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Abstract
Achieving a high Q-factor metamaterial unit for a precision sensing application is highly demanded in recent years, and most of the developed high-performance sensors based on the high-Q metamaterial units are due to the dielectric/magnetic property changes of the substrate/superstrate. In this paper, we propose a completely different sensing metamaterial unit configuration, with good sensing sensitivity and precision properties, based on the thermally tunable liquid metals. Specifically, a basic thermally tunable metamaterial unit, the mercury-inspired split ring resonator (SRR), is firstly presented to theoretically show the magnetic resonance and negative permeability frequency band shift properties under different background temperatures. Then, considering the radiation loss mechanism of the conventional SRR metamaterial unit and based on the physically reliable ability of liquid metals, the modified mercury-inspired Fano and toroidal resonators with a large frequency tuning range and high Q-factor are developed and discussed. The numerical demonstrations have shown that the designed Fano and toroidal resonators have much better sensing precision performances compared to the conventional SRR for the temperature sensing application. The experimental demonstrations have also been used to verify the proposed mercury-based toroidal resonators, and good agreements are achieved.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterial is a kind of man-made subwavelength-scale structure with novel electromagnetic properties, not found in nature [1]. According to different application requirements, one can select appropriate substrate materials, design subwavelength-scale metallic/dielectric units with different shapes, sizes and rotation directions, and make the array with subwavelength periodic or aperiodic feature. As a result, the designed metamaterial can control the incident electromagnetic wave as demanded. For the composed metamaterial, the substrate material property and the metallic/dielectric unit features have significant influences on the electromagnetic response characteristics. Therefore, the active controllable metamaterials based on elastic substrates, fluid media and other specific substrate materials, and/or consisted of the fluid metallic resonators have shown obvious advantages in real-time dynamic tuning and on-demanded controlling of incident electromagnetic wave, including the amplitude, phase, polarization mode, and frequency [2–3]. And a variety of high-performance tunable/controllable/reconfigurable metamaterials and microwave/optical functional devices are reported in the past several years [4–7].
In those reported active tunable metamaterials, the diodes/transistors, MEMS devices, graphene, and phase change materials are used to integrate (add) into the conventional metamaterial units [8–12]; and alternatively, the graphene, MEMS structure, phase change materials, and memory alloy can also be used to construct directly the metamaterial units and array [13–15]. Then, by adjusting the applied DC voltage, the intensity and direction of external DC electric/magnetic field or light field, and/or the magnitude and direction of stress, the electromagnetic response characteristics of metamaterials are dynamically tuned, and then the transmission/reflection EM wave can be dynamically controlled.
Most of the previously reported active tunable metamaterials are in solid-state. The fluid metamaterial, as a newly developed metamaterial in recent years [4,16–19], has excited much attention and has wide applications, such as the high-precision microfluidic sensing and conformal applications [4]. Similar to the solid-state metamaterials, the reported fluid metamaterials mainly have two types: (1) realized by loading fluids as substrates, such as the liquid crystal, water/water-based solutions, and low-loss organic solutions [20–30]; and (2) consisted directly by the liquid metals, such as the mercury, EGaIn, and Galinstan [31–40]. For the previously mentioned first kind of liquid metamaterials, the EM responses can be tuned by changing the applied DC voltage, the intensity and direction of external DC electric/magnetic field, and the concentrations of the water/water-based solutions. On the other hand, the second kind of liquid metamaterials has shown better performances for electromagnetic wave controlling applications, in terms of the controlling ranges. However, for such second kind of reported liquid metal-based metamaterials, the previously reported EM wave response controlling methods are limited in pressure [31–40]. Moreover, only the EM wave manipulation application for the liquid metal-based metamaterials is proposed in recent years. Therefore, it is highly recommended to broaden the controlling techniques and extend the real applications for such kind liquid metamaterial.
As well known, the liquid metals including the mercury, EGaIn, and Galinstan are all temperature sensitive materials. If those metals are used to construct the metamaterial units, the EM responses of metamaterials can also be accordingly controlled by changing the background temperature. In this paper, therefore, we use the very naturally controlling method, namely the thermally-tuning method, to adjust the EM response properties of the liquid metal-based metamaterials. Specifically, the mercury is firstly used to design the basic split ring resonator (SRR), and the thermally-tunable properties are confirmed by the theoretical calculation based on the thermal expansion of mercury, and also verified by finite element modelling. Then, most importantly, to achieve a high Q-factor metamaterial unit for the high-performance temperature sensing application, the modified Fano resonator and toroidal resonator configurations are proposed based on the mercury. Lastly, the thermally-tunable performance for the proposed high-Q mercury-based metamaterials are experimentally demonstrated. Compared to the previously reported liquid metal-based metamaterials [31–40] only focusing on the EM manipulation by adjusting the pressure acted on the metamaterials, here we opened a completely new avenue to control the EM response and found an important application by designing several new liquid metal-based high-Q metamaterial units.
