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Abstract
In this work, a polarization-free coding metasurface is proposed to manipulate circularly polarized waves. Compared to a Pancharatnam-Berry phase metasurface, the proposed design not only allows for overcoming anti-symmetrical response characteristics between orthogonal circularly polarized states to enable achieving identical functionality under both right-handed and left-handed circularly polarized wave illuminations and avoiding polarization-conversion losses but also offers additional degree of freedom in the control of handedness. As a proof-of-concept demonstration, a polarization-free multi-bit coding metasurface is designed to realize helicity-switched holograms in the microwave region. Experimental measurements performed on a fabricated prototype reveal outstanding imaging quality with extremely high imaging efficiency above 76% for arbitrary polarizations at 10 GHz. Our proposed method expands the route in manipulating circularly polarized waves and can be applied over the whole electromagnetic spectrum for wavefront manipulation.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurface, a subcategory of metamaterial, exhibits versatile abilities in manipulating the key properties of the scattered wave such as amplitude, phase and polarization [1–3]. Generally, metasurfaces are composed of two-dimensional (2D) array of meta-atoms with specially designed configurations and orientation angles [4–6]. Compared to the bulky volume of three-dimensional (3D) metamaterials, metasurfaces present the advantages of low losses, low cost and thin profile, providing compatible and promising potentials in engineering applications. Moreover, due to their ability in manipulating electromagnetic waves, metasurfaces have offered a new paradigm for applications in a wide frequency spectrum from optical to radio frequencies, such as flat lenses [7–9], high-resolution holograms [10–14], orbital angular momentum (OAM) generators [15,16], cloaking devices [17,18], detection imaging [19], spoof surface plasmon polaritons [20–23], retroreflectors [24–26], beam-steering antennas [27,28] and other functional devices [29–33]. Particularly, in microwave regime, the holographic metasurface offers a mechanism to achieve accurate and elaborate control of electromagnetic near-field rather than traditional far-field manipulation, which can be profitable to short-range communication systems, detection, security, data storage, and information processing [34–36]. Recently, the concept of coding metasurfaces has been proposed [37], and applied in beam manipulation [38], diffuse scattering [39], energy radiation control [40], wireless communications [41,42] and harmonic manipulations [43]. Based on out-of-phase responses, binary coding elements for the simplest 1-bit coding metasurface are “0” and “1”, corresponding to “0” and “π” phase response, respectively. Such coding principle can be extended from 1-bit to multiple bits. Holography is one of the most promising imaging techniques to record and reconstruct full wave information of objects [44]. Compared to conventional holograms, metasurface can provide unprecedented spatial resolution, low noise and high precision of reconstructed images. Based on different phase retrieval algorithms like Gerchberg-Saxton (GS) [45], computer-generated holograms can be elaborately designed with sub-wavelength meta-atoms to encode the holographic information of object patterns calculated by a computer. The fascinating features of coding metasurfaces are particularly advantageous in this regard, yielding to digital meta-holography [46,47]. Though polarization-insensitive metasurfaces have been demonstrated in many platforms both in reflection and transmission modes, they only dealt with the manipulation of incident linear polarizations. The benefits and freedom offered by such kind of metasurface for circular polarized waves were not considered [48–51].
Recently, we proposed a metamirror for multi-focusing with any desired focusing fashion based on the Pancharatnam-Berry (P-B) phase concept, which has been widely explored for metasurface engineering to flexibly manipulate circularly polarized (CP) incident waves [52]. However, the intrinsic nature of the P-B phase produces anti-symmetrical (equal and opposite) response characteristics between orthogonal CP states, which means that identical functionality cannot be achieved under right-handed and left-handed circularly polarized (RHCP and LHCP) waves. To overcome this limitation, we propose to manipulate CP waves with polarization-free metasurface having more degrees of freedom. Moreover, different from the P-B phase element based helicity-preserving metamirror (reflecting a CP wave to similar circular polarization in the opposite direction), the proposed helicity-switching mirror only reverses the radiation direction of the CP wave, as shown in Fig. 1(b), and thus avoids polarization-conversion losses during the process. As shown in Fig. 1(b), the control of handedness is an important characteristic that distinguishes our proposed polarization-free metasurface from the P-B phase based metasurface [53]. This kind of characteristic offers additional degree of freedom in the control of handedness of circularly polarized waves, such as the design of helicity-switching metamirror [53] or helicity-preserving metalens which cannot be achieved by P-B phase based metasurface. Based on the design method, a helicity-switched hologram is demonstrated utilizing a polarization-free multi-bit coding metasurface, as shown in Fig. 1. The proposed metasurface is constructed by ground-backed metallic ring structure, which enables to provide full reflection phase of 2π. By elaborately designing the diameter of the ring, a group of eight digital states (“000” to “111”) is extracted to encode the holographic information calculated by a modified weighted Gerchberg-Saxton (GSW) algorithm. Experimental verifications performed on a fabricated prototype agree qualitatively with the theoretical predictions and numerical simulations, validating the feasibility and high imaging quality of the proposed helicity-switched multi-bit coding meta-hologram.
