Introduction

Surface plasmon resonance (SPR) sensors are gaining increased attention in the field of optical sensing owing to their high sensitivity and label-free detection capabilities [1]. The unique optical properties of SPR enable the development of many nanodevices, such as optical switches [2, 3], meta-lens [4,5,6], sensors [7,8,9,10,11], surface-enhanced raman scattering [12, 13], lithography [14, 15], and perfect absorber [16, 17]. SPR sensors can overcome the diffraction limit and achieve higher precision detection than traditional optical sensors. Additionally, SPR is sensitive to changes in the refractive index (RI) of the material in the field-enhancement region. The RI of the surrounding medium, which affects the propagation of surface plasmons, can be accurately measured by analyzing the movement of the resonance angle [18] or wavelength [19, 20]. This property makes SPR sensors highly suitable for a wide range of applications, such as biomedical research [10, 21], environmental monitoring [22], food safety [23], and pharmaceutical analysis [24, 25]. Additionally, RI sensors have been widely studied for detecting trace substances, amongst which RI sensors based on SPR with self-reference characteristics have the broadest application. Refractive index sensors based on SPR mainly include prism composite structures [26], grating composite structures [27,28,29] and metal-insulator-metal (MIM) waveguide structures [30,31,32,33,34]. Among them, the prism composite structure has the disadvantage of being large and unfavorable for integration, while the MIM waveguide structure is unfavorable for realizing self-reference characteristics [35, 36]. The grating composite structure has the advantages of integrability and the possibility of self-reference.

Self-reference is a unique characteristic that can realize a reference comparison in a system, thereby significantly reducing the interference of external factors on the system [26, 37,38,39]. Therefore, numerous research has focused on the design and preparation of SPR sensors with high sensitivity and self-reference characteristics. Maji et al. proposed a self-referential hybrid Tamm plasmon polariton sensor that achieved a 200 nm/refractive index unit (RIU) sensitivity for sensing in liquid environments [21]. Wang et al. proposed a composite structure of nano-elliptical cylindrical arrays with gold films that can excite magnetic plasmon polariton (MPP) modes and localized surface plasmon (LSP) modes. The MPP mode and LSP mode achieved detection with a sensitivity of 52.09 nm/RIU and 522.76 nm/RIU for analytes (n = 1.0–1.6) [40]. Sun et al. proposed a multilayer dielectric nano-disk array with gold thin-film composite structure sensor to obtain the sensitivity and FOM of the sensing channel at 672 nm/RIU and 1050 RIU-1 in the analyte RI range of 1.33–1.38, respectively. The sensitivity of the reference mode was 46 nm/RIU [41]. These systems benefit from self-referencing as the sensitivity of the referencing channel is extremely low. However, the sensing channel is still limited by either a low sensitivity, low FOM, or a small detection range of the RI of the analyte.

To address these limitations, we propose a plasmonic RI sensor based on a square hole array and a gold film coupling structure. This design provides a self-reference characteristic with high anti-interference and improves sensitivity. The sensor has two resonance modes with different functions: one for self-reference (propagating along the interface between the gold film and the silicon dioxide substrate) and the other for sensing (propagating along the interface between gold nano-square hole arrays and analyte). The nano-square hole and gold film composite structure has a wider sensing range to detect gas and liquid analytes than most other systems discussed in the literature. Moreover, the rotating square aperture arrays and the rotation of the polarization direction of the incident light are discussed. Rotating the direction of the square hole array is beneficial for enhancing the signal intensities of the reference and sensing channels. Rotating the polarization direction of the incident light had no effect on the reflection spectra that is excited by the composite structure, indicating that the composite structure had little restraint on the polarization direction of the incident light. Moreover, the simple design of the sensor structure facilitated large-area processing.