2. Basic mercury-based SRR design and demonstrations
Here we start the discussions of a regular SRR configurations as the basic thermally-tunable liquid metamaterial. Following the basic metamaterial unit, the proposed mercury-based SRR is shown in Fig. 1(a). As can be seen, one additional sphere with radii larger than the cylinder radii is designed, because of the basic thermal expansion property of mercury with coefficient: γ=(1/V0)/(ΔV/ΔT) = 0.18×10−3/°C. Here V0 is the initial volume of the mercury injected into the cylinder glass tube, and ΔV is the volume changing amount of the mercury when the environment temperature change is ΔT. That means one can get larger mercury volume changing amount with larger mercury storage size. This requirement is based on the same mechanism of the widely used regular mercury-based thermometer, and also be used in this paper. Based on the SRR configuration and the parameters shown in Fig. 1(b), the mercury-bar length within the glass tube can be easily obtained after simple equation evolution:
With the temperature changing ΔT, we can theoretically obtain the resonant frequency shift of the mercury-based SRR as:
Fig. 1. (a)-(c) The systematic representations for the proposed mercury-based SRR, (d) the effectively circuit model of the SRR, (e) simulation mode used in HFSS, and (f),(g) the simulated S-parameters and calculated effectively media parameters.
Here LΔT, CΔT are, respectively, the changing amounts of the effectively inductance and capacitance based on the basic effectively circuit model shown in Fig. 1(d).
To quantitatively understand the EM response changing performance for the designed mercury-based SRR, we perform the numerical simulation with HFSS software. Firstly, the validations of the mercury-based SRR and SRR + wire configurations are discussed. As can be seen in Fig. 1(e), the proposed structure is placed in the center of a waveguide with PEC boundaries at top and bottom sides and PMC boundaries at back and front sides. The left and right sides of the waveguide are the input and output wave ports. As an example, the mercury-based SRR is worked around 3 GHz with the chosen structure parameters: l0 = 21.42 mm, r = 4 mm, d1 = 0.1 mm, d2 = 0.25 mm, d3 = 1.2 mm, and d4 = 1.4 mm. The simulated initial transmission and reflection for the mercury-based SRR unit are shown in Fig. 1(f) (solid lines). Based on the regular effective media parameter retrieval method [41], the effective permittivity and permeability of the mercury-based SRR are obtained and shown in Figs. 1(f) and 1(g) (solid lines). It can be seen that the proposed mercury-based SRR has the regular magnetic resonance response around 3.34 GHz, and the retrieved permittivity curve shows the anti-electric resonance and the permeability curve shows the regular magnetic resonance with negative permeability values around 3.5 GHz. It means that the mercury-based SRR can achieve the regular magnetic resonance response, like the regular solid-state metallic SRR structure. Similarly, if we add a regular metallic wire into the mercury-based SRR, the double negative properties can be obtained with the negative refractive index frequency band around 3.5 GHz, shown as the dashed lines in Figs. 1(f) and 1(g).
Then, we manually change the mercury bar length in HFSS, from 21.42 mm to 24.97 mm, and collect the transmission curves as concluded in Figs. 2(a) and 2(b) (top panels). The corresponding temperature changing based on the Eq. (1) is shown in Fig. 2 as well. Moreover, the retrieved effective permeability curves for the mercury-based SRR, and the effective refractive index for the mercury-SRR and wire configuration are concluded in Figs. 2(a) and 2(b) (bottom panels). It is shown that with the increase of the mercury bar length (correspondingly the increase of temperature from 0°C to 49.2°C), the transmission shapes are almost not changed but the resonant frequency for each state is shifted to lower frequency. Accordingly, the retrieved permeability curves and the refractive index curves are also shifted to lower frequency with almost unchanged bandwidth. Figure 2(c) shows the collected resonant frequency shift under different mercury bar lengths and the corresponding temperature changings. As can be seen, a linear changing feature is obtained in the range from 0°C to 30°C. When the temperature is increased close to 50 °C, the increased mercury bar length makes the split of the SRR very small. As a result, the resonance frequency is very sensitive with the change of temperature in such area. From Fig. 2(c), we can get the tuning ability of the mercury-metamaterial in the linear range as a scale factor (S) of 7.2 MHz/°C. This is also scaled to the temperature sensing sensitivity of about 1.4×10−7 °C/Hz. This sensitivity is better than most of the reported temperature sensing platform based on the metamaterials. It should be noticed that we can further enhance the sensitivity performance with larger mercury sphere and thinner mercury bar for the SRR structure, based on Eq. (1). This property can be confirmed in next section.
