# Multiple Physical Quantities Janus Metastructure Sensor Based on PSHE

^{*}

## Abstract

**:**

## 1. Introduction

^{4}times, which is convenient for experimental observation. Researchers have also found that the PSHE phenomenon can be effectively enhanced by introducing a graphene layer and tuning its chemical potential [18]. These findings provide ideas for improving PSHE in the terahertz (THz) range.

^{5}μm/RIU under optimal pumping power and could distinguish normal gastric cells and corresponding cancer cells. Zhu et al. [24] designed a Tamm structure, which was able to achieve RI detection with S = 2804 mm/RIU in a THz band with a resolution of up to 10

^{−8}RIU by using PSHE. Kumar et al. [25] reported a PSHE plasma sensor based on a graphene monolayer under a THz environment. It could realize the gas sensor and the detection limit was up to 10

^{−5}RIU, which could be useful for the early detection of airborne viruses such as SARS-CoV-2. All of the above reports could realize the detection of the physical quantity in the THz range through PSHE and could have an excellent sensing performance, but, unfortunately, the realized functions are single. Liu et al. [26] proposed a PSHE sensor for high-precision RI detection and graphene layers’ number detection. By locking the corresponding angle of the PSHE peak, the sensor could detect the RI of S = 127.85°/RIU and the 1~9 layers’ number of graphene layers with S = 4.54°/layer. The multifunctional sensor provided a new idea for the research of related fields and exhibited certain research values.

## 2. The Theoretical Model

^{H}

_{−}and right-handed circularly polarized component δ

^{H}

_{−}. The RI of dielectrics A and B are n

_{A}= 1.7 and n

_{B}= 2, respectively. It should be emphasized that Leiwin et al. [28] derived the expression of effective permittivity and permeability of composite materials based on the Mie resonance theory and that the required RI could be obtained in a wide range. This technology has been applied in practice [29], so the dielectric RI set in this JMS is reasonable and available. According to the Herzberger equation, in the THz band, RI of Si is considered to be n

_{Si}= 3.419 [30]. The electric field conductivity σ of graphene is composed of intraband σ

_{intra}and interband σ

_{inter}[31].

_{B}, $\u0127$, e, T, μ

_{C}, and τ represent the angular frequency, Boltzmann’s constant, Planck’s constant, electron charge, temperature, chemical potential, and carrier relaxation time, respectively. There is a specific functional relationship between the conductivity and the chemical potential of graphene, which is different from that of ordinary dielectric. Assuming that the electronic energy band of a graphene layer is not affected by adjacent elements, the effective dielectric constant ε

_{G}of graphene can be written as [31]:

_{0}is the vacuum dielectric constant. So, the RI of graphene layer is written as n

_{G}= (ε

_{G})

^{1/2}. For the ordinary dielectric and graphene layers, their transfer matrix can be expressed as [32]:

_{jz}= ω/cn

_{i}sinθ

_{i}is the component of the wave vector on the z-axis; the speed of light in a vacuum is symbolized by c. The definition of s-wave and p-wave can be referred to Ref. [33]. η

_{i}is the light conductivity; for s-wave, η

_{i}= (ε

_{0}/μ

_{0})

^{1/2}n

_{i}cosθ

_{i}. For p-wave, then η

_{i}= (ε

_{0}/μ

_{0})

^{1/2}n

_{i}/cosθ

_{i}. ε

_{0}and μ

_{0}are vacuum dielectric constants and permeability, respectively. The transmission matrix of (AB)

^{6}(GSi)

^{3}(AB)

^{4}is [32]:

^{2}and T = |t|

^{2}separately represent reflectance (R) and transmittance (T). The absorptance (A) is written through [32]:

_{0}represents the beam waist and o is the polarization operator. Left-handed and right-handed circular polarized beams are represented by o = 1 and o = −1, respectively. The horizontal and vertical polarization states are separately symbolized by H and V. A matrix of coefficients between an incident and reflected electric fields can be expressed as [34]:

_{0}symbolizes the number of waves in free space. r

^{p}and r

^{s}represent the Fresnel reflection coefficients of the p-wave and s-wave, respectively. According to Equations (8) and (9), the expression of the spectrum of the reflection angle can be obtained [34]:

^{H}

_{r}= (1 + r

^{s}/r

^{p})cotθ

_{i}/k

_{0}and δ

^{V}

_{r}= (1 + r

^{p}/r

^{s})cotθ

_{i}/k

_{0}. ${\tilde{E}}_{r\pm}$ can be written in a similar style to Equation (8). ${\phi}^{s}$ and ${\phi}^{p}$ symbolize the phase of r

^{s}and r

^{p}. For the reflected light, the PSHE lateral displacement of the left-handed and right-handed components can be expressed as [34]:

^{H}

_{−}.

