Sensing Performance of Triple-Band Terahertz Metamaterial Absorber Based on Snowﬂake-Shaped Resonators

: Terahertz metamaterial absorbers are important functional devices for liquid analyte detection. In contrast to general metamaterial absorbers with single-layer metasurfaces that possess only one resonant mode, a triple-band terahertz metamaterial absorber formed by a single layer of symmetrically arrayed snowﬂake-shaped resonators was proposed in this study. The simulation results showed that the absorption of the metamaterial absorber reached 97.43% at 0.550 THz, 79.22% at 1.249 THz, and 99.02% at 1.867 THz with narrow resonant peaks. The resonant frequencies were sensitive to the refractive index of the surrounding medium at a ﬁxed analyte thickness, which would play an important role in the performance of the sensor for detecting changes in the surrounding refractive index. The maximum value of the refractive index sensitivity was 137.70 GHz/RIU, 306.25 GHz/RIU, and 473.86 GHz/RIU, with a ﬁgure of merit ( FoM ) of 3.14, 2.33, and 6.46, respectively, for refractive index values ranging from 1.0 to 2.2 under three resonant modes. It is worth noting that most of the liquid samples showed a refractive index ranging from 1.0 to 2.0. Furthermore, the identiﬁcation of peanut oil, carbon disulﬁde, and turpentine was considered to verify that the proposed terahertz sensor could be used for high-sensitivity liquid detection and has broad development prospects in the ﬁeld of detecting and sensing.


Introduction
Liquid analytes are commonly found in the industrial and biomedical fields; thus, the study of liquid sensing is of great significance [1,2].Due to the unique characteristics of low photon energy and strong penetration possessed by terahertz (THz) waves [3][4][5], sensors based on THz modulation are recognized as nondestructive inspection tools.These sensors can directly calculate the refractive index of analytes through the noncontact measurement of the changes in the absorption spectrum [6,7].Microfluidic chips are widely used for the sensing and detection of small amounts of liquid analyte to improve the detection capability [8][9][10].However, the sensing accuracy and stability of THz sensors are still limited by the weak response of natural materials to THz waves, which would certainly limit the sensing sensitivity and accuracy for liquid analytes with similar refractive indexes.
Terahertz absorbers are of great significance, and utilizing metamaterials is recognized as a potential path to enhancing the responses to THz waves [11].Hence, metamaterial absorbers have been studied extensively, with a view to minimizing both the transmission and the reflectivity.The metamaterial absorber with X-shaped resonators reported by Mirzaei et al. [12] could be used to detect DNA in liquid, showing over 85% absorption at 0.85 THz and good selectivity for DNA detection.Janneh et al. [13] reported a metasurface absorber that exhibited perfect absorption, a high quality factor, and a refractive index sensitivity of 187.5 GHz/RIU (gigahertz per refractive index unit).Zhang et al. [10] combined metamaterials with a multi-channel microfluidic chip that achieved a refractive index sensitivity of 223 GHz/RIU at 1.96 THz.Due to the excellent sensing performance of the THz metamaterial absorber mentioned above, the THz metamaterial absorber is considered a promising device for liquid sensing [13][14][15][16].For instance, in 2020, Wang et al. [17] reported an absorber sensor based on a three-dimensional split-ring resonator (SRR) array and microfluidic channel that could be used as a refractive index sensor with a refractive index frequency sensitivity reaching 379 GHz/RIU.Leaky modes are also an important form of electromagnetic field propagation.Cheng et al. [18] experimentally demonstrated the properties of leaky waves generated inside the air gap between a high-index prism and a metal-dielectric-metal metasurface that could be strongly engineered by the geometrical parameters of the metasurface.
Very recently, multi-band metamaterial absorbers have attracted intense attention due to their potential applications in spectroscopic detection [19].Compared with traditional single-band metamaterial absorbers, multi-band metamaterial absorbers can realize highly accurate sensing and detection through the multi-point matching of information.Generally, a metamaterial absorber with a single-layer patterned structure shows only one resonant mode.Though a multi-band absorber can be obtained by a multi-layer metasurface, this kind of design leads to a heavy and thick structure.To avoid the thick structure caused by multi-layer metasurfaces, in 2021, Pang et al. [20] designed a dual-band THz metamaterial absorber with a single-layer metasurface whose absorption reached 99% at both 0.387 THz and 0.694 THz.Lan et al. [21] theoretically and experimentally demonstrated a THz biosensor with an intense wave-matter-overlap microfluidic channel.The resonant modes exhibited ultrahigh normalized sensitivities of 0.47/RIU and 0.51/RIU at 0.76 THz and 1.28 THz, respectively.To reduce the strong absorption of THz by water when detecting solution samples and to improve the sensitivity of the sensor, Yang et al. [22] proposed two dual-band THz sensors based on a metamaterial absorber integrated with microfluidics whose refractive index sensitivity could reach 300 GHz/RIU.Lu et al. [23] proposed an ultrathin terahertz dual-band perfect metamaterial absorber using an asymmetric doublesplit-ring resonator.Yao et al. [24] reported a triple-band metamaterial absorber using a multi-split-electric-ring resonator for sensing applications with maximal sensitivities of 0.119 THz/RIU, 0.248 THz/RIU, and 0.662 THz/RIU.Furthermore, the absorption bands could be continually expanded to the ultra-broadband range using hyperbolic metamaterials (HMMs), which typically comprise a metal-dielectric multilayer structure [25,26].
Therefore, it is very important to find powerful terahertz absorbers that are characterized by strong multi-band terahertz absorption; high quality factors; high compatibility; and a simple, ultra-thin structure consisting of a single-layer metasurface.In this research, we aimed to achieve the above goal using snowflake-shaped resonators.This study demonstrates a novel and simple design for a triple-band THz metamaterial absorber formed by a patterned metallic layer and a metallic ground plane separated by a dielectric layer.The designed THz metamaterial absorber showed three resonant modes that exhibited high absorption values of 97.43% at 0.550 THz, 79.22% at 1.249 THz, and 99.02% at 1.867 THz.The quality factor of the absorber was 26.01, 17.83, and 58.04, respectively, indicating extremely sharp absorption peaks.The absorption mechanism of the three resonant modes was explored.Furthermore, the sensing performance of the proposed absorber was investigated in terms of the surrounding refractive index.It was found that the maximum value of the refractive index sensitivity S was 473.86 GHz/RIU and the maximum FoM was 6.46 for a refractive index ranging from 1.0 to 2.2 at the resonant frequency of f 3 .The proposed THz absorber with these superior performance indicators could be implemented in the field of label-free sensing and non-contact detection.

