Metamaterials, as artificially engineered materials with periodic or quasiperiodic subwavelength arrays, have achieved significant attention and application because of their novel and exotic characteristics not found in natural materials [1,2]. As components of metamaterials, small scatterers or apertures have the characteristics to flexibly manipulate physical waves [1–3]. A metasurface is a new type of 2D metamaterial [4,5], which has been widely studied and continuously concerned due to its excellent resonance characteristics of ultra-thin thickness, light weight, and high absorbance, usually designed as subwavelength composite microstructures [6–10]. For electromagnetic (EM) waves, metamaterials greatly improve EM control capabilities in different frequency regimes, leading to some fascinating applications in theory and practice, such as negative refractive index, perfect absorbers, and polarization control devices [1,3,5,7,9,10]. The abundant functions have also been expanded to artificial intelligence and other fields [11,12]. In the field of acoustics, metamaterials can be used to display novel and peculiar properties to produce negative equivalent mass density and negative bulk elastic modulus [13–16], and to achieve functions such as noise absorption [17–19] and negative refraction [20]. In the infrared band, almost perfect absorption efficiency can be achieved on the subwavelength scale for incident light [21]. Therefore, this gives metamaterials a huge scope of development in the fields of noise reduction, acoustical insulation EM stealth thermal camouflage [22], etc., attracting more and more researchers in the field of metamaterials [21,22].

At present, effective detection methods have evolved from single spectrum and single physical field detection to integrated detection of visible light, microwave, infrared, acoustic waves [10,17,19,21–23], etc. It shows a trend towards wide band, multi-spectrum, and composite physical field detection. Moreover, metamaterial application scenarios often encompass a multitude of physical domains, making functional compatibility across different physical domains paramount for material adaptability. However, the majority of metamaterial designs mainly regulate waves of the same physical field to achieve corresponding functionalities [21]. This means that it is challenging to implement compatible regulation of matter waves with different properties through a single metamaterial design architecture, due to the significant differences in the physical properties of these waves. Acoustic metamaterials can be designed with underwater sound insulation and noise reduction function, with ventilation and noise reduction function, or with energy collection function. However, due to the functional limitations of acoustic metamaterials, their application potential has not been fully stimulated, but there is little research on multi-functional acoustic metamaterials, the field exploration is not deep enough, and there is still a need for further exploration.

Luckily, several successful attempts have been made to design multi-spectrum, multi-function compatible disguised metamaterials. Emrose et al. introduced multilayer structures with the phase-change material Ge₂Sb₂Te₅ (GST) for use as broadband switchable absorbers in the infrared wavelength range [24]. Zhang et al. presented a thin metasurface with large microwave absorptivity and low infrared emissivity simultaneously [25]. Li et al. presented a transparent metamaterial absorber with simultaneously high optical transparency and broadband microwave absorption, which consists of a two-layer soda-lime glass substrate and three-layer patch-shaped indium tin oxide (ITO) films [26]. Safari et al. proposed a visible and RF transparent composite metasurface utilizing dielectric–metal spectrally selective coatings with high near-infrared control and low thermal emissivity [27]. Zhang et al. reported a digital metasurface platform that can be programmed optically to implement EM functions [28], including microwave cloaking, illusion, and vortex beam generation. Sandeep et al. proposed a coating to demonstrate high-temperature IR camouflage with efficient thermal management, which makes the coating transparent in the visible range (300–700 nm) and highly reflective in the IR region, so it can serve as a thermal camouflage in the infrared band [29]. Ma et al. proposed to embed machine-learning models in both gradient-based and non-gradient optimization loops for the automatic implementation of multi-functional metasurfaces, which had eight controllable responses subjected to different combinations of working frequencies and linear polarization states [30]. Zhang et al. proposed a heat-stable and visible-transparent infrared selective emitter (ISE) based on ITO/ZnS four-layer composite film and proposed for the first time a camouflage ISE that showed excellent selective radiation characteristics at 2.5–3 μm and 5–8 μm dual-non-detection bands [31]. The ISE has a transmittance of over 67% in the visible band. In the field of acoustics, Langfeldt et al. placed two semi-circular bulk blocks on the bottom surface of the film and successfully demonstrated that bandwidth can be increased by using multiple bulk or multilayer materials [23]. Han et al. proposed an in-tube hollow acoustic metamaterial with double Helmholtz resonators and asymmetric waveguides for wave manipulation that has a good absorption domain and good ventilation performance in the 550–874Hz and 1344–1688Hz ranges [32]. Liu et al. proposed a broadband underwater acoustic metamaterial based on the coupling effect of Rayl beam vibration and Fabry–Perot resonance. The Rayl beam vibration provides a strong acoustic absorption effect in the low-frequency range of 500 Hz to 3 kHz. The operating frequency of the Fabry–Perot resonance is 3 kHz to 10 kHz, which has a good sound absorption capacity in a wide range [33]. Liu et al. designed a novel acoustic metamaterial that, combined with membrane elements that do not require precise tension, can achieve a sound insulation capacity of 30 dB at the peak frequency of sound insulation and can convert incident sound energy into electrical energy, and the collected electrical power can reach 0.93 mW [34].

