Multi-function sensing applications based on high Q-factor multi-Fano resonances in an all-dielectric metastructure

A multi-function sensor based on an all-dielectric metastructure for temperature and refractive index sensing simultaneously is designed and analyzed in this paper. The structure is composed of a periodic array of silicon dimers placed on the silicon dioxide substrate. By breaking the symmetry of the structure, the ideal bound states in the continuum can be converted to the quasi-bound states in the continuum, and three Fano resonances are excited in the near-infrared wavelength. Combining with the electromagnetic field distributions, the resonant modes of three Fano resonances are analyzed as magnetic dipole, magnetic toroidal dipole, and electric toroidal dipole, respectively. The proposed sensor exhibits an impressive maximal Q-factor of 9352, with a modulation depth approaching 100%. Our investigation into temperature and refractive index sensing properties reveals a maximum temperature sensitivity of 60 pm/K. Regarding refractive index sensing, the sensitivity and figure of merit are determined to be 279.5 nm/RIU and 2055.1 RIU-1, respectively. These findings underscore the potential of the all-dielectric metastructure for simultaneous multi-parameter measurements. The sensor's versatility suggests promising applications in biological and chemical sensing.


Introduction
It is essential to accurately measure temperature and refractive index in the chemical industry, biological sensing, and environmental monitoring [1].Various structures, such as silica bottle resonator [2], surface plasmonic waveguide [3], and photonic crystal [4], have been used for simultaneous measurement of temperature and refractive index, which are limited in terms of size, sensitivity, and integration capabilities [5].Dielectric materials present low thermal conductivity and ohmic loss compared to metallic materials [6], which is believed to further contribute to the development of sensors [7], bidirectional optical switches [8], and filters [9].All-dielectric metastructures have the characteristics of small size and compatibility with CMOS systems, which are more appropriate for the development of miniaturized and integrated modern optical systems [10].In addition, by adjusting the physical parameters and geometry shape of metastructures, it is possible to exhibit remarkable electromagnetic properties, thus enabling the realization of excellent resonance characteristics [11,12].
Fano resonance is an asymmetric spectral profile phenomenon caused by the destruction of interference between continuous and discrete local states [13,14].An efficient approach to generating high Q-factor Fano resonance is on the basis of bound states in the continuum (BIC) in all-dielectric metastructures [15][16][17][18].An ideal BIC is a mathematical model existing in an ideal lossless structure, which cannot be used for practical applications due to the characteristics of an exceptionally thin linewidth and an infinitely high Q-factor [19][20][21].However, by using the method of symmetry breaks in the metastructures, the radiation channel with the outside is established, which allows ideal BIC is disturbed and converted to the quasi-BIC, leading to limited linewidth and high Q-factor [22][23][24].
Due to significant near-field enhancement and narrow spectral characteristics, high Q-factor Fano resonance is extensively applied in high-performance sensors [25,26].Liao et al. proposed a temperature sensor based on a grating-like metastructure, which achieved the maximum Q-factor of 4400 and the maximum sensitivity of 68.7 pm/°C [27].Yu et al. proposed a refractive index sensor based on an asymmetric semi-circular metastructure, which achieved the maximum Q-factor of 2617, the sensitivity of 300 nm/RIU, and the FOM of 440 RIU −1 [28].Ye et al. presented a rhombus metastructure to achieve a refractive index sensor, the sensitivity and FOM are 255 nm/RIU and 477 RIU −1 , respectively [29].Sensors are a typical application of high Q-factor Fano resonance, but few studies have achieved multi-function sensors for simultaneous measurement of the temperature and refractive index based on all-dielectric metastructures.Therefore, it is meaningful to design a metastructure that can excite high Q-factor multi-Fano resonances, which is used as a multi-function sensor.
In this paper, a multi-function sensor for simultaneous measurement of temperature and refractive index based on an all-dielectric metastructure is designed.The structure consists of Si dimer and periodically aligns on a SiO 2 substrate.The finite-difference time-domain (FDTD) method is adopted to simulate and analyze the optical properties of the designed structure.By tuning the length of Si dimer, the symmetry of the structure is broken, which converts the BIC to the quasi-BIC.Three high Q-factor Fano resonances with the modulation depth of nearly 100% are excited.The temperature and refractive index sensing properties of the proposed structure are investigated.The sensitivity to the temperature can reach 60 pm/K.For refractive index sensing, the sensitivity (S) and the figure of merit (FOM) are 279.5 nm/RIU and 2055.1 RIU −1 , respectively.The results show that the structure can achieve a multi-function sensor, which provides a further step in the development of high-performance sensors.