Structures and Methods
So far, great efforts have been devoted to broadening the frequency range of the electromagnetic response of metastructures.The most straightforward approach is to superimpose different resonant modes in the system [27].Inspired by the shape of a snowflake, which possesses branches of different sizes and distributions, Figure 1a,b show schematic Photonics 2022, 9, 777 3 of 11 diagrams of the triple-band THz metamaterial absorber, which comprises a sandwich structure of a metasurface top layer resting on the dielectric substrate and a bottom layer of a continuous metallic plane.The topside metasurface is composed of periodically arrayed snowflake-shaped cells, as shown in Figure 1c.The material of both the top and the bottom layers was chosen to be copper (Al), due to its excellent electrical conductivity.The material used for the intermediate dielectric layer was polytetrafluoroethylene (PTEE), whose permittivity is ε = 2.1.
ulations using the commercial electromagnetic solver CST Studio Suite 2019 to determine the geometric parameters of the metamaterial absorber shown in Figure 1b,c, which were as follows: the period of the cells g = 120 μm; the line-width of cells w = 5 μm; the length of the center square a = 8 μm; the length of the main branch of each snowflake-shaped cell b = 50 μm; the length of the two groups of sub-branches on each main branch, c1 = 45 μm and c2 = 30 μm, respectively; the distance from the sub-branches to the center, h1 = 16.95 μm and h2 = 32.77μm, respectively; and the angle between the main branch and the auxiliary branch α = 45°.The thickness of the intermediate dielectric layer t = 8 μm, the thickness of the top layer t1 = 0.3 μm, and the thickness of the bottom continuous Al layer t2 = 2 μm were set to be higher than the skin depth to ensure that the absorber worked in the free transmission mode.The proposed structure was simulated using periodic boundary conditions in the x and y directions with Px = Py = P.A plane beam polarized along the xdirection was vertically incident on the absorber, as shown in Figure 1b, and periodic boundary conditions were used in the x and y directions.Furthermore, transmission and reflection were calculated under far-field conditions to reveal the physical mechanisms.

