A High-Temperature and Frequency-Reconfigurable Multilayer Frequency Selective Surface Using Liquid Metal

A high-temperature and frequency-reconfigurable multilayer frequency selective surface (FSS) based on liquid metal is proposed in this work. After construction of a multilayer dielectric cavity with specific dielectric-shaped pillars and the injection of liquid metal (EGaIn) into each layer of the cavity, the liquid metal and dielectric pillars form a slot-type bandpass FSS, and frequency reconfiguration is realized by switching the injection layer. A prototype of the proposed FSS was designed, fabricated and measured. The measured results validated the design well. The good conductivity and fluidity of the liquid metal are utilized to realize the reconfigurable electromagnetic performance of the proposed FSS. This works in the C-band (5 GHz) and Ku band (13 GHz) and has a frequency switching time between 13.1 to 14.2 s. Moreover, due to the good thermal conductivity of liquid metal, the flowing liquid metal can take away heat, and the multilayer FSS can work as cooling plate. The heat transfer performance was investigated by numerical simulations. A 1000 °C plane heat source was set on the bottom surface of the double-layer FSS. The average temperature on the top surface was 62.2 °C, when the liquid metal fluid in the FSS had a speed of 1 m/s. The proposed multilayer FSS has strong potential for applications in some special application fields involving stealth and hypersonic aircraft.

etching or 3D printing FSS elements onto an existing singlesided copper clad laminate [12]- [13]. Simultaneously, to adapt to complex and changeable service environments, a reconfigurable FSS has been proposed, the structure of which can be manually or automatically switched to match the current electromagnetic environment. Research on reconfigurable FSSs began in 1972 when Lee et al. designed a folded surface by loading lumped elements onto an FSS [14]. Azemi et al. used a metal resonant helix structure to control the stop band or pass band of an FSS by adjusting the height of the helix [15]. Ebrahimi et al. realized a secondorder bandpass FSS with an adjustable passband by using a varactor diode [16]. The former is a mechanically adjustable FSS, and the latter is an electronically controlled FSS. The devices used mainly include PIN diodes, varactor diodes and MEMS switches [17]- [18]. Meanwhile, the hypersonic requirement results in high-temperature ablation (hundreds or even more than thousands of degrees). These current FSS technologies cannot meet the requirements of the hightemperature hypersonic working conditions. Liquid metal has good fluidity and high thermal conductivity at room temperature. It has been used as the cooling medium for forced liquid cooling, which provides a solution to the "thermal barrier" problems caused by the high integration of electronic equipment and high-speed operation of packaging systems and hypersonic aircraft [19]. Moreover, liquid metal offers electrical conductivity. Therefore, it is not only applied in the fluid heat transfer field [20]- [21] but also in the microwave electromagnetic field [22].
In 2009, scientists found that the liquid metal eutectic gallium-indium (EGaIn) is nontoxic and has all the electromagnetic characteristics needed by an antenna. Therefore, it is being researched as a promising new material for reconfigurable antennas [23]. Song et al. introduced liquid metal into a 3D printing microchannel to form an Eshaped patch antenna and realized multipolarization reconfiguration of the antenna by switching the continuous flow of liquid metal in the microchannels [24]- [25]. Liu et al. injected liquid metal into a PDMS microchannel and placed it on a square substrate to form a slot antenna and achieved antenna frequency and polarization reconstruction by controlling the length and direction of liquid metal flow [26]. Chen et al. introduced liquid metal into a glass medium to form a dielectric resonant antenna and achieved +45°, -45° and y-axis polarization reconstruction by controlling the channel and direction of flow of the liquid metal in the medium [27]. A pattern-reconfigurable Yagi-Uda antenna based on liquid metal was presented by Hao et al. [28]. The liquid metal alloy (LMA) was used to design a metasurface with switchable reflection phases, which serves as the superstrate of an antenna array to manipulate its scattering features [29]. Liquid metal can also be applied in FSS. Ghosh [33]. However, the above applications only use part of the properties of liquid metal; e.g., electrical conductivity and fluidity, or thermal conductivity and fluidity. There is no research on the application of all three properties to realize both electromagnetic and heat dissipation functions at the same time. This work proposes a reconfigurable bandpass slot-type multilayer liquid metal FSS that also has a high heat transfer capacity. Unlike the traditional FSS, this work uses all three properties of liquid metal: the electrical conductivity, fluidity and thermal conductivity. Therefore, the proposed multilayer FSS has good performance in both frequency selection and heat transfer and has strong potential for applications in specific scenarios; e.g., stealth and hypersonic aircraft.

