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Abstract
In this paper, a transparent absorption-diffusion-integrated metamaterial (ADMM) based on standing-up lattice structure is proposed which takes full advantage of electromagnetic absorption and destructive interference simultaneously for the suppression of broadband backward scattering within a wide angular domain, especially for the lower-frequency scattering. The proposed ADMM is constituted by two kinds of rhombic and squared ITO lattices arranged in a pseudorandom distribution and then backed with ITO film. Calculation, simulation, and experimental measurement show that the proposed ADMM can achieve low scattering with normalized reflection less than 0.1 in the frequency band of 6.1-21.0GHz. In addition, owing to the standing-up lattice structure, the averaged optical transmittance of our ADMM reaches the optimal value of around 82.1% in the visible wavelength range of 380-780nm, promising an excellent optical transparency. The proposed comprehensive scheme provides an effective way to achieve broadband scattering suppression and high compatibility with optical transparency, enabling a wide range of applications in the window glass of stealth armament, electromagnetic compatibility facility and photovoltaic solar device.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Owing to more freedom in engineering light-matter interaction, metamaterial (MM) consists of subwavelength meta-atoms have been deeply investigated in their capacity of negative refraction [1,2], energy harvesting [3,4], wavefront modulation [5,6], scattering control [7,8] and so on. As one of the most concerned aspects, investigation on how to reduce the backward scattering based on the scheme of subwavelength structure has always being a hot topic of fundamental and applied research due to the increasing demands of stealth technology, electromagnetic shielding, detection, and wireless communication.
Aiming at low backward scattering performance, MA with the capability of inhibiting the reflected and transmitted electromagnetic waves provides an effective approach to reduce the backward scattering almost for all directions of upper space. The perfect MA based on metal-dielectric-metal configuration was firstly proposed which acquired near unity absorption at any frequency [9]. With the emerging metamaterials, a series of single-, dual-, multi- and broad-band MAs based on the three-layered construction were flexibly gained [10–22]. However, when the total thickness is given as a fixed value, broadband MAs with the overlapped multiple resonances are hard to expand the operating bandwidth to the lower frequency. On the other hand, metasurface with the capability of diffusing the far-field distribution also provides an alternative way to the suppression of backward scattering. The diffusion-like metasurface makes full use of destructive interference from two anti-phase elements to reshape the far-field pattern [23,24]. After that, a fundamental innovation was proposed which assembles multiple lossless elements together in digital coding method to achieve more flexible manipulation of far-field distribution for backward scattering reduction [25–28]. Owing to the two-dimensional subwavelength structure, the diffusion-like metasurfaces exhibit obvious advantage in the thin thickness. Unfortunately, the proposed metasurface hardly achieve the wide-angle scattering reduction for the stealth applications under bistatic detections.
Inspired by the aforementioned discussion, the comprehensive scheme was proposed which combines the advantages of two schemes together for the pursuit of excellent backward scattering reduction. For example, Qu et al. developed an absorptive coding metasurface, demonstrating better performance of backward scattering reduction than the original traditional lossless coding metasurface and periodic MA [29]. Then, Cui et al. proposed a systematical design scheme of metasurface with incorporation of absorption-diffusion-integrated performance for broadband microwave antireflection [30]. However, the former researches with incorporation of electromagnetic absorption and destructive interference always concentrated on the planar structure. In fact, three-dimensional subwavelength structure introduced to MM had been demonstrated to excite multiple resonances for further performance improvements [15,16]. Meanwhile, the suitable scheme also provides an effective solution to the contradiction in the original planar MM, such as the standing-up ITO resonator used in the transparent broadband absorption MM [31]. Inspired by this, the comprehensive scheme of absorption-diffusion-integrated design based on three-dimensional subwavelength structure is still expected.