## 3. Analysis and Discussion of Performances

_{C}of the graphene can be adjusted [31]. How to change the graphene layer μ

_{C,}refer to Ref. [35]. In order to explain the generation of δ

^{H}

_{−}peak and the choice of μ

_{C}, taking the EWs propagation from the forward direction at the frequency of 5.52 THz to detect the RI of dielectric B n

_{B}as an example. Figure 2 displays the real and imaginary parts of the graphene surface conductivity σ at different μ

_{C}. According to Equation (1), μ

_{C}affects the σ and the σ increases with the rise of μ

_{C}. According to Equation (2), the change of σ will further change the permittivity of graphene layers, which are at different positions in the structure, thus affecting the effective permittivity and impedance of the whole structure. As a result, when EWs propagate through the structure, the electromagnetic properties such as reflection coefficient will be changed. Here, it takes the four classical μ

_{C}of 0.2 eV, 0.4 eV, 0.6 eV, and 0.8 eV. Figure 3 shows the relationship between the absolute values |r

^{s}| and |r

^{p}| of Fresnel coefficients and the θ at different μ

_{C}. The solid yellow and dashed green lines severally symbolize the reflection coefficient curves of |r

^{s}| and |r

^{p}|. The variation of μ

_{C}will affect the σ, thus altering the Fresnel coefficients and regulating δ

^{H}

_{−}. Moreover, the energy is localized and the reflection gap is created, where |r

^{s}| and |r

^{p}| drop quickly to produce defect peaks as a result of the introduction of the defect layer. Under various μ

_{C}, the reflection gap is produced at different θ. As can be seen from Figure 3a–d, the θ corresponding to the curve peaks of |r

^{s}| and |r

^{p}| gradually become smaller. When μ

_{C}= 0.6 eV, the peak value of |r

^{p}| reaches the minimum at 18.67°, where the defect peak generates |r

^{p}| = 0.002. By the beam displacement of Equation (11), the division of the spin correlation primarily depends on the part of |r

^{s}|/|r

^{p}|, thus the |r

^{s}|/|r

^{p}| might reach a high value close to the defect peak of r

^{p}|, resulting in the peak of δ

^{H}

_{−}. In Figure 4, this theory is put to the test. Figure 4a,b displays the δ

^{H}

_{−}values at various μ

_{C}and, as μ

_{C}rises, the δ

^{H}

_{−}peak progressively shifts to a small angle. δ

^{H}

_{−}produces the highest peak at 18.76°; δ

^{H}

_{−}= 2.46 × 10

^{−4}m when μ

_{C}= 0.6 eV. δ

^{H}

_{−}peaks at μ

_{C}of 0.2 eV, 0.4 eV, and 0.8 eV are small, the values are 2.94 × 10

^{−6}m, −1.02 × 10

^{−6}m, and −1.14 × 10

^{−6}m, belonging to θ of 19.48°, 29.7°, and 33.07°, respectively. To choose the suitable μ

_{C}with greater certainty, Figure 3c shows the changing pattern of the δ

^{H}

_{−}peak values corresponding to different μ

_{C}within the n

_{B}range of 2~2.4. It is evident that the peak value of δ

^{H}

_{−}at μ

_{C}= 0.6 eV is substantially higher than values at other μ

_{C}and that it varies greatly with the RI. The choice of μ

_{C}= 0.6 eV has great sensing performance because the multiple physical quantities detection is accomplished by locking the δ

^{H}

_{−}peak.