Fig. 2. Numerical demonstrations for the tunability of mercury-based metamaterials at different temperatures. (a) simulated transmissions and retrieved permeability curves for the SRR, (b) simulated transmissions and retrieved refractive index curves for the SRR + wire, and (c) the resonant frequency shift, Q-factor, and FOM of the mercury-based SRR under different mercury bar lengths and correspondingly the temperature changing amounts.
3. Modified mercury-based Fano resonator design and demonstrations
In previous section, we have numerically demonstrated that the mercury can be used to design the high-sensitivity metamaterial unit for the high-performance temperature sensing application. However, to get more precision temperature sensing performance, the metamaterial unit should have higher Q-factor (equivalently narrow resonance frequency bandwidth) to get the larger figure-of-merit (FOM): S/Δf. Here Δf represents the 3-dB resonance frequency bandwidth and Δf = f0/Q. From the numerical simulation shown in previous section, we can find that the Q-factor of the SRR is in the range of 100 to 110 and the FOM is about 0.24/°C within the linear sensitivity area [see Fig. 2(c), bottom two panels], not such large for the high precision sensing applications. This is mainly due to the radiation loss (represented by Rr) of the regular SRR configuration and the ohm loss (represented by Ro) of the used mercy. Such two loss sources (R = Rr + Ro) contribute to the low Q-factor for the designed mercy-based SRR. In the past several years, many kinds of high Q-factor resonators are proposed and developed including, especially, the asymmetry Fano resonator [42,43], toroidal resonator [44,45], and anapole resonator [46–49]. Based on the high Q-factor performances of those metamaterial units, the sensing applications are proposed accordingly [43,50].
Therefore, obviously the above-mentioned high Q-factor metamaterial units can be used to design the mercury-based liquid metamaterial for the high-precision temperature sensing application. However, the original Fano, toroidal, or anapole resonator configurations are difficult to directly constructed by using mercury. Here, based on the fluid nature and the classic thermal expansion rate of the mercury and based on the design experiences obtained in previous section, we firstly propose a modified mercury-based Fano resonator, as shown in Fig. 3(a) (yellow part is the designed new resonator, and light blue part is the low-loss glass used to hold the mercury which will be discussed in next experimental demonstration section). As can be seen, the split is offset from the center of the resonator, so the Fano mode can be excited if the electromagnetic wave is incident along z-axis with polarization along x-axis. Theoretically, in the Fano resonator a circular current loop can be excited with non-radiation loss, and it can be interacted with the dipole response, resulting in a very sharp asymmetric resonance line shape with high Q-factor [42,43]. Moreover, the large cylinder shown in Fig. 3(a) is used to store more mercury so larger mercury bar increase/decrease under smaller temperature changing can be achieved (as mentioned in previously section based on the fixed expansion rate of mercury).
Fig. 3. Design and demonstrations for the modified mercury based Fano resonator. (a) schematic representation with parameter definitions, (b) simulated transmission curves under different gf, (c) surface current distributions, (d) simulated transmission curves under different sf, and (e) the resonant frequency shift, Q-factor, and FOM of the mercury-based Fano resonator under different mercury bar length and correspondingly the temperature changing.
As a schematic analysis, the electromagnetic wave response of the proposed mercury-based Fano resonator in a wide frequency band is numerically investigated with the initial used structural parameters: af=27.3 mm, bf=18.2 mm, cf=15.2 mm, df=0.4 mm, ef=8.4 mm, hf=6 mm, and rf=3 mm. And the period boundaries along x-axis and y-axis are set in the numerical modeling with Floquet ports along z-axis. To numerically reveal the Fano mode appeared in the designed resonator, we firstly set the split placed in the center with parameter gf=0 mm and a small split of 1 mm. At such situation, the electromagnetic wave response should be a classic electric dipole mode as shown in Fig. 3(b) (black line). When the split with fixed 1-mm gap size is shifted from the center to the one side of the resonator [see Fig. 3(a)], two additional resonances are appeared, seen in the simulated transmission curves in Fig. 3(b). It is obviously that the much shaper asymmetric transmission features are obtained, and such resonances are the so-called Fano modes which have been explained widely in Ref. [42,43]. The retrieved surface current distributions at such three resonance frequencies (for the case of gf=7.5 mm) are shown in Fig. 3(c). As can be seen, for each resonance, most of the currents are concentrated at different places of the mercury bar.
