameters on Fano resonances are investigated, and independent tunability of multiple Fano resonances can be realized by adjusting the structural parameters of different resonators. Finally, the plasmonic sensor is explored for the simultaneous determination of two water-soluble vitamins.

Structure design and theoretical analysis

We design a simple and compact plasmonic sensor structure which is comprised of a MIM S-shaped waveguide with baffle, an analogous C-shaped resonator (ACR), and a T-shaped resonator with an annular cavity (TRAC), as illustrated in Fig. 1. Silver and gold are broadly employed for RI sensing among all plasmonic materials [19, 20], while the silver is chosen as a metallic material which is mainly attributed to its cheaper and low-loss properties [21]. For the easy oxidation of silver, it can be covered with a thin layer of silica to avoid direct contact with air [22]. The orange and white areas represent metallic silver and air, respectively. To ensure that only the fundamental transverse-magnetic (TM0) mode is transmitted in the waveguide structure, the widths of both the S-shaped waveguide and the resonators are fixed to w = 50 nm, and the radius of the arc at the bend is fixed to r = 25 nm [23]. For the S-shaped waveguide, the ACR and the TRAC are situated on its left and right sides, and the coupling distances in the x and y directions are represented by g1 and g2, respectively. Moreover, the thickness of baffle in the waveguide is defined as t. The ACR can be considered as one rectangular ring with a gap. The length and width of the rectangular ring and the height of the gap are indicated by L1, W1, and H1, respectively. Similarly, the TRAC can be also disassembled into one big rectangle, one connected gap and one ring. The lengths of the big rectangle and the connected gap are H2 and L2, while the inner and outer radii of the ring are denoted by R1 and r1, respectively. In addition, the refractive indices (RIs) of the medium materials within the MIM waveguide, ACR, and TRAC are defined as n, n1, and n2, respectively. Then, the plasmonic sensor structure is constructed and simulated employing the finite element method (FEM). Since the calculation results of 2D model and 3D model are almost identical when the thickness in the z direction is out of 1 μm [24]. Thus, to boost calculation efficiency, all structures are calculated based on the 2D model.

Fig. 1
figure 1

Schematic diagram of the plasmonic sensor structure

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In the simulation process, SPPs are passed from the left input port to the right output port of the MIM waveguide, and the powers (Pin and Pout) at the input and output ports are examined. Thereby, the transmittance (T) is able to be calculated by T = Pout/Pin. Additionally, two mode couplers can be integrated into the ports of S-shaped waveguide, respectively. They can effectively contribute to convert between dielectric mode and plasmonic mode [25, 26]. To absorb the escaping electromagnetic (EM) waves, we set up perfect matching layers around the simulation area. The permittivity of air is εi = 1.0. Silver, as a metallic material, exhibits a relative permittivity (εm) as a function of frequency and can be described by the classic Drude model [27]:

$$\varepsilon_{m} (\omega ) = \varepsilon_{\infty } - \frac{{\omega_{p}^{2} }}{\omega (\omega + i\gamma )},$$
(1)

where ꞷ represents the angular frequency of incident photons, while parameters γ, ꞷp, and ε∞ are the damping attenuation frequency, the plasmonic resonance frequency, and the permittivity at infinite frequency, respectively. And the values of these parameters for silver are set to γ = 2.73 × 1013 rad/s, ꞷp = 1.38 × 1016 rad/s, and ε∞ = 3.7. Since the waveguide width is much smaller than the wavelength of the incident light, only the TM0 mode is propagated in the waveguide. The dispersion equation of TM0 mode in the waveguide can be given as follows [28]:

$$\tanh (\frac{{w\sqrt {\beta^{2} - \varepsilon_{i} k_{0}^{2} } }}{2}) + \frac{{\varepsilon_{i} \sqrt {\beta^{2} - \varepsilon_{m} k_{0}^{2} } }}{{\varepsilon_{m} \sqrt {\beta^{2} - \varepsilon_{i} k_{0}^{2} } }} = 0,$$
(2)

Here, k0 = 2π/λ0 and ꞵ are the wave vectors of SPPs in free space and in MIM waveguide. Thus, the effective RI (neff) is described as neff = ꞵ/k0. Then based on the standing wave theory, the resonance is excited when the wavelength of incident light satisfies the phase matching condition of resonator. And the resonance wavelength (λres) can be represented as [29]

$$\lambda_{res} = \frac{{2L_{eff} {\text{Re}} (n_{eff} )}}{{m - \tfrac{{\varphi_{ref} }}{\pi }}},$$
(3)

where Leff is the effective length of resonator, Re(neff) is the real part of effective RI, and \(\varphi_{ref}\) is the reflection phase shift of SPPs. The positive integer m indicates the order of resonance.