Fig. 1. (a) Schematic diagram of the proposed helicity-switched meta-hologram based on the polarization-free multi-bit coding metasurface. Identical images of capital letter “H” can be projected under RHCP and LHCP wave illuminations. (b) Structural details of the coding particle.
2. Design of the coding element
The coding particle structure to construct the polarization-free coding metasurface is presented in Fig. 1(b). A metallic ring structure printed on a ground-backed dielectric substrate is utilized as the elementary coding particle due to its characteristics of symmetric geometry and easy fabrication. Structures with identical reflection or transmission response for x- and y-polarizations such as the square or cross loop can be applied for the design of the polarization-free metasurface. F4B dielectric spacer is chosen as substrate with thickness t = 2 mm (only λ0/15), dielectric constant εr = 3 and loss tangent tan δ = 0.0015. The size of the unit cell is p = 10 mm and the width of the ring is w = 0.4 mm. The outer diameter d is varied to achieve the desired 3-bit coding particles. Due to the symmetric geometry, the EM responses of the coding particle are identical for arbitrary linearly polarized waves, providing polarization-free functionality. For convenience, the response under a y-polarized incident EM wave is analyzed. The proposed unit cell is simulated using the commercial software CST Microwave Studio by applying unit periodic boundary conditions in x- and y-directions. By changing the outer diameter d, the phase change can cover the whole range of 2π, while the amplitude of the reflection coefficient keeps above 0.98. Although continuous phase control across a 2π range can be achieved by continuously varying the radius of the ring, a 3-bit coding level is adopted here as a good tradeoff between design complexity and discretization losses, which is sufficient to provide high-efficiency manipulation of electromagnetic waves [38,46,54]. A unit cell without metallic structure on the substrate is utilized here to operate as code “000”, which not only simplifies the design process, but also relaxes fabrication tolerance requirements and reduces the mutual coupling between unit cells. Figure 2(a) shows the reflection amplitude spectra of the 3-bit coding particles extracted from the simulation results, and Fig. 2(b) depicts the reflection phase spectra. The design details of the different 3-bit coding particles are presented in Fig. 2(c). Since arbitrary polarization can be decomposed into x- and y-polarizations, the 3-bit coding particles can also be applied to CP waves. As the reflection response for incident x- and y-polarizations is totally identical, perfect helicity switching can be achieved for incident CP waves using the polarization-free coding particle.
Fig. 2. Design of the coding particles. (a) and (b) Reflection amplitude spectra and reflection phase spectra of the 3-bit coding particles, respectively, under y-polarized incident wave. (c) Design details of the 3-bit coding particles using different-scale ring structure.
3. Design of the coding meta-hologram
In order to achieve the desired helicity-switched hologram, the coding map across the metasurface is derived using the modified GSW retrieval algorithm [55,56]. To consider high resolution, the imaging plane here is designed to be 2.7λ0 (z = 80 mm) away from the meta-hologram. Due to the limited focal distances with respect to the working wavelength, the Fraunhofer diffraction of the optical domain is modified by Green’s function. The method consists in selecting ideal point sources as virtual sources and place them at pre-designed hotspots. Considering there are N hotspots located at (xn, yn, zn) (n = 1 to N), the phase delay at the position of each coding element ϕ (xm, ym, zm) (m = 1 to M) can be retrieved by superposing the electromagnetic field generated by all the virtual sources described by Green’s function. Accordingly, the reconstructed electric field is converged to the predesigned hotspots. In order to keep uniform intensity distribution among hotspots, a weighted factor wn is introduced to reduce intensity difference among N hotspots. An iterative procedure between the holography imaging and meta-hologram is proposed to obtain the uniform intensity profile of the target image as follows:
Fig. 3. (a) Coding maps of the 3-bit coding metasurface. (b) Theoretical results of the electric field intensity distributions. (c) and (d) Simulated reflected electric intensity distributions under linear x- and y-polarized incidence, respectively. (e) and (f) Simulated reflected electric intensity distributions of cross- and co-polarized component under LHCP incidence, respectively. (g) and (h) Simulated reflected electric intensity distributions of the cross- and co-polarized component under RHCP incidence, respectively.
