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Abstract
Impedance metasurface can establish a link between an electromagnetic surface wave and spatial wave and hence has attracted much attention of researchers in recent years. The holographic method, which is well known in the optical area, has also the great ability to shape the radiated beams in the microwave band by introducing the concept of surface impedance. Here, we propose a method to shape the radiated beams at two different wavelengths using single-layer multiplexing holographic impedance metasurface with in-plane feeding. For one wavelength, the generated broadside beam in the far field has the left-hand circular polarization, while the broadside beam in the other wavelength has the right-hand circular polarization. The radiation performance under different wavelengths are controlled independently due to the novel design of two eigen-modes in the impedance unit cell, in which the ratio of the two wavelengths can be large enough. To verify the proposed design experimentally, we fabricate a metasurface sample, and good agreement is observed between the simulation and measurement results.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, metasurfaces [1–7] have become the research focus and hotspot in the electromagnetic community due to their advantages of low profile, low loss, low cost, and multi-functional designs. Generally defined as the two-dimensional artificial electromagnetic media, the metasurfaces are composed of homogeneous or inhomogeneous subwavelength unit cells. According to the two forms of the electromagnetic waves, i.e., the spatial wave and the surface wave, there are also two categories of methods for modeling and designing the metasurfaces in different applications.
For the spatial waves, the metasurfaces can be modeled by the method of generalized sheet transition condition [8,9], from which the reflection and transmission coefficients of the metausrfaces can be calculated. The method of generalized Snell’s law [10–12] was introduced to tailor the metasurfaces with abrupt transmission phase by covering 360 degrees, which can accomplish the wavefront manipulations under cross polarizations. However, the transmission efficiency has the limitation of 25% [13] due to the polarization conversion. Huygens surface [14–18] can solve this problem by equally exciting the responses of electric and magnetic dipoles of the unit cells, and theoretical 100% transmission efficiency of the EM wave can be realized. For the surface waves, the metausrfaces can be modeled by effective surface impedance, which can describe the relationship between the electric and magnetic fields under the surface-wave modes on the metasurfaces. Accordingly, the holographic impedance antenna [19–22] that can realize the arbitrary beam forming in the far field had been proposed. Due to the connection between the effective surface impedance and surface refraction on the metasurface, the corresponding surface lenses [23,24] and surface waveguides [25,26] had been presented to flexiblely control the wavefronts of the surface waves.
The widely used holographic technology [27] in optical imaging has been enormously promoted due to the rapid developments of metasurfaces. Ni at al. proposed an ultrathin single layer hologram composed of complementary V-type nano units to generate arbitrary optical images [28] based on the theory of wavefront shaping. Meanwhile, three-dimensional optical images had been reconstructed [29] by eliminating the undesired effects of multiple diffractions. Multiple images [30] with diverse polarizations and angles had been generated using geometric metasurfaces under single-beam incidence, and multiplexing dual images were constructed using dual illuminations with orthogonal polarizations [31]. By exciting the shared hologram under surface plasmon polariton (SPP) waves from four directions [32], the corresponding four multiplexed images were generated. In addition, optical multi-images had been reconstructed by diversely excited modes of orbital angular momentum (OAM) respectively [33]. Dynamic three-dimensional holographic technology [34] was also realized by combining space channel metasurface and high-speed dynamic structured laser beam modulation module. However, all above-mentioned spatial holograms were dependent on the design of single wavelength.
In the microwave band, the hologram can be reconfigurable [35] using programmable and active methods. Based on the theory of Fabry-Perot cavity, the leaky-mode hologram can be reconstructed by in-plane feeding metasurface [36] with low profile. Actually, the development of antenna in the microwave band has more valuable applications due to the method of holographic reproduction, and various designs such as circular isoflux [37], multi-beam [38,39], multi-function [40] and arbitrarily synthesized beam shaping [41] antennas. And also, the quasi- dual-frequency holographic antenna based on the holographic impedance surface had been presented [42], but the hybrid multiplexing hologram had mutual interference for the two frequencies and the ratio between the two frequencies is small due to the intrinsical defect of the design method.
