Introduction

Surface plasmon polaritons (SPPs) arise from the interaction between incident photons and electrons on the surface of a metal, giving rise to electromagnetic wave [1, 2]. SPPs are able to propagate along metal-dielectric or metal-air interfaces, and their electric field strengths decay very little horizontally but decrease exponentially in the vertical direction [3, 4]. It is capable of breaking the diffraction limit, allowing sub-wavelength manipulation and transmission [5]. With their low-dimensional high intensity and sub-wavelength properties, SPPs possess excellent capabilities as carriers of energy and signal, and their ability to combine at sub-wavelength scales enables the creation of diverse optical devices, such as multi-wavelength decomposition multiplexers [6, 7], thin-film solar cells [7, 8], photoelectric detector [9, 10], and Wiener sensors [11].

SPPs can be stimulated by an external optical field present at the boundary of a metal-to-dielectric [12]. And optical waveguides made of different types of metals and high refractive index dielectric materials can be used to excite SPP, including Metal-Dielectric-Metal waveguides [13, 14]. Among them, the MIM waveguide can play a good role in limiting the SPPs and realize a longer transmission distance as well as a smaller loss during transmission [15]. Therefore, various structures composed of MIM waveguides and coupling cavities have already extensively studied and developed. The coupling cavity can have a variety of shapes including polygons, which can be adjusted to fulfil different functions [16].

The MIM waveguide based sensors are also capable of producing non-linear optical effects such as Fano resonance [17, 18].The Fano resonance is a type of linear syntony appearance that arises from the coupling between broad continuous states and narrow discrete states in an atomic system, exhibiting asymmetry [19]. In the SPP system, the Fano resonance is generated by the mechanism that when light is incident into the MIM waveguide, it produces bright modes that can be directly coupled, which have flatter spectral lines. However, some of the metal nanoparticles cannot be directly excited by light and require coupling of light modes in order to be excited, which are called dark modes and have narrower and sharper spectral lines. When the two modes interfere with each other, Fano resonance phenomenon occurs, creating a sharp asymmetric curve. Different from the Lorentz resonance, the Fano resonance has a distinctly asymmetric spectrum. The distinct and asymmetric line shape of the Fano resonance is achieved by the interference of scattering amplitudes from the discrete narrowband and continuous broadband modes [20, 21]. The rapid changes in oscillation and frequency give the Fano resonance a narrow full width at half maximum (FWHM) [22]. Since the Fano resonance smaller FWHM has a strong spatial magnetic field binding ability and the linear asymmetry cuts steeply, small changes in the surroundings and geometry of the MIM waveguide structure will cause a large shift in the Fano resonance wave peak, which is a method for analyzing and characterizing the resolution of the instrument [23].

In addition, the Fano resonance is very sensitive to changes in the structural parameters of the sensor, so the use of waveguide-coupled resonant cavities is an important method for the preparation of refractive index sensors. In order to improve the performance of refractive index sensors, various waveguide-based refractive index sensor structures have emerged. Tathfif et al. proposed a refractive index sensor structure based on a concentric triple ring resonator with a sensitivity as high as 3639.79 nm/RIU, where in the refractive index range of 1.30 to 1.40 showing a maximum sensitivity of 7530.49 nm/RIU at refractive index range between 1.30 and 1.40 [24]. Another sensor structure with a groove and a Square-Ring Resonator of MIM waveguide shows a maximum sensitivity of 1074.88 nm/RIU with a FOM of 32.4 [25]. The pressure sensor structure loaded with an array of silver nanorods has a maximum pressure sensitivity of 25.4 nm/MPa [26]. Rashid et al. [27, 28] reported Co-shaped refractive index sensor structure embedded with gold nanorods with optimal structural sensitivity up to 6227.6 nm/RIU. Refractive index sensor based on three circular rings coupled with metal–insulator-metal straight waveguide with maximum sensitivity up to 3573.3 nm/RIU and FOM of 21.9. Hassan et al. [29, 30] presented a refractive index sensor of a rectangular ohmic cavity and a Concentric Double-Ring Resonator coupled with two MIM waveguides with a maximum sensitivity of 1070 nm/RIU. Another double rectangular silver trough vertically coupled with a pair of dielectric-metal-dielectric (DMD) waveguide refractive index sensor structure with a maximum sensitivity of 1228.67 nm/RIU.