However, it should be noted that the characteristic scale boundary in different spectra has not been broken out, which limits the further coupling with different physics fields. Therefore, the waves in the acoustic field cannot be modulated in EM modulation devices. The existing acoustic metasurface cannot be applied in the EM field. There are few attempts to concentrate different physical fields on the same metasurface for regulation. Therefore, designing a multi-functional metasurface based on multi-physical field coupling effects represents a significant challenge. It is a fundamental development trend in the future application of metamaterials.

In this research, a devisable metasurface with characteristic scale compatibility is proposed. Waves in microwave, infrared, and acoustic fields can be modulated simultaneously in the reduced characteristic scale, which can realize the multi-physics functions compatibility. As Fig. 1 shows, the devisable metasurface consists of a single porous layer of a metasurface that incorporates a back cavity. To verify the compatibility performance, three typical functions in microwave, infrared, and acoustic fields are chosen to simulate and experiment. In the microwave band, broadband backward scattering reduction can be achieved at 8–10 GHz. In the infrared band, the metasurface is configured with infrared transmission color blocks of 0.8, 0.6, and 0.4, resulting in digital camouflage functionality. Digital camouflage can be used in complex environments, where low infrared radiation and high infrared radiation coexist, such as forests, bushes, and densely populated construction areas. Significantly, the material is compatible with the acoustic physical field in the application of the EM field, enabling acoustic effects and offering certain sound absorption performance in the middle- and low-frequency bands (160–410 Hz). This metasurface architecture bridges the gap between different physical fields and effectively integrates the microwave, infrared, and acoustic fields. This design is important in concealed camouflage design for ships, submarines, aircraft, and other vehicles. It offers new directions for the integration of acoustic-EM physical fields, with great application values in smart skin, disguise protection, aviation manufacturing, submarine designing, and so on.

As shown in Fig. 2(a), the metasurface proposed in this paper consists of two parts: the upper part is a multi-functional EM metasurface layer consisting of an open resonant metal square ring and a non-invasive inset metal patch, and the resonant ring realizes a broadband polarization conversion by forming an angle of 45 deg with the line polarization direction of the incident EM wave, which achieves a highly efficient polarization conversion at 8–12 GHz, and thus achieves specific modulations of the reflective EM wave. The special advantage of using a polarization rotator is that it can provide a lot of infrared devisable space for the independent functional design at microwave and infrared bands. The non-metallic area in the middle and around the open resonant metal square ring is embedded with metal patches of different sizes, which can modulate the infrared emissivity of different meta-atoms and realize the overall infrared digital camouflage function. The macroscopic representation for the infrared band can expand the infrared characteristic scale from micron to millimeter scale. At the same time, quarter-circle arcs are dug out around each meta-atom. Then the meta-atoms and the cavity portion form a microperforated plate structure with an amount of Helmholtz cavities. The microperforated plate can realize acoustic absorption and noise reduction by losing the sound waves that entered the structure. The oscillation loss mechanism can reduce the sound wave characteristic scale from meter to millimeter scale. Thus, the waves in microwave, infrared, and acoustic fields can be modulated simultaneously in the metasurface at a millimeter scale.