Structural Design of the Triple-Band THz Metamaterial Absorber
The absorption (A) could be calculated by

R S =
(2) where T and R are the transmission and reflection, respectively, and S11 and S21 are the reflection coefficient and transmission coefficient, respectively.Since the thickness of the We implemented a careful design and optimization process involving full-wave simulations using the commercial electromagnetic solver CST Studio Suite 2019 to determine the geometric parameters of the metamaterial absorber shown in Figure 1b,c, which were as follows: the period of the cells g = 120 µm; the line-width of cells w = 5 µm; the length of the center square a = 8 µm; the length of the main branch of each snowflake-shaped cell b = 50 µm; the length of the two groups of sub-branches on each main branch, c 1 = 45 µm and c 2 = 30 µm, respectively; the distance from the sub-branches to the center, h 1 = 16.95 µm and h 2 = 32.77µm, respectively; and the angle between the main branch and the auxiliary branch α = 45 • .The thickness of the intermediate dielectric layer t = 8 µm, the thickness of the top layer t 1 = 0.3 µm, and the thickness of the bottom continuous Al layer t 2 = 2 µm were set to be higher than the skin depth to ensure that the absorber worked in the free transmission mode.The proposed structure was simulated using periodic boundary conditions in the x and y directions with P x = P y = P.A plane beam polarized along the x-direction was vertically incident on the absorber, as shown in Figure 1b, and periodic boundary conditions were used in the x and y directions.Furthermore, transmission and reflection were calculated under far-field conditions to reveal the physical mechanisms.

Structural Design of the Triple-Band THz Metamaterial Absorber
The absorption (A) could be calculated by where T and R are the transmission and reflection, respectively, and S 11 and S 21 are the reflection coefficient and transmission coefficient, respectively.Since the thickness of the continuous Al layer was greater than the skin depth, the transmission of the proposed absorber was suppressed (T = 0), so the absorption (A) could be expressed as A = 1 − R [28].
The simulated absorption and reflection spectra of the proposed absorber at normal incidence are shown in Figure 2. It is obvious that the proposed absorber had three resonant modes at the frequency range of 0.2 to 1.8 THz.The resonant frequencies and the corre-sponding absorption values were as follows: f 1 = 0.550 THz, A(f 1 ) = 97.43%;f 2 = 1.249THz, A(f 2 ) = 79.22%; and f 3 = 1.867THz, A(f 3 ) = 99.02%.Triple-band effective absorption was achieved.The full width at half maximum (FWHM) values were FWHM(f 1 ) = 21.14GHz, FWHM(f 2 ) = 70.05GHz, and FWHM(f 3 ) = 58.04GHz, indicating that the absorption spectra were narrow.The quality factor (Q factor) of the absorber was defined as: where f is the resonant frequency.The Q factors were Q(f 1 ) = 26.01,Q(f 2 ) = 17.83, and Q(f 3 ) = 58.04,indicating that the absorption peaks were extremely sharp.
Based on the interaction between the incident terahertz waves and the metamaterial absorber, the as-designed metamaterial absorber could still maintain an excellent terahertz absorption performance at an oblique TEM wave incidence.The angular dependence of the absorption performance was investigated, as depicted in Figure 3.The absorption spectrum was nearly independent of the incident angle below 60° for TE polarization, as shown in Figure 3a.Meanwhile, the metamaterial absorber exhibited a high quality factor for all resonance modes, even when the incident angle was increased to 60° for both TE and TM polarization.Based on the interaction between the incident terahertz waves and the metamaterial absorber, the as-designed metamaterial absorber could still maintain an excellent terahertz absorption performance at an oblique TEM wave incidence.The angular dependence of the absorption performance was investigated, as depicted in Figure 3.The absorption spectrum was nearly independent of the incident angle below 60 • for TE polarization, as shown in Figure 3a.Meanwhile, the metamaterial absorber exhibited a high quality factor for all resonance modes, even when the incident angle was increased to 60 • for both TE and TM polarization.

