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Abstract
In the paper, a quasi-symmetrical structure reconfigurable metasurfaces (QSRMS) is proposed to generate the full-polarization electromagnetic (EM) holographic imaging. A combination of metasurfaces and varactor that involves the position and the gap of loading varactor is explored to achieve low-loss characteristics. The loading of the capacitor allows the element of reconfigurable metasurfaces (RMS) to present quasi-central symmetry, thus reducing the coupling between co- and cross-polarization. Therefore, the phase shift of 310° and the amplitude loss of 1.3 dB in the two orthogonal directions are acquired at 5.2 GHz. And the 3dB-loss bandwidth reaches 15.67%. Based on the dual-polarization QSRMS, the amplitude and phase modulation (APM) of the EM field are implemented simultaneously using L-BFGS-B algorithm. The implementation process of holographic imaging shows that all polarization state of the Poincaré sphere can be realized by designing the phase distribution of the QSRMS. Furthermore, the multi-polarization multiplexing holographic imaging is also investigated in this research, indicating that the polarization carrying capacity (PCC) can be enhanced by increasing the aperture of the metasurfaces. The results of simulation and experiment reveal that there will be a broad application prospect in next-generation large-scale, multi-channel EM intellisense systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Perfect realization of electromagnetic (EM) waves modulation is one of the essential directions of next-generation intellisense system, the emergence of metasurfaces has dramatically expanded the method of EM modulation. Metasurfaces, as two-dimensional forms of artificial EM metamaterials, have simple structure, reliable performance, and unique EM properties that ordinary materials do not have, such as, negative dielectric constant [1], magnetic permeability [2], and double negative property [3], etc.
Over the past two decades’ exploration and development of metasurfaces, the same laws of EM waves modulation have been gradually obtained, including amplitude [4–6], phase [7–10], and polarization [11–16] modulation. Based on the flexible capability of metasurfaces, the diffractive device has been replaced by metasurfaces in holographic imaging system. By designing the singular structure of metasurfaces, the EM wavefront can be controlled to change the distribution of near-field electromagnetic energy and realize large-scale microwave holographic imaging [17,18]. By virtue of Pancharatnam-Berry (PB) phase and different orientation angle increments, a full-polarization metasurfaces [19] is designed to implement multi-directional meta-hologram. Although multi-directional polarization multiplexing technology as a basis for the holographic display of complex object has greatly improved the imaging channel, the coupling of direction and polarization cannot guarantee the diversity of polarization in the same direction. To address such issue, the APM metasurfaces is designed to generate full-polarization patterns in the same direction by simultaneously customizing the two orthogonal components of EM waves [20]. Based on a leaky-type 2-bit resonance phase, a low-profile holographic coding Fabry–Perot metasurfaces is proposed [21] to demonstrate that the quality improvement of holographic image depends on the degree of phase quantization accuracy.
By combining the electric tunable devices (materials) with the fixed metasurfaces, the RMS has been designed in recent years and has been used to realize multiple EM properties. The rapid development of amplitude [22,23], phase [24–27], and polarization RMS [28,29] have further enhanced the comprehensive control ability of EM waves. With the application of RMS in the diffraction surface, holography [30] has developed from static picture holography to dynamic film holography. A reprogrammable hologram is proposed based on coding metasurfaces [31]. The element incorporating a PIN diode can be switched between ‘1’ and ‘0’ by the external voltage. A 1-bit polarization-controlled metasurfaces [32] can be achieved by integrating four varactors in an element of fixed metasurfaces, which can be programmed with two independent coding sequences simultaneously. Hence, the metasurfaces have a powerful capacity of controlling the co- and cross-polarized waves, respectively. However, high amplitude loss and complex DC structure are problems to be urgently solved.
Based on the holographic principle applicable to solve reverse engineering problems, any desired EM field distribution can be excited by the RMS. Therefore, the core of realizing multi-channel and dynamic holographic imaging lies in the design of the RMS. The difficulty of designing the RMS is how to obtain the required high performance such as, low loss, wide bandwidth, and multi-polarization by intelligently integrating the tunable device with the metasurfaces.
To address the problems, a dual-RMS with low loss, low profile, and a wide phase shift is deigned in this paper. The reconfigurable mechanism of RMS based on varactors is studied. And the methods to achieve low loss and wide phase shift are proposed in the paper. The quasi-symmetric resonant structure is designed to reduce the polarization coupling in the x- and y-directions of the metasurfaces, and reconfigurable phases in the orthogonal directions of RMS are acquired. Based on the L-BFGS-B algorithm, the holographic imaging in any polarization state can be generated using the designed dual-RMS.