4. Results and discussion
To demonstrate our proposed helicity-switched hologram, the 3-bit coding metasurface is designed and simulated to project the image of capital letter “H”. Since the proposed coding elements can achieve nearly uniform reflection amplitude and multi-level phase coverage, any desired images can be theoretically achieved with high imaging efficiency based on the proposed GSW algorithm. The metasurface consists of 41 × 41 unit cells with an overall size of 410 mm × 410 mm. In the near-field imaging simulations, the metasurface is subjected to open boundary conditions along x- and y- axes, and is illuminated by linear x-polarized, linear y-polarized, RHCP and LHCP waves. Figure 3(b) shows the theoretical calculated results, and Figs. 3(c) and 3(d) present the simulated reflected electric field intensity distributions in the imaging plane under linear x- and y-polarized wave incidences. Although the reflection responses of the coding elements for x- and y-polarized incidences are identical, the metasurface is anisotropic in x- and y-directions, which results in minor differences between images of x- and y-polarized incidences, as shown in Figs. 3(c) and 3(d). Figures 3(e) and 3(f) depict the simulated reflected electric field intensity distributions of cross- and co-polarized component under LHCP wave illumination, respectively, and Figs. 3(g) and 3(h) show the simulated reflected electric field intensity distributions of cross- and co-polarized component under RHCP wave illumination, respectively. The simulated results show high imaging quality and good agreement with the theoretical results for arbitrarily polarized wave illuminations. Moreover, it can be clearly observed from Figs. 3(e)-(f) that the energy of the incident CP wave is totally transformed into the cross-polarized component, indicating the perfect helicity-switching ability. To study the performance of the proposed metasurface under oblique incidence, the simulated results under LCP incidence at different oblique incidence angles of 10°, 20° and 30° are shown in Fig. 4. It can be observed that the proposed metasurface can still achieve reasonable performance under an oblique incidence angle of 30°.
Fig. 4. Simulated reflected electric intensity distributions under LCP incidence at different oblique angles: (a) at 10°. (b) at 20°. (c) at 30°.
To experimentally validate the performances of the proposed helicity-switched meta-hologram, a sample is fabricated using conventional printed circuit board (PCB) technique, as depicted by the photography in Fig. 5(a). Measurements are performed using a near field scanning system, as illustrated by the experimental setup schematic in Fig. 5(b). A feeding horn antenna is placed 130 cm away from the metasurface to launch quasi-plane waves at 10 GHz. The electric field mapping is performed by using an EFS-105-12 fiber-optic active antenna [57], which has a small purely dielectric head of 6.6 × 6.6 mm2 with an optical fiber connection that allows obtaining a negligible field perturbation and eliminating the possibility of having a scattered field on metallic parts and coaxial cables for accurate measurement results. The fibre optic active antenna is fixed on two orthogonal translation stages controlled by a motion controller to measure the amplitude and phase of the electric field. Both the feeding horn antenna and the field-sensing probe are connected to a vector network analyzer (VNA) to measure the reflection coefficients. Since reflection coefficient in the imaging plane of the metamirror involves both incident and reflected electric fields, another measurement without the metamirror is performed to collect only the incident electric field as reference. The reference data is then subtracted from the first measurement (with metamirror) to obtain only the reflected electric field. For CP waves, electric field polarized along x- and y-axes is measured respectively, and the LHCP and RHCP components are calculated as:
Fig. 5. (a) Photography of fabricated sample. (b) Illustration of experimental setup. (c) and (d) Measured reflected electric intensity distribution under x- and y-polarized incidence, respectively. (e) and (f) Measured reflected electric intensity distribution of the cross- and co-polarized component under LHCP incidence, respectively. (g) and (h) Measured reflected electric intensity distribution of the cross- and co-polarized component under RHCP incidence, respectively.
Fig. 6. Measured reflected electric intensity distributions: (a) under LCP incidence at 9.5 GHz. (b) under LCP incidence at 10.5 GHz. (c) under RCP incidence at 9.5 GHz. (d) under RCP incidence at 10.5 GHz.
5. Conclusion
In summary, a polarization-free 3-bit coding reflective metasurface is designed and validated for high efficiency helicity-switched hologram realization. The proposed polarization-free metasurface enables overcoming anti-symmetrical (equal and opposite) response characteristics between orthogonal circularly polarized states and allows achieving identical functionality for incident CP waves without polarization conversion losses. The performed experimental measurement achieves high imaging efficiency above 76% for arbitrarily polarized waves, and shows near perfect helicity-switching conversion efficiency for incident CP waves. The proposed ultra-thin polarization-free metamirror based helicity-switched hologram expands the route to manipulate CP waves, and can find potential applications in data storage, high-resolution imaging lenses, and antenna systems.
Funding
State Key Laboratory of Millimeter Waves (K202001); National Natural Science Foundation of China (61701141).
Disclosures
The authors declare no conflicts of interest.
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