II. MULTILAYER FSS ELEMENT DESIGN
The element structure diagram of the proposed frequencyreconfigurable multilayer liquid metal FSS is shown in Fig.  1. There are three substrates constituting a two-layer structure: the upper layer has four Y-shaped pillars, and the lower layer has one cross-shaped pillar. The center of each Y-shaped pillar is located at the center of the upper element of 1/4 size, and the center of the cross-shaped pillar is located at the center of the lower element. The cross-shaped pillar includes two branches, and the centers of the two branches overlap and are distributed in a connected structure at an angle of 90°. The Y-shaped pillar includes three branches, and the three branches are distributed in a connected structure of a circular array at an angle of 120°, with one of the branches parallel to the side boundary of the element. When the four side boundaries of each layer are sealed and the space between pillars and substrates is filled with liquid metal, the upper layer can work as a bandpass slot-type FSS at a specific frequency band, and the lower layer can function as an FSS at other frequency bands. Moreover, the liquid metal works as the electrical conductor, and the dielectric pillars work as slots. Other kinds of slot elements can also be adopted to replace the Y-or cross-shaped pillars. Each layer controls one specific frequency band. For example, in this work, if a C-band FSS is needed, the liquid metal is injected into the lower layer with the cross-shaped pillars and leaves the upper layer empty. If a Ku-band FSS is needed, the liquid metal is injected into the upper layer with the Y-shaped pillars and leaves the lower layer empty. When the liquid metal is switched among the different layers, the frequency reconfiguration of the FSS is realized. The switching time depends on the flow speed of the liquid metal and the total space volume between pillars.
The advantages of the proposed multilayer liquid metal FSS are significant: any classic slot FSS element can be employed, any range of the frequency band can be reconfigured, more layers (meaning more frequency bands) are easy to realize, and reconfiguration of the other electromagnetic characteristics (such as the polarization) can VOLUME XX, 2021 3 be conveniently realized. Moreover, the liquid metal is a good heat conducting medium. If a fluid circuit is constructed and the dielectric material of the substrates and pillars is replaced with a high-temperature material (such as ceramics), the proposed liquid metal FSS can also be used as an efficient cooling plate and has strong potential applicability in high temperature environment, such as stealth and hypersonic aircraft.

III. DESIGN PARAMETER ANALYSIS
The basic design flow of the proposed multilayer liquid metal FSS is as follows: 1) define the specified frequency bands of the FSS; 2) select the number of layers and slot element type of each layer; 3) design the dimensional parameters of the pillar in each layer; and 4) optimize the parameters of all pillars in the multilayer FSS.
The specified frequency bands of this work are the C-band (5 GHz) and Ku-band (13 GHz). A double-layer FSS structure can meet the frequency requirements, and classic cross-shaped [34] and Y-shaped [35] slot elements (pillars) are adopted here for the C-and Ku-bands, respectively. There are four design parameters for the Y-shaped (WY and LY) and cross-shaped (LS and WS) pillars. There are two parameters for the distance between pillars (PS for crossshaped and PY for Y-shaped), and two parameters for the heights of the substrate (H') and pillars (H). Considering cost and processing capability, polymethyl methacrylate (PMMA) is used as dielectric substrate and pillars instead of ceramics. Its permittivity is 2.57, and the loss tangent is 0.0078. The liquid metal is EGaIn (68.5% gallium, 21.5% indium, 10% tin), and the electrical conductivity is 6.8 × 10^6 S•m -1 .