Model and simulation
Figure 1 shows the schematic diagram of the proposed metastructure laid on the SiO 2 substrate, which consists of asymmetric Si dimer.The thickness of Si dimer is H 1 , the thickness of SiO 2 substrate is H 2 , the length of Si dimer is L, the widths of Si dimer are W 1 and W 2 respectively, the distance between Si dimer is d, and the asymmetry parameter δ is given as δ = L 1 −L 2 .The periods are P x and P y in the x and y directions.The electric field is y-polarized (polarization angle is 90 • ), and the plane wave is incident perpendicular to the structure along the z-direction.The simulation results are solved using the FDTD method.In the z direction, the perfectly matched layer (PML) is set as well as the periodic boundary conditions are used in the x and y directions.The material characteristics of Si and SiO 2 are obtained in the Palik handbook [30].The real and imaginary parts of the refractive index of Si and SiO 2 in the experimental wave band are shown in Fig. 1(c)-(d).

Results and discussion
When d = 40 nm , W 1 = 150 nm , W 2 = 130 nm , H 1 = 120 nm , H 2 = 220 nm , P x = P y = 700 nm , L = 600 nm , L 1 = 370 nm , L 2 = 300 nm , the impedance of the structure are shown in Fig. 2(a), which indicates the degree that the structure impedes incident light.Meanwhile, the transmission spectra of symmetrical ( δ = 0 nm ) and asymmetrical ( δ = 70 nm ) metastructures are analyzed in Fig. 2(b).For δ = 0 nm ( L 1 = L 2 = 300 nm ), one Fano resonance appears at λ = 1162.67nm .When the symmetry of the structure is broken at δ = 70 nm (L 1 = 370 nm , L 2 = 300 nm ), two new Fano resonances appear at λ = 1128.32nm (R1) and λ = 1271.86nm (R3), respectively.The original Fano resonance shows a redshift at λ = 1186.96nm (R2).The performance of Fano resonance can be evaluated by the Q-factor and modulation depth, which can be qualitatively analyzed by the following expression [31]: Where a 1 , a 2 , and b are defined as real numbers, the resonant frequency is ω 0 , γ is the overall damping loss, and the Q-factor is defined as [32]: In Fig. 2(c), the fitting result at λ = 1271.86nm (R3) is consistent with the calculated result using FDTD.The Q-factors of R1, R2, and R3 are 4179, 733, 9352, respectively.In addition, the modulation depth is defined as [33]: ) in which T peak and T dip are respectively the transmission amplitude at the peak and dip of Fano resonance.The calculated modulation depths of R1, R2, and R3 are 98.9%, 98.9%, 99.1%,