Absorption Mechanism of Triple-Band THz Metamaterial Absorber
In order to gain insight into the absorption mechanism of the absorber and the characteristics of the resonant modes, the distribution of electromagnetic field and surface currents on the top of the snowflake-shaped unit cell were illustrated for a TE-polarized wave with normal incidence.The spatial distributions of the electric field for the three resonant modes, shown in Figure 4, indicated that the snowflake-shaped structure could stimulate strong absorption resonance and produce a strong electric field located near the sidewalls of the branches of the snowflake structure, which could effectively excite surface plasmon resonances (SPRs) in the unit cells [29].Figure 4a shows that the electric field was mainly concentrated at both sub-branch groups (c 1 and c 2 ) and the apex of the main branches along the y-axis at resonant frequency f 1 = 0.550 THz.The electric field was mainly focused on the outer sub-branches (c 1 ) along the x-axis at resonant frequency f 2 = 1.249THz, as shown in Figure 4b.In the simulation results depicted in Figure 4c, the electric field was obviously concentrated in the inner sub-branches (c 2 ) along the x-axis at resonant frequency f 3 = 1.867THz.It is worth noting that the resonant modes were excited by the SPRs at different locations in the snowflake-shaped unit cell.

Absorption Mechanism of Triple-Band THz Metamaterial Absorber
In order to gain insight into the absorption mechanism of the absorber and the characteristics of the resonant modes, the distribution of electromagnetic field and surface currents on the top of the snowflake-shaped unit cell were illustrated for a TE-polarized wave with normal incidence.The spatial distributions of the electric field for the three resonant modes, shown in Figure 4, indicated that the snowflake-shaped structure could stimulate strong absorption resonance and produce a strong electric field located near the sidewalls of the branches of the snowflake structure, which could effectively excite surface plasmon resonances (SPRs) in the unit cells [29].Figure 4a shows that the electric field was mainly concentrated at both sub-branch groups (c1 and c2) and the apex of the main branches along the y-axis at resonant frequency f1 = 0.550 THz.The electric field was mainly focused on the outer sub-branches (c1) along the x-axis at resonant frequency f2 = 1.249THz, as shown in Figure 4b.In the simulation results depicted in Figure 4c, the electric field was obviously concentrated in the inner sub-branches (c2) along the x-axis at resonant frequency f3 = 1.867THz.It is worth noting that the resonant modes were excited by the SPRs at different locations in the snowflake-shaped unit cell.Figure 5 shows the magnetic field distribution results of the simulation that included field monitors at the corresponding resonant frequencies f1, f2, and f3.The magnetic field was mainly gathered around the main branches and the sub-branches in the y direction at resonant frequency f1 = 0.550 THz, while it was concentrated around the outer and inner sub-branches c1 and c2 in the x direction at resonant frequency f2 = 1.249THz and f3 = 1.867THz, respectively.The simulated surface currents on the top of the unit cell under the three resonant modes were illustrated for a linearly TE-polarized wave with a normal incidence (Figure 6).In the case of f1 = 0.550 THz, most of the currents were primarily confined at the edge of the branches in the y direction (Figure 6a).At f2 = 1.249THz and f3 = 1.867THz, the currents were observed to behave similarly to those in the previous scenario, being concentrated at different positions in the outer and inner sub-branches, respectively, in the x direction (Figure 6b,c).Due to the symmetry of the unit cell, the electric field, magnetic field, and induced surface currents at the surface had the same distributions for both TE and TM waves [30].Figure 5 shows the magnetic field distribution results of the simulation that included field monitors at the corresponding resonant frequencies f 1 , f 2 , and f 3 .The magnetic field was mainly gathered around the main branches and the sub-branches in the y direction at resonant frequency f 1 = 0.550 THz, while it was concentrated around the outer and inner sub-branches c 1 and c 2 in the x direction at resonant frequency f 2 = 1.249THz and f 3 = 1.867THz, respectively.The simulated surface currents on the top of the unit cell under the three resonant modes were illustrated for a linearly TE-polarized wave with a normal incidence (Figure 6).In the case of f 1 = 0.550 THz, most of the currents were primarily confined at the edge of the branches in the y direction (Figure 6a).At f 2 = 1.249THz and f 3 = 1.867THz, the currents were observed to behave similarly to those in the previous scenario, being concentrated at different positions in the outer and inner sub-branches, respectively, in the x direction (Figure 6b,c).Due to the symmetry of the unit cell, the electric field, magnetic field, and induced surface currents at the surface had the same distributions for both TE and TM waves [30].