_{C}, RI modulation will have an impact on the size of the Fresnel reflection coefficients |r

^{s}| and |r

^{p}|. As a result, both δ

^{H}

_{−}peak and θ vary accordingly. So, RI detection can be accomplished by locking the corresponding θ of the δ

^{H}

_{−}peak. The dielectric B layers are selected as the detection region. When EWs propagate forward at 5.52 THz, Figure 5a indicates that continuous θ of the δ

^{H}

_{−}peak exhibits a good linear fitting relationship (LFR) in the range of n

_{B}from 2 to 2.4. In this scope, the values of δ

^{H}

_{−}are greater than 6.89 × 10

^{−5}m, which can ensure basic detectability. Using the linear fitting method, equidistant locations along the horizontal axis are chosen in order to produce the LFR. Figure 5b exhibits the LFR between n

_{B}and θ. In the range of RI of 2~2.4, the LFR is θ = 81.35 n

_{B}− 142.4. R

^{2}is applied to evaluate the quality of linear fit. R

^{2}= 0.9928 proves that the sensor is reliable and S can reach 81.38°/RIU. Figure 6 displays the RI detection performance under the condition of EWs backward propagation at f = 5.62 THz. As exhibited in Figure 6a, with the increase in n

_{B}from 2 to 2.09, the θ of the δ

^{H}

_{−}peak exhibits linear change along with δ

^{H}

_{−}> 5.87 × 10

^{−5}m. Figure 6b demonstrates the LFR between n

_{B}and θ. Between RI from 2 to 2.09, the LFR is θ = 99.3n

_{B}−156.3 and the S is up to 99.3 °/RIU. R

^{2}= 0.9928 indicates that the detection is reliable. Because EWs incident forward and backward separately have different RI detection performance in the common range of 2~2.09, an unknown RI is detected simultaneously. The δ

^{H}

_{−}peak is examined to have a maximum at θ = 20.3° on the forward scale and a maximum at θ = 42.3° on the backward scale. Through the corresponding forward and backward LFR, the unknown RI can be obtained as 2, which can mutually verify the accuracy of the test results.

^{H}

_{−}peak. On the forward scale, by investigating the changes in θ with dB from 2 to 2.35 μm, the relationship between θ and dB is established and depicted in Figure 7. Figure 7a displays the phenomenon of continuous variation of δ

^{H}

_{−}in the range of dB = 2~2.35 μm; δ

^{H}

_{−}is greater than 2.18 × 10

^{−4}m. The results show a linear distribution in a certain measurement range and, by further exploring the relationship between the two physical quantities, a fitting curve of θ and dB is obtained. The LFR is θ = 64.84 dB−109.6. The R

^{2}is found to be high, at 0.9904. S, an important indicator of sensor performance, is measured to be as high as 64.68 °/μm, indicating the high performance of the sensor manufacturing.

^{H}

_{−}peak values are greater than 2.18 × 10

^{−4}m in the dB scope of 1.85~2.02 μm. Figure 8b selects six data points at the same intervals for linear fitting to verify the strong LFR. The results exhibit that, as the thickness varies from 1.85 to 2.02 μm, the LFR is θ = 70.07 dB−102.3, with an R

^{2}of 0.9993. The S is 70.07°/μm, indicating further possibilities for sensor fabrication.

^{H}

_{−}peak. As the angle θ increases in the range of 27°~47° and 20°~40°, the δ

^{H}

_{−}peak produces a blue shift, respectively. Meanwhile, the corresponding δ

^{H}

_{−}peaks still remain larger than 9.93 × 10

^{−5}m and 1.05 × 10

^{−6}m, proving basic detectability. With the purpose of exploring their linear relationship, the correlative LFRs δ

^{H}

_{−}= 0.02238θ + 4.911 and δ

^{H}

_{−}= 0.02348θ + 7.64 are presented in Figure 9b and Figure 10b; 0.02238 THz/° and 0.02348 THz/° are the S compared with the magnetized plasma angle sensor with S up to 1.325 × 10

