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Abstract
Complex amplitude modulation metasurfaces (CAMM) that can independently control both amplitude and phase have fostered a broad research interest worldwide due to its more robust wave manipulation capability than metasurfaces that can only adjust phase. Although many CAMM structures have been reported, they still suffer from limitations such as low transmittance, complicated structure, polarization dependence, high cost, and difficulty in fabrication. This work proposes a high-transmission polarization-independent CAMM operating in an ultra-wide millimeter-wave frequency range from 30 to 50 GHz realized by cost-effective and easily implementable manners. Three CAMMs are designed to generate complicated millimeter-wave beams like holographic imaging beam, Airy beam, and vortex knot beam. The presented simulation and experimental results clearly demonstrate the effectiveness of the CAMMs. This work presents a new paradigm for CAMM that can be readily extended to other frequency bands. It may also advance further applications of millimeter-wave beams in communication, imaging and detection.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
There has been a continuous escalation in interest in manipulating electromagnetic (EM) waves at will. Many of the properties of EM waves, such as amplitude, phase, polarization, frequency and angular momentum, can be flexibly modulated and act as information carrier for diversified applications in communications [1–5], video transmission [6], imaging [7–9], holography [10–12] and detection [13–15]. As the two-dimensional embodiment of metamaterials, metasurface has exhibited unprecedented capability and flexibility in EM wavefront modulation [16–23].
Depending on the wavefront manipulation method, metasurfaces can be categorized into phase modulation metasurfaces (PMM) [24–30] and complex amplitude modulation metasurfaces (CAMM) [31–38], with the former only being capable of tuning the phase of EM waves (without altering the amplitude) while the latter can control both phase and amplitude. Although the PMM has been successfully applied in a wealth of applications, the lack of amplitude tuning ability is still a big limitation. For example, applying PMMs to realize holography requires large amount of computational burden to iteratively calculate the required phase distribution on the metasurface. Moreover, some other advanced applications are difficult or even impossible to be realized by PMMs. In contrast, CAMM can offer complex manipulation to the EM wavefront and thus enable many applications like the generation of some special-structured EM beams and greatly facilitate the design procedure of some applications such as high-quality holography. For instance, the image quality and resolution of PMM-based holograms are obviously inferior to those of the CAMM-based holograms [36]. Complex-amplitude hologram can provide high-quality images free of ghost images and undesired diffraction orders. CAMMs can also realize full-space reflective/transmissive modulation [39], which cannot be handled by PMMs.
Many works on CAMMs operating in the microwave band have been reported. Although interesting applications have been demonstrated by microwave CAMMs, they still suffer from some shortcomings. First, the previous CAMMs do not have very high transmittance. The largest obtainable transmission coefficient (S21) of the meta-atom is usually no larger than 0.9, mainly due to the losses in the applied metal and dielectric materials. Second, many CAMMs are expensive and difficult to fabricate because the meta-atom has complicated multi-layer structures. Thus, high-efficiency and easily implementable CAMMs become an urgent demand.
Owing to the great potential of millimeter waves in 5G and 6G communications as well as imaging and detection applications, metasurfaces operating in the millimeter-wave region have attracted many research endeavors [40–45]. Compared to the microwave band, the millimeter-wave region is endowed with finer image resolution for imaging/detection applications and higher data capacity for communications and information transmission. Compared to the THz band, the millimeter-wave region is advantageous in terms of transmission distance and system cost. Therefore, it is very meaningful to investigate CAMMs in the millimeter-wave region. However, to the best of the authors’ knowledge, no CAMM has been reported in the millimeter-wave region, greatly limiting many metasurface-based fascinating applications in this promising band. To bridge this gap, in this work we propose a high-transmission CAMM operating in a wide millimeter-wave frequency range from 30 to 50 GHz fabricated by cost-effective and easily implementable manners. The proposed meta-atom is composed of a dielectric layer and a metallic layer that can independently modulate the amplitude and phase of millimeter waves. The dielectric layer is realized by 3D-printing technique and the metallic layer is fabricated by mechanical machining, which are both cost-effective manufacture technologies. Another feature of the meta-atom is that it is also insensitive to incident polarization, significantly enriching the application scenarios of the proposed CAMM. Simulation results of the meta-atom show that the amplitude and phase modulation are almost independent of each other, which greatly facilitates the design procedure of the proposed CAMM for different applications. As a proof of concept, three CAMMs are engineered for different applications including millimeter-wave holography, launching of a 2-D millimeter-wave Airy beam, and generation of a 3-D millimeter-wave vortex knot. Experimental measurements of all the reported applications are in excellent agreement with the corresponding simulated results or theoretical calculation. This work presents a new paradigm to accomplish complex amplitude modulation in the millimeter-wave region and is meaningful to a plethora of metasurface-based applications. The proposed CAMM structure is also readily to be extended to other frequency bands.