The upper metasurface is composed of a metal back plate, dielectric layer, and metal pattern unit from bottom to top. The specific parameters are: the period of the upper metasurface unit is a=8.00mm, the edge length of the open resonant metal square ring is b=6.00mm, the width of the square ring is d=0.5mm, the width of the square ring is l=2.00mm, the aperture diameter around the meta-atom is r=0.30mm, the thickness of the metal layer pattern is h1=0.018mm, the dielectric layer is h2=3.50mm, the metal backplane is h3=0.018mm, cavity thickness D=35mm, and cavity wall thickness h=2.00mm. Helmholtz cavity material for the acoustic performance has almost no effect; considering the overall coherence of the metasurface, the cavity material is selected with the same dielectric layer as the metasurface. All metals mentioned are copper and all substrates are F4B (with a dielectric constant of 2.65 and a loss tangent of 0.001).

By setting the angle between the polarization direction of the linearly polarized wave and the open resonant square ring to 45 deg in CST, the square ring forms an efficient polarization rotator, which can realize the cross-polarization conversion of the reflective EM wave; the effect is shown in Figs. 3(a) and 3(c). When the x-polarized EM wave is incident, strong resonance occurs at the three frequency points of 5.2 GHz, 7.9 GHz, and 11.5 GHz. The polarization conversion rate (PCR) is more than 90% in the range of 7.1–12.5 GHz. The PCR is calculated as follows [35]: PCR=rxy2rxx2+rxy2=ryx2ryy2+ryx2,(1)where rxx=ryy represents co-polarization and rxy=ryx indicates cross-polarization. According to Eq. (1), the PCR is calculated and shown in Fig. 2(c) as well. The PCR is nearly 90% from 7.1 GHz to 12.5 GHz. Due to the equivalence of the co-polarization and cross-polarization, the reflectance rxx=ryy and rxy=ryx.

To explain the process of polarization conversion, we take y-polarization as the incident wave, and the u- and v-coordinate system is introduced. The u-axis is along a 45 deg direction concerning the y-axis and perpendicular to the v-axis, as shown in Fig. 3(b). Then we consider that the incident EM wave is polarized along the y-axis. The electric field can be decomposed into two orthogonal components (directions u→ and v→). Hence, the electric field of the incident EM wave can be expressed as Eq. (2) [35–37]: E→=u→Eiueiφu+v→Eiveiφv,(2)where u→ and v→ are the meta-atom vectors in the u- and v-axes, respectively. The electric field of the reflected wave can be written as Eq. (3) [35–37]: E→r=u→ruEiueiφu+v→rvEiveiφv,(3)in which ru and rv are the reflection coefficients along the u- and v-axis, respectively. When the EM wave is incident into the surface, the electrons motivated by the waves will move along the copper pattern, and the equivalent direction is the u-axis, which means the other direction z-axis will not affect the performance of the EM waves (be equivalent to the perfect electric conductor), so Δϕv=0 and ru=rv. However, in the u-axis direction, because of the resonance oscillation between the surface current and bottom current, the phase of the reflected waves will change, and when Δφ=π, the field synthesized by Eru and Erv will be changed to the x-direction. Therefore, the direction of reflective polarization is rotated by 90 deg [38].

If the open square ring is rotated by 90 deg while the polarization direction of the incident EM wave remains unchanged, according to Eqs. (2) and (3), the new reflected EM wave formed can be expressed with Eq. (4) [37,38]: E→r2=u→Eiuei(φu+π)+v→Eivei(φv+π).(4)

This means that the new reflective EM wave still undergoes cross-polarization rotation, but the reflective phase changes by 180 deg, and the magnitude remains the same. To confirm the above theory, the phase and amplitude of the reflective EM waves before and after the rotation of the square ring are compared at CST, and the results are shown in Figs. 3(d)–3(f), which are consistent with the theoretical analysis. According to the theory of coded metasurfaces, the meta-atom before rotation is denoted as code 0, and the meta-atom after rotation is denoted as code 1 [39]. Specific modulation of reflective EM waves can be realized by arranging the meta-atoms of the two codes, which can realize RCS reduction.