^{−4}THz/° [37]. The JMS is more responsive to the changes in θ. R

^{2}are all 0.99, indicating the high quality of the LFR. The above research presents that the sensor exhibits multiscale different θ detection ranges and the LFRs of detection are excellent, with sensitive response and exact detection, thus providing a novel and stable way to detect weak θ change in the THz band.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Zhu, Y.; Cao, L.; Merkel, A.; Fan, S.-W.; Vincent, B.; Assouar, B. Janus Acoustic Metascreen with Nonreciprocal and Reconfigurable Phase Modulations. Nat. Commun.
**2021**, 12, 7089. [Google Scholar] [CrossRef] [PubMed] - De Gennes P, G. Mechanical properties of polymer interfaces. Butterworth-Heinemann Phys. Polym. Surf. Interfaces
**1992**, 1992, 55–71. [Google Scholar] - Casagrande, C. Janus beads-realization and 1st observation of interfacial properties. Europhys. Lett.
**1998**, 306, 1423–1425. [Google Scholar] - Walther, A.; Müller, A.H.E. Janus Particles. Soft Matter.
**2008**, 4, 663–668. [Google Scholar] [CrossRef] [PubMed] - Hu, S.-H.; Gao, X. Nanocomposites with Spatially Separated Functionalities for Combined Imaging and Magnetolytic Therapy. J. Am. Chem. Soc.
**2010**, 132, 7234–7237. [Google Scholar] [CrossRef] - Wu, L.Y.; Ross, B.M.; Hong, S.; Lee, L.P. Bioinspired Nanocorals with Decoupled Cellular Targeting and Sensing Functionality. Small
**2010**, 6, 503–507. [Google Scholar] [CrossRef] - Jiang, J.; Gu, H.; Shao, H.; Devlin, E.; Papaefthymiou, G.C.; Ying, J.Y. Bifunctional Fe
_{3}O_{4}–Ag Heterodimer Nanoparticles for Two-Photon Fluorescence Imaging and Magnetic Manipulation. Adv. Mater.**2008**, 20, 4403–4407. [Google Scholar] [CrossRef] - Huck, C.; Vogt, J.; Sendner, M.; Hengstler, D.; Neubrech, F.; Pucci, A. Plasmonic Enhancement of Infrared Vibrational Signals: Nanoslits versus Nanorods. ACS Photonics
**2015**, 2, 1489–1497. [Google Scholar] [CrossRef] - Liu, L.; Zhang, X.; Kenney, M.; Su, X.; Xu, N.; Ouyang, C.; Shi, Y.; Han, J.; Zhang, W.; Zhang, S. Broadband Metasurfaces with Simultaneous Control of Phase and Amplitude. Adv. Mater.
**2014**, 26, 5031–5036. [Google Scholar] [CrossRef] - Cong, L.; Xu, N.; Han, J.; Zhang, W.; Singh, R. A Tunable Dispersion-Free Terahertz Metadevice with Pancharatnam–Berry-Phase-Enabled Modulation and Polarization Control. Adv. Mater.
**2015**, 27, 6630–6636. [Google Scholar] [CrossRef] - Chen, M.L.N.; Jiang, L.J.; Sha, W.E.I. Artificial Perfect Electric Conductor-Perfect Magnetic Conductor Anisotropic Metasurface for Generating Orbital Angular Momentum of Microwave with Nearly Perfect Conversion Efficiency. J. Appl. Phys.
**2016**, 119, 064506. [Google Scholar] [CrossRef] - Yu, Y.; Chen, Y.; Hu, H.; Xue, W.; Yvind, K.; Mork, J. Nonreciprocal Transmission in a Nonlinear Photonic-Crystal Fano Structure with Broken Symmetry. Laser Photonics Rev.