In this study, we propose and research a structure for nanoscale refractive index sensor that is based on an MIM waveguide, which comprises an MIM bus waveguide and a U-shaped ring resonator with three stubs (URRS). The investigation explores the disseminate performance of the sensing structure through the utilization of finite element method (FEM) and Coupling Mode Theory (CMT) [31]. The U-shaped cavity with three stubs, which is deliberately designed, improves light trapping capabilities and sensing performance in contrast to the traditional ring cavity [32]. Since the Fano resonance spectrum is highly sensitive to the arguments of geometric structure of the designed structure, this study aims to analyze the impact of the geometrical parameters of the URRS structure on the disseminate performance characteristics of the Fano resonance spectrum. These geometrical parameters comprise the outer radius of the URRS, the height of the URRS, the length of the three stubs, and the spacing between the MIM waveguide and the URRS structure.

Geometry Structure and Analysis Methods

We present the 2D and 3D schematic of the proposed structure in Fig. 1, which consist of URRS structure coupled to the waveguide and an MIM waveguide. The U-shaped cavity was selected because it offers the advantages of both circular cavity, which can provide a smooth reflection surface, and square cavity, which can provide a parallel reflection surface. The square cavity is capable of adjusting the vertical distance, while the straight waveguides aid in the transmission of light. However, coupling the waveguide in the vertical direction to the MIM bus waveguide results the sensor’s bandwidth widen, leading to performance degradation. Circular resonators are one of the best choices for sensor structure design because they exhibit good performance when coupled to MIM waveguides. However, in the process of increasing the radius, the increase in the area of a circular cavity perpendicular to the horizontal direction leads to the increase of the sensor loss, which affects the performance of the sensor. In the end, we choose the URRS structure. The fabrication process of the sensor is shown in Fig. 2, where a sufficient silver layer (yellow part) is prepared by chemical vapor deposition on a silicon substrate (gray part), and then the desired silver layer structure is obtained by electron beam etching. After comparing data from several simulation experiments, we finally determined that the structure is characterized by the following set of geometric arguments: g = 15 nm, \({R}_{1}\) = 210 nm, \({r}_{1}\) = \({R}_{1}\)  − 50 nm, l = 180 nm, d = 205 nm.

Fig. 1
figure 1

a 2D diagram of URRS structure. b 3D schematic of the URRS structure

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Fig. 2
figure 2

Schematic diagram of sensor fabrication

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The equation for the TM0 mode of the MIM waveguide is as follows [33]:

$${\text{tanh}}\left(k\omega \right)=-\frac{2k{\alpha }_{c}}{{k}^{2}+{p}^{2}{\alpha }_{c}}$$
(1)

where \(p={\varepsilon }_{in}/{\varepsilon }_{m}\), \({\varepsilon }_{in}\), and \({\varepsilon }_{m}\) signify the value of dielectric constants of dielectrics and metals, respectively. The wave vector in the waveguide is described as \(k=2\pi /\lambda\), whereas in free space it can be denoted as \({k}_{0}=2\pi /{\lambda }_{0}\), and \({\alpha }_{c}={[{{k}_{0}}^{2}\times ({\varepsilon }_{{\text{in}}}-{\varepsilon }_{{\text{m}}})+k]}^\frac{1}{2}\).