Sensing Characteristics of Triple-Band THz Metamaterial Absorber
Figure 7a-c show the absorption of the proposed THz metamaterial absorber under different analytes (refractive indexes n changing from 1 to 2.2) with an analyte thickness of h = 5 µm, as shown in Figure 1b.It can be seen that the absorption changed as the refractive index n varied for all three resonant modes.For instance, the absorption at resonant frequency f 1 = 0.550 THz dropped from 97.43% to 1.05% when the analyte refractive index n changed from 1 to 2.2, as shown in Figure 7a.Furthermore, the resonant frequency gradually redshifted for all three resonant modes when the analyte refractive index n changed from 1 to 2.2 with an interval of 0.2, as shown in Figure 7.In order to determine the sensing performance of the proposed THz metamaterial absorber, we analyzed the relationship between the variation in the refractive index n and the frequency shifting for the three resonant modes (Figure 8), which was confirmed to represent linear fitting.
Moreover, the sensitivity S could be defined as the slope of the fitted line according to the following formula [31]: where ∆f is the variation in resonant frequency caused by changing the refractive index ∆n.The sensitivities for the three resonant modes were S(f 1 ) = 97.94GHz/RIU, S(f 2 ) = 216.50GHz/RIU, and S(f 3 ) = 377.34GHz/RIU.
Figure 5 shows the magnetic field distribution results of the simulation that included field monitors at the corresponding resonant frequencies f1, f2, and f3.The magnetic field was mainly gathered around the main branches and the sub-branches in the y direction at resonant frequency f1 = 0.550 THz, while it was concentrated around the outer and inner sub-branches c1 and c2 in the x direction at resonant frequency f2 = 1.249THz and f3 = 1.867THz, respectively.The simulated surface currents on the top of the unit cell under the three resonant modes were illustrated for a linearly TE-polarized wave with a normal incidence (Figure 6).In the case of f1 = 0.550 THz, most of the currents were primarily confined at the edge of the branches in the y direction (Figure 6a).At f2 = 1.249THz and f3 = 1.867THz, the currents were observed to behave similarly to those in the previous scenario, being concentrated at different positions in the outer and inner sub-branches, respectively, in the x direction (Figure 6b,c).Due to the symmetry of the unit cell, the electric field, magnetic field, and induced surface currents at the surface had the same distributions for both TE and TM waves [30].

Sensing Characteristics of Triple-Band THz Metamaterial Absorber
Figure 7a-c show the absorption of the proposed THz metamaterial absorber under different analytes (refractive indexes n changing from 1 to 2.2) with an analyte thickness of h = 5 μm, as shown in Figure 1b.It can be seen that the absorption changed as the refractive index n varied for all three resonant modes.For instance, the absorption at resonant frequency f1 = 0.550 THz dropped from 97.43% to 1.05% when the analyte refractive index n changed from 1 to 2.2, as shown in Figure 7a.Furthermore, the resonant frequency gradually redshifted for all three resonant modes when the analyte refractive index n changed from 1 to 2.2 with an interval of 0.2, as shown in Figure 7.In order to determine the sensing performance of the proposed THz metamaterial absorber, we analyzed the relationship between the variation in the refractive index n and the frequency shifting for the three resonant modes (Figure 8), which was confirmed to represent linear fitting.Moreover, the sensitivity S could be defined as the slope of the fitted line according to the following formula [31]: where ∆f is the variation in resonant frequency caused by changing the refractive index ∆n.The sensitivities for the three resonant modes were S(f1) = 97.94GHz/RIU, S(f2) = 216.50GHz/RIU, and S(f3) = 377.34GHz/RIU.

