Multiphysical Digital Coding Metamaterials for Independent Control of

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A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions Cheng Zhang, Wen Kang Cao, Jin Yang, Jun Chen Ke, Ming Zheng Chen, Li Ting Wu, Qiang Cheng, and Tie Jun Cui ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b02490 • Publication Date (Web): 12 Apr 2019 Downloaded from http://pubs.acs.org on April 12, 2019

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ACS Applied Materials & Interfaces

A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions Cheng Zhang1,‡, Wen Kang Cao1,‡, Jin Yang1, Jun Chen Ke1, Ming Zheng Chen1, Li Ting Wu1, Qiang Cheng1,*, and Tie Jun Cui1,* 1State

Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China

‡These authors contributed equally *Corresponding author E-mail: [email protected]; [email protected]

Keywords: Metamaterial, bi-functional metamaterial, digital coding metamaterial, acoustic wave, electromagnetic wave, dual physical domains

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Abstract Fabricating materials with customized characteristics for both electromagnetic (EM) and acoustic waves remain a significant challenge using the current technology, since the demand of multi-physical manipulation requires a variety of material parameters that are hard to satisfy in nature. However, the emergence of artificially structured materials provides new degree of freedom to tailor the wave-matter interactions in dual physical domains at the subwavelength scale. Here, a bi-functional digital coding metamaterial (MM) is proposed to engineer the propagation behaviors of EM and acoustic waves simultaneously and independently. Four kinds of rigid pillars with various material properties are employed to serve as the 1-bit reflectiontype digital meta-atoms with antiphase responses in both frequency spectra, thus offering the opportunities of independent field controls as desired. The MM demonstrates excellent performance of scattering manipulations from 5700 Hz to 8000 Hz in the acoustic region, and 5.80 GHz to 6.15 GHz in the microwave region. The bi-functional MM is verified through fullwave simulations and experimental measurements with good agreements, which stands out as a powerful tool for the related applications in the future.


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Introduction It has been a long dream to control the electromagnetic (EM) and sound waves simultaneously in a desired fashion. Restricted by the EM and mechanical properties of natural materials, it is almost an impossible mission to find the candidate to meet the demands of wave manipulations in such two different spectra. In the past a few years, driven by the rapid advent of artificial structured metamaterials (MMs), deliberate design of material parameters becomes possible,14

allowing for precise control of waves in a broad physical range at deep subwavelength scale

and opening a door for multi-physical manipulations in the meantime. The EM MMs are usually constituted by periodic arrays of electric and/or magnetic particles, with unprecedented physical responses barely found in nature,5-7 such as invisible cloaks,8-9 super-lens,10 negative refraction,11-12 and omnidirectional absorption.13 Such ideas are extended to the acoustic region, which greatly enrich the modulation methods of sound waves.14-15 With the gradient index MMs,16-18 more and more fascinating phenomena were discovered in addressing the challenge of multi-physical controls, such as the invisible cloak for both static electric current and heat flux,19-20 and the cloak for the acoustic, EM and water wave simultaneously.21 However, the design rules are rather complex and the functionalities are quite limited. More recently, a simple strategy is demonstrated to achieve pronounced sound insulation and EM absorption/diffusion with a double membrane structure coated with Indium Tin Oxide (ITO) films,22-23 but the cavity structure is unfit for a variety of acoustic applications in practice. In addition, the huge quantities of the meta-atoms with different shapes or geometries also brought significant challenges to the design complexity and global optimization. Aiming to



circumvent this problem, digital coding MMs provide a promising avenue to alleviate the burden in design, and show outstanding abilities during wave-matter interactions.24 In general, the coding MM is composed of low loss elements with finite types of phase states, as can be encoded by the binary digits. For instance, the n-bit coding MM have 2n basic elements with equal reflection/transmission amplitudes and the phase interval of 2 2n . It was shown that the coding MM played important roles in the control of wave propagation, scattering and radiation,25-29 and displayed enormous potentials to adjust wave amplitude, phase or spectrum characteristics dynamically with the aid of digital signal processors.30-31 Later the idea was pushed into the acoustic regime,32-33 with similar trends observed in the elastic systems. In this paper, for the first time to our knowledge, we demonstrate the design, fabrication, and characterization of a novel bi-functional digital coding MM to engineer the scattering properties of EM and acoustic waves independently. The designed MM is constituted by four kinds of rigid pillars with different materials, which have nearly unity reflection amplitudes and anti-phase responses suitable for 1-bit meta-atoms in both EM and acoustic domains, making it possible to achieve the goal of independent field manipulations in a predefined fashion. We show that the EM and acoustic scattering characteristics can be modified at the same time by simply altering the coding sequences of the meta-atoms for both waves, which are confirmed by simulations and measurements with good agreements.