Here, we propose a surface impedance hologram under two different wavelengths which are well separated to realize two radiated beams at the corresponding wavelengths with different circular polarizations. To independently control different functions under different wavelengths, we propose a new subwavelength surface-impedance unit whose dispersion performance can be freely tailored under two transverse-magnetic (TM) eigen-modes. We show that the surface impedance hologram can radiate a broadside beam with the left-hand circular polarization (LHCP) at the low frequency, and the other broadside beam with the right-hand circular polarization (RHCP) at the high frequency. Both numerical simulations and mearsured results validate our design method, which have good agreements.
2. Dual-wavelength impedance holographic metasurfaces
2.1 Principle of holographic impedance surface for reconstructing radiated beams
The impedance surface which establish the relationship between the surface wave and spatial wave, is applied to record the hologram which can be excited to reconstruct the radiated beams in the far field. The holographic impedance metasurface is usually defined as [20]
where ${\psi _{ref}}$ and ${\psi _{obj}}$ represent the wave function of the reference wave and object wave the same as the defination in traditional optical holography. And the values of X and M represent the average surface impedance and modulated depth of whole impedance metasurface respectively. From the Eq. (1), we can know that the maximum value of surface impedance should be X + M, and the minimum value of the surface impedance should be X-M. To reconstruct the object wave, the impedance metasurface should be excited by the reference wave ${\psi _{ref}}$ which is the surface wave or current generated from the source. Correspondingly, the information of wave front $|{\psi _{ref}}{|^2}{\psi _{obj}}$ will come out and the arbitary shape of radiated beam can be tailored according to the artificial definition of ${\psi _{obj}}$.The generation of the impedance hologram should depend on the wavelength or frequency due to the property of Eq. (1). For the coherent hologram, the frequency of the excited source should be the same as the working frequency of designed hologram. If the ${\psi _{ref}}$ excited by the source and the ${\psi _{obj}}$ we required are determined in detail, the impedance hologram can be synthetically generated by the impedance unit cells which range of surface impedance should be from X-M to X + M. Here, we propose the design that the surface impedance ${Z_s}$ can be independently controlled under two different wavelengths, and accordingly, the different object waves which represent the radiated functions under corresponding wavelengths will be reproduced. In our design shown in Fig. 1, we intend to realize the broadside beams with LHCP at low frequency (${\lambda _1}$) and RHCP at high frequency (${\lambda _2}$). The wave function of reference wave is defined as ${\psi _{ref\_{\lambda _i}}} = {e^{ - j{k_{0i}}{n_i}\rho }}$ where the superscript i = 1 or 2, ${k_{0i}}$ and ${n_i}$ indicate the wave number in free space and effective surface refractive index under different wavelengths respectively. And $\rho$ means the distance from the source to the superposition of the impedance unit. This kind of reference wave can be regarded as the surface cylindrical wave which can be launched by the electric dipole. And that the polarized mode of the excited surface current is transverse magnetic, which polarization of electrical field is along the direction of wave propagation. Assuming that the dielectric loss is neglected, the surface impedance will be pure reactance. To realize the circularly-polarized broadside radiation beams, the impedance hologram of imaginary part should be recorded as [22]
Fig. 1. Schematic diagram of the overall single-layer holographic impedance metasurface which can realize the radiations under LHCP and RHCP under corresponding wavelengths. The in-plane feed of source located at the center of metasurface can have the good performance of real low profile.
2.2 Design of impedance surface unit for the dual wavelength hologram
To complete the design which is shown in Fig. 1, the most important issue is to realize the unit cells which not only satisfy the impedance range requirement, but also can be independently controlled under both wavelengths according to Eq. (2). The proposed new impedance surface unit cell shown in Fig. 2(a) is the single-layer texture and has two degrees of freedom to tailor the surface impedance of texture under two frequencies respectively. The total metallic structure on the top of the impedance unit cell is composed of two parts which are the square ring outside and the patch without cross inside. Due to the analytical method of equivalent circuit for periodic structure, the opposite adjacent edges of outside square rings between two neighboring units can be considered as the capacitor C1 and the complementary cross inside the patch can be regarded as the capacitor C2, it is because the arm of cross structure can be mainly equivalent to the inductor which means that its approximate complementary structure will be mainly regards as the capacitor.