2. Theoretical fundamentals and meta-atom design
The structure of the proposed meta-atom for CAMM operating in millimeter-wave regime from 30 to 50 GHz is shown in Fig. 1(a), which is composed of a square metallic ring (yellow) and a square dielectric tube (light blue). The metallic ring, which can be easily fabricated by mechanical machining, is designed to only modulate the amplitude of transmitted wave by tuning the size of the square hole. The dieletric tube, made of low-loss polymer material via 3-D printing technique, mainly controls the phase of the tranmitted wave without altering the amplitude. Therefore, the amplitude and phase can be largely tuned in an independent manner and the entire CAMM can be easily and cost-effectively fabricated.
Fig. 1. Structure and simulation results of the designed complex-amplitude modulation meta-atom. (a) Structure of the meta-atom. (b) Dimensions of the meta-atom. (c) Simulated transmission coefficient |S21| of the proposed matched phase tuning module using different h. (d) Simulated transmitted amplitude and phase at 40 GHz obtained by sweeping b and h. For any target amplitude |S21| and phase θ, b and h can be respectively determined by the left and right image
The square metallic ring, shown in yellow in Fig. 1(b), has a thickness of t = 0.1 mm, an inner dimension of b and an outer dimension of w = 3.75 mm that is half of the wavelength in vacuum at the center frequency 40 GHz. The square hole can be considered as an aperture antenna. As suggested by the well-established antenna theory [46], the field amplitude transmitting the aperture is approximately proportional to the aperture size, enabling felxible modulation of the amplitude of transmitted wave. Since the aperture has a square shape, its tranmission property is independent of the incident polarization. We apply CST Microwave Studio to simulate the meta-atom by sweeping b from 0 to 3.75 mm. The first image plotted in Fig. 1(d) demonstrates the nearly liear adjustablity of the transmission amplitude via varying b.
As for the phase manipulation module, adjusting the height h of the square dielectric tube (with an outer dimension of w and an inner dimension of g2) can effectively manipulate the phase of wave traversing the tube, shown in Fig. 1(b). This dielectric tube is referred to as the phase tuning module. Besides the phase tunability, the dielectric tube is desired to exhibit high transmission, i.e., low reflection. For some previously reported dielectric-based phase tuning modules, only discrete values of h can render ultralow reflectivity based on the quarter-wavelength transformer theory and only discrete phase tuning can be obtained with high transmission [47], which greatly hinders related applications. To realize continuous phase tuning ability while maintaining high transmission, we add two matching layers on both ends of the dielectric tube to form a matched phase tuning module. For the sake of convenience each matching layer is also implemented by a square dielectric tube of height d, outer dimension w and inner dimension g1. As suggested by the quarter-wavelength transformer theory, perfect matching between the air and the phase tuning module (with an inner dimension of g2) occurs if the following condition is satisfied [48].
The next step is to determine d, g1 and g2. Theoretically, any value of g2 can render a pair of g1 and d for perfect matching. However, from a practical perspective, there is some tradeoff needs to be considered. On one hand, the larger the g1 and g2, the less printing material is consumed in fabrication that is meaningful for reducing the cost and weight of the structure. On the other hand, larger g1 and g2 lead to thinner walls of the dielectric tubes, which demands a larger h for phase tuning and a larger d for matching. In addition, dielectric tubes with thin walls may be challenging to be printed and the structure can be very fragile. We then use CST to optimize d, g1 and g2 and obtain the final values as d = 1.62 mm, g1 = 1.55 mm, and g2 = 1 mm, which are fixed in all the meta-atoms. These parameters lead to the largest h = 17.9 mm utilized in this work. Figure 1(c) shows the simulated transmission coefficient |S21| of the entire dielectric tube with differernt h in a frequency range from 30 to 50 GHz. Observing all presented |S21| results are larger than 0.99 in the design bandwidth, it is proved that the matched phase tuning module has a high transmittance in a ultrawide frequency range (50% relative bandwidth) and the transmission is almost independent of h.