According to Kirchhoff’s law [24,40,41], the ratio of the spectral radiance of any object to its spectral absorptivity is independent of the nature of the object. The absorptivity is constantly equal to the radiative capacity of an absolute blackbody at the same temperature. In thermal equilibrium, the emissivity and absorptivity of an object are numerically equal for a given temperature and wavelength. For a wavelength-impermeable material, the reflectance can be obtained from a measurement of the reflectance. The absorbance is obtained by Eq. (5): ε=α=1−ρ.(5)

The emissivity is a property of the material itself, and most common metals are high-reflectivity materials with low absorptivity. Therefore, they are more commonly used in coating-based infrared low-emissivity materials, especially precious metals such as Au, Pt, and Ag. Some common metals also have lower emissivity with low cost, such as Al, Cu, and Zn. The copper powder coating emissivity at room temperature is 0.1 [21,25,31], and the aluminum powder coating emissivity at room temperature is 0.15. For the mixed combination of metal and non-metal surfaces in the macroscopic scale of infrared detection, it can be approximated as an average of the treatment according to the empirical equation ε=εm·fm+εd·(1−fm),(6)where ε is the symbol of emissivity, εm represents the metal emissivity, εd represents the dielectric emissivity, and fm represents the occupation ratio [40,42].

There is a large amount of non-metallic space around the original open square ring, which provides the possibility of a digital infrared emissivity design for the meta-atom unit. By insetting metal patches of the same thickness as the non-metallic areas, the occupation ratio on the surface of the meta-atom can be changed to realize the multifaceted design of the infrared emissivity.

The specific design idea is shown in Fig. 4(a). Considering the gradient design requirement of digital infrared emissivity, three modes of meta-atoms with infrared emissivity of 0.8, 0.6, and 0.4 are proposed, which correspond to the occupation ratio of 0.125, 0.375, and 0.625, respectively. To ensure the effect of infrared gradient emissivity while minimizing the impact on microwave performance, the embedded metal patch is cut so that the incident EM wave cannot form a large-scale eddy current within the metal patch affecting the function of the main polarization converter. According to the simulation results in Fig. 4(b), the meta-atoms’ co-polarization conversion rate, cross-polarization conversion rate, polarization conversion rate, and cross-polarization phase of the three occupation ratio designs all maintain good performance over 8–10 GHz. The cross-polarization reflective difference phase is less than 40 deg between 4 and 16 GHz, which balances the infrared performance and microwave performance. The surface currents of the three meta-atoms at the resonance frequency point in Figs. 4(c) and 4(d) show that the embedded metal patches tightly bind the induced currents in a limited area, reducing the coupled resonance with the open metal ring.

The sound absorption structure of the microperforated plate is composed of three parts, microperforated plate, rigid wall surface, and cavity, as shown in Fig. 5(a). According to acoustic knowledge and the transfer matrix method, the relationship of the upper sound pressure P1, the lower sound pressure P2, the upper particle vibration velocity V1, and the lower particle vibration velocity V2 of the microperforated plate can be expressed by Eq. (7): {[P1V1]=T1[P2V2],T1=[1ZMPP01],(7)where T1 is the transfer matrix of the microperforated plate. Similarly, as Fig. 5(b) shows, the relationship among the upper sound pressure P2, the lower sound pressure P3, the vibration velocity of the upper left particle V2, and the vibration velocity of the lower particle V3 can be expressed by Eq. (8): {[P2V2]=T2[P3V3],T2=[cos(kD)jρcsin(kD)jρcsin(kD)cos(kD)],(8)where T2 is the transfer matrix of the space cavity behind the plate, and k=ω/c is the wave number. By synthesizing Eqs. (7) and (8), the following formula can be obtained by using the transfer matrix method: {[P1V1]=T1T2[P3V3],T1T2=[T11T12T21T22]=[cos(kD)+jZMPPρcsin(kD)jρcsin(kD)+ZMPPcos(kD)j1ρcsin(kD)cos(kD)],(9)where D is the depth of the cavity, i.e., the distance from the microperforated plate to the rigid wall.