Sensing Characteristics of Triple-Band THz Metamaterial Absorber
Figure 7a-c show the absorption of the proposed THz metamaterial absorber under different analytes (refractive indexes n changing from 1 to 2.2) with an analyte thickness of h = 5 μm, as shown in Figure 1b.It can be seen that the absorption changed as the refractive index n varied for all three resonant modes.For instance, the absorption at resonant frequency f1 = 0.550 THz dropped from 97.43% to 1.05% when the analyte refractive index n changed from 1 to 2.2, as shown in Figure 7a.Furthermore, the resonant frequency gradually redshifted for all three resonant modes when the analyte refractive index n changed from 1 to 2.2 with an interval of 0.2, as shown in Figure 7.In order to determine the sensing performance of the proposed THz metamaterial absorber, we analyzed the relationship between the variation in the refractive index n and the frequency shifting for the three resonant modes (Figure 8), which was confirmed to represent linear fitting.Moreover, the sensitivity S could be defined as the slope of the fitted line according to the following formula [31]: where ∆f is the variation in resonant frequency caused by changing the refractive index ∆n.The sensitivities for the three resonant modes were S(f1) = 97.94GHz/RIU, S(f2) = 216.50GHz/RIU, and S(f3) = 377.34GHz/RIU.The volume of analytes also affected the sensitivity S of the proposed sensor.Figure 9a-c show simulated resonant frequency shifting maps as functions of different analyte thickness values h ranging from 5 to 25 µm for the three resonant modes.Figure 9d shows the influence of the analyte thickness h on the sensitivity of the sensor.The refractive index sensitivity at resonant frequencies f 1 and f 2 achieved the maximum value of S(f 1 ) = 137.70GHz/RIU and S(f 2 ) = 306.25 GHz/RIU when the analyte thickness h was 20 µm.The maximum value of the refractive index sensitivity at the highest resonant frequency S(f 3 ) = 473.86GHz/RIU appeared when h = 15 µm.However, the refractive index sensitivity S decreased as the analyte thickness h continued to increase, which was caused by two phenomena.On the one hand, the refraction and dissipation of terahertz waves in the liquid analyte changed as the analyte thickness continually increased, which led to variations in the absorption spectra.On the other hand, the refractive index sensitivity of an absorption sensor with a certain structure is limited to an ultimate value.Hence, the refractive index sensitivity did not continuously increase or even decrease when the thickness of the analyte was higher than 15~20 µm.Considering the refractive index sensitivity S, it could be concluded that the optimum analyte thickness h was 15 or 20 µm.In addition to sensitivity S, we also used the figure of merit (FoM) as another coefficient for assessing the sensing performance of the proposed absorber, which could be defined as: Photonics 2022, 9, x FOR PEER REVIEW 7 of 12 The volume of analytes also affected the sensitivity S of the proposed sensor.Figure 9a-c show simulated resonant frequency shifting maps as functions of different analyte thickness values h ranging from 5 to 25 μm for the three resonant modes.Figure 9d shows the influence of the analyte thickness h on the sensitivity of the sensor.The refractive index sensitivity at resonant frequencies f1 and f2 achieved the maximum value of S(f1) = 137.70GHz/RIU and S(f2) = 306.25 GHz/RIU when the analyte thickness h was 20 μm.The maximum value of the refractive index sensitivity at the highest resonant frequency S(f3) = 473.86GHz/RIU appeared when h = 15 μm.However, the refractive index sensitivity S decreased as the analyte thickness h continued to increase, which was caused by two phenomena.On the one hand, the refraction and dissipation of terahertz waves in the liquid analyte changed as the analyte thickness continually increased, which led to variations in the absorption spectra.On the other hand, the refractive index sensitivity of an absorption sensor with a certain structure is limited to an ultimate value.Hence, the refractive index sensitivity did not continuously increase or even decrease when the thickness of the analyte was higher than 15~20 μm.Considering the refractive index sensitivity S, it could be concluded that the optimum analyte thickness h was 15 or 20 μm.In addition to sensitivity S, we also used the figure of merit (FoM) as another coefficient for assessing the sensing performance of the proposed absorber, which could be defined as: The FoM at resonant frequencies f1, f2, and f3 was FoM(f1) = 3.14, FoM(f2) = 2.33, and FoM(f3) = 6.46, respectively, with an analyte thicknes h = 20 μm.Table 1 shows the absorption, sensitivity, Q factor, and FoM of our device and the designs proposed in previous works.It can be seen that the sensing performance of our device was either superior or comparable to that of the other reported works.In order to verify the liquid detection performance of the proposed THz sensor, we analyzed the absorption spectra (Figure 10) of the absorber with and without the analyte coating, which was set as carbon disulfide with a refractive index n = 1.628.We chose turpentine with a permittivity of 2.2, carbon disulfide with a permittivity of 2.6, and peanut oil with a permittivity of 3.0 as the three different liquid analytes.There are two ways to model an analyte in CST Studio Suite 2019 simulation software.The first is to directly The FoM at resonant frequencies f 1 , f 2 , and f 3 was FoM(f 1 ) = 3.14, FoM(f 2 ) = 2.33, and FoM(f 3 ) = 6.46, respectively, with an analyte thicknes h = 20 µm.Table 1 shows the absorption, sensitivity, Q factor, and FoM of our device and the designs proposed in previous works.It can be seen that the sensing performance of our device was either superior or comparable to that of the other reported works.In order to verify the liquid detection performance of the proposed THz sensor, we analyzed the absorption spectra (Figure 10) of the absorber with and without the analyte coating, which was set as carbon disulfide with a refractive index n = 1.628.We chose turpentine with a permittivity of 2.2, carbon disulfide with a permittivity of 2.6, and peanut oil with a permittivity of 3.0 as the three different liquid analytes.There are two ways to model an analyte in CST Studio Suite 2019 simulation software.The first is to directly choose the corresponding material in the material library.The second is to set the permittivity of the analyte ε according to n = ε 1/2 for non-magnetic materials, where n is the refractive index of the analyte.Figure 11a-c show the simulated absorption spectra results for these liquid analytes with a thickness of h = 20 µm.As can be seen, it was easy to distinguish the different liquid analytes according to the locations of the absorption peaks at the resonant frequencies f 1 , f 2 , and f 3 .Hence, the three liquid analytes could be identified using the proposed THz sensor.The locations of the resonant frequencies f 1 , f 2 , and f 3 for the different liquid analytes are shown in Figure 11d.When the analyte was peanut oil, the resonant frequencies f 1 , f 2 , and f 3 were located at 0.450, 1.016, and 1.522 THz, respectively, according to the simulation results shown in Figure 11d.Compared with the refractive index n = 1 of the surrounding air, the resonant frequency shift was ∆f 1 = 96.5 GHz, ∆f 2 = 222.86GHz, and ∆f 3 = 337.29 GHz, respectively.Based on the calculated results for the refractive index sensitivity S(f 1 ) = 137.70GHz/RIU, S(f 2 ) = 306.25 GHz/RIU, and S(f 3 ) = 462.16GHz/RIU, the refractive index of the liquid analytes n could be derived by the following formulas: Ref. [24] 0.64