In this paper, we develop a transparent ADMM based on the standing-up lattice structure which can highly effective suppression of broadband backward scattering within a wide angular domain, especially for the lower-frequency scattering. As a proof, two kinds of rhombic and squared lattices fabricated by ITO film are assembled together in a pseudorandom distribution and then backed with ITO backplane in the proposed ADMM. Theoretical research shows that the designed standing-up ITO lattice with moderate sheet resistance can flexibly control its electric and magnetic resonances. With the optimized reflected amplitudes and phases of the two elements, the electromagnetic absorption and destructive interference can be inspired simultaneously under normal incident wave, contributing low scattering performance with normalized reflection less than 0.1 in the frequency band of 6.1-21.0GHz. In addition, owing to the standing-up lattice structure, our ADMM is also equipped with excellent optical transparency with averaged transmittance of around 82.1% in the wavelength range of 380-780nm, enabling extensive applications from military equipment to civil facility.
2. Theoretical analysis
The fundamental theory supporting the absorption-diffusion-integrated designs originates from the planar array theory [32]. As the schematic diagram shown in Fig. 1(a), MM including two kinds of elements arranged in the two-dimensional array of M × N randomly with the thickness of d. Under the excitation of normal indent wave, the array factor can be represented by
where β(m,n) is the initial phase, θ and φ are the elevation and azimuth angle for an arbitrary scattering direction. Multiple resonances inspired by the two elements can be flexibly gained, and their corresponding reflection coefficient amplitudes A0 and A1 as well as reflection phase P1 and P2 will also be changed. Based on this, the normalized reflection R for the proposed metamaterial composed of element 0 and element 1 follows the relationshipHere, it should be noted that the ratio k is defined as k = n0/(n0 + n1), where n0 and n1 are the total number of element 0 and element 1, respectively. Thus, it is evident that the ratios, reflection coefficient amplitudes, and reflection phases of the selected two elements play important roles for the achievements of low backward scattering in our absorption-diffusion-integrated design. In order to give a detailed illustration based on the aforementioned formula, the phase difference Pd = P1-P0 and the ratio k between the two elements is introduced here as independent variables under the following conditions of I: A1 = 1 A0 = 1, II: A1 = 1 A0 = 0.7, III: A1 = 1 A0 = 0.3, and IV: A1 = 1 A0 = 0.1, and the calculated normalized reflection spectra are given in Figs. 1(b)-1(e). In Fig. 1(b), when the reflection coefficient amplitudes of two elements are equal to 1, the proposed metamaterial can be simplified as chessboard reflector [19–21], and the low scattering performance with normalized reflection less than 0.1 can be achieved in the well-known phase difference range of 180 ± 37° under the condition of optimal ratio k = 0.5. Then, with the decreasing amplitude of reflection coefficient A1 from 0.7 to 0.1, there will be more freedom for the available phased difference Pd combined with suitable ratio k to achieve desired low backward reflection. Particularly, in Fig. 1(e), the obvious difference of reflection coefficient amplitudes realized by the two elements just like alternate distribution of absorption peaks in the spectrum, and the highly effective backward scattering reduction will be easily achieved. Thus, it can be concluded that the alternate distribution of absorption peaks in the spectrum combined with optimized phase difference will help our ADMM to make full use of electromagnetic absorption and destructive interference simultaneously for the achievement of extremely low scattering performance in a wider frequency band.
Fig. 1 (a) Schematic diagram of the transparent ADMM based on the combination of two kinds of standing-up lattice elements. Calculated reflection spectra of the ADMM based on different reflection coefficient amplitude combinations of (b) A0 = 1, A1 = 1; (c) A0 = 1, A1 = 0.7; (d) A0 = 1, A1 = 0.3; (e) A0 = 1, A1 = 0.1 under normal incident wave.
3. Design strategy
There are three steps in the design process of our proposed ADMM based on standing-up lattice. The first step is to design two kinds of standing-up lattice structures which can acquire alternate distribution of absorption peaks and desired phase difference in a wider frequency band. Then, theoretical calculation needs to be carried out for the determination of required ratio k as well as theoretical calculation of backward reflection. The final step is arrangement optimization of the two elements in the ADMM to obtain approving simulation close to the calculation.