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Figure 1. Schematic of the proposed MM illuminated by the normally incident EM wave (a) and acoustic wave (b). The proposed MM is composed by four basic elements serving as 1-bit units in dual-physical domains at the same time.

Theory and design The configuration of the proposed MM is shown in Figure 1, which shows different scattering features under illumination from EM (Figure 1a) and acoustic (Figure 1b) waves in the normal direction. It is an all-dielectric MM, consisting of four basic elements with identical periodicities but distinct material properties. A metallic ground is located at the bottom to block the backward scattering. Table 1 gives the density, sound velocity, and dielectric constant of air and the substrate materials termed from Sub1 to Sub4 for the elements described in Figure 1. It is clear that the densities (ρ) of the selected substrates are much larger than that of air, giving rise to significant impedance (defined as Z=ρc, where c represents the sound velocity) mismatch when sound is travelling normally from free space into any of them. Thereby, nearly total reflection of the incident sound can be realized with ultralow absorption. On this basis, we can easily shape the wavefront of the echo signal, if proper phase profiles are introduced along the



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interface by tailoring the geometries of scatters. It is worth emphasizing that the substrates make great difference in the dielectric constants from Table 1, implying that the elements can respond distinctly to the external EM illuminations. Here, Sub4 is made of copper with high electrical conductivity (5.96×107 S/m), and the corresponding dielectric constant approaches infinity near low frequencies.

Table 1. Material parameters of the MM substrates and air Density

Sound Velocity

[kg/m3]

[m/s]

air

1.29

343.0

1.0

Sub1

2385.8

322.3

10.2(1+i0.001)

Sub2

2137.0

384.9

6.2(1+i0.001)

Sub3

3021.7

269.9

25.0(1+i0.0015)

Sub4

8930.0

5010.0

-

Name

Dielectric Constant


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Figure 2. (a) Evolution of the 1-bit meta-atom design from the acoustic regime to both EM and acoustic regimes simultaneously. (b) Simulated acoustic reflection amplitude and phase spectra for the four metaatoms, and the phase difference between ‘0’ and ‘1’ units in the observation bandwidth. (c) Simulated EM reflection amplitude and phase spectra for the four meta-atoms, and the phase difference between ‘0’ and ‘1’ units within the observation bandwidth.

Figure 2a gives an overview of the design procedure for meta-atoms encoded in both acoustic and EM regimes. Initially, we built two square pillars using any solid material in Table 1, with the same period of 5.0 mm but various heights of H0 and H1 respectively. The heights



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are deliberately differed to create an antiphase reflection response while keeping large reflection amplitude. Theoretically, the reflection characteristics are almost invariant to the substrate change from Sub1 to Sub4, since all of them can be regarded as hard medium when interacted with the incoming sound. In this paper, the square pillar heights are chosen to be H0=15 mm and H1=2.5 mm. The height difference is equal to a quarter wavelength of free space at the operation frequency f=6860 Hz. As will be shown later in Table 2, the reflection amplitudes of the two structures are approximately unity, while the reflected phases remain out of phase around this frequency, hence successfully meets the demand of 1-bit acoustic coding MM. For convenience, the digits ‘0’ and ‘1’ are taken to describe the binary elements in which the corresponding height are H0 and H1, respectively.

Table 2. Reflection coefficients of the Elements 1#-4#. Frequency

Element 1

Element 2

Element 3

Element 4

6860 Hz

0.999∠34.2°

0.999∠34.2°

0.999∠-145.6°

0.999∠-145.6°

6.0 GHz

0.997∠-213.8°

0.962∠-39.1°

0.966∠-224.4°

0.999∠-43.4°

Next we further investigate the EM reflection properties of the designed square pillars. In order to create disparate EM responses for each square pillar, the variance of substrate permittivity is introduced, leading to four kinds of units as illustrated in the third column of Figure 2a. Specifically, the first two meta-atoms are made of Sub1 and Sub2, with the total height of H0, while the latter two are composed of Sub3 and Sub4, with the total height of H1. To reveal the bi-functional behaviors of the four elements, full wave simulations are made to inspect the reflection coefficients within the bandwidth of 5.0-8.0 kHz in the sound regime, and