Conclusions
In conclusion, we presented a novel triple-band snowflake-shaped metamaterial absorber design based on a sandwich structure.The absorption at the three resonant frequencies was 97.43%, 79.22%, and 99.02%, respectively.Moreover, the sensing properties of the proposed THz absorber were demonstrated with different analyte thicknesses, ranging from 5 to 25 μm, and different refractive indexes, ranging from 1.0 to 2.2, for the three resonant modes.The maximum value of the refractive index sensitivity was 137.70 GHz/RIU, 306.25 GHz/RIU, and 473.86 GHz/RIU for the three resonant frequencies.The identification of peanut oil, carbon disulfide, and turpentine indicated that compared with the resonant frequencies f1 and f3, the resonant frequency f2 was closer to the exact refractive index of the surroundings.Based on Equations ( 7)-( 9), the calculated refractive index of peanut oil was n 1 = 1.701, n 2 = 1.727, and n 3 = 1.712 according to the different resonant modes.Similarly, the calculated refractive index of carbon disulfide was n 1 = 1.620, n 2 = 1.627, and n 3 = 1.616 according to the different resonant modes, while the calculated refractive index of turpentine was n 1 = 1.440, n 2 = 1.471, and n 3 = 1.434.Since the known refractive indexes of peanut oil, carbon disulfide, and turpentine are 1.715, 1.628, and 1.472, respectively, it can be seen that the refractive index n 2 calculated by the resonant frequency f 2 was more accurate than those calculated by the resonant frequencies f 1 and f 3 , due to the larger deviation introduced by the linear fitting of the refractive index sensitivity for the resonant frequencies f 1 and f 3 compared to f 2 .

