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Abstract
Metasurfaces with complex-amplitude modulation are superior in power regulation and hologram imaging resolution compared with those with phase-only modulation. Nevertheless, a single-cell metasurface with multi-band independent phase and amplitude controls is still a great challenge for the circularly polarized incidences. In this work, we propose and design a single-substrate-layer single-cell metasurface with independent complex-amplitude modulations at two discrete frequencies. Based on this emerging technique, a bi-spectral meta-hologram is designed and verified by both full-wave simulations and experiments, which could reconstruct two Chinese characters at the imaging plane at two frequencies. The proposed method shows great potential in multifunctional meta-devices with enhanced performance.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The arbitrary manipulation of the electromagnetic (EM) waves has been of great importance for science and engineering societies. Prisms and lenses are the traditional methods to shape the lights through accumulated phase change on the optical path within natural materials. In the past several decades, metamaterials have attracted great attention as a new-generation method to tailor the EM near- or far-fields based on the extraordinary effective medium parameters (e.g., electric permittivity, magnetic permeability, and refractive index) [1,2], which could lead to unusual functions, such as perfect imaging [3,4], negative refraction [5,6] and invisible cloaking [7,8]. As a two-dimensional (2D) version of metamaterials, metasurfaces could arbitrarily tailor the wavefronts by introducing abrupt discontinuities (e.g., amplitude, phase, and/or polarization) within a deep subwavelength thickness [9–12]. Thus, metasurfaces are of great interest for many applications, including holograms [13,14], analog computing [15,16], and metalens [11,12,17].
In addition to the traditional metasurface with phase modulation, the metasurface incorporating amplitude modulation enables better performance in modifying power distribution and improving hologram quality [11,18–20]. Recently, multi-band single-cell metasurfaces and polarization multiplexing metasurfaces have been reported in order to increase the number of operation channels [21–27], among which the multi-band metasurface with complex-amplitude modulation could be obtained according to the Malus's law for linearly polarized (LP) waves [24,28]. However, a single-cell metasurface with multi-band independent phase and amplitude modulations is still challenging for circularly polarizated (CP) waves, which is resulted from the strong coupling between resonators. Moreover, efficiency is an important criterion for metasurfaces, which is settled by adopting the dielectric metasurface, the reflective type metasurface and the multi-substrate-layer transmissive metasurface [29–35]. Although a tri-band reflection geometric metasurface is reported with 2-level amplitude controls [36], a higher level amplitude modulation would be required for better power regulations. Furthermore, a high-efficiency transmissive metasurface with single-layer substrate would be preferable and more practical in practical applications, which could avoid feeding blockage compared to the reflective metasurfaces.
In this work, we demonstrate a methodology to achieve a transmissive geometric metasurface with independent complex-amplitude modulations at two frequencies for the CP waves. The proposed meta-atom consists of two identical metallic layers printed on both sides of a subwavelength-thick dielectric. The metallic layers are perforated with a modified complementary split-ring resonator (MCSRR) and a circular hole, where an electric field coupled resonator (ELCR) is placed in the center. The judiciously designed structure guarantees almost non-coupling between the two resonators, which permits independent complex-amplitude modulations at two operating frequencies. Besides, a dual-channel meta-hologram was designed, fabricated, and characterized to explore the power regulation capability of the proposed metasurface, where the experimental results agree very well with the simulated ones.