2. Principle of the Full-Polarization Electromagnetic Holographic Imaging
2.1 Full-polarization representation
The full-polarization EM holographic imaging is illustrated in Fig. 1. By exciting the QSRMS with a specific phase distribution, the different polarized EM fields can appear in the imaging area, where all of the polarization states of EM waves propagating in the OZ direction can be expressed with the Poincaré sphere from Fig. 1(a). The polarization path Equation with the orthogonal linear polarized components Ex = excos(ωt-kz+δx) and Ey = eycos(ωt-kz+δy) can be expressed as:
Fig. 1. Full-polarization EM holographic imaging based on QSRMS. (a) The polarization states ofthe Poincaré sphere. (b) The element of QSRMS.
At the point M (S1, 0, 0) in Fig. 1(a), the angular quantity (φ=0, χ=0) represents the linear polarization state with the vibration direction paralleling to the OX-axis and ey = 0. Similarly, the symmetry point M′ (-S1, 0, 0) of M represents the linear polarization state paralleling to the OY direction. At the point Q (0, S2, 0), the angular quantity (φ=45°, χ=0) represents the linear polarization state with an angle of 45° to the OX-axis, and there is ex = ey. On the north pole N (0, 0, S3), δ= (2n+1/2)π and tanα=1, that is, the vibration of Ex is π/2 ahead of Ey, so the north pole represents right-handed circularly polarized (RHCP) EM waves. In the same way, the south pole S represents left-handed circularly polarized (LHCP) EM waves. The elliptical polarization state of EM waves is characterized by stokes parameters (S1, S2, S3) on the Poincaré sphere except the equator and the poles. Each point on the spherical shell corresponds to the polarization state of the EM waves one-to-one. So, all the polarization states on the Poincaré sphere can be realized by designing the δ and tanα of the two orthogonal components, which can be modulated by the QSRMS.
2.2 Design of QSRMS element
As shown in Fig. 1(b) and Fig. 2, the metasurfaces element consists of an upper metal resonance structure, a dielectric layer, and a metal ground. The two grooves are etched in the metal patch to load the orthogonal isolation varactors for the adjustment of the reflection phase and amplitude of EM waves in orthogonal polarized states. The varactors are connected to the DC bias circuit through the via-hole, respectively, and the DC bias provides all the power for the varactor in Fig. 2(b). Two capacitors at the symmetrical position of the varactors are loaded so that the element exhibits a quasi-symmetric structure. The Taconic-LTL is used as dielectric substrate with the dielectric constant of 2.55, and loss tangent of 0.0006. The thickness h = 1.524 mm, b = 13 mm, and a = 10 mm.
Fig. 2. The element structure of metasurfaces. (a) The equivalent circuit parameters of capacitor and varactor. (b) Three views of the element and bias control circuit.
The capacitance change of the varactor has a significant impact on the distribution of induced current in Visualization 1. According to the Huygens radiation principle, the evolution of induced current distribution, as secondary radiation, indicating that the resonance characteristics of the radiation structure have changed. The amplitude and phase of the element will shift accordingly, as shown in Fig. 3. The phase shift of the metasurfaces is caused by the change of resonance frequency point. However, at the resonance point, the impedances of the varactor and the space wave are matched, exhibiting high impedance characteristics. So, partial EM wave energy has been absorbed by metasurfaces, and the amplitude loss has increased sharply. The selected operating frequency point would deviate from the resonance point to ensure that EM wave energy is reflected to the utmost. However, this will result in a phase shift of less than 360°. Hence, the design difficulty lies in the design of the element structure for a wider coverage of phase modulation range at lower losses. Equation (2) is defined to describe our design goals:
Fig. 3. The (a) phase and (b) amplitude of metasurfaces vary with capacitance of the varactor (in the case of loading position (x = 3.5, y = 0), w = 0.2 mm and the p = 0.3pF).
Fig. 4. (a) f and (b) g vary with the position (x, y) (in the case of w = 0.2 mm and p = 0.3pF), (c) f and (d) g vary with the gap width w (in the case of (x = 3.5, y = 0), and p = 0.3pF).