**2015**, 9, 241–247. [Google Scholar] [CrossRef] - Chen, C.; Ye, X.; Sun, J.; Chen, Y.; Huang, C.; Xiao, X.; Song, W.; Zhu, S.; Li, T. Bifacial-Metasurface-Enabled Pancake Metalens with Polarized Space Folding. Optica
**2022**, 9, 1314–1322. [Google Scholar] [CrossRef] - Yang, P.; He, J.; Ju, Y.; Zhang, Q.; Wu, Y.; Xia, Z.; Chen, L.; Tang, S. Dual-Mode Integrated Janus Films with Highly Efficient NaH
_{2}PO_{2}-Enhanced Infrared Radiative Cooling and Solar Heating for Year-Round Thermal Management. Adv. Sci.**2023**, 10, 2206176. [Google Scholar] [CrossRef] [PubMed] - Kavokin, A.; Malpuech, G.; Glazov, M. Optical Spin Hall Effect. Phys. Rev. Lett.
**2005**, 95, 136601. [Google Scholar] [CrossRef] - Zhou, X.; Ling, X.; Luo, H.; Wen, S. Identifying Graphene Layers via Spin Hall Effect of Light. Appl. Phys. Lett.
**2012**, 101, 251602. [Google Scholar] [CrossRef] - Hosten, O.; Kwiat, P. Observation of the spin Hall effect of light via weak measurements. Science
**2008**, 319, 787–790. [Google Scholar] [CrossRef] - Dong, P.; Cheng, J.; Da, H.; Yan, X. Spin Hall Effect of Transmitted Light for Graphene–Silica Aerogel Photonic Crystal in Terahertz Region. Opt. Commun.
**2021**, 485, 126744. [Google Scholar] [CrossRef] - Bing, P.; Sui, J.; Wu, G. Analysis of dual-channel simultaneous detection of photonic crystal fiber sensors. Plasmonics
**2020**, 15, 1071–1076. [Google Scholar] [CrossRef] - Khansili, N.; Rattu, G.; Krishna, P.M. Label-Free Optical Biosensors for Food and Biological Sensor Applications. Sens. Actuators B Chem.
**2018**, 265, 35–49. [Google Scholar] [CrossRef] - Lin, S.; Xu, X.; Hu, F.; Chen, Z.; Wang, Y.; Zhang, L.; Peng, Z.; Li, D.; Zeng, L.; Chen, Y.; et al. Using Antibody Modified Terahertz Metamaterial Biosensor to Detect Concentration of Carcinoembryonic Antigen. IEEE J. Sel. Top. Quantum Electron.
**2021**, 27, 1–7. [Google Scholar] [CrossRef] - Huang, T.-J.; Zhao, J.; Yin, L.-Z.; Liu, P.-K. Terahertz Subwavelength Edge Detection Based on Dispersion-Induced Plasmons. Opt. Lett.
**2021**, 46, 2746–2749. [Google Scholar] [CrossRef] [PubMed] - Cheng, J.; Xiang, Y.; Xu, J.; Liu, S.; Dong, P. Highly Sensitive Refractive Index Sensing Based on Photonic Spin Hall Effect and Its Application on Cancer Detection. IEEE Sens. J.
**2022**, 22, 12754–12760. [Google Scholar] [CrossRef] - Zhu, W.; Xu, H.; Pan, J.; Zhang, S.; Zheng, H.; Zhong, Y.; Yu, J.; Chen, Z. Black Phosphorus Terahertz Sensing Based on Photonic Spin Hall Effect. Opt. Express
**2020**, 28, 25869–25878. [Google Scholar] [CrossRef] [PubMed] - Kumar, P.; Sharma, A.K.; Prajapati, Y.K. Graphene-Based Plasmonic Sensor at THz Frequency with Photonic Spin Hall Effect Assisted by Magneto-Optic Phenomenon. Plasmonics
**2022**, 17, 957–963. [Google Scholar] [CrossRef] [PubMed] - Liu, S.; Yin, X.; Zhao, H. Dual-Function Photonic Spin Hall Effect Sensor for High-Precision Refractive Index Sensing and Graphene Layer Detection. Opt. Express
**2022**, 30, 31925–31936. [Google Scholar] [CrossRef] [PubMed] - Guo, S.; Hu, C.; Zhang, H. Ultra-Wide Unidirectional Infrared Absorber Based on 1D Gyromagnetic Photonic Crystals Concatenated with General Fibonacci Quasi-Periodic Structure in Transverse Magnetization. J. Opt.