Results and discussion
When d = 40 nm, W 1 = 150 nm, W 2 = 130 nm, H 1 = 120 nm, H 2 = 220 nm, P x =P y = 700 nm, L = 600 nm, L 1 = 370 nm, L 2 = 300 nm, the impedance of the structure is shown in Fig. 2(a), which indicates the degree that the structure impedes incident light.Meanwhile, the transmission spectra of symmetrical (δ = 0 nm) and asymmetrical (δ = 70 nm) metastructures are analyzed in Fig. 2(b).For δ = 0 nm (L 1 =L 2 = 300 nm), one Fano resonance appears at λ = 1162.67nm.When the symmetry of the structure is broken at δ = 70 nm (L 1 = 370 nm, L 2 = 300 nm), two new Fano resonances appear at λ = 1128.32nm (R1) and λ = 1271.86nm (R3), respectively.The original Fano resonance shows a redshift at λ = 1186.96nm (R2).The performance of Fano resonance can be evaluated by the Q-factor and modulation depth, which can be qualitatively analyzed by the following expression [31]: Where a 1 , a 2 , and b are defined as real numbers, the resonant frequency is ω 0 , γ is the overall damping loss, and the Q-factor is defined as [32]: In Fig. 2(c), the fitting result at λ = 1271.86nm (R3) is consistent with the calculated result using FDTD.The Q-factors of R1, R2, and R3 are 4179, 733, 9352, respectively.In addition, the approaching 100%.Therefore, it can be found that multiple Fano resonances with excellent performance are excited in the designed structure.The transmission spectra are simulated with different asymmetry parameters δ in Fig. 3 (a).For δ = 0 nm , there are no Fano resonances at λ = 1128.32nm (R1) and λ = 1271.86nm (R3).The resonant mode is the ideal BIC mode, and the Q-factor is infinite.When δ ≠ 0 nm , the difference between L 1 and L 2 breaks the symmetry of the structure, which makes the ideal BIC disturbed and converted to the quasi-BIC.In Fig. 3 (a), Fano resonances appear at λ = 1128.32nm (R1) and λ = 1271.86nm (R3) as δ increases.Meanwhile, the larger the δ is and the wider the radiation channel is, resulting in more energy radiating into the free space, so the linewidths of two quasi-BIC-induced Fano resonances increase.In addition, the relationship between the radiative Q-factor of quasi-BIC-induced Fano resonances and the asymmetry degree α is discussed in Fig. 3(b).The radiative Q-factor is given as [34]: 4) in which Q 0 is a constant decided by the designed metastructure, and α is the degree of asymmetry.The α = ΔS/S , where ΔS is the increased area of Si material relative to the symmetrical structure and S is the area of the Si material for δ = 0 nm .In Fig. 3  modulation depth is defined as [33]: in which T peak and T dip are respectively the transmission amplitude at the peak and dip of Fano resonance.The calculated modulation depths of R1, R2, and R3 are 98.9%, 98.9%, 99.1%, approaching 100%.Therefore, it can be found that multiple Fano resonances with excellent performance are excited in the designed structure.
The transmission spectra are simulated with different asymmetry parameters δ in Fig. 3(a).For δ = 0 nm, there are no Fano resonances at λ = 1128.32nm (R1) and λ = 1271.86nm (R3).The resonant mode is the ideal BIC mode, and the Q-factor is infinite.When δ ≠ 0 nm, the difference between L 1 and L 2 breaks the symmetry of the structure, which makes the ideal BIC disturbed and converted to the quasi-BIC.In Fig. 3(a), Fano resonances appear at λ = 1128.32nm (R1) and λ = 1271.86nm (R3) as δ increases.Meanwhile, the larger the δ is and the wider the radiation channel is, resulting in more energy radiating into the free space, so the linewidths of two quasi-BIC-induced Fano resonances increase.In addition, the relationship between the radiative Q-factor of quasi-BIC-induced Fano resonances and the asymmetry degree α is discussed in Fig. 3(b).The radiative Q-factor is given as [34]: in which Q 0 is a constant decided by the designed metastructure, and α is the degree of asymmetry.The α = ∆S/S, where ∆S is the increased area of Si material relative to the symmetrical structure and S is the area of the Si material for δ = 0 nm.In Fig. 3   Further, the transmission spectra with different geometric parameters are analyzed.In Fig. 5(a), it can be seen that three Fano resonances generate a significant redshift as the thickness H varies from 715 nm to 745 nm.This is attributed to the fact that the effective refractive index Further, the transmission spectra with different geometric parameters are analyzed.In Fig. 5(a), it can be seen that three Fano resonances generate a significant redshift as the thickness H 1 varies from 110 nm to 130 nm.This is attributed to the fact that the effective refractive index of the metastructure increases with the increase in thickness.As shown in Fig. 5(b), when the length L varies from 590 nm to 610 nm, Fano resonance at R3 has a significant redshift compared to Fano resonances at R1 and R2, which indicates that the near-field interaction between cells in the structure generates a little effect on resonances at R1 and R2.In Fig. 5(c), it can be seen that three Fano resonances generate different degrees of red-shift as the period P increases from 690 nm to 710 nm.So, the resonant wavelength corresponding to Fano resonances can be adjusted by varying geometric parameters.
The temperature and refractive index sensing properties of the proposed structure are investigated.The changes of temperature and refractive index generate spectra shift.The relationship between the spectral shift and changes of temperature and refractive index can be described by the following equation [1]:  Further, the transmission spectra with different geometric parameters are analyzed.In Fig. 5(a), it can be seen that three Fano resonances generate a significant redshift as the thickness H varies from 715 nm to 745 nm.This is attributed to the fact that the effective refractive index Where i refers to three Fano resonances, T represents temperature, n and dn/dT are refractive index and thermo-optic coefficient of the ambient medium.The first and third terms of the equation represent the spectra shift generated by independent changes of refractive index and temperature, while the second term is the spectra shift resulting from thermo-optic effect of the ambient medium.After taking the inverse operation, the variation of temperature and refractive index can be obtained from the following equation [1]: Where S T1 and S T2 are temperature sensitivity coefficients, S n1 and S n2 are refractive index sensitivity coefficients, dn/dT is the thermo-optical coefficient of the ambient medium, which can be obtained from relative references or calculated under the assumption ∆n = 0. From Eq. ( 6), dn/dT can be calculated as: As a result, ∆n and ∆T can be measured simultaneously by using Eq. ( 6).The next step is to determine the sensitivity coefficients.
First, when temperature changes in the environment where the structure is located, the refractive index of materials varies because of the thermo-optic effect.The thermo-optic coefficients of Si and SiO 2 are 2.01 × 10 -4 and 8.40 × 10 -6 , which are obtained from an experimental measurement [35,36].Figure 6(a) presents the transmission spectra at different temperatures.The structure is surrounded by air, whose thermo-optic effects are not considered.Meanwhile, it is worth noting that the nonuniform distribution of temperature is ignored.Therefore, the structure is assumed to be in an environment with uniform temperature.As shown in Fig. 6    The temperature sensitivity is used to evaluate the performance of the sensors and is defined as [5]: Where ∆λ is the offset of resonant wavelength and ∆T is the variation of temperature.
The S can be calculated as 45 pm/K, 60 pm/K and 50 pm/K.For the Fano resonance at R3, the Fano resonance can shift a full-width at half-maximum (FWHM) toward the long wavelength when the temperature increases only by 2.5 K.In addition, one of the main bottlenecks of temperature sensors is long response time, therefore the modulation speed is limited.Similar modulation is achieved using a silicon-based resonant antenna, changing the temperature by 40 K with a response time of 70 µs [37].The response time can be estimated at the same µs level the temperature is varied by 30 K, which is expected to enable the temperature sensors at an acceptable rate.Combined with narrow linewidth, temperature sensitivity and response time, the designed metastructure can be a temperature sensor with excellent performance.
