Introduction

Due to the advantages of high sensitivity, high selectivity, low cost, and so on,1,2,3 optical biosensors play an important role in modern biomedical, material, and environmental monitoring applications.

In recent years, metasurfaces4,5,6 have emerged as a crucial area for advancing the development of optical sensing technology. Metasurfaces are optical devices composed of subwavelength structures that can be designed reasonably to achieve specific functions.7,8,9 For optical sensing, metasurfaces can confine light to micro/nanoscale electromagnetic hotspots to improve sensitivity. In addition, due to the important role played by the anopole mode in regulating the light field,10,11 the anopole metasurface can also be applied to optical sensing.12 Metasurface optical sensors have been applied in many works.13,14,15,16

Refractive index sensors are one of the most common types of optical biosensors.17,18,19 When the refractive index of the analyte increases, it will cause a redshift of resonance. The sensitivity is defined as the ratio of the shift of the resonance peak to the change in refractive index.20 In addition, the change in resonance intensity can also be used as a detection indicator for refractive index sensing.21 However, the main problem currently limiting the performance of refractive index sensors is the weak interaction between the light field and the analyte, resulting in low sensitivity. At present, most methods enhance the interaction between light and analytes by increasing the Q factor, including the coupling of localized surface plasmon resonance with surface lattice modes, high-refractive-index dielectric materials, and Fano resonance structures.22,23,24 Due to the near-field enhancement and strong nonlinear effects, toroidal dipole resonance also can significantly enhance the interaction between light and matter.25,26 Therefore, Wang et al.27 designed the toroidal dipole to achieve high sensitivity by using a strong electric field generated near the microstructure interface around the toroidal dipole. Moreover, as a new method for achieving an infinite Q factor, bound states in the continuum (BIC) have been proposed.27,28,29,30 High-Q and high-sensitivity sensing can be achieved by quasi-BICs.31,32,33 Although the BIC can achieve high Q factor and high figure of merit (FOM), most studies have found that electric field enhancement is localized in a small area, resulting in weak interaction between light and analytes, and the sensitivity is still not suboptimal.

Plasma plays a crucial role in confining and manipulating local electromagnetic fields. However, in optical frequencies, metals exhibit significant losses, leading to a low Q factor. Moreover, fabrication tolerances can reduce the Q factor, which results in an inability to achieve high-performance refractive index sensing. Due to the low loss of dielectric material, all-dielectric metasurfaces with high Q can be achieved. Therefore, we have designed a conical hole structure for all-dielectric metasurfaces. The toroidal dipole resonance mode achieved by using the conical hole structure not only can achieve a high Q factor, but also can achieve large-area electric field enhancement, thus achieving high refractive index sensitivity sensing and high FOM. We also confirm the strong robustness of the structure.

Structure and Model

Figure 1 shows the designed all-dielectric conical hole unit structure. The side length L of the unit is 1 μm, height H is 0.2 μm, and the upper diameter D of the conical hole is 0.7 μm. The material is glass (LaSF), with a fixed refractive index of 1.8. Here, the finite element method (FEM) is used for simulation, with the electric field polarized in the X direction and the wave vector incident perpendicular to the metasurface in the Z direction. Periodic conditions are set in the X and Y directions, and the Z direction is defined as a perfectly matched layer. To avoid interference, the monitor is placed at a distance of 10 μm from the surface of the structure.

Fig. 1
figure 1

(a) The three-dimensional unit structure of the metasurface; (b) cross-section of the unit structure.

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Results and Discussion

Firstly, the effect of the conical hole bottom radius on the transmission of the structure was studied. The circular hole can obtain two obvious resonances when the bottom radius is 0.35 μm, as indicated in Fig. 2a. As the bottom radius of the conical hole decreases to 0 μm, the resonance line width of long wavelengths is significantly reduced, while the change in short wavelength resonance is not very significant. The narrower the resonance peak, the higher the Q factor obtained. Therefore, the bottom radius of the conical hole chosen here is 0 μm for further research. As shown in Fig. 2b, the wavelengths of the two resonances are 1.087 μm and 1.255 μm, and the corresponding Q factors are 1767.4 and 173.7. Compared to the Q factor of resonance at 1.255 μm, the Q factor of resonance at 1.087 μm is about 10 times higher.

Fig. 2
figure 2

(a) Transmission with varying bottom radius; (b) transmission of the bottom radius of 0 μm.