2. Principle and structure design
2.1 Pancharatnam-Berry phase modulation
Under the Pancharatnam-Berry phase (PB phase) principle, the CP light could be tailored by an anisotropic structure through changing the in-plane orientation of the meta-atom. While a right-/left-polarized (RCP/LCP) wave $({E_i^R/E_i^L} )$ is illuminated onto a meta-atom rotated by an angle of θ, the LCP/RCP component of the transmissive scattering waves $({E_t^R/E_t^L} )$ could be described as [37,38]
Figure 1(a) demonstrates the schematic diagram of the proposed dual-band complex-amplitude meta-hologram. While an LCP spherical wave is impinging on the metasurface, the cross-polarized component of the transmitted field is detected and two holographic images of ‘仁’ (mercy in Chinese) and ‘和’ (peace in Chinese) can be reconstructed at f1 and f2, respectively. Figures 1(b) and 1(c) show the three-dimensional (3D) and top views of the proposed high-efficiency dual-band meta-atom. It can be seen from Figs. 1(b) and 1(c) that both the top and bottom metallic layers of the meta-atom are etched with an MCSRR and a circular hole, in the center of which an ELCR is placed. The outer radius, inner radius, width and incision gap width of the MCSRR are denoted as (r1o, r1i, w1, g1), the radius of the circular hole is denoted as rc, and the structural parameters of the ELCR are denoted as (r2, w2, l1, l2). Furthermore, the orientation angles of the MCSRR and ELCR are represented as θ1 and θ2 with respect to the x-axis, respectively. The thicknesses of the metal and substrate are denoted as tm and ts, respectively. In the designed example, the substrate and metal are chosen to be the commercially available F4B (dielectric constant εr = 2.2, loss tangent tanδ = 0.001, ts = 1.5 mm) and copper (conductivity = 5.96 × 107 S/m, tm = 0.035 mm), respectively. Besides, the operating frequencies of the dual-band meta-atom are selected to be f1 = 10 and f2 = 15 GHz. The geometric parameters of the high-efficiency dual-band meta-atom are optimized by employing the CST microwave studio, where periodic boundary conditions are applied in both x- and y-directions to emulate an infinite array. The structural parameters of the MCSRR and ELCR are optimized to be (r1o, r1i, w1, g1) = (4.2, 3.8, 0.2, 0.2) and (r2, w2, l1, l2) = (2.6, 0.2, 2.2, 2.05) (unit: mm), respectively. Furthermore, the periodicity p and the radius of the hole rc have been set as 8.6 mm and 3 mm, respectively.
Fig. 1. (a) Schematic demonstration of the proposed frequency-multiplexed meta-hologram consisting of the dual-band complex-amplitude meta-atom. (b), (c) The three-dimensional and top views of the proposed dual-band meta-atom.
Figures 2(a) and 2(b) plot the instantaneously surface current distributions on the metallic layer of the proposed high-efficiency dual-band meta-atom at 10 and 15 GHz while illuminated by an LCP wave, respectively. It is observed that the surface current flows along the MCSRR (ELCR) at 10 GHz (15 GHz) and is cut off at the circular hole, which implies that there is barely any couplings between the two resonators. Such a de-coupling feature guarantees the independence of the two resonators, which means that the EM characteristics of one resonator would not be affected by the alteration of the other one. Figures 2(c) and 2(e) (Figs. 2(d) and 2(f)) demonstrate the transmitted RCP phase and amplitude profiles at 10 GHz (15 GHz) under a normal LCP incidence while rotating the MCSRR and ELCR, respectively. It could be seen that the phase at 10 GHz (15 GHz) is twice correlated with the θ1 (θ2) while independent with θ2 (θ1). In the meanwhile, the amplitude holds almost constant of >0.8 (>0.7) at 10 GHz (15 GHz) when the orientation angles of the two resonators (i.e., θ1 and θ2) are changed from 0 to π, indicating a good isolation between the resonators.
Fig. 2. (a), (b) The current distributions of the high-efficiency dual-band meta-atom at 10 and 15 GHz. (c), (d) The geometric phase profiles of the dual-band meta-atom at 10 GHz and 15 GHz with respect to θ1 and θ2. (e), (f) The amplitude profiles at 10 and 15 GHz.