Considering the practical thermal expansion route of the mercury-based Fano resonator, we also numerically investigate the changing properties of the electromagnetic wave response when altering another parameter sf. As shown in Fig. 3(d), when the parameter gf=0 mm is unchanged (representing the mercury bar length is increased from the center point), the three resonances are down-shifted with the increase of the mercury bar length (sf). Specifically, the first and second resonance frequencies (f1 and f2) show the larger shifting range. This is mainly due to the fact that most of the currents are concentrated in the left mercury bar. So next we mainly focus on these two Fano resonance modes.
Specifically, based on the above obtained results, we can get the temperature sensing sensitivity according to the simple relationship of,
4. Modified toroidal resonator design and demonstration
At above section, we have numerically analyzed and verified that the mercury-based Fano resonator can achieve very sensitivity and precision properties. However, it needs the rigorous period boundary along x- and y-axis, which is very hard to realize in practical application condition. For the miniaturized metamaterial-inspired sensing application, only one or several metamaterial units can be used. Considering this limit, we change the rigorous period boundary to the perfect E boundary along x-axis and perfect H boundary along y-axis. Now the original Fano resonance modes are changed to the toroidal resonance modes due to the mirror symmetric property [44,50,51], as shown in Fig. 4(a). Specifically, within the toroidal resonator, the magnetic field can be effectually confined by multi current loops generated in the asymmetric resonator arranged as the mirror symmetric manner, so the new magnetic dipole with the so-called toroidal moment can be excited. This can also achieve very sharp resonance line shape with large Q-factor [51].
Fig. 4. Demonstrations for the modified mercury based toroidal resonator. (a) Surface current distributions, (b) simulated transmission curves under different gf, (c) the Q-factors under different gf, (d) simulated transmission curves under different sf, and (e) the resonant frequency shift, Q-factor, and FOM under different mercury bar length and correspondingly the temperature changing.
Therefore, with the same simulation structural parameters shown in Sec. 3, the numerical transmission curves under different parameters gf and sf are shown in Figs. 4(b) and 4(d). As can be seen, firstly for the new boundary setting, more clean transmissions are obtained for the different parameter values, with only two modes shown in the simulated frequency range. The collected Q-factors for the two toroidal modes when altering the parameter gf are shown Fig. 4(c), which indicate the moderate Q values but still much larger than Q-factor of mercury-based SRR. Specifically, when changing the parameter sf (representing the real temperature increase condition), the frequency of the first toroidal resonance mode is shifted faster than the second mode, similar to the Fano resonance condition. So it can be used for the temperature sensing application. The collected frequency shift and Q-factor changing properties, and the calculated scale factor (S) and FOM are all shown in Fig. 4(e). As can be seen, the good sensitivity (6.39×10−8 °C/Hz) in a very wide linear range is obtained. This large linear dynamic range is very important for the practical temperature sensing application.
Table 1 concludes the numerical performances for the discussed three resonators, including the temperature sensing sensitivity, linear dynamic range, Q factor, and FOM. It can be known that the new designed mercury-based Fano resonator and toroidal resonator have much larger sensitivity with more precision sensing performances. And considering the practical application limit, the toroidal resonator has acceptable sensing performance. Next, we will experimentally demonstrate the toroidal resonator in a real rectangular waveguide.
Table 1. Supplementary materials supported in OSA journals
To experimentally investigate the designed toroidal resonator, we fabricated a single-cell porotype as shown in Fig. 5(a). Specifically, the low-loss silica glass container is firstly fabricated by using precision laser etching technique with the scale bar, then another silica glass plate is used to cover the container, and the container and plate are stuck by UV glue. Then, the mercury is injected by a syringe via small through-hole connected to the container. Lastly, the fabricated toroidal resonator is placed at the center of a regular S-band rectangular waveguide, as shown in Fig. 5(b), and the whole measurement system is established as shown in Fig. 5(c). The background temperature is controlled by heating the metallic rectangular waveguide (model WR430, operating frequency band: 1.72-2.61 GHz), and the temperature closed to the mercury-based toroidal resonator is monitored by a commercial thermometer.