Structure Design and Theoretical Foundations

The three-dimensional (3D) schematic and planar projection of the nano-square hole arrary and gold film composite structure are shown in Fig. 1. The composite structure mainly consists of a silicon dioxide substrate, gold film, and gold square hole arrays. The analytes were placed above the nano-square hole and gold film composite structure. The structural parameters of the sensor include the square hole length a, the depth h, the simulation period P, the gold film thickness d, the angle α between the length of the square hole (labeled by the blue dotted line in Fig. 1(b)) and the x-axis, and the angle β between the direction of polarization of the incident light and the x-axis. The reflectance spectrum and electric field distributions of the composite structure were simulated using the finite-difference time-domain (FDTD) method. The schematic x-y plane of the composite structure is shown in Fig. 1(b), where z = 20 nm is the plane of the lower surface of the gold film. In the simulation, the mesh size was set to 8 × 8 × 8 nm, the number of monitoring points was set to 10000, the incident light was a plane wave with the initial polarization along x-direction. The red dotted box represents the selected simulation unit. The x- and y-directions were subject to periodic boundary conditions, and the z-direction used a perfectly matched layer (PML). The main operational principle is as follows: the square hole array acts as a two-dimensional (2D) grating for optical momentum compensation to excite the SPR and the position of the field enhancement is regulated in the square hole. This enables the excitation of two independent propagating surface plasmon resonances (PSPRs) at the top and bottom of the gold film, facilitating self-referential sensing for detecting the RI of the analyte. The steps to fabricate of this sensor are simple, and large-scale fabrication can be achieved through electron beam evaporation and lithography. First, a gold film of thickness d is deposited on the substrate surface by electron beam evaporation. Then, negative photoresist is spin-coated on the gold film surface. Subsequently, the complementary structure of the proposed composite structure is etched through exposure and development steps. Next, a gold layer of thickness h is deposited on the surface of the complementary structure using electron beam evaporation. Finally, the proposed composite structure is obtained by removing the photoresist. In practical refractive index sensing detection: First, the analyte is placed on the upper surface of the composite structure. Then, for detection, the incident light is irradiated perpendicularly on the upper surface of the composite structure through the beam splitter. Finally, the reflected light from the surface of the composite structure is reflected through the beam splitter and measured by a spectrometer [19].

Fig. 1
figure 1

(a) Three-dimensional schematic and (b) planar projection of the square hole array gold film coupling structure

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The square-hole array was used as a 2D grating to satisfy the wave vector matching condition for exciting the SPR as follows:

$${k}_{light}+{k}_{grating}={k}_{SPR}$$
(1)

where klight, kgranting, and kSPR correspond to the wave vector of the incident light, grating compensation and excited SPR, respectively.

Two PSPR modes were excited in this study: one that occurred at the gold film-analyte interface and the other at the gold film-substrate interface. The SPR is mainly excited at the interface between the metal and the medium. The dielectric constant of the metal is closely related to the wavelength of the incident light. This relationship can be accurately described using the Drude model [9]. Therefore, the PSPR mode at the gold film-analyte interface follows the relationship:

$${k}_{SPR}={k}_{0}{n}_{a}\text{sin}\theta +2\pi \frac{\sqrt{{n}^{2}+{m}^{2}}}{P}=\frac{2\pi }{{\lambda }_{0}}\sqrt{\frac{\text{Re}({\varepsilon }_{m})\times {n}_{a}^{2}}{\text{Re}({\varepsilon }_{m})+{n}_{a}^{2}}}$$
(2)

where θ is the incident angle of incident light, n and m are diffraction orders, the simulation period (P), and εm is the dielectric constant of the metal. Equation (2) can be further simplified as follows

$$\lambda_{res}=\frac{P}{\sqrt{{n}^{2}+{m}^{2}}}\sqrt{\frac{\text{Re}({\varepsilon }_{m})\times {n}_{a}^{2}}{\text{Re}({\varepsilon }_{m})+{n}_{a}^{2}}}$$
(3)

where λres is the resonance wavelength of PSPR mode. According to Eq. (3), the resonance wavelength of the PSPR can be calculated. The resonance wavelength of PSPR is tuned by the simulation period (P), the dielectric constant of the metal (εm), the diffraction order (n and m), and the RI of the analyte (na), but is insensitive to the size of the metal nanoparticles. Based on this principle, the reliability of the PSPR mode simulations can be accurately assessed.

The field enhancement region of the PSPR mode propagating along the undersurface of the gold film is the substrate environment. Therefore, Eq. (3) is modified to establish the following relationship:

$${\lambda }_{res}^{\prime}=\frac{P}{\sqrt{{(n^{\prime})}^{2}+{(m^{\prime})}^{2}}}\sqrt{\frac{\text{Re}({\varepsilon }_{m})\times {n}_{s}^{2}}{\text{Re}({\varepsilon }_{m})+{n}_{s}^{2}}}$$
(4)

where \(\lambda_{res}^{\prime}\) represents the resonance wavelength, n' and m' are diffraction orders, and ns is the RI of the substrate.