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5.0-8.0 GHz in the EM regime. The commercial numerical solvers COMSOL Multiphysics 5.3a and CST Microwave studio 2014 are employed respectively in the acoustic and EM simulations, where periodic boundaries are applied around the structure, and normal incidence is taken into account. At sound frequencies, all the elements demonstrate high reflectance as expected (see Figure 2b). The square pillars with the same heights owns nearly identical phase responses, and the relative phase retardation is 180°±30° between the elements 1(2) and 3(4) from 5.7 kHz to 8.0 kHz, which confirms the wideband performance of the 1-bit acoustic element design discussed above. In the microwave regime, the four meta-atoms are also highly reflective with little loss across the band of interest (Figure 2c), as can be understood by the impedance mismatch between the high dielectric constant resonator and free space. In the meanwhile, the four phase traces in Figure 2c nearly intersect at two points at 6.0 GHz. A phase difference of near 180 degrees is displayed in Table 2, implying that the element 1(3) and element 2(4) in Figure 2a can serve as ‘0’ and ‘1’ units separately for the sake of EM control. Moreover, the phase difference between the elements 1(3) and 2(4) varies from 150° to 210° (180°±30°) under normal incidence of plane EM wave from 5.80 GHz to 6.15 GHz, indicating that the 1-bit EM coding particles can operate over the relative bandwidth of 5.8% in this case. So far we have realized a bi-functional element which can be encoded individually in two physical domains, such as ‘0/0’, ‘0/1’, ‘1/0’, ‘1/1’ where the binary digits on both sides of the slash “/” stand for the corresponding codes for 1-bit EM/acoustic coding meta-atoms respectively. The proposed approach is very general for independent control of dual fields, if we can synthesize the phase profile of the reflected wave with proper coding sequences.



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From the theory of digital coding MMs,34-35 under the illumination of EM or acoustic waves, the scattering pattern of the MM can be determined by the superposition of the far fields from the unit cells: f ( , )  f e ( , ) M

N

  exp i  (m, n)  k0 D sin  [(m  1 2) cos   (n  1 2)sin  ]，

(1)

m 1 n 1

where m, n are the row and column numbers in the MM. D is the element periodicity. θ, φ, and k0 are the elevation, azimuth angles and the wavenumber of the free space respectively; φ(m, n) is the reflection phase of the lattice (m, n), and fe(θ, φ) is the pattern function of single unit. Indeed, we are able to regulate the scattered beams by solving the element phases inversely through the method of iterative fast Fourier transform.36-37 To validate our findings, three cases are provided to demonstrate independent modulations of various physical fields. Two kinds of supercells comprising 10×10 identical ‘0’ or ‘1’ elements are adopted to constitute the whole MM. In Case I, a minimal repeating coding matrix for 1-bit coding MM is selected as 1 0 0 0  M1 =  , 1 1 0 1

(2)

implying that the EM coding particles are placed alternatively by the sequence of ‘101010…’ across the row, but remain invariant along the column direction, and vice versa for the acoustic particles (Figure 3a). This is a typical phase pattern for the coding MM, corresponding to two scattering mainlobes symmetrically distributed with respect to the normal direction.38 From the generalized Snell’s laws, the deflection angle can be evaluated as  = sin 1     , where λ represents the free-space wavelength, and Γ stands for the physical length of the period with gradient phase respectively. In the simulation, the corresponding values are Γ=100 mm and


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λ=50 mm for both EM and acoustic waves at 6.0 GHz and 6860 Hz respectively. When excited by EM and acoustic plane waves along the normal direction, a pair of identical scattering beams emerge as depicted in Figures 3d and 3g, showing excellent accordance with the theoretical predictions. The beam splitting phenomenon can be ascribed to the introduced phase gradients in ±x or ±y directions.39-40 As revealed in Figures 4a-4f, the deflection angles both for EM (Figures 4a-4c) and acoustic waves (Figures 4d-4f) are gradually reduced within the ranges of (5.80-6.15 GHz) and (5.7-8.0 kHz), since  /  tends to be decreased when the frequency goes up. To further demonstrate the independent manipulation capability of the MM, two additional coding schemes are also proposed for the 1-bit MM with 1 1 0 0 M2 = , 1 0 0 1 

(3)

0 0 1 0 M3 =  .  1 1 0 1

(4)

and

In the former case described by Eq. (3), the ‘0’ and ‘1’ units are arranged alternatively in one dimension for the EM wave at 6.0 GHz, and two dimensions for acoustic wave at 6860 Hz as shown in Figure 3b, while in the latter case the inverse strategy is considered (Figure 3c) on the basis of Eq. (4). As is well known, the two dimensional alternant chessboard phase profile is usually characterized by four scattering mainlobes due to the equal amplitudes of phase gradients in both ±x and ±y directions.41 Such property is well validated by the simulation results in Figures 3h and 3f, corresponding to the EM and acoustic situations respectively. Nevertheless, the scattering trends illustrated in Figures 3e and 3i look the same to those in



Case I, since identical coding sequences are utilized to engineer the wavefronts of the scattering waves.

Figure 3. Schematic of the patterned MM, and the corresponding EM scattering patterns at 6.0 GHz and acoustic ones at 6860 Hz under normal incidence. (a-c) The repeating coding matrices are M1, M2 and M3 respectively. (d-f) and (g-i) are the three-dimensional EM and acoustic scattering patterns corresponding to the MMs in (a)-(c).