The simulated transmission results provided in Fig. 1(d) can be used to find b and h of the meta-atom, which are obtained by sweeping b from 0 to 3.75 mm and h from 0 to 18 mm. For any target transmission amplitude |S21| and phase θ of a meta-atom, b and h can be respectively determined by the left and right image in Fig. 1(d). As can be perceived from Fig. 1(d), the modulation of amplitude and phase are largely decoupled. This property greatly facilitates the design of the required meta-atoms. Therefore, any target complex amplitude can be easily obtained by constructing the meta-atom as suggested by Fig. 1(d). For convenience, the meta-atoms in this work are designed with eight discrete amplitudes (from 0.125 to 1 with a step of 0.125) and eight discrete phases (from 45° to 360° with a step of 45°). This leads to in total 64 different meta-atoms that are utilized to form CAMMs for different applications.
Apart from the broadband high transmission and complex modulation features, the meta-atom is also polarization insensitive, rendering it very robust for tremendous applications. This merit is essentially offered by the symmetry of the meta-atom structure.
The proposed design method can be extended to other bands including microwave and THz regions since the fabrication technique is largely the same. It is also theoretically valid for the IR or visible band. It is possible to realize dielectric meta-atoms working in the optical band with dielectric constant adjustable by changing the structure [49]. But it may be challenging to fabricate the proposed structure. First, the obtainable variation range of the dielectric constant in the optical regime may not be big enough to apply the proposed design. Second, the three-layer dielectric structure may be quite difficult and costly to fabricate. Third, the commonly applied materials for optical metamaterials usually have nonlinear effect and it is hard to control the polarization in such materials.
3. Results of generated complicated millimeter-wave beams
We engineer three CAMMs for complicated millimeter-wave beam generation to validate the proposed broadband high-transmission polarization-independent complex-amplitude meta-atom. The first one is a hologram generator, the second one is a vortex knot generator and the third one is an Airy beam generator. Photos of the three fabricated CAMMs are shown in Fig. 2. Generation of these complicated beams in the millimeter-wave region has profound implications for a wealth of important disciplines like imaging and information transmission, but has rarely been covered by previous research endeavors. Simulation and experimental results are both provided to prove the effectiveness of the CAMMs. For the sake of simplicity, the feature of polarization independence is only proved by the hologram generator, which does not compromise the generality of this work.
Fig. 2. Photos of the three fabricated CAMMs for (a) hologram generator, (b) vortex knot generator, and (c) Airy beam generator. The upper row shows the metallic layer and the lower row shows the dielectric layer
3.1. Hologram generator
Holography is an efficient way for information transfer because it has a large storage capability for phase and amplitude [50–53]. In this section, a polarization-independent hologram of letter ‘S’ is designed and verified in a wide millimeter-wave frequency band from 30 to 50 GHz. Design of the CAMM for hologram generator is based on propagation compensation algorithm that is described in the supplementary information. The hologram is intended to be constructed on a plane 100 mm behind the designed CAMM. As suggested by the algorithm, applying a CAMM to achieve a high-resolution hologram is much more efficient than utilizing a PMM since the latter demands dramatically more iterations than the former and the quality of the hologram is inferior to that obtained by the former.
Figure 3(a) illustrates the schematic diagram of simulation setup, which is performed using CST. Four sets of simulations are conducted, which respectively use incident plane waves with different polarizations (XP, YP, LCP and RCP) as the excitation source. After passing through the CAMM-based hologram generator, the transmitted field intensity is recorded for different polarizations and displayed in Fig. 3(c). The hologram ‘S’ apparently manifests itself and the results subject to different polarizations bear excellent coincidence, verifying the polarization independence feature of the CAMM.
Fig. 3. Setup and results of the hologram generator. (a) Schematic diagram of simulation setup. (b) Experimental setup. (c) Simulated hologram results at 40 GHz using different polarizations. (d) Experimental hologram results from 30 to 50 GHz using different polarizations. Size of the images is 200 mm × 200 mm.
We fabricate the CAMM as displayed in Fig. 2(a). The metallic layer of the designed CAMMs is fabricated by mechanical machining using a 0.1-mm-thick steel plate. The dielectric layer is made by a 3D printer using the Grey Pro Resin material from Formlabs. Because the dielectric tube in the meta-atom has very thin walls, some supporting materials are needed to support the dielectric structure. We have to remove these supporting materials before the measurement. However, for the fabricated structure in the current case, it is difficult to thoroughly eliminate the supporting materials. Since the supporting material has a larger loss than the Grey Pro Resin material, the residual supporting materials inevitably degrade the measured beam quality.