Results and Discussion

Figure 2 shows the reflectance spectrum of the proposed sensor in a liquid environment and the electric field distribution for Modes 1 and 2. The results indicate that the sensor operates well in a liquid environment. Here the parameters of the square-hole array composite structure are: a = 700 nm, h = 50 nm, d = 30 nm, P = 1050 nm, α = 45° and β = 0°. The reflectance spectrum in Fig. 2(a), indicates that Modes 1 and 2 are (1, 0)-order PSPR modes propagating along the undersurface of the gold film and the upper surface of the nano-square hole array, respectively. The reflectivity at the resonance wavelength is 0.59 for Mode 1 and 0.02 for Mode 2, which presents low reflectivity with a strong detection signal. Figure 2(b–e) exhibit the electric field distributions of Modes 1 and 2 at RI of 1.33 for the analyte. In Fig. 2(b) and (d), Mode 1 is mainly caused by the PSPR, which occurs at the interface between the gold film and the silicon dioxide substrate, propagates along the bottom surface of the gold film, and continuously decay in the -z-direction. Mode 1 has a strong electric field enhancement effect in the substrate, but not in the analyte environment. Therefore, the results suggest that Mode 1 is insensitive to changes in analyte RI and has a self-referential function. Similarly, the analysis of Fig. 2(c) and (e) shows that Mode 2 is a PSPR that occurs and propagates along the upper surface of the gold nano-square-hole array. The field-enhanced region of Mode 2 occurs mainly in the analyte environments and continuously decays in intensity along the z-direction thereby suggesting that Mode 2 strongly interacts with the analyte environment [42]. This phenomenon indicates that Mode 2 is sensitive to changes in the analyte RI and can be used as a sensing mode. The analysis of the electric field distribution, indicates that the composite structure has self-reference characteristic. Moreover, the sensing performance for the composite structure is discussed in detail later in this paper.

Fig. 2
figure 2

(a) The reflectance spectrum of the proposed sensor in a liquid environment. (b–e) Electric field distribution at the resonance wavelength. (b) Mode 1 at x–z cross-section with y = 0 nm, (c) Mode 2 at x-z cross-section with y = 0 nm, (d) Mode 1 at x-y cross-section with z = 20 nm, and (e) Mode 2 at x-y cross-section with z = 50 nm

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The parameters were optimized to further explain the plasmonic effects excited by the sensor. As shown in Fig. 3, the reflectance spectrum of the composite structures was investigated by varying the angle (α) of the square aperture array and the polarization direction of the incident light. In Fig. 3(a), the reflectivity at the dip of Modes 1 and 2 decreases slightly as α changes from 0° to 45° in 5° incremental steps. Here, α = 45° was considered as the optical value. In Fig. 3(b), the reflectance spectrum of the sensor is almost constant as β changes. This indicates that the sensor has almost no condition for the polarization direction of the incident light, which is beneficial for practical applications. Both SPR modes excited by the proposed sensor are PSPR modes, which are insensitive to variations in geometric parameters of individual nano-square holes. Furthermore, based on the arrangement, the proposed structure belongs to a square dot array arrangement. Therefore, for the PSPR mode, from a physical perspective, the change in the polarization direction of the incident light does not affect the reflectance spectrum of the composite structure. The sensing modes are mainly caused by the PSPR modes that propagate along the upper surface of the gold film and decay in the z-direction. The self-reference mode is mainly caused by the PSPR mode that propagates along the lower surface of the gold film and decays in the -z direction. The excitation sensing mode only needs to satisfy the momentum matching condition, and the incident light is directly incident on the upper surface of the composite structure. However, for the self-reference mode, the energy of the incident light needs to penetrate the gold film and be coupled to the lower surface of the gold film. This results in the signal strength of the sensing mode usually higher than that of the self-reference mode [41].