Fig. 5. Experimental demonstrations for the designed toroidal resonator. (a) fabricated mercury-based toroidal resonator, (b) sample-under-test placed in the center of WR430 rectangular waveguide, (c) the whole measurement system, (d),(e) the measured transmissions under different temperatures, and (f) the collected and calculated sensitivity, Q-factor, and FOM.
Before collecting the transmission curves based on the vector network analyzer (Agilent 5230A), the whole systems shown in Fig. 5(c) is calibrated by regular TRL calibration procedure. Then we start the background temperature from the environment temperature 26℃ and gradually increase the temperature to 38 ℃. The collected transmission curves are concluded in Fig. 5(d), and part of the curves are also replotted at Fig. 5(e). As can be seen, when the background temperature is increased from 26℃ to 38 ℃, the resonance frequency of the toroidal resonator is down shifted from 2.418 GHz to 2.221 GHz, with almost linear feature, as shown in Fig. 5(f). At the same time the measured Q-factor is also collected in Fig. 5(f), with average Q-value of 80; so the calculated scale factor of 16.4 MHz/℃ (the corresponding sensitivity is 6.01×10−8 °C/Hz) and FOM of about 0.59/℃ can be achieved. As can be seen, the similar sensitivity compared to the numerical result shown in Fig. 4 is obtained.
5. Discussion
As shown in Fig. 5, however, it should be noticed that the measured resonance strength, Q-factor, and FOM are much smaller than the numerical results shown in Fig. 4. After carefully analysis, we found that those decreased performances are mainly due to the following several aspects. Firstly, as shown in Fig. 6(a), when only one toroidal resonator is used in the regular rectangular waveguide exactly the same case in experiments, the resonance frequency and resonance strength are similar with the measured results shown in Fig. 5. But the simulated Q-factor can be kept well (closed to 900), similar to the results for unit modelling configuration shown in Fig. 4. When more toroidal resonators with increased numbers are placed in the rectangular waveguide with the mirror symmetric arrangement, the resonance frequency is down shifted, the resonance strength is enlarged strongly, and the Q-factor are not changed too much. That means the period arrangements have slight effects on the Q-factor and FOM for the proposed resonator. This can also be confirmed by the unit configuration modelling. As can be seen in Fig. 6(b), when we enlarge the period of the resonator along x-axis, the resonance frequency is increased, the resonance strength is gradually reduced with slight decrease in Q-factor. While the resonance feature is not changed obviously when the period along y-axis is enlarged, as shown in Fig. 6(c).
Fig. 6. Numerical discussion for the resonance performances of the toroidal resonator. (a) resonance features for different unit numbers, with inset plot for the different dielectric losses, (b) and (c) resonance features for different period space along x-axis and y-axis, respectively.
Besides, the dielectric losses of the used glass and UV glue in sample fabrication and experiments will have the major impact for the Q-factor. As shown in the inset of Fig. 6(a), when the effective dielectric loss used in simulation is 0.002, the resonance strength will be decreased with the reduced Q-factor of about 300. Moreover, the un-perfect micro-tube fabrication and assembling process for the sample will also affect the final measurement results, making the decrease of the Q-factor.
6. Conclusion
In conclusion, three mercury-based thermally-tunable metamaterial units, including the SRR, modified Fano and toroidal resonators, are proposed and discussed in this paper. Based on the designed thermally-tunable liquid metamaterial units, the temperature sensing sensitivity and precision performances are analyzed, and the Fano and toroidal resonators with much higher Q-factor and FOM are proposed for future high-performance temperature sensing applications.
Funding
National Natural Science Foundation of China (61601093, 61701082, 61901095, 61971113); National Key Research and Development Program of China (2018AAA0103203, 2018YFB180210); Special Project for Research and Development in Key areas of Guangdong Province (2019B010141001, 2019B010142001); Sichuan Province Science and Technology Support Program (2019YFG0120, 2019YFG0418, 2020YFG0039, 2021YFG0013, 2021YFH0133); Ministry of Education-China Mobile Research Fund Project (MCM20180104); Fundamental Research Funds for the Central Universities (ZYGX2019Z022); Yibin Science and Technology Planning Program (2018ZSF001, 2019GY001); Intelligent Terminal Key Laboratory of Sichuan Province (SCITLAB-0010).
Disclosures
The authors declare no conflicts of interest.
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