We then perform experimental characterization based on the setup in Fig. 3(b) [54]. The excitation wave is generated by a y-polarized WR-22 20-dB standard gain horn antenna in conjunction with a dielectric lens. The field traversing the CAMM is captured by another y-polarized WR-22 horn antenna deployed on the other side of the CAMM. These two antennas are directly connected to the two ports of a vector network analyzer (Keysight Technologies, N5227A) and both the amplitude and phase of the S21 parameter are measured. The receiving antenna is placed on a motorized stage and scanned in the plane where the hologram ‘S’ is designed to be formed. The measured S21 on the scanning plane form the amplitude and phase distributions of the generated millimeter-wave beam. In total four sets of measurements are conducted by changing the polarizations of transmitting and receiving antennas, which aims to synthesize circular polarization. To be specific, XP (x-polarized) excitation with XP measurement, XP excitation with YP (y-polarized) measurement, YP excitation with YP measurement, and YP excitation with XP measurement. The x-polarized excitation wave can be obtained by simply rotating the y-polarized antenna by 90°. The experimental results are shown in Fig. 3(d). The hologram is clear in a wide frequency range with different incident polarizations, which demonstrates the ultra-wideband and polarization-independent property of the proposed CAMM.
The simulated and measured efficiency is given in Table 1, which is averaged over the entire bandwidth. This efficiency is the field efficiency. Only the dielectric layer is used in the simulation and experiments, in which the receiving antenna is put directly behind the dielectric layer to do the scanning. This is because the dielectric layer theoretically does not tune the amplitude while the metallic layer does. Another set of measurement is also conducted by measuring the field without any sample, which serves as the reference. The simulated efficiency is 90% while the measured efficiency is 77%. This is probably because the residual supporting material in the dielectric layer induces more attenuation of the wave. Another possible reason is the fabrication error when printing the dielectric layer.
Table 1. Simulated and measured efficiency of the dielectric layer of the three CAMMs
3.2. Vortex knot generator
Vortex knot is a fascinating EM wave structure in 3-D holographic imaging owing to its complex topology and has applications in precision shaping of nodal structures such as the design of optical landscapes for blue-detuned trapping [55] and super-resolved fluorescent imaging [56]. Different from traditional holographic technique in which the object of interest usually has stronger field than the background (i.e., bright part), the field in the knot region is weaker than its background, i.e., the knot occupies the dark region. This feature offers a new creative approach for imaging and field manipulation [57].
In order to generate a vortex knot that consists of two rings, as schematically depicted in Fig. 3(a), the explicit expression of the initial wavefront can be described by
Fig. 4. Theoretical, simulated and experimental results of the vortex knot generator at different propagation distances. Size of the images is 200 mm × 200 mm.
3.3. Airy beam generator
Airy beam is widely recognized for its curved parabolic trajectory, non-diffraction propogation and self-healing property [59–62]. Airy beams may find applications in wireless communications, wireless power transfer and imaging [63]. Only quasi-non-diffraction Airy beam can be generated in reality since the ideal Airy beam has infinite energy. The 2-D quasi-Airy beam has a truncated initial field distribution as follows [64].
Fig. 6. Simulated and experimental results of the Airy beam generator. (a) Simulated amplitude at 40 GHz in xy cut planes. (b) Measured amplitude at 30, 35, 40, 45 and 50 GHz in xy cut planes. (c) Simulated amplitude at 40 GHz in an oblique cut plane along the axis of symmetry of the Airy beam. The plotted propagation distance is up to 550 mm. (d) Measured amplitude at 30, 35, 40, 45 and 50 GHz in the same oblique cut plane as (c).
4. Conclusion
In this work, an ultra-wideband high-transmission polarization-independent CAMM operating from 30 to 50 GHz is presented. A metallic ring is applied to modulate the amplitude and a dielectric matched phase tuning module controls the phase. Compared with traditional reported CAMMs in the microwave region, the proposed meta-atom is more advantageous in terms of bandwidth, transmission efficiency, cost efficiency, ease of fabrication and polarization independence. Three applications based on the proposed CAMM are engineered, including hologram, vortex knot and Airy beam. The achieved simulation and experimental results undoubtedly verify the outstanding properties of the designed CAMMs. This work may enable further applications of millimeter-wave beams in communication, imaging and detecting systems with enhanced performance.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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