Then, the transmission spectra at different environmental refractive indexes are analyzed.As shown in Fig. 7(a)-(c), it is clear that transmission spectra have a significant redshift.The corresponding linear fitting of the relationship between the resonant wavelength and the various refractive indexes are simultaneously shown in Fig. 7(d).To evaluate the performance of refractive Then, the transmission spectra at different environmental refractive indexes are analyzed.As shown in Fig. 7(a)-(c), it is clear that transmission spectra have a significant redshift.The corresponding linear fitting of the relationship between the resonant wavelength and the various refractive indexes are simultaneously shown in Fig. 7(d).To evaluate the performance of refractive index sensor, the two main performance indicators which include the sensitivity (S) and the figure of merit (FOM) are analyzed.Here, S is given by [22]: where Δλ is the offset of resonant wavelength and Δn is the variation of refractive index.The FOM can be obtained using [22]: (10) Where FWHM represents the full-width at half-maximum of Fano resonance.
The S of three Fano resonances calculated by equation are 231.5 nm/RIU, 132.5 nm/RIU, and 279.5 nm/RIU.The FOM values are 857.4RIU -1 , 81.8 RIU -1 , and 2055.1 RIU -1 .The designed metastructure can be applied as a high-performance refractive index sensor.index sensor, the two main performance indicators which include the sensitivity (S) and the figure of merit (FOM) are analyzed.Here, S is given by [17]: where ∆λ is the offset of resonant wavelength and ∆n is the variation of refractive index.The FOM can be obtained using [17]: Where FWHM represents the full-width at half-maximum of Fano resonance.The S of three Fano resonances calculated by equation are 231.5 nm/RIU, 132.5 nm/RIU, and 279.5 nm/RIU.The FOM values are 857.4RIU −1 , 81.8 RIU −1 , and 2055.1 RIU −1 .The designed metastructure can be applied as a high-performance refractive index sensor.
In addition, the transmission spectra are simulated when the refractive indexes change from 1.0 to 1.5.In Fig. 8(a), it is also found that the transmission spectra have a significant redshift.The corresponding linear fitting of the relationship between the resonant wavelength and the various refractive indexes are simultaneously shown in Fig. 8(b).The calculated S of three Fano resonances are 254.6 nm/RIU, 176.9 nm/RIU, and 255.1 nm/RIU, as well as FOM values reach 943 RIU −1 ,109 RIU −1 and 1876 RIU −1 .The designed metastructure is also suitable for detecting liquids with refractive indexes in the range of 1.3-1.5, such as sucrose solution (n = 1.3412) [22], water (n = 1.333) [26], glycerin (n = 1.394) [26], NaCl (n = 1.351) [38], ethanol (n = 1.352) [39], carbon tetrachloride (n = 1.4489) [40], which is widely used in sensing fields.In particular, the proposed structure can be used to measure different blood group In addition, the transmission spectra are simulated when the refractive indexes change from 1.0 to 1.5.In Fig. 8 (a), it is also found that the transmission spectra have a significant redshift.The corresponding linear fitting of the relationship between the resonant wavelength and the various refractive indexes are simultaneously shown in Fig. 8(b).The calculated S of three Fano resonances are 254.6 nm/RIU, 176.9 nm/RIU, and 255.1 nm/RIU, as well as FOM values reach 943 RIU -1 ,109 RIU -1 and 1876 RIU -1 .The designed metastructure is also suitable for detecting liquids with refractive indexes in the range of 1.3-1.5, such as sucrose solution ( n = 1.3412 ) [22], water ( n = 1.333 ) [26], glycerin ( n = 1.394 ) [26], NaCl ( n = 1.351 ) [38], ethanol ( n = 1.352 ) [39], carbon tetrachloride ( n = 1.4489 ) [40], which is widely used in sensing fields.In particular, the proposed structure can be used to measure different blood group components.Combining experimentally measured refractive index values for different blood components, the refractive indexes range from 1.33 to 1.40 and can be assumed as follows [41,42]: blood plasma ( n = 1.35 ), white blood cells ( nWBC = 1.36 ), Hemoglobin ( nHb = 1.38 ), and red blood cells ( nRBC = 1.40 ).At the same time, measurements at different temperatures can be realized, avoiding the influence of temperature factors on the results.Thus, the proposed metastructure has potential in the field of biosensing.components.Combining experimentally measured refractive index values for different blood components, the refractive indexes range from 1.33 to 1.40 and can be assumed as follows [41,42]: blood plasma (n plasma =1.35), white blood cells (n WBC =1.36), Hemoglobin (n Hb =1.38), and red blood cells (n RBC =1.40).At the same time, measurements at different temperatures can be realized, avoiding the influence of temperature factors on the results.Thus, the proposed metastructure has potential in the field of biosensing.
When temperature increases from 293.15 K to 323.15 K and refractive index increases from 1.0 to 1.08, the sensitivity to temperature and refractive index are obtained from the aforementioned simulations.The calculated sensitivity values of R1 and R3 Fano resonances are substituted into Eq.( 6), the matrix can be obtained by the following equation: 231.5 nm/RIU 45 pm/K 279.5 nm/RIU 50 pm/K Therefore, simultaneous measurement of temperature and refractive index is realized after obtaining the wavelength shifts of Fano resonances.The comparisons of sensitivity to the temperature and refractive index calculated in this paper with the proposed works in the references are shown in Table 1.It can be seen that the proposed structure can achieve high sensitivity to the temperature and refractive index, which has excellent sensing performance.
In addition, when δ = 70 nm, the transmission spectra at the polarization angles of 0 • , 15 • , 30 • , 45 • , 60 • , and 90 • are simulated to investigate the switching properties.As shown in ethanol ( n = 1.352 ) [39], carbon tetrachloride ( n = 1.4489 ) [40], which is widely used in sensing fields.In particular, the proposed structure can be used to measure different blood group components.Combining experimentally measured refractive index values for different blood components, the refractive indexes range from 1.33 to 1.40 and can be assumed as follows [41,42]: blood plasma (n plasma = 1.35 ), white blood cells (n WBC = 1.36 ), Hemoglobin (n Hb = 1.38 ), and red blood cells (n RBC = 1.40 ).At the same time, measurements at different temperatures can be realized, avoiding the influence of temperature factors on the results.Thus, the proposed metastructure has potential in the field of biosensing.When temperature increases from 293.15 K to 323.15 K and refractive index increases from 1.0 to 1.08, the sensitivity to temperature and refractive index are obtained from the aforementioned simulations.The calculated sensitivity values of R2 and R3 Fano resonances are substituted into Eq.( 6), the matrix can be obtained by the following equation:  Theta-shaped all-dielectric metasurface 42.71 278.9 [43] Asymmetric dimer all-dielectric metastructure 60 279.5This work Fig. 9(a)-(b), the transmission amplitudes of three Fano resonance peaks gradually decrease without significant wavelength shift when the polarization angle changes from 90 • to 0 • .When the polarization angle is 0 • , the Fano resonances disappear.The results indicate that Fano resonances are polarization-dependent and can be excited at the specific polarization direction of the incident light.Therefore, the proposed structure can achieve multi-wavelength optical switches and shows better performance compared with the plasmonic metastructure optical switches [44,45].
The designed metastructure has the advantages of a simple structure, a mature fabrication process and compatibility with the CMOS process, which is beneficial to realize large-scale semiconductor chip integration.Although this study was only verified through simulation, the feasibility of the experiment with the proposed metastructure is shown in Fig. 10.The preparation process consists of the following steps: cleaning of the silicon on insulator (SOI) substrate, low-pressure chemical vapor deposition (LPCVD), spin coating of the ZEP520 resist, electron beam lithography (EBL), development, inductively coupled plasma (ICP) etching and removal of the resist.With just a few simple processes, the required metastructure can be fabricated.In addition, the metastructure has a certain tolerance in the preparation process.The designed metastructure has the advantages of a simple structure, a mature fabrication process and compatibility with the CMOS process, which is beneficial to realize large-scale semiconductor chip integration.Although this study was only verified through simulation, the feasibility of the experiment with the proposed metastructure is shown in Fig. 10.The preparation process consists of the following steps: cleaning of the silicon on insulator (SOI) substrate, low-pressure chemical vapor deposition (LPCVD), spin coating of the ZEP520 resist, electron beam lithography (EBL), development, inductively coupled plasma (ICP) etching and removal of the resist.With just a few simple processes, the required metastructure can be fabricated.In addition, the metastructure has a certain tolerance in the preparation process.

