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Abstract
In this work, we report the realization of broadband binary-reflection-phase metasurfaces that simultaneously exhibit undistorted transmission wavefront. Such a unique functionality is bestowed by leveraging mirror symmetry in the metasurface design. Under the normal incidence of waves polarized along the mirror surface, a broadband binary-phase pattern with π phase difference is induced in the cross-polarized reflection, while the co-polarized transmission and reflection are unaffected by the binary-phase pattern. Consequently, the cross-polarized reflection can be flexibly manipulated by designing the binary-phase pattern, without distorting the wavefront in transmission. The phenomena of reflected-beam splitting and undistorted transmission wavefront are hereby experimentally validated in a broad bandwidth from 8 GHz to 13 GHz. Our findings reveal a unique mechanism to realize independent manipulation of reflection with undistorted transmission wavefront in a broad spectrum, which has potential implications in meta-domes and reconfigurable intelligent surfaces.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces [1,2], consisting of a two-dimensional array of subwavelength nanostructures, have been demonstrated to exhibit strong capabilities to manipulate the propagation of electromagnetic waves at frequencies ranging from microwave to visible. Up to now, many novel mechanisms for metasurfaces have been revealed, such as generalized Snell’s law [3–5], Huygens’ metasurface [6,7], Pancharatnam-Berry-phase metasurfaces [8,9], space-time metasurface [10,11], and so on. These mechanisms further inspired various metasurface devices, including achromatic metalens [12–15], antireflection coatings [16–21], ultrathin invisibility cloaks [17,22–26], vortex beam generator [27–30], polarization converter [31–35], parity-protected meta-gratings [36], high-efficiency holograms [37,38], and high-capacity holograms [39,40] etc. Tunable metasurfaces [41–46] that can dynamically change the functionalities based on tuning mechanisms, such as optical, electro-optical, magnetic, and thermal tuning, and lumped-element tuning with voltage, greatly enhance the potential of metasurfaces for practical applications. Among them, tunable lumped-element metasurface is naturally compatible with the coding metasurfaces [47,48], where each unit cell offers discrete amplitude/phase response states as “bits”, giving rise to the programmable metasurface [48,49] paradigm in a systematic and scalable way. Furthermore, the reconfigurable intelligent surfaces [50–53] even further extend the functionality and potential of programmable metasurfaces by including the ability of incidence perception, communication with each other, and information processing.
In most previous metasurfaces that allow both reflection and transmission, the wavefronts in reflection and transmission of metasurfaces are strongly correlated. Such a correlation is attributed to the fact that most modifications of the meta-atom influence both the reflection and transmission simultaneously. However, in many scenarios, when the reflection is modulated, the transmission is required to maintain the wavefront of incidence so as to conserve the carried information. Typical cases include camouflaged dome for radars [54] at the microwave frequency and transparent materials with diffuse reflection [55] in the visible frequency regime. Such a requirement is challenging to meet for classical metasurfaces, especially over a broad spectrum.
Very recently, the so-called flip-component metasurfaces [54,55] have been proposed to control the reflection without affecting the transmission wavefronts. Flip-component metasurfaces are composed of two types of meta-atoms, which are the flipped counterparts of each other. The reciprocity and space-inversion symmetry guarantee a broadband undistorted transmission wavefront, regardless of the arrangement of meta-atoms. On the contrary, the reflection of the flip-component metasurface can be engineered by designing the arrangement of the meta-atoms because of the distinct reflection phases of the two meta-atoms. However, the reflection phase difference between the two meta-atoms is dispersive and thus limits the reflection functionality to a narrow operating bandwidth.