Generally, for the sensing properties of plasmonic sensors, sensitivity (S) and figure of merit (FOM) are two important evaluation parameters, and they can be calculated by the following equations, respectively [30].

$$S = \frac{{\Delta \lambda_{res} }}{\Delta n},$$
(4)
$$FOM = \frac{\Delta T}{{T\Delta n}},$$
(5)

Here, \(\Delta n\) is the RI change, while \(\Delta \lambda_{res}\) and \(\Delta T\) are the corresponding changes in the resonance wavelength and the transmittance.

Numerical results and discussion

The default parameter settings are listed in Table 1. So far, electron beam lithography (EBL), nano-imprint lithography (NIL), and focused ion beam (FIB) lithography are commonly employed to fabricate nanoscale photonic devices [31]. Among them, EBL with sub-10 nm resolution can satisfy the required accuracy of the designed structure [32]. Firstly, a silver layer with sufficient thickness is deposited on the Si substrate utilizing the magnetron sputtering method. Subsequently, the silver layer is covered with a polymethyl methacrylate resist, and the desired pattern is created on its surface using an electron beam. The exposed areas undergo chemical development and silver etching, followed by removal of the resist from the surface.

Table 1 Summary of the default parameter settings
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To study the optical properties of the proposed plasmonic sensor, the transmission spectra of sensor structure without resonators, sensor structure without baffle, and the whole structure are numerically simulated and displayed in Fig. 2a. According to the formation conditions of Fano resonance, it can be seen from the black dashed line in Fig. 2a that the sensor structure without resonator generates a continuous spectrum with low transmittance. Whereas for the spectrum of the sensor structure without baffle, the red dashed line exhibits two narrow discrete states. Therefore, the whole structure is capable of exciting the dual Fano resonances (FR1 and FR2), as seen in the blue solid line. Moreover, the simulated values are verified by matching the transmission spectra to the Fano profile (FP). The theoretical FP values can be obtained by Fano liner equation [33]:

$$F(\lambda ) = \frac{A(q + b)}{{(1 + b^{2} )}}, b = \frac{{(\frac{1}{\lambda } - \frac{1}{{\lambda_{res} }})\lambda_{res}^{2} }}{\Delta \lambda }.$$
(6)

where q is Fano factor. A and \(\Delta \lambda\) stand for the amplitude and linewidth of Fano resonance. The FP values of FR2 and FR1 are fitted, as depicted in Fig. 2b and c. The q values for FR2 and FR1 are calculated to be − 56.9765 and − 56.7682, respectively. It can be seen that there is a great agreement between the FEM simulated values and the FP fitted values. Then, to further investigate the formation mechanism of FR1 and FR2, the transmission spectra of the structures with different resonators and the distributions of magnetic fields at FR1 and FR2 are also analyzed, as presented in Fig. 3. It can be seen that FR1 can be excited only when the ACR exists. Similarly, FR2 can be excited only when the TRAC is present. Combining with the magnetic field distributions at the corresponding resonance wavelengths, the energy at FR1 is primarily concentrated in the ACR, and the energy at FR2 is mainly focused in the TRAC. In addition, both of them keep high transmittance at the Pout. As a result, it can be indicated that FR1 and FR2 originate from the ACR and the TRAC, respectively.