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Figure 4. Two dimensional EM (a-c) and acoustic (d-f) scattering patterns of the proposed bi-functional MM respectively in the yoz plane and xoz plane at different frequencies under the coding sequence of M1.

Experimental and Discussion To validate our findings, we fabricate a sample as shown in Figure 5a with the same geometric parameters as those used in the simulation. The periodic coding elements are produced via Computerized Numerical Control (CNC) with a high precision of 0.05 mm. The whole size of the sample is 400×400 mm2. In the experiment, only the coding sequence of M1 is considered during the fabrication of the sample. The EM experiment is carried out in the microwave anechoic chamber. The detailed measurement setup can be found in Figure 5a. The sample is placed before a wideband



transmitting horn antenna on a rotatory stage. A receiving antenna is located far away from the sample to record the far-field scattering pattern at different directions (not shown here). Both the feeding antenna and the sample are mounted on a supporting board with the distance of 1.8 m. The rotatory stage runs at the interval of 0.1°, thus we can observe the scattering properties with high precision. Due to the limitation of the test system, only the scattering waves in the horizontal plane can be obtained. Figure 5b shows the measured H-plane scattering patterns of the sample. A pair of scattering beams appear at the angles of ±30° with respect to the surface normal at 6.0 GHz (Figure 5b). The E-plane scattering pattern of the sample is plotted in Figure 5c by rotating the sample clockwise 90 degrees in the xoy plane, while the feed horn stays still. The excellent agreement between numerical and the experiment results in Figures 5b-5c confirms the theoretical analyses in the previous section. The acoustic performance of the sample is also measured using a home-built system as shown in Figure 6a.42 The test region is surrounded by the sound absorption materials to reduce undesired scatterings from the background. Due to the instrument and site restrictions, only the near field can be detected to inspect the acoustic behaviors of the sample. An array of 8 speakers with the interval of 50 mm is used to generate quasi-plane waves from the top. A 1/4-in microphone (MAP416, BSWA Technology Co., Ltd.) (Figure 6a) acts as the sensor to receive the total sound pressure within the scanning plane, with the aid of two dimensional moving stages. The sound pressure distribution in a cut plane above the sample (shadow region in Figure 6b) can be obtained by moving the microphone with equal step of λ/25 at 6860 Hz. From the comparison of the simulated and measured results in Figures 6c-6d, the wave splitting phenomenon can be observed obviously, which in turn validates the theoretical analysis in


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previous section.

Conclusion In conclusion, we have demonstrated the design and experimental characterization of a bifunctional coding MM in both EM and acoustic fields. The pillar shaped element is used to generate specific phase responses for the two waves by changing the materials and geometries, which is suitable to act as the 1-bit coding meta-atoms in each domain, thereby greatly facilitate the independent wave manipulations at will. The scattering features of the MMs can be deliberately adjusted with the changes of the coding sequences, making it possible to create various functionalities such as beam splitting, beam scanning or beam tilting in both domains. The numerical and experimental results demonstrate the good performance of the proposed MM. Our findings can be used as the reflect-array antenna for EM radiation as well as the sonar array for directive sound emission, which can be used in the scenarios such as safety detection, or oil exploration requiring multi-physical sensors. The thickness of the sample is just 15.0 mm, and the designed meta-atom is the particle at deep sub-wavelength scale. It is worth noting that the bulk density of the sample (1.36×103 kg/m3) is far less than that of pure copper (8.96×103 kg/m3), similar to the densities of Acrylonitrile Butadiene Styrene (ABS, 1.07×103 kg/m3) or photopolymer resin (1.31×103 kg/m3). In general, it is a lightweight and low-profile MM suitable for the engineering applications. Moreover, since the MM is composed of ceramic matrix composites, it also shows excellent environment adaptability and stable performances.



Figure 5. (a) Photograph of the fabricated sample and the EM experimental setup in the microwave chamber. (b-c) Measured and simulated H- and E-plane scattering patterns under the illumination of y-polarized plane waves at 6.0 GHz.

Figure 6. Photograph (a) and schematic (b) of the experimental setup to mapper the acoustic near field in a cut plane above the sample. (c-d) Simulated and measured acoustic near fields within the cut plane at 6860 Hz.


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Acknowledgments This work is supported by the National Key Research and Development Program of China (2017YFA0700201, 2017YFA0700202, 2017YFA0700203), the National Science Foundation of China (61631007, 61138001, 61371035, 11227904, 61731010, 61571117, 61501112, 61501117, 61522106, 61722106, 61701107, and 61701108), the 111 Project (111-2-05), the Natural Science Foundation of Jiangsu Province (BK20150020), the Fundamental Research Funds for Central Universities (KYCX17_0091), Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX17_0091), and the Scientific Research Foundation of Graduate School of Southeast University (YBJJ1812).

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