In this work, we demonstrate binary-reflection-phase metasurfaces (BRPMs) that simultaneously support broadband configurable reflection and undistorted transmission wavefront as schematically shown in Fig. 1. The metasurfaces are composed of two types of meta-atoms, which are the mirror image to each other, as schematically shown in the inset in Fig. 1. The materials and the architecture of the meta-atoms can be arbitrary. Mirror symmetry plays a crucial role in this design. Assuming a linear-polarized normal incidence with the electric field parallel to the mirror plane, the transmission of the two meta-atoms are identical in the co-polarization, which is strictly protected by mirror symmetry between the two meta-atoms and hence is regardless of the specific architecture and materials of the meta-atoms. Therefore, the wavefront in the transmission is unchanged in a broad spectrum, regardless of how the meta-atoms are arranged. On the contrary, the reflections of the two meta-atoms have a phase difference of 0 and $\mathrm{\pi}$, separately for the co- and cross-polarizations in a broad spectrum, which is also rigorously protected by mirror symmetry. The $\mathrm{\pi}$ phase difference enables broadband binary-reflection-phase pattern and hence configurable reflections by engineering the arrangement of the two meta-atoms, which has been thoroughly studied in previous coding metasurfaces. As an example, we design metasurfaces that simultaneously support broadband reflected-beam splitting and undistorted transmission wavefront. This functionality of the metasurfaces is verified by numerical simulations and both near-field and far-field microwave experiments. Our work provides a unique approach based on mirror symmetry to independently control the reflection while keeping the transmission wavefront unchanged in a broad spectrum.
Fig. 1. Schematic diagram of the BRPM that simultaneously supports broadband configurable reflection and undistorted transmission. (Inset) Mirror symmetry between the meta-atoms guarantees the y-polarized scattering or the x-polarized scattering are of identical intensity and are separately in-phase or out-of-phase. The blue and red arrows depict the electric field of the y- and x- polarizations.
2. Principle of the BRPM based on mirror symmetry
To tailor the wavefront in the reflection and simultaneously keep the wavefront in the transmission the same as the incidence, as schematically shown in Fig. 1, a configurable phase-shift pattern or a homogeneous phase-shift pattern should be separately imposed on the reflected or transmitted waves. Such two decoupled phase-shift patterns can be obtained by arranging two types of meta-atoms with distinct reflections and identical transmission. To achieve these two types of meta-atoms, we consider a pair of meta-atoms with arbitrary shapes and materials, as schematically shown in the inset in Fig. 1, which are the mirror images of each other with the mirror in the y-z plane, and assume an illumination of a y-polarized (with electric field in y direction) normal incidence propagating in –z direction. Due to mirror symmetry of the meta-atoms and incidence, the y-polarized scattering or the x-polarized (with electric field in x direction) scattering are of identical intensity and are separately in-phase or out-of-phase. It is worth noting that such identical intensity and in-phase or out-of-phase features are protected by mirror symmetry and hence are independent of the specific geometric parameters and materials of the meta-atoms, as well as the frequency. By eliminating the x-polarized component, the transmissions of the two meta-atoms with pure y-polarization are identical, leading to a homogeneous transmission-phase pattern and hence unchanged wavefront in the transmission, regardless of the arrangement of the meta-atoms in a metasurface. On the contrary, x-polarized reflection of such metasurface can be configured by engineering the arrangement of the two meta-atoms to form a binary-reflection-phase pattern with the phase difference of $\mathrm{\pi}$. Meanwhile, a specular reflection component with y-polarization occurs in parts of the spectrum.
By using this method, we design a pair of meta-atoms composed of two layers of copper structures, which are separated by a dielectric layer, as shown in the upper panel in Fig. 2(a). The first layer contains two tilted copper patches and the second layer is a copper layer with narrow slits as shown in the lower panel in Fig. 2(a). The detailed structural parameters of the meta-atom are specified in the figure caption. The first layer with structures asymmetric about the y-direction is used to generate both x- and y-polarized scatterings under y-polarized incidence propagating in –z direction and the second layer with slit structure functions as a broadband polarizer that allows only y-polarized waves in the transmission, as schematically shown in Fig. 2(b). Numerical simulations based on the finite-element method are carried