At this time, considering the rigid wall surface of the sound-absorbing structure of the microperforated plate, i.e., the boundary condition V3=0, the acoustic impedance Z of the sound-absorbing structure of the microperforated plate can be obtained: Z=P1V1=T11T21=ZMPP−jρccot(ωDc).(10)

Under normal incidence conditions, the sound absorption coefficient of the microperforated plate can be obtained by combining Eqs. (9) and (10): α=4R(1+R)2+(ωM−cotωDc)2.(11)

When the resonant frequency f is satisfied, the sound absorption coefficient can reach the maximum: ωM−cotωDc=0,(12)αmax=4R(1+R)2.(13)

To gain a deeper understanding of the compatibility regulation mechanism of the metasurface for electromagnetic and acoustic fields, CST is employed to observe the electric field distribution of the meta-atom design across three frequency points: 8, 9, and 10 GHz. The outcomes are depicted in Fig. 6(a). The metal backing plate positioned between the microperforated plate cavity and the metasurface plays a pivotal role in effectively confining the electromagnetic fields within a specific portion of the metasurface. This framework ensures that the cavity’s presence does not hinder the ability to regulate reflective microwaves or compromise its infrared camouflage emission performance. The sound absorption characteristics of the microperforated plate are independent of the material’s rigidity, enabling seamless integration of its architecture with traditional multi-spectrum super-surfaces. This integration fosters the achievement of multi-physical field regulation compatibility. On the other hand, the holes from the microperforated plate will not affect the microwave and infrared camouflage. The method of inversion is used to infer the equivalent medium parameters from S-parameters, and the results are shown in Figs. 6(b) and 6(c). The equivalent medium parameters of the metasurface are not changed after adding the holes. The polarization conversion performance is kept the same as the metasurface without holes in Figs. 6(d) and 6(e). So the acoustic performance and EM performance can be individually designed and optimized.

Figure 7(a) demonstrates the overall design idea of the microperforated plate metasurface. In the microwave band, by introducing the P-B phase theory and the design idea of the coded metasurface [43,44], the meta-atom before the rotation is remembered as the coded ‘0’. The meta-atom after the rotation is remembered as the coded ‘1’, which realizes the dual beam fractalization of the reflective electromagnetic wave by the arrangement of the ‘000001111100000 ……’, and then realizes the RCS reduction in the backscattering [45]. In the infrared band, the meta-atoms with three occupation ratios of 0.8, 0.6, and 0.4 (named mode 0, mode 1, and mode 2, respectively) are randomly arranged in the ratio of 1:2:1 to form an infrared imaging effect with digital camouflage feature. In the acoustic wave band, multiple meta-atoms are arranged in combination to form a microperforated plate structure with the cavity underneath to realize the acoustic absorption effect [46]. Figures 7(d)–7(f) show the simulation performance under microwave, acoustic, and infrared waves in turn.

COMSOL Multiphysics software is used for simulation. Since the impedance tube method is used to measure the sound absorption coefficient in the experimental validation of this paper, and the impedance tube method limits the shape and parameters of the metamaterials, to facilitate comparison with the experimental results, some metamaterial architectures are extracted from the simulation process in this section to form rectangular and columnar metasurfaces as shown in Fig. 7(b). To prove the rectangular and columnar metasurfaces have completely identical acoustic performance, the sound pressure level (PSL) distributions are simulated and shown in Fig. 7(c), in which the PSL distributions are identical. The acoustic absorptivity curves of the microperforated plate metasurface and conventional metasurface are shown in Fig. 7(d), and the simulation results show that the microperforated plate metasurface has a certain acoustic absorption in the range of 20–1600 Hz, whereas the traditional electromagnetic super-surface material has no acoustic absorption at all, and the architecture makes the electromagnetic metamaterial achieve a breakthrough in acoustic performance from scratch, and the sound absorption coefficient is greater than 0.5 in the range of 191.1–326.4 Hz, which has a good sound absorption effect.

In the microwave band, the far-field simulation of the whole metasurface is carried out by using CST as shown in Fig. 7(e), which results in the distribution map of the overall RCS and the beam fractal map, from which the reflected electromagnetic wave becomes a two-beam fractal, and the RCS of the perpendicular direction is scaled down. In the infrared band, the infrared distribution of the metasurface is simulated by combining the empirical formula of the infrared emissivity using MATLAB, which results in the effects shown in Fig. 7(f), and the metasurface exhibits the typical digital characteristics of the infrared.