The air and silver materials are respectively stand for the white region and yellow region in Fig. 1a. The use of silver as a filler material has the advantage of ensuring a high field in the system and reducing power consumption. Considering the devised silver layer structure, we need to deposit sufficient silver layer on the bottom substrate through chemical vapor deposition and subsequently obtain the devised structure by utilizing electron beam etching. The relative dielectric permittivity of air, denoted as \({\varepsilon }_{d}\), is equal to 1. The dielectric constant, which is known as relative permittivity of Ag can be described by the Debye-Drude dispersion model as follows [34]:

$$\varepsilon \left(\omega \right)={\varepsilon }_{\infty }+\frac{{\varepsilon }_{s}-{\varepsilon }_{\infty }}{1+i\tau \omega }+\frac{\sigma }{i\omega {\varepsilon }_{0}}$$
(2)

In Formula (2), the conductivity and relaxation time of Ag are \(\upsigma =1.1486\times {10}^{7}S/m\) and \(\uptau =7.35\times {10}^{-15}s\), respectively. \({\varepsilon }_{\infty }\) is when Ag is shielded by a strong magnetic field, its dielectric constant reaches infinity, which is assigned a value of \({\varepsilon }_{\infty }=3.8344\). \({\varepsilon }_{s}\) is the dielectric constant of Ag in an electrostatic field, which is assigned a value of \({\varepsilon }_{s}=-9530.5\).

In this paper, three parameters, namely sensitivity (S), full width at half maximum (FWHM), and figure of merit (FOM), can be employed to assess the performance of the proposed sensor structure. Among them, sensitivity (S) is a critical performance metric used to evaluate nanoscale refractive index sensors. It quantifies the relationship between the refractive index change and the peak drift, providing valuable insights into the sensor’s effectiveness; FWHM represents the width of the transmission spectral line at half its peak height, which usually represents the clarity of the transmission spectrum line; and the FOM is a comprehensive representation of the sensor’s performance and therefore needs to be considered in combination with both sensitivity and FWHM. The sensitivity (S) and the figure of merit (FOM) can be mathematically described by the following equations, respectively [35, 36]:

$$S=\Delta \lambda /\Delta n$$
(3)
$$FOM=S/FWHM$$
(4)

where \(\Delta n\) and \(\Delta \lambda\) represent changes in wavelength and refractive index, respectively.

In the next part of this paper, we will employ the simulation of the designed sensor structure using COMSOL Multiphysics 5.4a software to build a 2D geometric model with greatly reduced computational complexity and analyze its propagation characteristics using the finite element method (FEM) [37, 38]. To achieve precise computational accuracy, the MIM waveguide and URRS structure regions undergo mesh dissection using ultra-fine triangles. This meticulous selection guarantees reliable results in the analysis. Furthermore, to effectively absorb the outward reflected waves, a perfectly matched layer is incorporated into the structure. The experimental procedure is shown in Fig. 3. Specifically, the MIM waveguide and URRS structures are firstly drawn on the silver substrate, and then an ultra-fine triangular mesh is used to delineate the model structure, set the refractive index, and finally derive the calculation results.

Fig. 3
figure 3

Schematic diagram of the experimental process

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Simulation Results and Analysis

Since the Fano resonance is essential to the performance of sensors, we will focus on exploring its creation and characterization. This investigation aims to better understand the properties of Fano resonance, ultimately improving the overall sensor performance. The geometric parameters for the structure have been established as follows: g = 15 nm, \({R}_{1}\) = 210 nm, \({r}_{1}\) = \({R}_{1}\)  − 50 nm, l = 180 nm, d = 205 nm. As shown in Fig. 4, in the transmission spectrum in the designed structure, there are two resonance dips with sharp and asymmetric dip profiles, clearly different from the symmetric profile formed by the Lorentz resonance, which is a sign of the formation of the Fano resonance. D2(\({\lambda }_{0}\) = 1894 nm) and D1(\({\lambda }_{0}\) = 2150 nm) represent dip 2 and dip 1 of the Fano resonance, respectively. It can be seen from the Fig. 4 that the transmittance of D1 is significantly lower than that of D2. By calculating the S (sensitivity) of the two resonance inclinations, it can be obtained that the S of D1 is 2900 nm/RIU, and the S of D2 is 2280 nm/RIU. The two inclinations are located at different resonance wavelengths, and the variation of the resonance wavelength produces inclinations in different resonance modes, which are caused by the sensing properties of the structure. Note that the inclination sensitivity at the D2 position is smaller than that of D1 and the transmittance is too high, so we will not discuss the D2 position resonance inclination in the subsequent study.