out to investigate the designed meta-atoms. In the simulation, unit-cell boundary conditions are applied to sides of meta-atoms to mimic an infinite array. Two ports in front of and behind the meta-atoms are used to calculate the reflection and transmission coefficients and each port supports two modes corresponding to the x- and y-polarizations. A loss-free dielectric spacer is assumed. The calculated x- and y-polarized transmittances (${T_x}$ and ${T_y}$) and transmission phase of the y-polarized transmission (${\varphi _{{t_y}}}$) under y-polarized normal incidence are shown in Fig. 2(c), the x- and y-polarized reflectances (${R_x}$ and ${R_y}$) and the corresponding reflection phases (${\varphi _{{r_x}}}\textrm{}$ and ${\varphi _{{r_y}}}$) in Fig. 2(d), where the solid lines and symbols depict the meta-atom I and meta-atom II separately. From Fig. 2(c), it is found that the transmission of the two meta-atoms has only the y-polarized component and that the transmittances and transmission phases of the two meta-atoms are identical in the frequency range of 8-13 GHz. From Fig. 2(d), it is found that the y-polarized reflections of the two meta-atoms are of identical intensity and in-phase while the x-polarized reflections are of identical intensity but $\pi $-phase difference. We note that both the identical intensities and in-phase and out-phase properties of scattering in the two meta-atoms are independent of the frequency. However, for practical applications in metasurfaces, on the one hand, at low frequencies where the wavelength is much larger than the size of meta-atoms, the reflected and transmitted properties of the meta-atom can be barely tailored by engineering its geometric parameters. On the other hand, at high frequencies where the wavelength is much smaller than the meta-atoms, a diffraction effect might occur depending on the periodicity in the metasurface. Therefore, here we focused on a finite frequency range of 8-13 GHz. At a frequency range of 10.7 -12.1 GHz (the shaded region), the out-phase x-polarized reflections dominate and the intensity of y-polarized reflection is less than 5% due to the destructive interference. And a minimum y-polarized reflection near zero occurs at 11.4 GHz.
Fig. 2. Design of the meta-atoms in the BRPM. (a) (upper panels) A pair of meta-atoms that are mirror images of each other with the mirror in the y-z plane. Each meta-atom is composed of a layer of tilted copper patches (the 1st layer) and a copper layer with slits (the 2nd layer), which are separated by a dielectric spacer. (lower panels) Bottom view of the meta-atoms. The lattice constant of meta-atom is $p = 12.5\textrm{mm}$. The width and length of the copper patches are separately $a = 8.4\textrm{mm}$ and $b = 3.8\textrm{mm}$. The distance between the two patches is $w = 0.44\textrm{mm}$. The width of the slit is ${d_s} = 0.25\textrm{mm}$ and the widths of the copper stripes are ${d_1} = 1\textrm{mm}$, ${d_2} = {d_3} = 4.75\textrm{mm}$, and ${d_4} = 1.25\textrm{mm}$, respectively. The dielectric spacer has a relative permittivity of ${\varepsilon _r} = 2.3$ and a thickness of $h = 3.3\textrm{mm}$. (b) Cut view of the meta-atom and the allowed polarization states in the incidence and transmission sides and inside the meta-atom. Blue and red arrows represent the y- and x-polarized waves respectively. (c) The calculated transmittances and transmission phases of the two meta-atoms. (d) The calculated reflectances and reflection phases of the two meta-atoms. The solid lines and symbols in (c) and (d) depict the meta-atomI and meta-atom II separately.
For a BRPM composed of the two types of meta-atoms shown in Fig. 2(a), a homogeneous phase pattern is imposed on the transmission with pure y-polarization and therefore the wavefront of the transmission is undistorted and maintains that of the incidence in a broad spectrum regardless of the arrangement of the meta-atoms. Such a homogeneous phase pattern is strictly protected by mirror symmetry between the two types of meta-atoms. On the contrary, the x-polarized reflection can be engineered by designing the arrangement of the meta-atoms to form a binary-reflection-phase pattern with a $\pi $-phase difference, which is also broadband thanks to mirror symmetry. A variety of functionalities could be realized with binary-phase patterns including beam splitting [56,48,57], diffuse reflection [56,48], focusing [58], and orbital-angular-momentum-beam generation [59]. The y-polarized specular reflection vanishes at frequencies ranging from 10.7 GHz to 12.1 GHz and occurs out of this band. Such specular reflection can be further suppressed in a broader frequency band by introducing mechanisms of broadband polarization conversion [34,35] in the meta-atoms while maintaining mirror symmetry between the two types of meta-atoms. For instance, the dispersion of polarization conversion of the metallic structures can be cancelled out by the thickness-dependent dispersion of the dielectric spacer [34].