Fig. 2. (a) Schematic diagram of the overall impedance unit cell which is composed of the top sheet layer and the grounded dielectric substrate. The equivalent circuit model is also given to approximatively and intuitively analyze the dispersive performance mainly controlled by ‘dout’ and ‘long’ under low and high frequencies respectively. The period of the unit cell is 6 mm. The F4B material with dielectric constant of 3 is selected as the substrate. The copper is applied to be the metal for top sheet layer. The size of ‘din’, ‘gap’, ‘width’ and ‘height’ are 3.6 mm, 0.1 mm, 1.2 mm and 1.5 mm respectively. (b) The corresponding results of partial dispersive curves. By changing the sizes of ‘dout’ from 4.8 mm to 5.2 mm with step of 0.05 mm and fixing the ‘long’ at 3.05 mm, the dispersive performance of the first TM mode can be tailored under 8.6 GHz. And by changing the sizes of ‘long’ from 2.7 mm to 3.4 mm with step of 0.1 mm and fixing the “dout” at 5 mm, the dispersive performance of the second TM mode can be tailored under 14.8 GHz.
Fig. 3. The simulation results for considering the mutual interference in the design of dispersive curves under two frequencies. (a) When the design is under 8.6 GHz with changing the sizes of ‘dout’ which are 4.8 mm (minimum), 5 mm (middle) and 5.2 mm (maximum), the sizes of ‘long’ are also be changed with 2.7 mm (minimum) and 3.4 mm (maximum) (b) When the design is under 14.8 GHz with changing the sizes of ‘long’ which are 2.7 mm (minimum), 3.05 mm (middle) and 3.4 mm (maximum), the sizes of ‘dout’ are also be changed with 4.8 mm (minimum) and 5.2 mm (maximum).
The two capacitors are key points to control the dispersion performance of the surface wave under two different frequencies which have large ratio. The size of ‘din’, ‘width’ and ‘gap’ which can determine the level of mutual interference for the two equivalent capacitors at two frequencies should be carefully considered. According to the theory of transmission line, the grounded dielectric can be regarded as inductor L which is nearly fixed. Thus, the equivalent model of shunt circuit of C1 with L, and the equivalent model of shunt circuit of C2 with L should be established according to the configuration of our proposed impedance unit under two frequencies, and correspondingly, the dispersive features of unit can be manipulated with tailoring the two capacitors by changing the sizes of ‘dout’ and ‘long’ of unit for low-frequency and high-frequency respectively. Accordingly, the the dispersive curves shown in Fig. 2(b) can be achieved under the full-wave eigen-mode simulation in the commercial software CST. For the simulation results of dispersive curves, this impedance unit can support the first and second TM modes with a small band gap, and the dispersive features of unit can be controlled during in the two modes. And the performance of the dispersion is directly relevant to the values of the surface impedance of the unit cells. Due to the general requirement [21] of X and M in Eq. (1) and (2), 8.6 GHz (${\lambda _{1}} \approx {34.88} \textrm{mm}$) and 14.8 GHz (${\lambda _{2}} \approx {20.27} \textrm{mm}$) are selected to be as the working frequencies of proposed dual-wavelength holographic impedance metasurface.
The mutual interference is the important issue in the design of two TM eigen-modes, and hence should be considered carefully. To operate the dispersion at 8.6 GHz by changing the size of ‘dout’, it should not be disturbed a lot by changing the size of ‘long’. Similarly, to operate the dispersion at 14.8 GHz by changing the size of ‘long’, it should not be influenced a lot by changing the size of ‘dout’. The relevant simulation results by considering the mutual interference in designing the dispersive curves under two frequencies are shown in Fig. 3. The good performance without disturbing dispersion has been observed. That is to say, the dispersive features of the impedance unit at two working frequencies in their corresponding TM eigen-modes can be designed independently.