In the pre-design process, the rhombic and squared lattice MAs are firstly selected here as the basic elements in our ADMM. As the schematic diagram shown in Fig. 2(a), the rhombic lattice MA is constituted by the standing-up rhombic lattice array, dielectric substrate, and reflective backplane. The ITO printed on an ultra-thin polyethylene terephthalate (PET) substrate is introduced here to fabricate the standing-up rhombic lattice array and background plane, and the achieved lattice is embedded into the polymethyl methacrylate (PMMA) substrate with the horizontal alignment of upper surface. The sheet resistance of the ITO film is R0. The thickness of the PET substrate is tp. For each unit cell of rhombic lattice MA, the side length and height of the standing-up rhombic lattice are a0 and s, while the side length and height of the PMMA substrate are P and d. Another element of squared latticed MA is shown in Fig. 2(b), the constitutive materials and structure parameters of the proposed MA are consistent with the former one except that the standing-up lattice fabricated by ITO film with sheet resistance of R1 is designed as squared lattice with the side length of a1. The ITO backplane for the two elements are equipped with the sheet resistance of R2 = 6.0Ω/sq, which can be approximated as specular reflection due to its averaged transmissivity is about 0.001. The relative permittivity of the PMMA and PET are 2.25(1-j0.001) and 2.8(1-j0.03), respectively. Numerical simulation is performed in the commercial software of CST Microwave Studio, and unit cell boundaries are used in both x and y directions as well as open boundary in z direction. As the former discussion in Fig. 1(e), the alternate distribution of absorption peaks and desired phase difference benefits for the achievement of low backward scattering performance in a broad frequency band, and thus the global optimization method based on genetic algorithm is applied to explore the desired combination of absorption and phase spectra. Meanwhile, it should be noted that the standing-up ITO lattice elements used here ensure the high compatibility with excellent optical transparency characteristic, leading to the increased profile of the total system. Accordingly, the obtained lower-frequency absorption can be optimized for the pursuit of broadband backward scattering suppression, especially for the lower-frequency scattering. After optimization, the structural parameters are given as follows: P = 8.0mm, d = 4.0mm, tp = 0.175mm, s = 2.0mm, a0 = 5.1mm, R0 = 18.0Ω/sq, a1 = 7.0mm, R1 = 250.0Ω/sq, and the simulated reflection coefficient amplitudes and reflection phases of the rhombic and squared lattice MAs under normal incident wave are illustrated in Figs. 2(c) and 2(d), respectively. In the reflection spectrum, the rhombic lattice MA with low sheet resistance has obvious dips distributing at both end of the frequency band of 6.0-20.7GHz, while the squared lattice MA with high sheet resistance have only one dip just in the middle frequency. Moreover, the simulated phase difference between the two elements is also close to 180° during the frequency band of 6.0-20.7GHz. Thus, the electromagnetic absorption and destructive interference can be comprehensively utilized in the ADMM for the suppression of backward scattering in a wider frequency band. Here, it worth discussing that the sheet resistance is a vital parameter for the distribution of absorption peaks in the standing-up lattice MA. Compared with the original broadband MA of overlapping adjacent absorption peaks, our proposed ADMM allows the constituent element with the freedom to enhance the lower-frequency absorption, which benefits for further improvement of the lower-frequency scattering suppression.
Fig. 2 (a) Schematic of the rhombic lattice MA. (b) Schematic of the squared latticed MA. (c) Simulated reflection spectra of the squared and rhombic lattice MAs. (d) Simulated phase spectra of the rhombic and squared lattice MAs as well as their phase difference.
To get insight into the fundamental physics, the electric field distributions in the y-z plane as well as the power loss distributions of the two MAs are monitored at the resonance frequencies. Figure 3(a) shows that there has an enhancement of electric field between the corners of rhombic lattice at the low frequency of 6.0GHz, and the obvious power loss takes place at the corners along x-axis direction. Figure 3(b) shows that a circulation of electric field marked by the pinked line is inspired between the rhombic lattice array and the ITO backplane at the high frequency of 20.7GHz, and the power loss almost concentrates on the lower edge of the four sides in rhombic lattice. Thus, the rhombic lattice MA with low sheet resistance can excite strong electric and magnetic resonances simultaneously. Figure 3(c) shows that there also has an enhancement in the space between adjacent squared lattice unit cell at the frequency of 13.2GHz, and the power loss almost concentrates on the sides of squared lattice along y-axis direction. The squared lattice MA with high sheet resistance just excites weaker electric resonance in the interest frequency band. Thus, it is demonstrated that the standing-up ITO lattice array with different sheet resistance mounted above the reflective backplane can acquire various resonance characteristic, which can completely replace the planar resistive frequency selective surface (FSS) for the applications of broadband backward reduction.