3. Reflected-beam splitting with undistorted transmission wavefront enabled by a BRPM
Without loss of generality, here we design a BRPM, which is referred to as BRPM I in the following, that functions as a one-dimensional reflected-beam splitter with undistorted transmission wavefront as shown in Fig. 3(a) by using the two meta-atoms in Fig. 2(a). The binary-reflection phase of this one-dimensional beam splitter is periodic in x direction and homogeneous in y direction. The unit cell of BRPM I is composed of a subset A and a subset B, which separately contain two meta-atoms I and two meta-atoms II as shown in Fig. 3(b). The length and width of a unit cell are ${L_x} = 50\; \textrm{mm}$ and ${L_y} = 12.5\; \textrm{mm}$. The phase of the y-polarized transmission along x-direction is a constant, while the phase of the x-polarized reflection is a binary function as schematically shown in Fig. 3(b). And y-polarized reflected phase is a constant similar to that of the y-polarized transmission. The transmission of the BRPM, which has only the y-polarized component, is undistorted and maintains the wavefront of the incidence due to the homogeneous y-polarized-transmission-phase pattern. On the contrary, the reflection of the BRPM is tailored. Due to the periodic phase distribution along the x direction, the x-polarized reflection follows:
where m represents the order of the reflections and can be integers, ${\theta _m}$ is the reflection angle of the $m\textrm{th}$ reflection in the x-z plane, $\lambda $ is the wavelength, ${L_x}$ is the period in the x-direction. In the $m\textrm{th}$-order reflection, the phase difference between reflections from the two subsets is where the first term stems from the geometric offset of ${L_x}/2$ between subsets A and B, while the second term is the mirror-symmetry-induced phase difference between the two subsets. By substituting Eq. (1) into Eq. (2), it is found that for m with even or odd values, the reflections from subsets A and B possess a $\Delta \mathrm{\Phi }$ of $\pi $ or $0$. Therefore, when m is even, the reflections vanished due to destructive interference. On the contrary, when m is odd, the reflections exist due to the constructive interference [57]. To fulfill the requirement $|{\textrm{sin}{\theta_m}} |\le 1$, the allowed odd value of m and the corresponding ${\theta _m}$ can be obtained from Eq. (1). The calculated m and ${\theta _m}$ for ${L_x} = 50\; \textrm{mm}$ are plotted in Fig. 3(c), where only reflections of $m ={\pm} 1$ exist. In addition, the y-polarized reflection exists only at frequencies out of the shaded region in Fig. 2(d) and obeys specular reflection rules due to the homogeneous phase distribution similar to the y-polarized transmission.Fig. 3. One-dimensional reflected-beam splitter with undistorted transmission wavefront enabled by a BRPM. (a) The arrangement of the two types of meta-atoms in the BRPM I with a side length of 25 cm. (b) Unit cell of the BRPM I consisting of two meta-atoms I and two meta-atoms II (upper panel). The phase-shift distributions of the x-polarized reflection and y-polarized transmission (lower panel). (c) The calculated (solid lines) propagation angle of the reflected beams. Diamonds, stars, and circles represent the simulated propagation angles at 10.6 GHz, 8 GHz, and 13 GHz. (d-f) The x-polarized (left panels) and y-polarized (right panels) electric-field distributions of the BRPM I under normal incidences with y-polarization at frequencies of 10.6 GHz (d), 8 GHz (e), and 13 GHz (f). Hollow arrows represent the incident beams. The unit of the coordinates is mm. (g) The simulated far-field scattering patterns at 10.6 GHz, 8 GHz, and 13 GHz. The energy proportion of each beam is listed.