3. Radiated beam reconstruction in simulation
3.1 Synthesis design of the impedance hologram
The values of the surface impedance of TM mode can be extracted from the dispersive curves according to the relationship which is given as
where $\phi$ represents the phase difference of the surface wave passing through the impedance unit, p is the period of the unit cell, ${k_0}$ and ${Z_0}$ are the wave number and characteristic impedance in free space respectively. And the corresponding calculated results of the surface impedance are shown in Fig. 4. For the design under 8.6 GHz, the values of surface impedance can be varied from 155.8 j$\Omega $ to 234.3 j$\Omega $ with changing the size of ‘dout’ from 4.8 mm to 5.2 mm. Thus, the values of n, X and M in the Eq. (2) will be 1.117, 195 j$\Omega $ and 39.2 j$\Omega $ under 8.6 GHz respectively. And for the design under 14.8 GHz, the values of surface impedance can be varied from 154.4 j$\Omega $ to 223.6 j$\Omega $ with changing the size of ‘long’ from 2.7 mm to 3.4 mm. Afterwards, the values of n, X and M in the Eq. (2) will be 1.107, 189 j$\Omega $ and 34.6 j$\Omega $ under 14.8 GHz respectively. And also, the ratio between M and X is around 0.20 and 0.18 under 8.6 GHz and 14.8 GHz, that means the good performance of the radiated beam reconstruction can be guaranteed due to the theory of holographic impedance antenna [21]. To synthetically generate the whole impedance metasurface under the required EM functions according to Eq. (2), the sizes determination of impedance unit located at each superposition on metasurfaces could be tailored followed by exponential and Gaussian fitting methods which are given asFig. 4. The extraction of the surface impedance based on the results of dispersive curves shown in Fig. (2). (a) With changing the sizes of ‘dout’, the values of surface impedance can vary from 155.8 j$\Omega $ to 234.3 j$\Omega $ under 8.6 GHz. (b) With changing the sizes of ‘long’, the values of surface impedance can vary from 154.4 j$\Omega $ to 223.6 j$\Omega $ under 14.8 GHz.
3.2 Full wave electromagnetic simulation results
According to the design requirement of LHCP under low frequency and RHCP under high frequency, the whole impedance metasurface is synthetically generated by combining the Eqs. (2), (4) and (5). Based on considering the radiation of the circular polarization, the contour of metasurface is designed under the circular shape which diameter is 249 mm. The coaxial connector which is located at the center of the metasurface is chosen as the feed, and the wave port is applied to be the source in the time domain solver of CST. The cylindrical surface wave will be excited by the feed and it will be modulated to be the fast wave which is the radiated beam by the impedance metasurface. Correspondingly, the simulation results of the three dimensional radiation patterns under the two frequencies are shown in Fig. 5.
Fig. 5. Simulation results of the three dimensional radiation patterns under the two working frequencies. (a) The radiation pattern of LHCP under 8.7 GHz and the maximum directivity is 18.7 dB. The corresponding aperture efficiency is 14.4%. (b) The radiation pattern of RHCP under 14.9 GHz and the maximum directivity is 19.7 dB. The corresponding aperture efficiency is 6.18%.
The best performances of the radiation patterns are observed under the 8.7 GHz and 14.9 GHz respectively which both have the frequency deviation of 0.1 GHz. And the direction of the main lobe has a little deviation of two degrees and one degree to our initial design under low frequency and high frequency respectively. They are mainly caused by several reasons that 1) the whole impedance metasurface is composed of the gradient quasi-period unit cells, however, the basic dispersive curves of unit cells are obtained by the eigen mode simulation under the period boundary conditions. 2) the mutual interference of the dispersive features which is shown in Fig. 3 can more or less influence the radiated performance under the two frequencies. 3) the imperfect fitting calculations of Eqs. (4) and (5) may introduce a little error in the synthesized work. The better performance of the radiated beam could be expected to be achieved under the global optimization and iteration of the massive variables of the impedance unit, however, this method will be very time consuming especially under the design of dual-wavelengths.