Conclusions
In summary, a multi-function sensor based on an all-dielectric metastructure composed of Si dimers periodically placed on a SiO 2 substrate is proposed.The difference between L 1 and L 2 breaks the symmetry of the structure, which makes the ideal BIC disturbed and converted to the quasi-BIC.Three Fano resonances with a high Q-factor and a high modulation depth are excited.The maximal Q-factor is 9352, and the modulation depth can approach 100%.The resonant modes of three Fano resonances, MD, MTD, and ETD, are obtained by analyzing the electromagnetic field distributions.Compared to other sensors, the simulation results show that the proposed structure enables simultaneous measurement of temperature and refractive index, avoiding their crosstalk.For temperature sensing, the maximum sensitivity to the temperature Fig. 9. Transmission spectra at the polarization angles of 0 • , 15    The designed metastructure has the advantages of a simple structure, a mature fabrication process and compatibility with the CMOS process, which is beneficial to realize large-scale semiconductor chip integration.Although this study was only verified through simulation, the feasibility of the experiment with the proposed metastructure is shown in Fig. 10.The preparation process consists of the following steps: cleaning of the silicon on insulator (SOI) substrate, low-pressure chemical vapor deposition (LPCVD), spin coating of the ZEP520 resist, electron beam lithography (EBL), development, inductively coupled plasma (ICP) etching and removal of the resist.With just a few simple processes, the required metastructure can be fabricated.In addition, the metastructure has a certain tolerance in the preparation process.