Figure 1 .
Figure 1.(a) Vertical view and (b) side view of the proposed triple-band THz metamaterial absorber.(c) Perspective view of the snowflake-shaped unit cell.

Figure 1 .
Figure 1.(a) Vertical view and (b) side view of the proposed triple-band THz metamaterial absorber.(c) Perspective view of the snowflake-shaped unit cell.

Figure 2 .
Figure 2. Absorption and reflection spectra of the triple-band THz metamaterial absorber.

Figure 3 .
Figure 3. Terahertz absorption in the case of TEM waves incident at different angles from 0° to 60° for (a) TE polarization and (b) TM polarization.

Figure 2 .
Figure 2. Absorption and reflection spectra of the triple-band THz metamaterial absorber.

Figure 2 .
Figure 2. Absorption and reflection spectra of the triple-band THz metamaterial absorber.

Figure 3 .
Figure 3. Terahertz absorption in the case of TEM waves incident at different angles from 0° to 60° for (a) TE polarization and (b) TM polarization.Figure 3. Terahertz absorption in the case of TEM waves incident at different angles from 0 • to 60 • for (a) TE polarization and (b) TM polarization.

Figure 3 .
Figure 3. Terahertz absorption in the case of TEM waves incident at different angles from 0° to 60° for (a) TE polarization and (b) TM polarization.Figure 3. Terahertz absorption in the case of TEM waves incident at different angles from 0 • to 60 • for (a) TE polarization and (b) TM polarization.

Figure 7 .
Figure 7. Absorption spectra of the THz metamaterial absorber when the refractive index of analyte n changed from 1 to 2.2 under the three resonant frequencies: (a) f1, (b) f2, and (c) f3.

Figure 7 .
Figure 7. Absorption spectra of the THz metamaterial absorber when the refractive index of analyte n changed from 1 to 2.2 under the three resonant frequencies: (a) f 1 , (b) f 2 , and (c) f 3 .

Figure 8 .
Figure 8.The functional relationship between resonant frequency shifting and the refractive index of the analytes n for three resonant modes with an analyte thickness h = 5 μm.

Figure 8 . 12 Figure 9 .
Figure 8.The functional relationship between resonant frequency shifting and the refractive index of the analytes n for three resonant modes with an analyte thickness h = 5 µm.Photonics 2022, 9, x FOR PEER REVIEW 8 of 12

Figure 9 .
Figure 9. Resonant frequency shifting maps as functions of analyte thickness at the three resonant frequencies (a) f 1 , (b) f 2 , and (c) f 3 .(d) Influence of the analyte thickness on the sensitivity of the sensor.

Figure 10 .
Figure 10.The absorption spectra of the absorber with and without the analyte coating.Figure 10.The absorption spectra of the absorber with and without the analyte coating.

Figure 10 . 12 Figure 11 .
Figure 10.The absorption spectra of the absorber with and without the analyte coating.Figure 10.The absorption spectra of the absorber with and without the analyte coating.Photonics 2022, 9, x FOR PEER REVIEW 10 of 12

Author
Contributions: L.M. wrote the paper; Y.L. conceived and designed the simulation; Y.Z. and W.G. conducted the editing and review.All authors have read and agreed to the published version of the manuscript.

3 Figure 11 .
Figure 11.(a) Simulated absorption spectra results for the three resonant frequencies (a) f 1 , (b) f 2 , and (c) f 3 .(d) Locations of the resonant frequencies f 1 , f 2 , and f 3 for different liquid analytes at frequencies ranging from 0.2 to 1.8 THz.

Table 1 .
Comparison of absorption, sensitivity, Q factor, and FoM of the resonant modes in the present study and in previous works.