The design parameters of the pillar in single layer were simulated and designed by Ansys HFSS. S 11 and S 21 of every single layer are shown in Fig. 2 (solid lines), and the parameters are listed in Table 1 (single layer column). It is clear that the transmission performance of the two singlelayer liquid metal FSSs is good.   The proposed two-layer frequency selective surface structure, when a single layer is filled with liquid metal, considers the vertical direction. The connected liquid metal increases the effective inductance, while the consecutive Yor cross-shaped pillars show large capacitance. To explain the resonance mechanism of the proposed FSS structure, simple circuit models are presented in Fig. 3. The design exhibits resonance in the form of a parallel combination (L 1 -C 1 ) resulting in a bandpass response at 4.99 GHz when the frequency selective surface works in the C-band, and in the form of a parallel combination (L 2 -C 2 ) resulting in a bandpass response at 12.98 GHz when the frequency selective surface works in the Ku-band. When the circuit models were implemented using Advanced Design System (ADS) software, the values of the lumped parameters were determined to be the followings: L 1 = 76.75 pH, C 1 = 13.23 pF, L 2 = 24.36 pH, and C 2 = 6.17 pF using the curve-fitting technique. The scattering parameters obtained from the circuit model were also compared with the simulated response as shown in Fig. 4, and they are in good agreement, thus validating the circuit model.  It is difficult to provide a set of equations relating the components of the electric circuit to the physical dimensions. But we can provide a set of qualitative relationships for changes in circuit element performance parameters as physical dimensions (LS, WS, LY, WY, H, and PS) change. When the proposed FSS works in C-band, C1 decreases and L1 increases when LS and WS increase. For Ku-band, when LY and WY increase, C2 decreases and L2 increases. As shown in Fig. 4 (c) and (d), the parameters L 1 and C 1 increase, the resonance frequency decreases. The same pattern is shown in Fig. 4 (e) and (f), when the parameters L 2 and C 2 are varied.
After the single cross-shaped layer (filled with liquid metal) is overlapped with the Y-shaped layer (no liquid metal filling) to form a double-layer FSS (working in the C-band), the transmission performance clearly degenerates, the resonance frequency shifts from 5.0 to 4.99 GHz, and the S 11 value rises from -26.42 to -16.75 dB, as shown in Fig. 2 (a).
When the single Y-shaped layer (filled with liquid metal) is overlapped with the cross-shaped layer (no liquid metal filling) to form the other double-layer FSS (working in the Ku-band), the transmission performance also degenerates, the resonance frequency shifts from 12.9 to 13.02 GHz, and the S 11 value rises from -24.54 to -16.72 dB, as shown in Fig.  2 (b).
The reason for the above outcome is the interaction of different layers and asymmetric dielectrics on the two sides of the liquid metal. Therefore, based on the single FSS layers, the parameters of the entire multilayer FSS must be optimized. Before optimization, parameter analysis is necessary to define the key design parameters. The values in Table 1 (double layer column, optimized parameters) are the initial dimensions used in the parameter analysis at C-band, and the values in Table 1 (single layer column) are used at Ku-band. Figs. 3-5 plot the simulation results for the double-layer element when all parameters are altered. Fig. 5 shows S 11 and S 21 in both the C-and Ku-bands when the element space (PS/PY) varies. The element space has a negligible impact on the transmission performance. Fig.  6 shows the results when the other parameters (LS, WS, LY, WY, H and H') vary in the C-band, and Fig. 7 shows the results when the same parameters vary in the Ku-band. The conclusion is clear: the parameters LS and WS have major effects on S 11 and S 21 in the C-band (as shown in Fig. 6 (a) and (b)), and the parameters LY and WY have major effects on S 11 and S 21 in the Ku-band (as shown in Fig. 7 (c) and (d)). Parameter H has no effect on the results in either the Cor Ku-band (as shown in Fig. 6 (e) and Fig. 7 (e)), but H' has a minor impact on the results in both the C-and Ku-bands (as shown in Fig. 6 (f) and Fig. 7 (f)). Considering the fluidity of liquid metal, the height (H) of pillars cannot be too small; it is fixed to 5 mm, and H' is fixed to 2 mm. The element space parameters PS and PY are fixed to 25.4 mm and 12.7 mm for the cross-shaped and Y-shaped FSS layers, respectively. The sensitivity of these parameters is consistent before and after optimization. Thus, only four parameters (LS, WS, LY, and WY) need to be optimized. Due to the considerable longitudinal dimension (H) of the proposed liquid metal double-layer FSS, the operation of the FSS for the case of large incident angles is investigated. To get the best transmission performance over a wide incident angle range, optimized parameters in Table 1 (double layer column) is used here. Three incident angles, 0°, 30° and 60° are considered for both the C-and Ku-bands. The S 11 results are shown in Fig. 8. The frequency shift rate is only 1%, and the frequency shift value is 50 MHz (from 5.01 to 4.96 GHz) at C-band and 130 MHz (from 12.99 to 12.86 GHz) at Kuband. Therefore, the considerable longitudinal dimension does not result in poor performance for oblique incidence at both C and Ku operation bands.