Conclusions
In summary, a multi-function sensor based on an all-dielectric metastructure composed of Si dimers periodically placed on a SiO 2 substrate is proposed.The difference between L 1 and L 2 breaks the symmetry of the structure, which makes the ideal BIC disturbed and converted to the quasi-BIC.Three Fano resonances with a high Q-factor and a high modulation depth are excited.The maximal Q-factor is 9352, and the modulation depth can approach 100%.The resonant modes of three Fano resonances, MD, MTD, and ETD, are obtained by analyzing the electromagnetic field distributions.Compared to other sensors, the simulation results show that the proposed structure enables simultaneous measurement of temperature and refractive index, avoiding their crosstalk.For temperature sensing, the maximum sensitivity to the temperature

Conclusions
In summary, a multi-function sensor based on an all-dielectric metastructure composed of Si dimers periodically placed on a SiO 2 substrate is proposed.The difference between L 1 and L 2 breaks the symmetry of the structure, which makes the ideal BIC disturbed and converted to the quasi-BIC.Three Fano resonances with a high Q-factor and a high modulation depth are excited.The maximal Q-factor is 9352, and the modulation depth can approach 100%.The resonant modes of three Fano resonances, MD, MTD, and ETD, are obtained by analyzing the electromagnetic field distributions.Compared to other sensors, the simulation results show that the proposed structure enables simultaneous measurement of temperature and refractive index, avoiding their crosstalk.For temperature sensing, the maximum sensitivity to the temperature is 60 pm/K.The same design is also used for refractive index sensing, which achieves a sensitivity of 279.5 nm/RIU and a figure of merit of 2055.1 RIU −1 .In addition, the transmission amplitudes of Fano resonances can be effectively modulated by changing the polarization direction of the incident light, which can be exploited for designing optical switches with excellent performance.The structure is characterized by high Q-factor Fano resonances, which have extensive applications in sensors as well as optical switches.