The scattering field distributions of the BRPM I under the illumination of a normal incident Gaussian beam with y-polarization are simulated by the finite-element method. In the simulation, the incident Gaussian beam is generated by using a field source. Open boundary conditions are applied to all boundaries of the simulated region to avoid undesired reflections. From the simulated results, the minimum y-polarized reflection is found at 10.6 GHz, which slightly deviates from 11.4 GHz in Fig. 2(d) due to the mutual coupling between neighboring meta-atoms and the finite width of the metasurface and the incident beam. The simulated electric-field distributions of the metasurface at 10.6 GHz, 8 GHz, and 13 GHz are separately shown in Fig. 3(d)-(f). At 10.6 GHz as shown in Fig. 3(d), the transmission of the BRPM I has only the y-polarized component and maintains the wavefront of the incident Gaussian beam. Meanwhile, the reflection has only the x-polarized component and propagates in the directions of ${\theta _{ {\pm} 1}} ={\pm} 34.4^\circ $, which are depicted by blue stars in Fig. 3(c) and agree well with the theoretical calculation. As shown in Fig. 3(e) and Fig. 3(f), at 8 GHz and 13 GHz, the undistorted transmission wavefront with y-polarization and two split reflection beams with x-polarization are observed. The propagation angles of ${\theta _{ {\pm} 1}} ={\pm} 46.7^\circ $ (${\theta _{ {\pm} 1}} ={\pm} 27.3^\circ $) for 8 GHz (13 GHz) are depicted by green diamonds (pink circles) in Fig. 3(c) and agree well with the theoretical calculation. We also investigate the far-field scattering pattern of the BRPM I and the energy carried by each scattered beam can be calculated by integrating the far-field scattering power in its space angle range. The simulated results at 10.6 GHz, 8 GHz, and 13 GHz are shown in Fig. 3(g). From Fig. 3(g), lobes in $180^\circ $ correspond to the transmission with an undistorted wavefront in the direction of the incidence. The transmission beams at 10.6 GHz, 8 GHz, and 13 GHz carry 38.4%, 59.5%, and 8.5% of the total energy, respectively. Lobes in the directions of ${\theta _{ {\pm} 1}} ={\pm} 34.4^\circ $, ${\pm} 46.7^\circ $, and ${\pm} 27.3^\circ $, which separately carry 30.1%, 2.6%, and 22.9% of the total energy, correspond to x-polarized reflections. In addition, it is seen that the y-polarized specular reflection in the direction of $0^\circ $ vanishes at 10.6 GHz and occurs at 8 GHz and 13 GHz, carrying 34.6% and 43.9% of the total energy. The consistency between the near-filed electric distributions in Figs. 3(d)–3(f) and the simulated far-field scattering patterns in Fig. 3(g) as well as the theoretical predictions verifies the undistorted transmission wavefront and tailored reflection in a broad spectrum.
We also verified the functionalities of the BRPM I by performing both near-field and far-field experiments. The top view of the fabricated BRPM I is shown in Fig. 4(a). The experimental setup for the near-field measurement is shown in Fig. 4(b). An emitting horn antenna 138 cm away from the metasurface is used to generate a quasi-Gaussian wave as the normal incidence. The near-field electric-field distributions in front of and behind BRPM I are measured by a probe mounted on a stepper motor. The x- and y-polarized electric fields are measured by placing the probe along the x and y directions, respectively. A KEYSIGHT N5224B network analyzer connecting the emitting horn antenna and the probe is used to obtain both the magnitude and phase of the electric field at the position of the probe. Absorbers surrounding the metasurface are used to prevent waves from bypassing the metasurface, considering that the width of the incident beam is broader than that of the metasurface. The measured scattered electric-field distributions at 10.6 GHz, 8 GHz, and 13 GHz are shown in Fig. 4(c)–4(e), which are in good agreement with the simulation results in Fig. 3(d)–3(f). Figure 4(f) shows the experimental setup for measuring the far-field scattering patterns. An emitting horn antenna and a receiving horn antenna are connected to the network analyzer and separately adopted to generate the normal incident beam and measure the electric field. The receiving horn antenna is mounted on a circular track, which can rotate around the BRPM I, to measure the electric field at each polar angle of $\theta $ in the x-z plane. The total far-field scattering pattern is the combination of electric fields in the x-z plane and y direction, which are measured by setting the receiving horn antenna parallel to the x-z plane and y direction. Absorbers surrounding the metasurface are also used to prevent waves from bypassing the BRPM I. The measured far-field scattering patterns at 10.6 GHz, 8 GHz, and 13 GHz are shown in Fig. 4(g). The shaded regions in Fig. 4(g) represent the directions where the far-field scattering can’t be obtained due to the finite size of the emitting and receiving horn antennas. The measured far-field scattering patterns are consistent with the measured near-field electric fields in Fig. 4(c)–4(e) and agree well with the far-field simulation results in Fig. 3 (g).