Fig. 3 Electric field distributions in the y-z plane and power loss distributions for (a) the rhombic lattice MA at 6.0GHz, (b) the rhombic lattice MA at 20.7GHz, (c) the squared lattice MA at 13.2GHz.
4. Broadband backward scattering reduction
The two kinds of MAs have succeeded in achieving the alternate distribution of absorption peaks and suitable phase difference during a wide frequency band, and then, the following theoretical calculation of their combination needs to be carried out to find the optimal value of k. According to the Eq. (2), the calculated backward reflection under the different ratio k in the proposed ADMM is given in Fig. 4(a). From the calculated reflection spectra, it is evident that the ratio of 0.5 is the best choice in our ADMM which contributes low scattering performance with normalized reflection less than 0.1 in the frequency band of 6.1-21.0GHz. Based on the theoretical model, the averaged energy ratio (AER) within the operating frequency band of 6.1-21.0GHz is calculated by the Eq. (3), and then performed in Fig. 4(b).
Obviously, a majority of the incident wave energy (64.2%) is absorbed by the ADMM and the partial incident wave energy (26.5%) is diffused into various directions of upper space. Only a little bit of the incident wave energy (8.7%) is reflected along the incident wave direction. Moreover, as shown in Table 1, the relative operating bandwidth with the normalized reflection less than 0.1 is also discussed here for our design as well as the recent achievements of transparent MAs and diffusers [30,33–35], and our ADMM exhibits larger relative bandwidth in contrast to the others. Based on this, comprehensive analysis concluded that the absorption-diffusion-integrated designs have an advantage in the enhancement of operating bandwidth compared to the former schemes depending on electromagnetic absorption or destructive interference solely. Meanwhile, owing to the comprehensive utilization of electromagnetic absorption and destructive interference in the ADMM, the original definition of phase difference with 180 ± 37° in the lossless meta-diffuser is no longer complied strictly, and thus the basic element in the ADMM is give with enough freedom to excite diversified resonances for achievement of the desired backward scattering reduction.Fig. 4 (a) Calculated reflection spectra of the ADMM with various ratio of k. (b) Averaged ratio of the absorption, diffusion, reflection, and transmission in the frequency band of 6.1-21.0GHz. (c) Schematic of the optimized ADMM. (d) Calculated and simulated reflection spectra for the optimized ADMM.
Table 1. Simulated reflection with the efficiency less than 0.1 of our work and recent achievements.
Full-wave simulation of the designed ADMM under the illumination of plane waves is carried out in CST Microwave Studio. In the simulation process, each kind of super-element consisting of 3 × 3 lattices is introduced to maximize the geometrical similarity and mimic the periodic boundary condition. Then, a complete ADMM consisting of 8 × 8 super-elements following the ratio of k = 0.5 is established which contains 32 super-elements of rhombic lattice MA and 32 super-elements of squared lattice MA. To make the simulation close to the former calculation as much as possible, the pseudorandom arrangement of the two super-elements in the ADMM needs to be repeatedly carried out until the accumulative error between them is less than a threshold value. Finally, the schematic of the desired ADMM is given in Fig. 4(c), and the simulated and calculated reflection spectra are also given in Fig. 4(d). The good agreement between the calculation and simulation conclusively validates our scheme.