IV. PARAMETER OPTIMIZATION AND PROTOTYPE FABRICATION
To obtain the optimum parameters of the proposed liquid metal double-layer FSS, the particle swarm optimization (PSO) algorithm [36] is used here, which starts with a population randomly located in the search space. The population of the potential solutions is called a swarm, and each individual solution within a swarm is called a particle. The optimization model can be described as follows: ( where LS, WS, LY, and WY are the design variables; the objective function is the minimum frequency shift between the request frequency (f 0 ) and simulated resonant frequency (f) at both the C-and Ku-bands; the superscripts C and Ku indicate the frequency band; w is the weight coefficient, and w 1 = w 2 = 0.5. The constraint conditions include S 11 and the upper and lower bounds of the design variables. The swarm number is 40, and the iteration number is 30. The resonant frequencies and S 11 values of the three states (single layer, double layer before optimization and double layer after optimization) are listed in Table 2, and the optimized parameters are listed in Table 1 (double layer  column). Clearly, the optimized liquid metal double-layer FSS has good performance in both the C-and Ku-bands. The S curves of the optimization results are plotted in Fig. 10 (dotted lines). The best way to manufacture the prototype of the optimized liquid metal double-layer FSS is integrated forming, regarding which there is no need to worry about liquid metal leakage. However, due to the limitations of cost and fabrication, the prototype of the optimized liquid metal double-layer FSS was divided into three parts, as shown in Fig. 9 (a). The Y-and cross-shaped pillars were fabricated by a high-precision computerized numerical control (CNC) machine on PMMA substrates separately and finally assembled together. The liquid metal was injected into or extracted out of the PMMA layer by a peristaltic pump. The front and back sides of the prototype are illustrated in Fig. 9 (b), where the silver part is the liquid metal, and the transparent component is the PMMA. The cross-shaped and Y-shaped slots can be seen clearly. The size of the prototype is 300 mm × 300 mm. There are 20 × 20 Y-shaped pillars in the upper layer and 10 × 10 cross-shaped pillars in the lower layer. There are also inlet and outlet tubes for liquid metal to flow in and out in each layer. The dielectric substrates, seal washers and bolts are used to seal the cavity and prevent liquid leakage.

. (a) Structure diagram and (b) photo of the liquid metal double-layer FSS prototype
As a reconfigurable frequency selective surface, there is an inlet tube for liquid metal to flow in and an outlet tube for liquid metal to flow out in each layer; the diameter of both the inlet and outlet is 5 mm, and the fluid speed of liquid metal is 1 m/s. The time to fill or evacuate the upper FSS cavity is 13.1 s, and the time to fill or evacuate the lower FSS cavity is 14.2 s. Therefore, the switching time to reconfigure from C-band to Ku-band and from Ku-band to C-band is 14.2 s for FSS switch-overs.