2.2 Amplitude modulation
In addition, for a better performance of power regulation, the 3-level amplitude modulation is also introduced for the dual-band meta-atom. The amplitude responses of the MCSRR and the modified double-C-slot resonator (MDCSR) are investigated firstly with varied r1o, as shown in Fig. 3(a), where the transmission amplitudes of the RCP wave at 10 GHz are changed from a minimum to 0.85 (0.5) for MCSRR (MDCSR) under a normal LCP incidence. Moreover, Fig. 3(b) plots the amplitudes at 15 GHz by altering the ELCR with different r2 and l2. The gray and green stars respectively mark the the max and half amplitudes in both Figs. 3(a) and 3(b), respectively, indicating that the half amplitudes A0.5 could be obtained at 10 and 15 GHz with the structural parameters of r1o = 3.85 mm in MDCSR and (r2, l2) = (2.2 mm, 0.6 mm) in ELCR as shown in Figs. 3(d) and 3(g), respectively. Furtherover, zero amplitudes can be achieved by removing the resonator or replacing the resonator with a non-resonant structure, which are utilized as demonstrated in Figs. 3(e) and 3(h) for 10 and 15 GHz, respectively.
Fig. 3. (a) The cross-polarized transmission amplitude at 10 GHz while resizing the MCSRR and MDCSR with varied r1o. (b) The cross-polarized transmission amplitude at 15 GHz while varying r2 and l2. (c)-(e) The top views of the single-band meta-atoms with MCSRR, MDCSR and no resonator, which have the normalized amplitudes of 1, 0.5 and 0 at 10 GHz, respectively. (f)-(h) The top views of the single-band meta-atoms with different parameters of the ELCR and the non-resonant ring, which have the normalized amplitudes of 1, 0.5 and 0 at 15 GHz, respectively. (i)-(q) The top views of the dual-band meta-atoms with different amplitude combinations at 10 and 15 GHz.
Figures 3(c)–3(q) plot all combinations of the proposed dual-band meta-atoms with 3-level amplitude modulation, where the first column (Figs. 3(c)–3(e)) and the first row (Figs. 3(f)–3(h)) represent the single-band meta-atom with the normalized amplitudes of 1, 0.5 and 0 at 10 and 15 GHz, respectively. It could be observed from Figs. 3(c)–3(e) that the 3-level amplitude modulation of the single-band meta-atom at 10 GHz can be obtained by employing the MCSRRs, MDCSRs and removing the proper resonators. Besides, the amplitude of the single-band meta-atom operating at 15 GHz could be adjusted through resizing the ELCR, and the zero amplitude can be achieved by replacing the ELCR with a non-resonant ring, as demonstrated in Figs. 3(f)–3(h). Moreover, as shown in Figs. 3(i)–3(q), the 3-level amplitude controls of the dual-band meta-atom represented as Am-n are realized by simply combining the single-band meta-atoms in the first column and the first row, where m and n denote the normalized amplitude levels at 10 and 15 GHz, respectively. Furthermore, the compensation phases (φ1, φ2) of the complex-amplitude meta-atoms Am-n are given at the bottom of Figs. 3(i)–3(q), which are resulted from the modifications of the resonators. More interesting, it could be seen from Figs. 3(i)–3(n) that when the amplitude at 10 GHz is held unchanged (i.e., A1-n and A0.5-n) and the ELCR is resized or replaced, the compensation phases remain constant with 0° and 228° at 10 GHz in each row. Additionally, the phases in Figs. 3(o)–3(q) (A0-n) could be neglected since the amplitude is zero at 10 GHz. Similar conclusions could be drawn from Figs. 3(i)–3(q) for 15 GHz, where the phases of Am-1 and Am-0.5 are fixed while the phases of Am-0 require no attention due to the zero amplitude, proving the good isolation between the resonators once again. Therefore, when a meta-atom with amplitude level of Am-n is required, a compensation phase would be added ahead for both 10 and 15 GHz, and the corresponding resonator would be rotated by a certain angle, which is the half of the compensation phase.
3. Results and discussion
Based on the proposed dual-band meta-atom, a dual-channel meta-hologram was designed and verified by both full-wave simulations and experiments. Theoretically, the meta-hologram generated by computer-generated holography (CGH) could be expressed by the diffraction equation as follows:
Fig. 4. Detailed process to retrieve the complex-amplitude patterns of a meta-hologram based on the iterative Gerchberg-Saxton (GS) algorithm.