Fig. 3
figure 3

Reflectance spectrum of composite structures at different values of (a) α and (b) β

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Figure 4 shows the reflectance spectrum of the optimization process for the side length a, depth h of the square holes in the composite structure, and thickness d of the gold film. Figure 4(a) shows that the resonance wavelengths of Modes 1 and 2 remain unchanged as a increases; indicating that the two modes are insensitive to changes in this parameter. However, significant effect was observed on the signal intensity obtained for a = 700 nm. In Fig. 4(b), the optimization of the square hole depth was obtained for h = 50 nm, based on the trade-off between the resonance wavelength of Modes 1 and 2. As Mode 1 was the referencing mode, the resonance wavelength of Mode 2 cannot approach to that of Mode 1. As the RI of the analyte increases, Mode 2 experiences a red-shift. If the resonance of Mode 2 is similar to that of Mode 1, the resonance wavelength of Mode 1 is affected, altering the sensitivity of Mode 1 and limiting the sensing range of the sensor. Therefore, this factor must to be considered during the parameter optimization. At h = 50 nm, the reflectivity of Mode 2 at the dip was extremely low, at approximately 0. For Fig. 4(c), as d increased, the reflectivity at the resonance wavelength for Mode 1 increased, Mode 2 decreased, and the full width at half maximum (FWHM) for both modes decreased. The resonance wavelengths and FWHM of Modes 1 and 2 were considered, resulting in d = 30 nm. Figure 4 shows that the resonance wavelengths of Modes 1 and 2 are insensitive to changes in a, h, and d, which further confirms that Modes 1 and 2 are PSPRs. The PSPR is sensitive to changes in the period of the composite structure, whereas the LSPR is sensitive to changes in the size and shape of the nanoparticles [20]. Based on the above analysis of parameter optimization, a = 700 nm, h = 50 nm, and d = 30 nm were obtained.

Fig. 4
figure 4

Reflectance spectrum for different values of (a) the side length a of the square hole, (b) the depth h of the square hole, and (c) the gold film thickness d

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Next, we examined the effect of the period (P) of the square hole array composite structure on the reflectance spectrum. The theoretical resonance wavelengths of Modes 1 and 2 excited by the composite structure were calculated according to the theoretical equations (Eqs. (3) and (4)). Figure 5(a) shows the reflectance spectrum as the period changes from 1000 to 1250 nm in steps of 50 nm. As the period increases, the resonance wavelengths of Modes 1 and 2 show a significant linear red-shift, which is characteristic of PSPR. In general, the closer the resonance wavelength of the PSPR (as the sensing mode) is to the deep infrared band, the higher the sensitivity of this mode. When P = 1050 nm, the resonance wavelength of Mode 1 was less than 0.6, which resulted in a trade-off value of P = 1050 nm.

Fig. 5
figure 5

(a) Reflectance spectrum of the sensor at different simulation periods. (b) Comparison between the simulation and theoretical analysis for PSPRs

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In addition, the comparison between the simulation results (shown in Fig. 5(a)) and the theoretical analysis results is shown in Fig. 5(b). The results of simulation calculations and theoretical analyses of Modes 1 and 2 were basically fitted, confirming the reliability of sensor. Theoretical analysis implies that Modes 1 and 2 are (1,0) modes ((n,m) = (n',m') = (1,0)).

The sensing performance of the proposed sensors and self-referencing characteristics were investigated based on the above analysis. Two crucial-parameters for sensing performance. One of the parameters are sensitivity (S) and FOM. The expressions for these two parameters are as follows:

$$S=\frac{\Delta \lambda }{\Delta n}$$
(5)
$$FOM=\frac{S}{FWHM}$$
(6)

where sensitivity (S) quantifies the sensing capability of the sensor, and the FOM quantifies the sensing accuracy.

The sensing performance of the composite structure was investigated based on optimal parameters. Figure 6 shows the sensing performance of the sensor in a liquid environment, where Fig. 6(a) shows the reflectance spectrum of the sensor in a liquid environment, with different colors corresponding to different reflectivity. As the refractive index increased, Modes 1 and 2 exhibited well linear sensitivities, and the resonance wavelengths of the self-reference mode (Mode 1) remained almost constant, whereas that of the sensing mode (Mode 2) is significantly red-shifted. The electric field enhancement region of Mode 1 is located mainly in the substrate environment, while the substrate material remains unchanged. Therefore, the resonance wavelength of Mode 1 remains almost constant when the refractive index of the analyte changes. In contrast, the electric field enhancement region of Mode 2 is located mainly in the analyte environment and is extremely sensitive to changes in the analyte. Mode 2 undergoes a significant linear redshift as the refractive index of the analyte increases. Meanwhile, the FWHMs of Modes 1 and 2 were nearly constant. The FWHMs of Modes 1 and 2 were 8.9 and 12.7 nm in the liquid environment, respectively. Figure 6(b) shows the relationship between the resonance wavelengths of the two modes and the RI of the different liquid analytes. The sensitivity of Mode 1 in the liquid environment was 21 nm/RIU, whereas the sensitivity and FOM of Mode 2 in the liquid environment were 1063 nm/RIU and 83 RIU-1, respectively. These results demonstrate the high sensitivity and self-reference characteristics of the proposed sensor in liquid environment.