In order to observe the absorption-diffusion-integrated performance, the three-dimensional scattering patterns of the proposed ADMM under the normal incident wave are given in Fig. 5(a) at the frequencies of 6.0, 10.0, 15.0, and 20.0GHz. From the scattering patterns, it is obvious that the reflected energy is dispersed into various directions in the upper space due to the destructive interference effect. By contrast, the scattering patterns of the PEC plate with the same dimension at the corresponding frequencies in Fig. 5(b) show sharp scattering pattern as well as extremely concentrated reflected energy along the incident wave direction. Moreover, the E-Plane and H-Plane scattering patterns for both of the ADMM and PEC plate are simultaneously given as comparisons in Figs. 5(c) and 5(d), respectively. A significant scattering reduction almost for all directions of the upper space is achieved in the ADMM during a broad frequency band, demonstrating the advantage of absorption-diffusion-integrated performance. Moreover, the E-Plane and H-Plane scattering patterns of the proposed ADMM and PEC plate under the different oblique incidences of TE and TM waves are also monitored in Fig. 6. For the incident angle of 20° in Fig. 6(a), the ADMM achieves scattering reduce almost for all direction of upper space as well as the significant scattering reduction along the mirror symmetry of incident wave for both TE and TM wave at the frequency of 6.0, 10.0, 15.0 and 20.0GHz. With the incident angle increased as 40° in Fig. 6(b), the scattering reduce almost for all direction of upper space is still achieved at the corresponding frequencies, but the reduction efficiency is less than the formers, especially for oblique incidence of TE wave. For the larger incident angle of 60° in Fig. 6(c), the highly effective scattering reduction is still achieved during the higher frequencies, and the ADMM achieves more desired scattering reduction under the oblique incidence of TM wave. Thus, it can be concluded that our ADMM is also equipped with wide-angle scattering reduction during a broad frequency band, especially for the oblique incidence of TM wave.
Fig. 5 Full wave simulated scattering patterns of (a) the proposed ADMM and (b) PEC plate with the same dimension at the frequencies of 6.0, 10.0, 15.0, and 20.0GHz. The scattering patterns at (c) E-Plane and (d) H-Plane for the ADMM and PEC plate at the frequencies of 6.0, 10.0, 15.0, and 20.0GHz.
Fig. 6 Full wave simulated scattering patterns of the proposed ADMM and PEC plate with the same dimension at the frequencies of 6.0, 10.0, 15.0, and 20.0GHz under the oblique TE and TM incident waves with the angle of (a) 20°, (b) 40° and (c) 60°.
5. High optical transmittance
Besides the achievement of broadband backward scattering reduction, the standing-up ITO lattice array mounted above the ITO backplane in the proposed ADMM also provides a support for high optical transmittance. In fact, in order to achieve broadband microwave absorption, the former achievements of transparent MA in the literature almost concentrated on the multi-layered structure, and their optical transmittance would be reduced with the increased layer of ITO FSS. As a proof, calculated optical transmittance of our standing-up lattice structure as well as the multi-layered structure can be performed based transfer matrix method (TMM) [36]. As shown in Fig. 7(a), the multi-layered structure is constituted by several combinations of ITO FSS and PMMA substrate as well as the ground layer of ITO backplane. For the ITO film, both the amplitude and phase of the transmitted and reflected waves should be considered due to the existence of film interface effect. For the PMMA substrate, by contrast, the surface roughness and bulk thickness prevent the film interference effect. Thus, when the thickness and refractive index of the ITO films and PMMA substrates are given, the optical transmittance of the multi-layered structure can be obtained by a hybrid of coherent and incoherent TMM calculations. For our multi-layered structure, the thickness of the ITO FSS and ground ITO backplane are 40.0 and 100.0nm, respectively. The refractive index of the PMMA is 1.49, while the ITO has frequency-dispersive refractive index ranging from 1.7 to 2.0 during the visible light wavelength range [37,38]. The calculated results for normal incident wave are presented in Fig. 7(b). With the increased ITO film from one layer to four layers, the optical transmittance during the optical wavelength rang of 380-780nm are gradually decreased, especially for higher frequencies. For our standing-up lattice structure, by contrast, the influence of standing-up ITO lattice on the optical transmittance is negligible due to its thin thickness, and the calculated optical transmittance spectrum is given in Fig. 7(b) marked with pink asterisk. From the calculated results, the standing-up lattice structure exhibits excellent optical transparency with averaged transmittance of around 82.1% in the wavelength range of 380-780nm, which is very close to that of one-layered planar MA. However, one-layered planar MA has never achieved desired broadband microwave scattering reduction comparable to our proposed ADMM. Thus, it can be concluded that the standing-up lattice structure constituted by ITO film in transparent MM can provide an effective approach to overcome the contradiction between extending operating bandwidth and keeping highly optical transmittance.