Fig. 2
figure 2

a Transmission spectra: sensor structure without resonators (black dashed line), sensor structure without baffle (red dashed line), and whole structure (blue solid line). b FEM and FP curves for FR2. c FEM and FP curves for FR1

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Fig. 3
figure 3

a The transmission spectra of only ACR, only TRAC, and the whole structure. The distributions of magnetic fields: b FR2, c FR1

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Next, the effects of structural parameters on the Fano resonances are explored. In Fig. 4a, the gap height H1 in the ACR is increased from 50 to 90 nm, with an increment of 10 nm. Other structural parameters are kept at the default settings. It can be observed that with the increase of H1, the FR1 exhibits a significant blueshift and accompanies a decrease in transmittance, whereas the FR2 remains unchanged. The reason for this phenomenon is that the reduction of H1 is equivalent to decreasing the effective length of the ACR. Based on Eq. (3), it is known that the diminishment of the effective length results in the reduction of the resonance wavelength; thereby, the FR1 exhibits a blueshift. Moreover, the increase in the gap height reduces the coupling length between the ACR and the S-shaped waveguide, which leads to a decrease in the transmittance of FR1. And from Fig. 4b, it can be found that there is a good linear relationship between the resonance wavelength of FR1 and H1, which has a linearity as high as 0.99954. Conversely, the length H2 of the big rectangle in the TRAC is decreased from 290 to 250 nm with an interval of 10 nm, as depicted in Fig. 5a. Other structural parameters are also maintained as the default settings. In this case, the resonance wavelength of FR2 exhibits a blueshift with the decrease of H2 and that of FR1 remains unchanged. The transmittance of FR2 also exhibits a slight decrease. The reason for this is consistent with the effect of H1 on FR1. It can also be noticed from Fig. 5b that the resonant wavelength of FR2 has an excellent linear relationship with H2 and the linearity reaches 0.99963. Therefore, the resonance wavelengths of FR1 and FR2 can be independently controlled by varying the corresponding structural parameters H1 and H2, respectively. Namely, the independent tuning of double Fano resonances can be realized.

Fig. 4
figure 4

a The transmission spectra of the structures with different parameters H1. b The linear fitting of the resonance wavelength with H1

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Fig. 5
figure 5

a The transmission spectra of the structures with different parameters H2. b The linear fitting of the resonance wavelength with H2

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When the RI of filled medium in the resonator is changed, the resonance wavelength of Fano resonance is also affected and exhibits extreme sensitivity. Thus, this mechanism is widely used in the study of RI sensing. In Fig. 6, by changing the RI (n1 or n2) of the medium within the different resonators, only the resonance wavelength of corresponding Fano resonance can be changed. This indicates that independent tunability of the FR1 and the FR2 can also be achieved by changing the RI of medium within different resonators. Then, since we expect the designed plasmonic sensor to be used for concentration determination in water-based solutions, we further investigate the sensing properties of the proposed structure, and the RIs (n1 = n2) of the mediums within the two resonators are regulated between 1.3 and 1.4, as shown in Fig. 7. As the RIs increase, both FR1 and FR2 show an obvious redshift and a decrease in transmittance. The RI and dielectric constant of the medium are positively correlated. Based on Eqs. (2) and (3), the increased dielectric constant leads to an increase in the effective RI within the resonator, which causes the resonant wavelength to exhibit a redshift. Moreover, the increase of effective RI also enhances the energy loss of SPPs, which leads to the decrease of transmittance. Figure 7b presents the linear fitting between the resonance wavelength and RI. According to Eq. (4), it is known that the slope of the fitting straight line represents the sensitivity of the corresponding resonance. Therefore, the sensitivities of FR1 and FR2 are 2400 nm/RIU and 1650 nm/RIU, respectively. Meanwhile, based on Eq. (5), we can obtain the FOM curve of the designed sensor, as shown in Fig. 8. It can be observed that there is a maximum FOM value of 95.86 RIU−1 at 2302 nm. Table 2 lists the performance comparison of this study with other published works in recent years. It can be demonstrated that the plasmonic sensor structure has favorable sensing characteristics.