**2020**, 22, 105101. [Google Scholar] [CrossRef] - Lewin, L. Electr. Engineers—Part III: Radio and Communic. Engineer
**1947**, 94, 65. [Google Scholar] - Liu, X.; Zhao, Q.; Lan, C.; Zhou, J. Isotropic Mie Resonance-Based Metamaterial Perfect Absorber. Appl. Phys. Lett.
**2013**, 103, 031910. [Google Scholar] [CrossRef] - Herzberger, M.; Salzberg, C.D. Refractive Indices of Infrared Optical Materials and Color Correction of Infrared Lenses. J. Opt. Soc. Am.
**1962**, 52, 420–427. [Google Scholar] [CrossRef] - Andryieuski, A.; Lavrinenko, A.V. Graphene Metamaterials Based Tunable Terahertz Absorber: Effective Surface Conductivity Approach. Opt. Express
**2013**, 21, 9144–9155. [Google Scholar] [CrossRef] [PubMed] - Qi, L.; Yang, Z.; Lan, F.; Gao, X.; Shi, Z. Properties of Obliquely Incident Electromagnetic Wave in One-Dimensional Magnetized Plasma Photonic Crystals. Phys. Plasmas
**2010**, 17, 042501. [Google Scholar] [CrossRef] - Fenton, E.W. Absence of Proximity Effect between S-Wave and p-Wave Superconductors. Solid State Commun.
**1980**, 34, 917–922. [Google Scholar] [CrossRef] - Gao, C.; Guo, B. Enhancement and Tuning of Spin Hall Effect of Light in Plasma Metamaterial Waveguide. Phys. Plasmas
**2017**, 24, 093520. [Google Scholar] [CrossRef] - Qi, L.; Liu, C.; Ali Shah, S.M. A Broad Dual-Band Switchable Graphene-Based Terahertz Metamaterial Absorber. Carbon
**2019**, 153, 179–188. [Google Scholar] [CrossRef] - Geim, A.K. Graphene: Status and Prospects. Science
**2009**, 324, 1530–1534. [Google Scholar] [CrossRef] - Xiang, Y.-T.; Wan, B.-F.; Zhang, H.-F. Multiscale and Multiple Physical Quantities Sensor Based on Nonreciprocal Evanescent Wave in the One-Dimensional Photonic Crystals. IEEE Sens. J.
**2021**, 21, 19984–19992. [Google Scholar] [CrossRef] - Zhang, Y.; Wang, L.; Jia, P.; Zhai, C.; An, G.; Liu, L.; Zhu, F.; Su, J. High-Sensitivity Refractive Index Sensor with Cascaded Dual-Core Photonic Crystal Fiber Based on Vernier Effect. Optik
**2022**, 256, 168488. [Google Scholar] [CrossRef] - Shi, X.; Han, Z. Enhanced Terahertz Fingerprint Detection with Ultrahigh Sensitivity Using the Cavity Defect Modes. Sci. Rep.
**2017**, 7, 13147. [Google Scholar] [CrossRef] - Zhao, Y.; Li, X.; Cai, L. A Reflective Intensity Modulated Fiber Tilt Angle Sensor Based on an All-Photonic Crystal Fiber Interferometer. Sens. Actuators A Phys.
**2016**, 244, 106–111. [Google Scholar] [CrossRef] - Wan, B.-F.; Zhou, Z.-W.; Xu, Y.; Zhang, H.-F. A Theoretical Proposal for a Refractive Index and Angle Sensor Based on One-Dimensional Photonic Crystals. IEEE Sens. J.
**2021**, 21, 331–338. [Google Scholar] [CrossRef]