In this example, the dual-channel meta-hologram is composed of 31 × 31 meta-atoms. As shown in Figs. 5(a) and 5(b), the Chinese characters ‘仁’ (‘mercy’ in English) and ‘和’ (‘peace’ in English) were selected as the target images for the meta-hologram at 10 and 15 GHz, respectively. Additionally, considering a spherical wave would be irradiated from a horn antenna to the meta-hologram with a distance of 300 mm in the experiment, a spherical compensation phase was included to transform the spherical wave to the plane wave [28]. The required digitized amplitude and the total phase profiles at 10 and 15 GHz are demonstrated in Figs. 5(c)–5(f).
Fig. 5. (a), (b) Target images of ‘仁’ (‘mercy’ in English) and ‘和’ (‘peace’ in English) for 10 and 15 GHz. (c), (d) The digitized amplitude profiles for the dual-band meta-holograms at 10 and 15 GHz. (e), (f) The phase profiles for the meta-hologram at 10 and (f) 15 GHz.
To verify the dual-channel meta-hologram, a prototype of the meta-device is fabricated through the standard printed circuit board (PCB) technology as shown in Fig. 6(a). To measure the intensities in the imaging plane, the measurement setup as shown in Fig. 6(b) was employed. A pair of LCP and RCP horn antennas were adopted as the transmitter and receiver, respectively, and a vector network analyzer (VNA) was employed as a field recorder. Moreover, the fabricated sample of the dual-band meta-hologram is measured, where the receiving antenna moves along the x- and y-directions with a step of 5 mm to map the 2D electric field intensity. Figures 6(c) and 6(d) plot the measured RCP intensities in the imaging plane, where the holographic images of ‘仁’ and ‘和’ could be observed at 10 and 15 GHz, respectively. Furthermore, the designed meta-hologram was also verified by full-wave simulation. Figures 6(e), 6(f) and Figs. 6(g), 6(h) plot the simulation intensities in the XY plane with z = 200 mm at both 10 and 15 GHz through the complex-amplitude hologram (CAH) and the phase-only hologram (POH), where the POH adopts the meta-atom with A1-1 and the identical phase distribution as CAH. Compared with the simulated results of POH, the holographic images of CAH have smoother contour lines and more homogeneous power distributions, which validates the better performance of the designed CAH and agrees very well with the measured ones.
Fig. 6. (a) The top view of the fabricated sample of the dual-channel meta-hologram. (b) The measurement setup of electromagnetic (EM) field scanning system. (c), (d) The measured right-circularly polarized (RCP) intensities of the complex-amplitude hologram (CAH) on the image plane (z = 200 mm) under a left-circularly polarized (LCP) incidence at 10 and 15 GHz. (e), (f) The simulated intensities of the CAH on the imaging plane with z = 200 mm at 10 and 15 GHz. (g), (h) The full-wave simulated RCP intensities of POH on the XY plane with z = 200 mm under an LCP incidence at 10 and 15 GHz.
Furthermore, the correlation coefficient (ρ) between the target image (T) and the reconstructed image (R) is adopted to evaluate the reconstruction image quality, which is expressed as [41]:
4. Conclusion
In summary, we have demonstrated a transmissive single-cell metasurface with complete 2π phase and 3-level amplitude controls for the CP waves. By taking advantage of the de-coupling feature between resonators, the independent complex-amplitude controls could be realized by adjusting the two resonators separately, including changing, altering, and replacing the resonators, which could enhance the power regulation capability and simplify the design process for multi-band geometric metasurfaces with complex-amplitude modulations. As a proof-of-concept demonstration, a dual-channel meta-hologram was numerically demonstrated and experimently verified, which could reconstruct the images of Chinese characters ‘仁’ (‘mercy’ in English) and ‘和’ (‘peace’ in English) at 10 and 15 GHz, respectively. The experimental results agree well with the full-wave simulation ones. The multidimensional manipulations of EM waves offered by the proposed metasurface could pave the way towards realizing multifunctional meta-devices for advanced communication and biological systems.
Funding
National Natural Science Foundation of China (61775060, 62171186).
Disclosures
The authors declare that there are 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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