Fig. 4
figure 4

Transmission spectrum of designed structures

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In order to find a better U-cavity structure, we compare the performance of various types of U-cavities, including a single U-resonator, a U-cavity with one stub, a U-cavity with two stubs, and a URRS structure, and plot their transmission spectra and as shown in Fig. 5. The black line shows the transmission spectral line of the single MIM waveguide, and it is evident that the curve maintains a high level of transmittance because there is no structure coupled to it for Fano resonance. The red line is the transmission spectrum of a single U-shaped cavity, which has a good shape and a calculated sensitivity of 1840 nm/RIU. The blue line is the transmission spectrum of a U-shaped cavity coupled with a stub, which has a slightly increased transmittance and a larger resonance tilt wavelength, with a sensitivity up to 2640 nm/RIU. The green line is the transmission spectrum of the URRS structure, which has a larger resonance tilt wavelength and a good transmission characteristic, and the green line is the transmission spectrum of a single MIM waveguide, which is coupled to a single MIM waveguide, and a good transmission characteristic. At the same time, its transmittance is also lower, and its ability to capture SPPs is also stronger, with a sensitivity as high as 2900 nm/RIU. We have investigated the magnetic field distribution at the resonant inclination (\(\lambda\) = 2150 nm) for single waveguide with various types of U-cavity structures. As shown in Fig. 6, it is found that SPPs can be coupled to various types of U-cavity structures via MIM waveguides, and the URRS structures have a stronger ability to gather magnetic fields compared to them. From Fig. 6d, it is apparent that most of the normalized magnetic field’s coupling through the MIM waveguide to the URRS structure happens in the URRS itself, with only a tiny fraction collected in the MIM waveguide. This observation indicates a remarkable resonance, which indicates a significant resonance phenomenon.

Fig. 5
figure 5

Transmission spectra of the single MIM waveguide (black line), the single U-shape cavity (red line), the U-shape cavity with one stub (blue line), and the URRS structure (green line)

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Fig. 6
figure 6

Magnetic field distribution at \(\lambda\) = 2150 nm of a single MIM waveguide; b single U-shape cavity; c U-shape cavity with one stub; d URRS structure

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In order to study the effect of refractive index (n) on the Fano resonance transmission spectrum, we have constant structural parameters: g = 15 nm, \({R}_{1}\) = 210 nm, \({r}_{1}\) = \({R}_{1}\)  − 50 nm, l = 180 nm, d = 205 nm. We have simulated n = 1.00, n = 1.01, n = 1.02, n = 1.03, n = 1.04, and n = 1.05RIU, respectively. The simulation results are shown in Fig. 7. From Fig. 7a, it is possible to see that when the refractive index n is changed from 1.00 to 1.05. The transmission spectra show an equidistant redshift with an equal change in refractive index, and the position of the dip trough changes, but the shape of the transmission spectra remains unchanged. In addition, the linear fit of the sensitivity is shown in Fig. 7b. The structure has an optimal performance with a sensitivity of up to 2900 nm/RIU and a FOM of 55.76. From the above analysis, it can be concluded that the structure can be applied to refractive index sensors.