Fig. 4. Experimental demonstration of reflected-beam splitting and undistorted transmission of the BRPM I. (a) Front view of the fabricated BRPM I. Inset shows a zoomed-in view. (b) Setup of the near-field measurements. (c-e) Measured near-field electric-field distributions of the BRPM I under y-polarized normal incidence at frequencies of 10.6 GHz, 8 GHz, and 13 GHz. Fields in the blank areas are not measured because of the considerable thickness of the absorber. Hollow arrows represent the incident beams. The unit of the coordinates is mm. (f) Setup of the far-field measurements. (g) Measured far-field scattering patterns of the BRPM I at frequencies of 10.6 GHz, 8 GHz, and 13 GHz.
As another example, we design a BRPM that functions as a two-dimensional reflected-beam splitter with an undistorted transmission wavefront as shown in Fig. 5(a) by using the two types of meta-atoms in Fig. 2(a). The binary-reflection phase of this two-dimensional beam splitter is periodic in both x and y directions. This BRPM is referred to as BRPM II in the following. The unit cell of the BRPM II consists of four subsets depicted by a, b, c, and d as shown in Fig. 5(b). Subsets a and d (b and c) are composed of a $2 \times 2$ array of meta-atom I(meta-atom II). The length and width of a unit cell are ${L_x} = 50\; \textrm{mm}$ and ${L_y} = 50\; \textrm{mm}$. Since phases of the y-polarized transmitted wave of the two meta-atoms are identical, the transmitted phase distribution of the unit cell is homogeneous as schematically shown in the top-right panel of Fig. 5(b), rendering an undistorted transmission wavefront of the BRPM II. On the contrary, the phase distribution of x-polarized reflection of the unit cell forms a two-dimensional binary-phase pattern as schematically shown in the bottle-right panel of Fig. 5(b) because of the $\mathrm{\pi}$-phase difference in the x-polarized reflections of the two meta-atoms. In addition, the y-polarized specular reflection would exist at frequencies out of the shaded region in Fig. 2(d).
Fig. 5. BRPM II functions as a two-dimensional reflected-beam splitter with an undistorted transmission wavefront. (a) Schematic diagram of the BRPM II. (b) (left panel) Unit cell of the BRPM II. (right panels) Homogeneous phase pattern of the y-polarized transmission and the binary-reflection-phase pattern of the x-polarized reflection. (c) Far-field scattering patterns of the BRPM II under normal incidence at 10.9 GHz, 8 GHz, and 13 GHz. (d,e) The near-field electric-field distributions of the BRPM II in the $\varphi = 45^\circ \textrm{}({\varphi = 225^\circ } )$ (d) and $\varphi = 135^\circ \textrm{}({\varphi = 315^\circ } )$ (e) planes at 10.9 GHz. Hollow arrows represent the incident beams. The unit of the coordinates is mm.
We then focus on x-polarized reflections. Since the unit cell is periodically repeated in both x and y directions, BRPM II possesses a two-dimensional binary-phase pattern for the x-polarized reflection. Due to the periodicity of the BRPM II, the reflected beam is diffracted into several orders and each order can be depicted by $({m,n} )$, where m and n are separately the orders in the x and y directions and are both integers. The azimuthal and polar angles of the direction of the $({\textrm{m},\textrm{n}} )$-order reflected beam are separately
It is found from Eq. (6) that when m is even, the radiations from subsets a and b have a phase difference of $\pi $, which causes them to cancel each other. The same is true for the radiations from subsets c and d. Through similar derivation, it is easy to know that when n is even, the radiations from subsets a and c (b and d) would cancel each other. Therefore, the second requirement for the allowed reflection orders is now clear, that is both m and n are odd. Taking into consideration these two requirements and ${L_x} = 50\; \textrm{mm}$, reflections with orders of (1,1), (1,-1), (-1,1), and (-1,-1) exist at frequencies larger than 8.48 GHz and reflections with orders of (3,3), (3,-3), (-3,3), and (-3,-3) exist at frequencies lager than 25.4 GHz.