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A higher Q factor does not necessarily lead to high refractive index sensitivity. Therefore, these two resonance modes need further research. To analyze the electromagnetic resonance modes of these two resonances, multipole decomposition can be performed by integrating the current density of the structure in the Cartesian coordinate system.34,35 Multipole resonance can be written in the form of the following current description:

Electric dipole (ED):

$$P=-\frac{1}{iw}\int j{d}^{3}r$$
(1)

Magnetic dipole (MD):

$$M=\frac{1}{2c}\int (r\times j){d}^{3}r$$
(2)

Toroidal dipole (TD):

$$T=\frac{1}{10c}\int \left[\left(r\cdot j\right)r-2{r}^{2}j\right]{d}^{3}r$$
(3)

Electric quadrupole (EQ):

$${Q}_{\alpha \beta }=-\frac{1}{2iw}\int \left[{r}_{\alpha }{j}_{\beta }+{r}_{\beta }{j}_{\alpha }-\frac{2}{3}(r\cdot j){\delta }_{\alpha \beta }\right]{d}^{3}r$$
(4)

Magnetic quadrupole (MQ):

$${M}_{\alpha \beta }=\frac{1}{3c}\int \left[{\left(r\times j\right)}_{\alpha }{r}_{\beta }+{\left(r\times j\right)}_{\beta }{r}_{\alpha }\right]{d}^{3}r$$
(5)

where j is the surface current density, c is the speed of light in vacuum, and r is the displacement vector. Only ED, MD, TD, EQ, and MQ have been calculated here, as shown in Fig. 3a. It can be observed that the resonance at 1.087 μm is mainly EQ and MD, while the resonance at 1.255 μm is mainly TD resonance. Meanwhile, the impedance of the metasurface can be calculated by the impedance formula. The formula is as follows:36

$$Z=\sqrt{\frac{{(1+{S}_{11})}^{2}-{S}_{21}^{2}}{{(1-{S}_{11})}^{2}-{S}_{21}^{2}}}$$
(6)

where \({S}_{11}\) and \({S}_{21}\) represent the reflection and transmission, respectively. As shown in Fig. 3b, the effective impedance of the two resonances is Z = 0.02 + 1.09i and Z = 0.00 + 0.79i. Because the transmission of the two resonances approaches zero, the real part of the impedance is close to zero, and the imaginary part of the impedance is close to 1.37

Fig. 3
figure 3

(a) Scattering power of multipole decomposition; (b) effective impedance of the metasurface.

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Since it is different from traditional EDs and MDs, the TD can greatly promote the interaction between light and matter, and is extremely sensitive to environmental changes. Equations (7) and (8) are the electric field radiation of traditional dipole and toroidal dipole resonance, respectively.38 From one of the equations, it can be seen that, compared to dipole resonance, the electric field of the TD is more sensitive to changes in environmental refractive index. By utilizing the characteristics of the TD, highly sensitive biosensing can be achieved. For refractive index sensing, the TD plays an important role, and future research needs to focus on TDs.

$${E}_{P}={n}^{2}{k}_{0}^{2}\left(\widehat{r}\times \widehat{r}\times \frac{\widehat{P}}{r}\right)$$
(7)
$${E}_{T}={n}^{3}{k}_{0}^{3}\left(\widehat{r}\times \widehat{r}\times \frac{\widehat{T}}{r}\right)$$
(8)

To further analyze the resonance modes, we analyzed the electromagnetic fields of these two resonances, as shown in Fig. 4. Figure 4a, c and b, d show the cross-section position at Z = 0 μm and X = 0 μm, respectively. Figure 4a shows the electric field at 1.255 μm. The black arrow indicates the current vector, and the blue arrow indicates the direction. The direction of the middle electric field and the upper and lower electric fields are opposite. The middle and upper electric fields can form an upward magnetic field, while the middle and lower magnetic fields can form a downward magnetic field, which is also proven by Fig. 4b. The white arrow in Fig. 4b represents the magnetic field vector, while the blue arrow represents the direction. The left upward magnetic field and the right downward magnetic field form the TD, which is also the main resonance mode of 1.255 μm. Figure 4c shows the electric field at 1.087 μm has four directions, which can form an EQ. In Fig. 4d, the magnetic field propagates only along the y-axis. Therefore, an MD is formed. Analyzing the electric and magnetic fields at 1.087 μm shows that EQ and MD are formed, which correspond to the multipole decomposition results in Fig. 3a.

Fig. 4
figure 4

(a), (c) Electric field and (b), (d) magnetic field of the conical hole at (a), (b) 1.255 μm and (c), (d) 1.087 μm, respectively. The black arrows are the current vector, the white arrows are the magnetic field vector, and the blue arrow indicates the direction (Color figure online).

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In addition to considering the resonance mode, attention should also be paid to the location and the size of the electric field enhancement area. Figure 5a and b shows the cross-section of the electric field of the resonance of 1.255 μm at Y = 0 μm and X = 0 μm, respectively. As shown in Fig. 5c and d, the cross-section is the electric field of the resonance of the 1.087 μm at Y = 0 μm and X = 0 μm, respectively. The electric fields of 1.255 μm and 1.087 μm show significant enhancement. However, the location of these two resonance enhancements is different. The resonance electric fields of 1.255 μm and 1.087 μm are mainly located inside and outside of the conical hole, respectively. Meanwhile, the difference in the size of the electric field enhancement area is not significant.

Fig. 5
figure 5

Electric field of the conical hole at (a), (b) 1.255 μm and (c), (d) 1.087 μm, respectively.

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Previous studies have confirmed that the thickness of the analyte layer has a significant impact on frequency shift. Firstly, the frequency shift will increase as the thickness of the analyte layer increases. When the thickness of the analyte layer increases to a threshold, no matter how the thickness of the analyte layer increases, the frequency shift will not increase significantly.39 The main reason for this phenomenon is that the electric field intensity decays exponentially in the vertical direction of the sample, resulting in a weak interaction between the electric field and the analyte. Therefore, when the analyte increases to a certain thickness, the frequency shift of the resonance peak will not change significantly.