Fig. 6
figure 6

(a) Reflectance spectrum of the proposed sensors in liquid environments. Different colors correspond to different reflectivity. (b) Relationship between resonance wavelength and RI of liquid analytes

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The sensor’s performance in a gas environment was further investigated to broaden its application range. First, Fig. 7 shows the reflectance spectrum of the sensor in a gas environment alongside the electric field distributions for Modes 1 and 2. Identical to the liquid environment, the composite structure can excite two PSPR modes in gas environments. For Fig. 7(b) and (d), Mode 1 is mainly caused by the PSPR, which occurs at the interface between the gold film and the silicon dioxide substrate. This mode, propagates along the underside of the gold film, and decays continuously along the -z-direction. For Fig. 7(c) and (e), Mode 2 is a PSPR that occurs and propagates along the interface between the gold nano-square hole arrays and analyte. The field enhancement region of Mode 2 occurs mainly at the top of the gold nano-square hole array and continuously decays in the z-direction. This demonstrates that the sensor still exhibits self-reference characteristics in a gas environment.

Fig. 7
figure 7

(a) Reflectance spectrum of the proposed sensors in a gas environment. (b–e) Electric field distribution at the resonance wavelength. (b) Mode 1 at x-z cross-section with y = 0 nm, (c) Mode 2 at x-z cross-section with y = 0 nm, (d) Mode 1 at x-y cross-section with z = 20 nm, and (e) Mode 2 at x-y cross-section with z = 50 nm

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This analysis provides ample evidence that the sensor exhibits self-reference characteristic. The sensing performance for gas environments is discussed in Fig. 8. Figure 8(a) shows the reflectance spectrum of the sensor in gas environments with different colors corresponding to different reflectivity. Modes 1 and 2 exhibited excellent linear sensitivities with increased RI. Figure 8(b) shows the relationship between the resonance wavelengths of the two modes and the RI of the different gas analytes. Similar to the analysis in Fig. 6, the sensitivity of Mode 1 was 0 nm/RIU. The FWHMs of Modes 1 and 2 were 7.7 nm and 10.3 nm in the gas environment, respectively. The sensitivity and FOM for Mode 2 in the gas environment were 1037 nm/RIU and 103 RIU-1. These results further illustrate that the sensor can perform well in gas and liquid environments.

Fig. 8
figure 8

(a) Reflectance spectrum of the proposed sensors in a gas environment. Different colors correspond to different reflectivity. (b) Relationship between resonance wavelength and RI of gas analytes

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The performance of the proposed sensor was compared with that of similar sensors previously reported and listed in Table 1 [43,44,45,46]. The proposed sensor allows for refractive index sensing with high sensitivity and FOM. In addition, the sensor exhibited excellent self-reference performance. A comprehensive comparison shows that our sensor outperforms the aforementioned studies.

Table 1 Comparison of the performance of the proposed sensor with that of other sensors from literature
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Conclusion

We propose a self-referential plasmonic sensor based on a square hole array and gold film composite structure. Its sensing performance and field-enhancement phenomena were analyzed using the FDTD method. The sensor can excite the PSPR mode on the top and bottom surfaces of the gold film. The PSPR mode excited on the lower surface of the gold film exhibited excellent self-reference performance, while the PSPR mode excited on the upper surface of the gold nano-square-hole array exhibited excellent sensing performance. The composite structure does not require the specification of the polarization direction of the incident light. At the optimized parameters (a = 700 nm, h = 50 nm, d = 30 nm, and P = 1050 nm), the sensor achieved high-sensitivity sensing at 1037 and 1063 nm/RIU in gas and liquid environments, respectively. This type of sensor can be widely used for biochemical detection.