Fig. 1 .
Fig. 1.(a) Schematic diagram of the proposed metastructure.(b) The geometrical parameters are defined as d = 40 nm, W 1 = 150 nm, W 2 = 130 nm, H 1 = 120 nm, H 2 = 220 nm, P x = P y = 700 nm, L = 600 nm.(c) The real and imaginary parts of the refractive index of Si.(d) The real and imaginary parts of the refractive index of SiO 2 .

Fig. 1 .
Fig. 1.(a) Schematic diagram of the proposed metastructure.(b) The geometrical parameters are defined as d = 40 nm, W 1 =150 nm, W 2 =130 nm, H 1 =120 nm, H 2 =220 nm, P x =P y =700 nm, L = 600 nm.(c) The real and imaginary parts of the refractive index of Si.(d) The real and imaginary parts of the refractive index of SiO 2 .

Fig. 2 .
Fig. 2. (a) The impedance of the structure when δ = 70 nm (b) Transmission spectra of symmetrical (δ = 0 nm) and asymmetrical (δ = 70 nm) metastructures.(c) The fitting result at λ = 1271.86nm (R3).The calculated result is shown as the blue solid line and the fitting result is shown as the red dashed line.

Fig. 2 .
Fig. 2. (a) The impedance of the structure when δ = 70 nm (b) Transmission spectra of symmetrical (δ = 0 nm) and asymmetrical (δ = 70 nm) metastructures.(c) The fitting result at λ = 1271.86nm (R3).The calculated result is shown as the blue solid line and the fitting result is shown as the red dashed line.

Fig. 3 .
Fig. 3. (a) Transmission spectra with different asymmetry parameters δ.(b) The relationship between radiative Q-factor and asymmetry degree α at R1 and R3.To further investigate the resonant modes of Fano resonances, the electromagnetic field distributions at λ = 1128.32nm (R1), λ = 1186.96nm (R2) and λ = 1271.86nm (R3) are analyzed in Fig. 4. For the resonant mode at R1, two current circles are generated in the x-y plane, and two arrows with same directions are formed in the x-z plane, which can be recognized as a magnetic dipole (MD) resonance oscillating along the z-direction.For the resonant mode at R2, two reversed current circles are formed in the x-y plane.Meanwhile, the magnetic field creates two reversed arrows to form a loop in the x-z plane, which indicates a magnetic toroidal dipole (MTD) resonance.For the resonant mode at R3, two arrows with opposite directions are formed in the x-y plane, and two magnetic loops with opposite directions are generated in the x-z plane, indicating an electric toroidal dipole (ETD) resonance.The TD resonance has unique properties compared to electric dipole (ED) and MD resonance.The structure can excite two different toroidal dipole resonances (ETD and MTD).

Fig. 4 .
Fig. 4. Electromagnetic field distributions at R1, R2 and R3.(a) Small black arrows represent the distributions of electric field vectors and the electric field directions are indicated by white arrows.(b) Small black arrows represent the distributions of magnetic field vectors and the magnetic field directions are represented by black arrows.