V. MEASUREMENT AND DISCUSSION
The prototype was fabricated and the transmission performance (S11 and S21) was tested in an anechoic chamber. The measured two-frequency band working states are provided here for verification of the simulated results. The microwave measurement setups are shown in Fig 10. As shown in Fig. 10 (a), the standard-gain transmitting and receiving antennas (with operating frequency ranging from 2 to 18 GHz, double-ridged horn antenna) are fixed on the ground, and the fixture is fixed on the turntable to measure transmission coefficient at different angular incidences. The FSS is then embedded in the window of fixture (300 mm × 300 mm) to measure its transmission coefficient (see Fig.  10(b)). The center of antennas and FSS is located on the same horizontal line, and the distance between the fixture and each antenna is 800 mm. We measured the transmission between the transmitting antenna and the receiving antenna with/without the prototype, and the difference between the transmission results was regarded as the transmission performance. respectively. There is also some difference between the simulated and measured results. The frequency offset may be attributed to leakage from the gaps between the edges of the prototype, the finite size of the prototypes, and the fabricated tolerance of the prototypes. In particular, the contact surfaces between the liquid metal and PMMA pillars are rough due to the formation of some microbubbles or gaps, as shown in Fig. 9 (b). We can see that the edges of the metal slots are not smooth enough. In our opinion, this is the main reason for the frequency offset. In addition, some liquid metal drops remain in the upper layer when the liquid metal is pumped into the lower layer, which may also affect the measured results. Even so, the measured results still validate the design well. The comparison with measured data varying the angle of incidence is shown in Fig. 12. The measured data deviates from the simulated data, and the angular stability is good for C-band and slightly worse for Ku-band. The frequency shift rate is 2.1% at C-band and 3% at Ku-band, the frequency shift value is 110 MHz (from 5.02 to 5.13 GHz) at C-band and 400 MHz (from 12.75 to 13.15 GHz) at Ku-band.  Table 3. A 1000 ℃ plane heat source, which corresponds to the aerodynamic heating temperature at a speed about 5 Ma, was set on the bottom surface of the double-layer FSS. Two fluids (liquid metal and air) were used for cooling the heat surface with an initial temperature 20 ℃. The fluid speed was fixed to 0.1 m/s. Four cases were studied here, 1) both Y-and cross-shaped layers are empty (air flows); 2) liquid metal flows in both Y-and cross-shaped layers; 3) liquid metal in the cross-shaped layer and air in Y-shaped layer; 4) liquid metal flows in the Y-shaped layer and air in crossshaped layer. The average and maximum temperatures on the top surface of the 4 cases are listed in Table 4.
From Table 4, Case 4 has the best cooling results. The reasons for this are that the air (low thermal conductivity) flows in cross-shaped layer and insulates the heat source in the bottom of the same layer, and the liquid metal (high thermal conductivity and good fluidity) flows in the Yshaped layer and cools the top surface.
It is well known that a higher fluid speed results in a higher cooling effect and lower temperature. The fluid speed of liquid metal rises to 1 m/s (marked as Case 4-HS in Table  4), and the average temperature is 62.2 ℃. This temperature is less than 80 ℃, which is the maximum working temperature for most electronic device. Hence, the proposed liquid metal double-layer FSS has a good cooling effect and application potential in hypersonic aircraft. The temperature and fluid speed nephograms of Case 4-HS are shown in Fig.  13 for reference.

VII. CONCLUSIONS
A frequency-reconfigurable liquid metal multilayer FSS was proposed, designed, fabricated, and measured in this work. Table 5 compares the proposed liquid metal FSS with other reconfigurable FSSs or antennas from prior works. It is clear from the table that none of the prior works utilized good electrical conductivity, fluidity and thermal conductivity of liquid metal to realize both the reconfigurable electromagnetic performance and heat transfer capability achieved in this work. Therefore, it can be used in certain special application fields. Its advantages are summarized as follows: 1) It has both good frequency selective performance and good capability for achieving satisfactory heat transfer performance. Therefore, it can meet the challenges of stealth and hypersonic aircraft in the future.
2) It easily switches from C-band to Ku-band or from Kuband to C-band. It also has potential to realize the reconfiguration of additional EM performance factors; e.g., polarization.
3) Any type of classic and advanced slot FSS elements can be used in the proposed liquid metal FSS and achieve different EM performance or functional combinations. 4) To achieve a better cooling effect, two fluids (air and liquid metal) can be used together where air flows in the layer which is close to the heat source, and liquid metal flows in the other layer.