Fig. 7 (a) Schematic of the standing-up ITO lattice structure and multi-layered ITO FSS structure. (b) The calculated optical transmittance spectra.
6. Experimental verification
To validate our proposed scheme, the optimized ADMM with the dimension of 192.0 × 192.0mm2 was fabricated in Fig. 8(a). In the fabrication process, the two layers of PMMA substrate with thickness of 2.0mm was introduced here as the transparent substrates, and one substrate was cut out with the designed patterns by laser cut technology for the fixation of standing-up ITO lattices. The two kinds of ITO films with the sheet resistance of R0 = 18.0Ω/sq and R1 = 250.0Ω/sq printed on the thin PET substrate with thickness of tf = 0.175mm were bent into the designed rhombic and squared lattices, and then filled into the gap of PMMA substrate. Then, the two layers of PMMA substrate and standing-up ITO lattices are glued together by the liquid adhesive of acrylics (JING HONG,1509). Lastly, a complete ITO film with resistance of R2 = 6.0Ω/sq was adhered to the ground of PMMA substrate, and the ADMM sample was finally achieved.
Fig. 8 (a) Photograph of the fabricated sample. (b) Simulated and measured reflection spectra for the fabricated sample. (c) Simulated and measured optical transmittance spectra for the fabricated sample.
The experimental measurement of the backward reflection was performed in an anechoic chamber. The measurement system is based on a network analyzer (Agilent, 8720ET) with four pairs of broadband antenna horns working in the frequency bands of 4-8, 8-12, 12-18, and 18-28GHz, respectively. In the process of measurement, the reflection from a metal plate with the same size as the fabricated sample is firstly measured for the sake of normalization, and then the measured reflection of the ADMM sample is gained in Fig. 8(b). The proximate agreement between simulation and measurement demonstrates that the our ADMM based on standing-up lattice structure make full use of electromagnetic absorption and destructive interference simultaneously for the achievement of highly effective and continuous backward scattering reduction in a broad frequency band. In addition, owing to its excellent optical transparency characteristic, the transmittance of our fabricated ADMM was also measured by the spectrograph (Ocean Optics, OFS-2500) during the visible light wavelength range of 380-780nm. As shown in Fig. 7(c), due to the two layers of separated PMMA in the transparent substrate and rough thickness of ITO film, the measured transmittance spectrum is lower than the simulated one at the lower and higher frequencies. However, the averaged value of the measured transmittance is about 78.9% which still ensures highly transparent performance for our naked eye.
7. Conclusions
In conclusion, we have proposed an ADMM based on the standing-up lattice structure which can achieve broadband scattering suppression within a wide angular domain as well as high compatibility with excellent optical transparency characteristic. In the implement of the ADMM, two kinds of rhombic and squared lattices fabricated by ITO film are assembled together in a pseudorandom distribution and then backed with reflective ITO backplane. Theoretical research shows that the designed standing-up ITO lattice with moderate sheet resistance can flexibly control its electric and magnetic resonances. After optimizing reflected amplitudes and phases of the two elements, the proposed ADMM can utilize electromagnetic absorption and destructive interference simultaneously under normal incident wave, contributing low scattering performance with normalized reflection less than 0.1 in the frequency band of 6.1-21.0GHz. In addition, owing to the standing-up lattice structure, our ADMM also exhibits excellent optical transparency with averaged transmittance of around 82.1% in the wavelength range of 380-780nm. Finally, the experimental measurements were performed to demonstrate our proposed scheme. It is believed that the concept of absorption-diffusion-integrated design based on standing-up lattice structure open the door to a wide range of applications, including stealth armament, electromagnetic compatibility facility, energy harvesting, and sensor.
Funding
National Natural Science Foundation of China (NSFC) (61471388, 61671467, 61501497 and 61771485); China Postdoctoral Science Foundation (2015M572561); Foundation for the Author of National Excellent Doctoral Dissertation of the People's Republic of China (201242).
Acknowledgments
We wish to thank Dr. W. Li (State key lab of advanced technology for materials synthesis and processing, Wuhan University of Technology) for the theoretical instruction of calculated optical transmittance, and Dr. M. Li (Key laboratory of advanced ceramic fibers and composites, National University of Defense Technology) for the experimental support of optical transmittance.
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