**Figure 1.**The structure diagram of the JMS is arranged asymmetrically by graphene layer and common dielectrics are filled with different colors. The entire structure is (AB)

^{N}

^{1}(GSi)

^{3}(AB)

^{N}

^{2}, where N

_{1}= 6 and N

_{2}= 4. The thickness of the dielectric A, dielectric B, Si, and graphene are dA = 4 μm, dB = 2 μm, dSi = 1 μm, and dG = 0.34 nm, respectively.

**Figure 3.**The reflection coefficient curves of |r

^{s}| and |r

^{p}| with different μ

_{C}; (

**a**) μ

_{C}= 0.2 eV, (

**b**) μ

_{C}= 0.4 eV, (

**c**) μ

_{C}= 0.6 eV, (

**d**) μ

_{C}= 0.8 eV.

**Figure 4.**When μ

_{C}changes and EWs are incident from the front; (

**a**,

**b**) the comparison plots of δ

^{H}

_{−}under n

_{B}= 2. (

**c**) Plots of δ

^{H}

_{−}peak values under different n

_{B}.

**Figure 5.**Schematic diagrams of the RI detection when EWs propagate forward; the detection scope is n

_{B}from 2 to 2.4. (

**a**) Continuous varying δ

^{H}

_{−}peaks. (

**b**) The LFR between n

_{B}and θ; the LFR is θ = 81.35 n

_{B}–142.4.

**Figure 6.**Schematic diagrams of the RI detection when EWs propagate backward; the detection scope is n

_{B}from 2 to 2.09. (

**a**) Continuous varying δ

^{H}

_{−}peaks. (

**b**) The LFR between n

_{B}and θ; the LFR is δ

^{H}

_{−}= 99.3 n

_{B}− 156.3.

**Figure 7.**Schematic diagrams of the thickness detection when EWs propagate forward; the detection scope is dB from 2 μm to 2.35 μm. (

**a**) Continuous varying δ

^{H}

_{−}peaks. (

**b**) The LFR between dB and θ; the LFR is θ = 64.84 dB−109.6.

**Figure 8.**Schematic diagrams of the thickness detection when EWs propagate backward; the detection scope is dB from 1.85 μm to 2.02 μm. (

**a**) Continuous varying δ

^{H}

_{−}peaks. (

**b**) The LFR between dB and θ; the LFR is θ = 70.07 dB−102.3.

**Figure 9.**Schematic diagrams of the angle detection when EWs propagate forward; the detection scope is θ from 27° to 47°. (

**a**) Continuous varying δ

^{H}

_{−}peaks. (

**b**) The LFR between θ and frequency; the LFR is f = 0.02238θ + 4.991.

**Figure 10.**Schematic diagrams of the angle detection when EWs propagate backward; the detection scope is θ from 20° to 40°. (

**a**) Continuous varying δ

^{H}

_{−}peaks. (

**b**) The LFR between θ and frequency; the LFR is f = 0.02348θ + 7.64.

RI | Thickness (μm) | Angle (°) | ||
---|---|---|---|---|

Forward | Range | 2~2.4 | 2~2.35 | 27~47 |

S | 81.35 °/RIU | 64.84 °/μm | 0.02238 THz/° | |

Backward | Range | 2~2.09 | 1.85~2.02 | 20~40 |

S | 99.3 °/RIU | 70.07 °/μm | 0.02348 THz/° |

Refs. | Janus | Multifunction | Physical Quantities Detection | |||
---|---|---|---|---|---|---|

[38] | No | No | RI | Range | 1.362~1.366 | |

S | 303,376 nm/RIU | |||||

[39] | No | No | Thickness | Range | 0~0.5 μm | |

S | / | |||||

[40] | No | No | Angle | Range | 0~45 | |

S | 55.67 pm/° | |||||

[37] | Yes | No | RI | Forward | Range | 1.35~2.09 |

S | 132 MHz/RIU | |||||

Backward | Range | 1~1.57 | ||||

S | 40.7 MHz/RIU | |||||

[41] | No | Yes | RI | Range | 2~2.7 | |

S | 32.3 THz/RIU | |||||

Angle | Range | 25°~70° | ||||

S | 0.5 THz/° | |||||

This work | Yes | Yes | RI | Forward | Range | 2~2.4 |

S | 81.35°/RIU | |||||

Backward | Range | 2~2.09 | ||||

S | 99.3°/RIU | |||||

Thickness | Indicated in the article | |||||

Angle | Indicated in the article |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sui, J.; Xu, J.; Liang, A.; Zou, J.; Wu, C.; Zhang, T.; Zhang, H.
Multiple Physical Quantities Janus Metastructure Sensor Based on PSHE. *Sensors* **2023**, *23*, 4747.
https://doi.org/10.3390/s23104747

**AMA Style**

Sui J, Xu J, Liang A, Zou J, Wu C, Zhang T, Zhang H.
Multiple Physical Quantities Janus Metastructure Sensor Based on PSHE. *Sensors*. 2023; 23(10):4747.
https://doi.org/10.3390/s23104747

**Chicago/Turabian Style**

Sui, Junyang, Jie Xu, Aowei Liang, Jiahao Zou, Chuanqi Wu, Tinghao Zhang, and Haifeng Zhang.
2023. "Multiple Physical Quantities Janus Metastructure Sensor Based on PSHE" *Sensors* 23, no. 10: 4747.
https://doi.org/10.3390/s23104747