The dual-polarization element is obtained by adding an x-polarized structure of the rotation of 90° and the original structure. The two varactors in the orthogonal direction can be controlled independently. However, there is a challenge to reduce the coupling between the x- and y-polarization directions. That is, the capacitance change of the varactor in x-direction does not affect the y-polarization characteristics of the element, and vice versa. Figure 5(a) shows the distribution of the induced electric field of the RMS without capacitor. It is obvious that the zero point of induced electric field deviates from x = 0, which will result in a stronger induced electric field at x = 0, affecting the induced current excited by y-polarized EM wave. The same goes for its orthogonal direction due to the non-rotational symmetry structure. And a strong coupling will appear eventually. So, the realization of low cross-polarization loss requires a centrosymmetric structure, meanwhile, a wide range of phase modulation is necessary to take into account. DC-OFF and AC-ON, the natural properties of capacitor, make each varactor work independently. The loading of the capacitor makes the resonance structure present quasi-central symmetry, which can reduce the deviation of the zero point of induced electric field in Fig. 5(b). From Visualization 1, the low-capacitance varactor is similar to the open-circuit transition, therefore, a low-capacitance capacitor is selected to be comparable to the varactor. The loading of capacitors lengthens the path of induced current, the operating frequency of the metasurfaces is reduced to 5.2 GHz.
The resonance structure exhibits quasi-central symmetry due to the loading of the capacitor, which can weaken the coupling between the x- and y-polarization directions. When the resonance occurs at the position (x = 3.5, y = 0) of the varactor, the gap w= 0.2 mm and the capacitance p = 0.3pF, it is shown in Fig. 3 that the amplitude and phase vary with capacitance of varactor, and the final result of maximum phase shift and minimum loss are shown in Fig. 6. It is evident that the phase modulation of 310° can be realized, while the amplitude loss is 1.3 dB at 5.2 GHz at the same time. And the 3dB-loss bandwidth reaches 15.67%.
3. Full-polarization electromagnetic holographic imaging
Benefiting from the biorthogonal polarization modulation of the QSRMS, the APM of the EM field is realized using L-BFGS-B algorithm. The APM of metasurfaces, involving the solution of space vector field un(r), is more complicated than the amplitude- or phase-modulation alone. Green's function of Rayleigh-Sommerfeld represents the fact that the complex amplitude at any point in the spatial field is expressed by the complex amplitudes of other points. The un(r) can be expressed as:
Equation (3) can be expressed in the following matrix form:
In Eq. (4), U represents the complex electric field of imaging surface with N pixels, N*M matrix is expressed as Z, representing the transition matrix, and the phase distribution of metasurfaces with M elements is expressed as Ф. As shown in Fig. 6, the phase distribution Ф can be adjusted from 0 to 310° by an external DC voltage source, and the amplitude distribution Am is a constant matrix [0.88]M×1. Therefore, the change in the complex matrix U of the spatial field is only determined by the variation of the imaginary matrix Ф of the QSRMS. The solution model of Ф is built:
Fig. 7. (a) The process of holographic imaging, (b) the complex amplitude distribution of U0, (c) the phase distribution Фx and Фy of the QSRMS, (d) the holographic imaging.
According to Fig. 7(c), the QSRMS in the two orthogonal directions are encoded respectively. After the QSRMS are excited by the linear polarized EM waves with an angle of 45° with the OX-axis, that is, to set the same amplitude and phase excitation in the x- and y-directions of metasurfaces, the holographic image results of the ring shape are distributed in Fig. 7(d). Similar to U0, the amplitudes of imaging surface in the x- and y-directions are proportionable, and the phase distribution between the x- and y-direction of five rings differs from 0°, 0°, 0°, 90°, -90° approximately. It can be seen from Fig. 7(a) that the energy distributions of the combined field approach 1:1.4:1:1:1 at five rings region. The polarization states of five rings are broadly consistent with the points M, Q, -M, N, and S by further investigating. It can be concluded that full-polarization holographic imaging is obtained by combining the electric fields of the imaging surface in both x- and y-directions.
By adjusting the phase distribution of QSRMS according to the amplitude and phase of the preset U0, the holographic imaging of any polarization represented by Poincaré sphere can be realized. So, it is not limited to five polarization modes. In addition, the influence of the QSRMS on the coexistence of multi-polarization mode (MPM) is explored in Fig. 8. The signal-to-noise ratios (SNRs) and root-mean-square error (RMSE) [33] characterizing the image quality are given in Fig. 9. The comprehensive imaging efficiency (CIE) is defined as the product of reflection efficiency and imaging efficiency [10,31], which is shown in Table 1.