According to the results shown in Fig. 5, the electric field is still enhanced at 0.5 μm from the surface of the structure. Therefore, we first investigated the variation in transmission with different thicknesses of analytes. As shown in Fig. 6a, the analyte has a refractive index of 1.5, and its transmission spectrum varies with its thickness. As the thickness of the analyte increases, the resonance peak of the two white dotted lines does not continue to increase at a thickness of about 1 μm. Therefore, the thickness of the analyte is chosen to be 1 μm, and the transmission obtained by varying the refractive index of the analyte is shown in Fig. 6b. As the refractive index of the analyte increases, the resonance peak exhibits a significant redshift. After calculation, the sensitivity of the resonance at 1.255 μm can reach 540 nm/RIU with a FOM (the ratio of the sensitivity to the full width of the half-peak) of 154.3, and sensitivity of the resonance at 1.087 μm can reach 749.6 nm/RIU. However, the resonance at 1.087 μm shows a significant decrease in intensity as the refractive index changes, which is not conducive to the detection of the signal. Therefore, resonance of 1.255 μm was chosen here for refractive index sensing.

Fig. 6
figure 6

(a) Transmission with varying analyte thickness; (b) transmission at 1-μm-thick analyte with analytes of different refractive indexes. The white dotted line in (a) shows the trend of the resonance with increasing analyte thickness.

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In addition, compared to the previous all-dielectric toroidal dipole resonance structure reported in Table I, the sensitivity and FOM obtained here are significantly increased. Although some studies have higher FOM values, the sensitivity is lower. The high FOM is because they can produce a very narrow line width and obtain a high Q factor. And the low sensitivity is mainly because the local electric field enhancement is small, or the electric field enhancement is located inside of the structure, resulting in a weak interaction between the electric field and the analyte. Our structure can achieve higher sensitivity because the electric field enhancement has a large area, and the electric field enhancement is mainly outside the structure, so it can fully enhance the interaction between the electric field and the analyte.

Table I Performance index parameters of refractive index sensing based on a toroidal dipole all-dielectric metasurface
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Considering the real fabrication tolerance, the conical hole is more difficult to fabricate in practice, and an ellipsoidal hole may be obtained in the end. Therefore, the conical hole is changed to an ellipsoid hole. The long axis L1 is 0.7 μm, and half of the short axis L2 is 0.2 μm, as shown in Fig. 7a. When the conical hole is changed to an elliptical hole, the transmission is obtained in Fig. 7b, and the Q factor of resonance at 1.222 μm is 54. Compared to the electric field of the conical hole in Fig. 5, the electric field of the ellipsoidal hole structure shown in Fig. 7c and d is weak, which leads to a low Q factor. However, there is an increase in the area of the electric field enhancement.

Fig. 7
figure 7

(a) The three-dimensional image and cross-section of the ellipsoidal hole; (b) transmission of the ellipsoidal hole; electric field of the ellipsoidal hole in the (c) XZ and (d) YZ planes.

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Next, we investigated the effect of the ellipsoidal hole on refractive index sensing. When the ellipsoidal hole covers the analyte with a thickness of 1 μm, the sensitivity of the TD obtained from the simulation in Fig. 8a can reach 590 nm/RIU and FOM of 62.6. Although structural changes lead to low Q factors, the increase in the area of the electric field enhances the light–matter interaction. Therefore, it can be found that the fabrication tolerance has very little effect on the refractive index sensing, which indicates that the structure has a certain robustness. This is of great significance for the practical application of the structure. In addition, when the height H of the conical hole is fixed, the resonance is redshifted, and the line width of the resonance peak is also narrowed as the thickness of the structure increases, as shown in Fig. 8b. Multiple resonance peaks also appear as the thickness of the structure increases. Multiple resonance peaks can appear in more abundant electromagnetic resonance modes, so the sensitivity detection of multiple resonance peaks can be realized based on the different thicknesses of the structure and multiple wavelengths, which can be further optimized to improve the refractive index sensitivity and FOM.

Fig. 8
figure 8

(a) Transmission of an ellipsoidal hole structure at 1-μm-thick analyte with analytes of different refractive indexes; (b) transmission of conical hole structure varying with increasing thickness of the structure.

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Conclusion

The all-dielectric conical hole structure obtains toroidal dipole resonance, which leads to significant enhancement of light–matter interaction and large-area electric field. Moreover, the refractive index sensitivity and FOM can reach 540 nm/RIU and 154.3, respectively. Compared to the previous all-dielectric toroidal dipole resonance metasurfaces, the conical hole structure indicates a substantial improvement in sensing performance. The modification of the conical hole into an elliptical hole retains high sensitivity, confirming that the structure has a certain robustness, which is of great significance for practical application. At the same time, by changing the thickness of the structure, multiple resonances can be realized, and thus high-sensitivity detection at multiple wavelengths can also be achieved based on multiple resonance modes.