Fig. 6
figure 6

a The transmission spectra of different RI n1 in ACR. b The transmission spectra of different RI n2 in TRAC

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Fig. 7
figure 7

a The transmission spectra of different RIs (n1 = n2) in resonators. b The linear fitting of the resonance wavelength and RIs

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Fig. 8
figure 8

The FOM curve of the designed sensor

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Table 2 Performance comparison with other published works
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Application

Upon the above conclusions, the double Fano resonances excited in this sensor are independently tunable. Therefore, it can be used for the simultaneous determination of two substances, which will greatly improve its efficiency in practical applications. At present, plasmonic sensors are often employed for the detection of bio-chemical analytes, such as glucose, blood samples, and glycerol [43,44,45]. Vitamins are a category of organic substances that are indispensable for the support of normal physiological activity in humans and animals. Most of them cannot be produced by the organism themselves and must be obtained from food [46]. In particular, the intake of vitamin B1 can effectively improve diseases such as indigestion and neuritis, but too much intake can also lead to metabolic abnormalities and even induce toxic symptoms. The injection of vitamin C can be an effective treatment for scurvy and play an adjunctive role in the treatment of some chronic diseases [47]. Nonetheless, excessive injections can also lead to pro-coagulation of red blood cells and increase the formation of thrombosis in the body [48]. Therefore, the precise measurement of their concentration is extremely significant in the medical field. Here, based on the plasmonic sensor designed in this study, the simultaneous measurement of two water-soluble vitamins (vitamin B1 and vitamin C) is discussed. At room temperature, the mathematical relationships between the RIs of vitamin B1 and vitamin C with respect to concentration are given below [49, 50].

$$n_{b} = 0.208607C_{vb1} + 1.33281,$$
(7)
$$n_{c} = 0.13596C_{vc} + 1.33480,$$
(8)

where nb and Cvb1 (g/ml) represent the RI and concentration of water-soluble vitamin B1. Similarly, nc and Cvc (%) are the RI and concentration of water-soluble vitamin C. Then, water-soluble vitamin B1 and vitamin C are filled into the ACR and the TRAC as the sensing mediators, respectively. As shown in Fig. 9a, the concentration Cvb1 of water-soluble vitamin B1 in the ACR is increased from 0.06 to 0.14 g/ml with a step of 0.02 g/ml. Meanwhile, the concentration Cvc of water-soluble vitamin C in the TRAC is decreased from 25 to 5% with an interval of 5%. It can be seen that FR1 exhibits redshift, while FR2 exhibits blueshift. This is also further validated the independence between the ACR and the TRAC. Figure 9b shows the linear fitting between the resonance wavelength and the concentration of the water-soluble vitamin. According to Eq. 4, the concentration sensitivity for the water-based solutions can be defined as \(S^{\prime} = \Delta \lambda_{res} /\Delta C\). Thus, with respect to the sensing of water-soluble vitamin B1 and vitamin C, the concentration sensitivities of FR1 and FR2 are as high as 500 nm·ml/g and 224 nm/Cvc, respectively. These results indicate that proposed plasmonic sensor structure can efficiently accomplish simultaneous measurements of water-soluble vitamin B1 and vitamin C.

Fig. 9
figure 9

a The transmission spectra: water-soluble vitamin B1 (ranging from 0.06 to 0.14 g/ml) and water-soluble vitamin C (ranging from 25 to 5%). b The linear fitting of the resonance wavelength and the concentration of water-soluble vitamin

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Conclusion

In summary, we design a plasmonic sensor structure that is consisted of a MIM S-shaped waveguide with baffle, an ACR, and a TRAC. Using the FEM, the transmission spectrum and magnetic fields of the sensor structure are simulated and analyzed. The structure is able to excite two Fano resonances which originate from different resonators. The independent tunability of the dual Fano resonances can be achieved by changing the structural parameters H1 and H2, while the linearities are as high as 0.99954 and 0.99963, respectively. Similarly, by varying the refractive index of the medium in different resonators, the Fano resonances can be also tuned independently, which greatly increases the flexibility of the plasmonic sensor. Then, based on the RI range of water-based solutions, the sensing properties of the structure are researched. The results show that the designed structure can obtain a maximum sensitivity of 2400 nm/RIU and FOM of 95.86 RIU−1. Furthermore, due to the independence of the dual Fano resonances, the plasmonic sensor enables simultaneous determination of water-soluble vitamin B1 (FR1) and vitamin C (FR2) and exhibits concentration sensitivities of 500 nm·ml/g and 224 nm/Cvc, respectively. These findings will provide valuable references for the exploitation of nano-photonic devices and high-density integrated circuits.