Fig. 8. The results of (a)one, (b) two, (c) three, (d) four, (e) five and (f) six polarization modes
Table 1. Comprehensive imaging efficiency
The results reveal that the multi-polarization holographic image can be easily achieved by changing the phase distribution of QSRMS. However, the increasingly complex and diversified polarization characteristics will cause a decrease in the imaging quality of the coexistence of MPM, indicating that the PCC of the fixed-aperture metasurfaces is limited. The holographic imaging of metasurfaces, which meets the conditions i SNR > 10 dB and ii; RMSE > 1, is considered to be effective. Otherwise, the image distribution cannot be recognized. So, PCC is defined as Eq. (9):
Where, S is an array containing the SNRs of all polarized holograms; R is an array containing the RMSEs of all polarized holograms, PCC is the number of elements in both S and R that satisfy SNR > 10 dB and RMSE > 1 at the same time. So, the PCC of the metasurfaces with 32*32 elements is six. The SNR of MPM is low because of the insufficient effective aperture of the metasurfaces. Therefore, Fig. 10 shows the simulation results of PCC of the metasurfaces with different sizes. It can be seen that the large-aperture metasurfaces take into account high-quality and high-PCC holographic imaging. The larger the aperture of the metasurfaces, the more significant contribution to the EM energy of the holographic imaging. Therefore, images with complex target features require more EM energy and more metasurfaces elements.4. Experiment and discussion
The experimental measurement environment is shown in Fig. 11. The diffraction surface consisting of an RMS with 32*32 elements is fabricated by printed circuit board (PCB) technology. In order that each varactor works independently, an independent DC input connector is designed for each varactor on the back of the metasurfaces and is connected to the Field-Programmable Gate Array (FPGA) through a flat cable. The plane wave illumination method with time domain gate technique is adopted to measure the responses of metasurfaces, as shown in Fig. 12, which demonstrates the accuracy of simulation results. The calculated phase is written to the RMS by FPGA. The near-field scanning system is used to measure the distribution of the holographic field. The excitation source is a horn antenna working in the C-band, which is connected to an Agilent 8722ES vector network analyzer (VNA). At the distance of 1500 mm from the metasurfaces, the E-plane of the horn antenna exhibits an angle of 45° in the horizontal direction, constant amplitude and in-phase excitation are obtained in the x- and y-direction of the RMS. The electric field probe realized using the Sub Miniature version A (SMA) is also connected to the VNA. The planar two-dimensional scanning is performed by fixing the SMA on a rail, with a scanning accuracy of 5 mm. The 300*300 mm plane area at five wavelengths from the RMS is set as the imaging surface, the moving speed of the guide rail is set to 5 mm/1s, and the duration of one scan is 1 h. Before measuring the metasurfaces holographic imaging, the field distribution of the horn antenna at the imaging surface is pre-measured as the reference is measured, the probe is bent horizontally and only the induction of the x-polarized field is achieved; similarly, when the probe is bent vertically, the y-polarized electric field is obtained. The measurement results are drawn in the form of complex amplitude in Fig. 13, the x- and y-linear polarizations are synthesized according to Eq. (10).
The measured results are well consistent with the simulation results in Fig. 7 and Fig. 13, and the SNR and RMSE are shown in Fig. 9, despite some deviations possibly caused by imperfect manufacturing level and the measurement environment. However, it should be believed that the deviations would be negligible as the continuous improvement of the manufacturing process and the further optimization of the measurement environment.Fig. 13. The measurement results of (a) one, (b) two, (c) three, (d) four, and (e) five polarization modes
5. Conclusion
In conclusion, the paper introduces the design method of dual-polarization QSRMS, which is applicable to realize the full-polarization EM holographic imaging. Such as methods of the loading position (3.5,0) of the varactor, the gap w = 0.2 mm of loading varactor, and the 0.3pF fixed capacitance are employed to reduce the amplitude loss of RMS. Hence, a large phase shift of 310° and the amplitude loss of 1.3 dB at 5.2 GHz are realized by this method. And the 3dB-loss bandwidth reaches 15.67%. It can be concluded from the designed result that the coupling between co- and cross-polarization of RMS can be reduced by designing quasi-central symmetry. The phase distributions in both orthogonal directions of the metasurfaces are concluded using L-BFGS-B algorithm. The multi-polarization holographic imaging is realized after the metasurfaces is excited by the linear polarized EM waves at an angle of 45° in the OX-axis. Similarly, the phase distribution of metasurfaces in any polarization state represented by the Poincaré sphere can be obtained by virtue of the preset complex amplitude U0 and L-BFGS-B algorithm. And the multi-polarization multiplexing holographic imaging is also investigated by changing the phase distribution of the metasurfaces. With the realization of MPM holographic imaging, the polarization multiplexing capability is enhanced. The PCC of MPM is also investigated in this research, proving that the PCC will improve as the aperture of the metasurfaces increases. The result of this research is expected to provide technical support for next-generation multi-channel holographic imaging.
Funding
National Postdoctoral Program for Innovative Talents (2019M653960, BX20180375); Natural Science Basic Research Program of Shaanxi Province (20200108, 2020022, 2020JM-350, 20210110); National Natural Science Foundation of China (61801508, 6217012409).
Disclosures
The authors declare that there are no conflicts of interest related to this paper.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
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