To further verify the compatibility performance of metasurfaces, we fabricated a prototype of metasurfaces through conventional printed circuit board (PCB) techniques. First, the glass cloth and PTFE resin were scientifically configured, the customized PTFE sheets were obtained under a strict process, then a series of processes such as machining, cutting, and drilling were carried out for the PTFE sheets to obtain several PTFE rings and two PTFE plates, and experimental samples were bonded using glue to obtain experimental prototypes; the obtained experimental prototypes are shown in Fig. 8(a). To meet the microwave and acoustic wave test conditions, two kinds of samples, square and cylindrical, were fabricated, respectively, in which the square sample is used for microwave and infrared band performance testing, with the size of 320mm×320mm, consisting of 1600 meta-atoms, which is consistent with the simulation conditions in the CST. The cylindrical sample is used for the acoustic wave testing, with the inner diameter of the sample being 9.8 cm, which is consistent with the simulation conditions in COMSOL.

The microwave experiment measuring system is illustrated in Fig. 8(a). The measurements were carried out in a microwave anechoic chamber based on a network analyzer (Agilent E8363B) with two pairs of broadband antenna horns whose frequency bands are 2–6 GHz and 6–12 GHz. To bring into correspondence with the simulation settings, the sample was rotated 45 deg and placed on the detection platform. In the case of a vertical incidence, the antenna was first aligned to the metal backplate, and the RCS data was normalized for calibration. Then, the antenna was aligned to the sample surface to measure the co-polarization reflection coefficient, and the RCS reduction data of the metasurface was directly obtained and shown in Fig. 8(b). Figure 8(b-i) gives the simulated RCS of the metasurface and copper plate in the incident direction, and the simulated RCS reduction in Fig. 8(b-ii) can be obtained from the difference values in Fig. 8(b-i). Compared to the simulation results, the measured results are approximately the same with slight frequency deviation, which was caused by the fabrication precision, experimental environment, and the finite number of meta-atom cells in the test sample. In addition, the measuring step size difference between the simulation and experiments will also cause errors between the experimental curve and simulated curve, in which the simulated step size is 0.2 GHz while the experimental step size is 0.03 GHz.

The infrared emissivity results with different occupation ratios were measured by the TSS-5X IR emissivity meter first. The infrared probe acts as the detector and the metasurface is fixed horizontally on a platform. An infrared detector was placed on the metasurface to obtain the infrared emissivity in mode 0, mode 1, and mode 2. The results are shown in Fig. 8(c), which shows the obvious characteristic of the gradient infrared emissivity and coincides well with the theoretical values. There are slight deviations among the data from the TSS-5X IR emissivity meter and theoretical values, which is possibly caused by the background environment and limitation of instrument precision. What is more, the roughness of the sample can also have a great influence on the actual infrared emissivity. Then, we used the infrared imager (Thermao GEAR) to realize the infrared imaging of the sample, which is shown in Fig. 8(d). Because of the different infrared emissivity of the surface, the sample has an obvious digital infrared camouflage effect. The main error is from the surface of the sample. The principle of infrared test equipment is the mirror reflection method, which is easily interfered with by the roughness of the sample surface. The rougher the surface of the sample, the greater the results of the test will be.

To further verify the robustness of our designed samples, we tested the infrared digital camouflage performance of the sample at different temperatures. Three temperature gradients of 50°C, 90°C, and 120°C were selected to observe the infrared properties of the samples. Figure 8(e) shows the infrared imaging results of the samples under 50°C, 90°C, and 120°C environments heated for 4 min, 8 min, and 12 min, respectively. At each temperature, the sample is gradually heated over time, which is conducive to the better realization of the camouflage function of the sample. At the same time, the sample still maintains infrared digital camouflage characteristics at different temperatures, indicating that the sample has good thermal robustness and thermal stability, proving that the sample can maintain stable performance in extreme temperature environments.