Fig. 3 .
Fig. 3. (a) Transmission spectra with different asymmetry parameters δ.(b) The relationship between radiative Q-factor and asymmetry degree α at R1 and R3.To further investigate the resonant modes of Fano resonances, the electromagnetic field distributions at λ = 1128.32nm (R1), λ = 1186.96nm(R2) and λ = 1271.86nm (R3) are analyzed in Fig.4.For the resonant mode at R1, two current circles are generated in the x-y plane, and two arrows with same directions are formed in the x-z plane, which can be recognized as a magnetic dipole (MD) resonance oscillating along the z-direction.For the resonant mode at R2, two reversed current circles are formed in the x-y plane.Meanwhile, the magnetic field creates two reversed arrows to form a loop in the x-z plane, which indicates a magnetic toroidal dipole (MTD) resonance.For the resonant mode at R3, two arrows with opposite directions are formed in the x-y plane, and two magnetic loops with opposite directions are generated in the x-z plane, indicating an electric toroidal dipole (ETD) resonance.The TD resonance has unique properties compared to electric dipole (ED) and MD resonance.The structure can excite two different toroidal dipole resonances (ETD and MTD).Further, the transmission spectra with different geometric parameters are analyzed.In Fig.5(a), it can be seen that three Fano resonances generate a significant redshift as the thickness H 1 varies from 110 nm to 130 nm.This is attributed to the fact that the effective refractive index of the metastructure increases with the increase in thickness.As shown in Fig.5(b), when the length L varies from 590 nm to 610 nm, Fano resonance at R3 has a significant redshift compared to Fano resonances at R1 and R2, which indicates that the near-field interaction between cells in the structure generates a little effect on resonances at R1 and R2.In Fig.5(c), it can be seen that three Fano resonances generate different degrees of red-shift as the period P increases from 690 nm to 710 nm.So, the resonant wavelength corresponding to Fano resonances can be adjusted by varying geometric parameters.The temperature and refractive index sensing properties of the proposed structure are investigated.The changes of temperature and refractive index generate spectra shift.The relationship between the spectral shift and changes of temperature and refractive index can be described by the following equation[1]: ) recognized as a magnetic dipole (MD) resonance oscillating along the z-direction.For the resonant mode at R2, two reversed current circles are formed in the x-y plane.Meanwhile, the magnetic field creates two reversed arrows to form a loop in the x-z plane, which indicates a magnetic toroidal dipole (MTD) resonance.For the resonant mode at R3, two arrows with opposite directions are formed in the x-y plane, and two magnetic loops with opposite directions are generated in the x-z plane, indicating an electric toroidal dipole (ETD) resonance.The TD resonance has unique properties compared to electric dipole (ED) and MD resonance.The structure can excite two different toroidal dipole resonances (ETD and MTD).

Fig. 4 .
Fig. 4. Electromagnetic field distributions at R1, R2 and R3.(a) Small black arrows represent the distributions of electric field vectors and the electric field directions are indicated by white arrows.(b) Small black arrows represent the distributions of magnetic field vectors and the magnetic field directions are represented by black arrows.

Fig. 4 .
Fig. 4. Electromagnetic field distributions at R1, R2 and R3.(a) Small black arrows represent the distributions of electric field vectors and the electric field directions are indicated by white arrows.(b) Small black arrows represent the distributions of magnetic field vectors and the magnetic field directions are represented by black arrows.
(a)-(c), three Fano resonances are redshifted as the temperature changes from 293.15 K to 323.15 K.

Figure 6 (
Figure 6(d)  shows corresponding linear fitting of the relationship between the resonant wavelength and various temperatures.The temperature sensitivity is used to evaluate the performance of the sensors and is defined as[5]:

Fig. 6 .
Fig. 6. (a)-(c) Transmission spectra of three Fano resonances at different temperatures.(d) Linear fitting of the relationship between the resonant wavelength and the various temperatures.

Fig. 6 .
Fig. 6. (a)-(c) Transmission spectra of three Fano resonances at different temperatures.(d) Linear fitting of the relationship between the resonant wavelength and the various temperatures.

Fig. 7 (
Fig. 7 (a)-(c) Transmission spectra of three resonance peaks at refractive indexes from 1.01 to 1.08.(d) Linear fitting of the relationship between the resonant wavelength and the various refractive indexes.

Fig. 7 .
Fig. 7. (a)-(c) Transmission spectra of three resonance peaks at refractive indexes from 1.01 to 1.08.(d) Linear fitting of the relationship between the resonant wavelength and the various refractive indexes.

Fig. 8 (
Fig. 8 (a) Transmission spectra when the refractive indices change from 1.0 to 1.5.(b) Linear fitting of the relationship between the resonant wavelength and the various refractive indexes.

Fig. 8 .
Fig. 8. (a) Transmission spectra when the refractive indexes change from 1.0 to 1.5.(b) Linear fitting of the relationship between the resonant wavelength and the various refractive indexes.