Fig. 7
figure 7

a Transmission spectra at different refractive indices. b Fitted line for the variation of inclination wavelength with refractive index

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The Fano reflection transmission spectra are highly sensitive to the geometrical parameters within a structure, both in terms of position and shape. The Fano resonance transmission spectrum can be significantly affected by even small variations in geometric parameters. Consequently, this article focuses on the influence of changes in parameters such as the radius of the U-shaped cavity structure on the Fano resonant transmission spectra. We investigated the effect of U-cavity structure on Fano resonance. The effect of URRS \({R}_{1}\) was investigated by setting \({R}_{1}\) to 195, 200, 205, 210, and 215 nm. In Fig. 8a, there is a significant red shift in the curve as \({R}_{1}\) increases, which is because of the increased ability of the USRR to converge the electric field, which shifts the resonance wavelengths to larger wavelengths. Figure 8b shows the sensitivity curve in good linearity, from the figure we can conclude that the sensitivity of the URRS varies from 2700 to 3000 nm/RIU when \({R}_{1}\) is varied from 195 to 215 nm at 5 nm intervals. This shows that \({R}_{1}\) is one of the important parameters to improve the sensitivity of the sensor. Yet, increasing the radius will result in an increase in the area of the cavity in the vertical direction, which will increase the loss of the sensor. Therefore, it is not advisable to set the radius \({R}_{1}\) too large in practical use, and we set \({R}_{1}\) to 210 nm.

Fig. 8
figure 8

a Transmission spectra of the URRS at different values of R 1. b Sensitivity fitting lines for different values of  R 1

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Subsequently, in order to better assess the impact of changes in the overall structural parameters of the URRS on the sensor performance. We evaluated the effect of changes in the height d of the URRS on the overall structural transmission characteristics. We varied the height d of the URRS from 175 to 215 nm and plotted its transmission spectrum as revealed in Fig. 9a. Figure 9a reveals that as d increases, the transmittance spectrum shows a significant red shift and a slight increase in transmittance. This is because the ability of the URRS structure to converge the electric field decreases as the resonant cavity height increases. As shown in Fig. 9b, the fitting diagram with a clear linear relationship between parameters and sensitivity exhibits a favorable linear correlation and the sensitivity varies from 2740 to 2980 with d. It can be concluded that varying d improves the sensitivity of the sensor to a certain extent, but the height of the URRS structure has a lesser effect on the performance of the sensor than the radius 

\({R}_{1}\).This is due to the rectangular resonant cavity changes the distance in the vertical direction, which is favorable to the propagation of light, yet the direct waveguide is too long will lead to the process of coupling in the MIM waveguide leads to the frequency bandwidth is too large, which reduces the performance of the sensing; therefore, to synthesize the sensor performance, we set the d to 205 nm.

Fig. 9
figure 9

a Transmission spectra of the URRS at different values of d. b Sensitivity fitting lines for different values of d

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The effect on the system properties was further investigated by varying the structural parameters of three stubs. We have extended the length of the three stubs from 170 to 210 nm, increasing the length in 10 nm increments and plotted the resonance spectra as shown in Fig. 10a. Figure 10a shows that as l increases, the transmission spectrum is red-shifted, the resonance wavelength increases, and the transmittance decreases significantly. This is due to the fact that as l increases, the resonator has a strong resonance inside the resonator, the strength of the electric field gathered inside the URRS increases, and the performance of the sensor is enhanced. Figure 10b shows the fitted curves of the sensitivity when the three stubs are varied, and it can be seen that the sensitivity of the URRS increases significantly from 2840 to 3160 nm/RIU when l is varied at intervals of 10 nm, which suggests that the length of the stubs, l, is also one of the important parameters for improving the sensitivity. However, from the transmission curve in Fig. 10a, it can be seen that the transmission curve deformation is larger with the increase of l. Although the increase of l can lead to the improvement of sensing performance, it will also make the FWHM of the transmission curve increase; therefore, in order to synthesize the performance of the sensors, we set l to 180 nm.