In the acoustic field, the sound absorption coefficient of the physical model in the frequency band of 50–1000 Hz was measured using an AWA6290T transfer function measurement system, and the experimental values were recorded and compared with the simulation results.

The acoustic absorption mechanism of the microperforated plate structure is unaffected by the material. The material used in this experiment PTFE is rigid, and the effect caused by the vibration of the structure itself is not considered, so it can be regarded as a rigid body. The acoustic impedance of air is 400kg/(m2·s), the acoustic impedance of PTFE is 1.3×106kg/(m2·s), and the difference of acoustic impedance between the two objects is defined as impedance mismatch; the more mismatch of acoustic impedance, the more energy is reflected at the boundary of the two media, i.e., when the effect of the reflection is better, the acoustic impedance of air is insignificant compared with the acoustic impedance of steel and therefore can be ignored. In the processing of the physical prototype, the sample parameter values are selected with the structural design parameters. During the processing of the physical sample, the parameter values of the sample are selected to be consistent with those of the structural design parameters. In the experimental process, the impedance tube should be added with three pieces of sponge pads with a diameter of 10 cm at one end to calibrate the equipment, improve the accuracy of the experimental measurements, and reduce the impact of errors. One end of the impedance tube is the input end, and the other end is the sound-absorbing end. The experimental sample is placed in the impedance tube and a sponge pad is placed at the sound-absorbing end to absorb the sound waves. The white noise generated by the data acquisition front-end is transmitted through a power amplifier to a loudspeaker, and the sound pressure signal in the pipe is captured by a transducer. The data is transmitted to the acoustic analyzer, and the software on the computer analyzes and calculates the data to obtain the experimental data; the experimental process is shown in Fig. 8(f-i).

The measured sound absorption coefficients of the samples are shown in Fig. 8(f-ii) Compared with the simulation results, although the measured values of the physical experiment and the simulation results do not exactly match, the curve trend is consistent, the overall data match is relatively high, and the experimental results have a better performance compared with the simulation results, so it can be considered that the experimental results are valid. The simulation results are consistent with the actual results, which prove the validity of the simulation, and it is feasible to judge the performance of the material through simulation. The reasons for the errors between simulation and physical experiment are as follows. (1) The multi-stage processing and a splicing process are used to manufacture experimental samples, and glue is used for bonding. Much glue is applied in the sticky position, resulting in the decreasing actual inner cavity volume. (2) The PTFE ring is not well combined when glue is used for multi-stage bonding, which forms the metamaterials of rough inner wall surface. The uneven inner wall increases the acoustic loss, resulting in the actual measurement results being better than the simulation results. (3) There are certain systematic errors in the measurement system, which are difficult to eliminate, but they do not cause a significant change in the acoustic absorption coefficient. (4) Due to processing accuracy and other process errors, it is difficult to accurately determine the hole diameter and the space between holes, which has a certain influence on acoustic performance. (5) Due to the microperforated plate structure, there is a viscous effect in the air part of the hole, and the damping effect of the thermal interaction is large, which has a certain influence on the acoustic performance.

In this study, we introduce an electromagnetic-acoustic multi-physics field-compatible tuned metasurface, which seamlessly integrates a microperforated plate structure with an electromagnetic metasurface. This integrated design allows for concurrent electromagnetic modulation and acoustic modulation by Helmholtz cavities. Within the microwave spectrum, the metasurface achieves cross-polarized rotation of linearly polarized waves through the polarization rotator of meta-atoms. Additionally, a 01-coded metasurface is constructed using P-B phase theory, resulting in RCS reduction within the 8–10 GHz frequency range. In the infrared domain, while maintaining microwave performance, metasurface units with varying occupation ratios are randomly discretely arranged to form a camouflage functional layer with infrared digital characteristics. Finally, in the acoustic frequency range, the aperture of the electromagnetic ultra-surface is combined with the cavity beneath, creating a microperforated plate structure composed of multiple Helmholtz cavities. This design effectively dissipates incoming acoustic waves, thereby realizing acoustic sound absorption and noise reduction capabilities. The microperforated plate structure in the acoustic band has no requirement for a material medium, so it can be composited with electromagnetic metasurfaces to realize simultaneous electromagnetic-acoustic multi-physical field modulation.