We perform finite-element-method simulations to investigate the scattering of the BRPM II under the illumination of a normal incident Gaussian beam with y-polarization. The simulation results indicate that the minimum y-polarized reflection occurs at 10.9 GHz, where all the reflections are x-polarized and can be totally tailored via the binary-reflection-phase distributions. The slight deviation between 10.9 GHz and 11.4 GHz where the y-polarized reflection is minimum under the periodic condition as shown in Fig. 2(d) should be attributed to the mutual coupling between the neighboring meta-atoms. The simulated far-field scattering patterns at frequencies of 10.9 GHz, 8 GHz, and 13 GHz are shown in Fig. 5(c). From the far-field scattering patterns at 10.9 GHz, it is found that the transmission is located in the direction of incidence with 37.4% of the total energy, indicating an unchanged wavefront of the incidence and that the reflection is scattered into four directions corresponding to the orders of (1,1), (1,-1), (-1,1), and (-1,-1) and each beam carries 15.1% of the total energy, verifying a beam splitting phenomenon. The near-field scattering field distributions in the $\varphi = 45^\circ $ ($\varphi = 225^\circ $) and $\varphi = 135^\circ $ ($\varphi = 315^\circ $) planes at 10.9 GHz are shown in Figs. 5(d) and 5(e). From the near-field distributions, it is observed that the y-polarized transmission maintains the wavefront of the incidence and that the x-polarized reflection is redistributed in directions of $\theta = 50.4^\circ $ in these two planes, which agree well with the far-field simulation results as well as the theoretical prediction of $\theta = 51.1^\circ $ through Eq. (3). The far-field scattering patterns at 8 GHz and 13 GHz in the middle and right panels in Fig. 5(c) indicate transmissions with unchanged wavefront and tailored reflections consist with the theoretical prediction that the orders of (1,1), (1,-1), (-1,1), and (-1,-1) appears at frequencies larger than 8.48 GHz and that a mirror reflection with y-polarization occurs at frequencies out of the shaded region in Fig. 2(d).
4. Discussion and conclusion
We note that the mechanism of BRPMs is fundamentally different from that of previously developed full-space metasurfaces [60–63]. The full-space metasurfaces require wave incidence with two orthogonal linear polarizations and manipulate the wavefronts of each polarization in either transmission or reflection. The BRPMs reported here can only manipulate the cross-polarized reflection while keeping the co-polarized transmission unaffected at the same time. But they only require wave incidence of a single linear polarization and exhibit the significant advantage of broad bandwidth. The function of ultra-broadband $\mathrm{\pi}$ reflection phase difference in BRPMs also makes them superior to the previously proposed random-flip metasurfaces, where the $\pi $ reflection phase difference is usually limited to a narrow band due to the frequency dispersion of meta-atoms. Such an advantage of broadband functionality is a result of leveraging mirror symmetry in the meta-atom design.
Recently, reconfigurable intelligent surfaces [50–53] that utilize active metasurfaces to dynamically control the reflection and transmission of electromagnetic waves have found solid applications in manipulating wireless communication channels and improving energy efficiency, making them a promising technology for future wireless communication systems. We note that the passive BRPMs enabling wavefront manipulation in the reflection and undistorted transmission wavefront in principle can be extended to active ones such as reconfigurable intelligent surfaces by introducing controllable units, e.g., diodes, in the meta-atom while maintaining mirror symmetry between meta-atoms.
In summary, we introduce the BRPM that combines broadband configurable reflection and broadband undistorted transmission wavefront. The BRPM is composed of a pair of meta-atoms, which are mirror images of each other. Under normal incident wave with polarization parallel to the mirror plane between the two meta-atoms, the mirror symmetry strictly guarantees that the co-polarized transmissions of the two types of meta-atoms are identical and their cross-polarized reflections are out-of-phase with identical intensity. By arranging the two types of meta-atoms, the cross-polarized reflection of the BRPM can be manipulated in a broad spectrum due to the broadband binary-phase pattern with $\mathrm{\pi}$ phase difference, though co-polarized specular reflection exists in some frequencies depending on the resonance of the meta-atoms. On the contrary, the wavefront in transmission is unchanged in a broad spectrum regardless of the arrangement of the meta-atoms due to the zero phase difference in transmission. The remarkable feature of the BRPM, hereby demonstrated both numerically and experimentally, opens a route toward broadband manipulation of reflection with an undistorted transmission wavefront.
Funding
National Natural Science Foundation of China (11974176, 12174188); National Key Research and Development Program of China (2020YFA0211300, 2022YFA1404303).
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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