Fig. 10
figure 10

a Transmission spectra of URRS at different values of the stubs length l. b Sensitivity fitting lines for different values of l

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Finally, we investigate the impact of the gap between the URRS structure and the MIM waveguide on the system’s transmission characteristics. We keep the other structural parameters fixed and the coupling distance g is adjusted from 10 to 30 nm at 5 nm intervals. as shown in Fig. 11a, the curve undergoes a significant blue shift and the transmittance gradually increases as g increases, which suggests that the coupling between the SPPs and the URRS is gradually weakened as g increases. The fitted lines of sensitivity at each coupling spacing are shown in Fig. 11b. Sensitivity decreases with increasing coupling spacing and reaches a maximum value of 2980 nm/RIU when g = 10 nm. However, it can be noticed from Fig. 11c that the value of FWHM increases dramatically when g is less than 15 nm, which leads to a relatively small value of FOM. Therefore, we choose g = 15 nm as the optimal coupling distance for the sensor. At this time, the sensitivity is 2900 nm/RIU and the FOM is 55.76.

After several simulation experiments, we derived the structural parameter values for the optimal sensitivity of the structure and compared them with the initial design parameters as shown in Table 1. We compared the URRS structure with existing structures as presented in Table 2, and it is evident that the designed structure outperforms many existing ones.

Table 1 Comparison of initial and final structural parameters
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Table 2 Comparison of data with other structures
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Fig. 11
figure 11

a Transmission spectra at different coupling gaps. b Sensitivity fitting lines for different g. c Variation of FWHM values for different coupling distances

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Application of the Structure in Alcohol Concentration Detection

The structure described in this paper has great promise for applications in the field of alcohol sensors. The principle is that the refractive index of the alcohol solution will change with the change of concentration, and the transmission spectrum of the sensor will be red-shifted with the increase of the refractive index, so based on the relationship between the alcohol concentration and the refractive index, we can calculate the concentration of the alcohol solution according to the position of the sensor transmission spectrum. The alcohol concentration sensor with URRS structure designed in this paper has the advantages of simple structure, low price, high sensitivity, and fast response speed.

The detection process is that different concentrations of alcohol solutions are injected into the MIM waveguide grooves, which the refractive indices vary based on changes in the concentration of the intermediate medium. The transmission spectrum of the structure undergoes positional shifts as the refractive index changes.

After multiple experiments, it has been proven that the relationship between the concentration of ethanol and the refractive index can be expressed by the following equation:

When the alcohol concentration is less than 50%:

$$C=2054.4n-2745.1$$
(5)

When the alcohol concentration is less than 80%:

$$C=2771.7n-3711.4$$
(6)

where n is the refractive index and C is the concentration of the alcohol solution.

We calculated the refractive indices of 1.336, 1.346, 1.356, 1.361, and 1.368 for 0%, 20%, 40%, 60%, and 80% concentrations of alcohol solutions, respectively. The transmission spectra and sensitivity fitting curves were obtained by COMSOL Multiphysics 5.4a software simulation as shown in Fig. 12a, b.

Fig. 12
figure 12

a Transmission spectra as a function of alcohol solution concentration. b Sensitivity fitting lines for alcohol solution concentration change

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From Fig. 12a, it can be obtained that the transmission spectra are more red-shifted at lower solution concentrations and less red-shifted at higher concentrations. The accuracy of the measurement can be ensured by linearly fitting the curve. From Fig. 12b, it can be seen that the sensitivity of this alcohol concentration sensor can be as high as 112.

Conclusions

In this paper, a nano refractive index sensor structure consisting of a MIM waveguide and a U-shaped ring resonator with three stubs (URRS) resonator is proposed. Subsequently, we analyze the effect of the variation of each structural parameter on the sensor performance. The simulation results show that increases in the outer radius \({R}_{1}\), height d, refractive index n, and the length l of the three stubs lead to a redshift of the transmission spectra, and changes in the coupling distance g lead to a blueshift of the transmission spectra. Among them, the variation of parameters R1 and l has a greater effect on the sensitivity of the sensor. The proposed sensor structure has an optimal sensitivity of up to 2900 nm/RIU and a FOM value of 55.76. Finally, we used it for alcohol solution concentration detection, and the sensitivity of this alcohol concentration sensor is up to 112. It provides a new option for high-precision nanoscale concentration sensors.