Due to the radiated deviation of the main lobe, the simulation results of two dimensional radiation patterns in the plane including the maximum directivities have been found and shown in Fig. (6). The side lobes of the radiation patterns are all below −10 dB and also the cross polarization at the main radiated directions are all below −15 dB under both working frequencies. Thus, the approximately anticipant result is achieved under our theoretical design and full wave simulation confirmation.
Fig. 6. The two dimensional radiation patterns in the elevation planes which include the maximum directivity under two frequencies. (a) The simulation results under 8.7 GHz, the directivity is also 18.7 dB. (b) The simulation results under 14.8 GHz, the directivity is also 19.7 dB.
4. Experimental validation
To further verify the validity of design method, the sample of the dual-wavelength holographic impedance metasurface is fabricated using Printed Circuit Board (PCB) technology and the two-dimensional far field radiation patterns are measured in microwave anechoic chamber. The commercial F4B with dielectric constant of 3 is selected as the dielectric substrate, and the copper which is chosen as the metal is at the both sides of the substrate. And the gold-plating technic is applied to avoid the oxidation reaction. Furthermore, the air hole with diameter of 0.3 millimeter is drilled at the center of the fabricated metasurface to achieve the proper inserting of SMA connector which is applied to be as our excited source.
In our measurement, the sample is placed on the circular platform, as shown in Fig. 7, in which the rotating step is one degree in the azimuth direction and the radiated electromagnetic power from the metasurface is caught by the receiving horn located at the other end of the chamber. The receiving horn has two ports which are RHCP and LHCP respectively, and the bandwidth of the horn is very large to cover the measured requirement of dual-frequnecy. Due to the theory of electromagnetic polarized receiving, the radiated power with LHCP should be received by the RHCP port of the horn and the power with RHCP should be received by the LHCP port of the horn, and the corresponding measurement results of the two-dimensional radiated patterns under different frequencies are shown in Fig. 8.
Fig. 7. Schematic diagram of the far field measurement in the microwave anechoic chamber and the zoom in view of the fabricated sample. The sample can be maintained by the blue foam which is placed on the rotating platform. The receiving horn which is not shown here is located on the opposite of the sample.
Fig. 8. (a) The comparison between the measurement and simulation results of LHCP radiated beam under the 8.7 GHz. (b) The comparison between the measurement and simulation results of RHCP radiated beam under the 14.9 GHz.
From Fig. 8, we observe that the measurement and simulation results of normalized directivities at the main radiation direction have good agreements, which verify the validity of our theoretical design. All side-lobes of the measured radiation patterns are below −10 dB compared to the main lobe. The cross-polar discrimination at the main radiated direction is below −15 dB under both frequencies, showing good performance of the circular polarization. The difference of the side-lobes between measurement and simulation results of the radiated patterns is mostly due to the fabrication error and the noise form the environment of chamber.
5. Conclusions
The new method to generate surface impedance hologram under two different wavelengths which have much larger ratio has been proposed. And the broadside radiated beams with different states of circular polarizations has been reconstructed corresponding to the different working frequencies. The dual-wavelength hologram is composed of the subwavelength surface impedance units which dispersive characteristics are independently tailored in two eigen-modes correspondingly. According to the theory of holography and synthesized design of metasurfaces, the achieving of distinct arbitrary shape of radiated beams under dual wavelengths is expected. Comparing with the reflector-array and transmitarray, the holographic impedance metasurfaces have the feature of real low-profile due to the in-plane feeding. The proposed metasurface can have the great prospect of applications in satellite remote sensing and communications, multi-functional radar detecting and multi-scale image system.
Funding
National Natural Science Foundation of China (61571117, 61631007, 61801262, 61901113); National Key Research and Development Program of China (2017YFA0700201, 2017YFA0700202, 2017YFA0700203); Fundamental Research Funds for the Central Universities (2242019K3DN06, 2242020R20010).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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