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Abstract
Structuring elements of gratings brings more freedom in manipulating diffraction waves, e.g., retroreflection using diffraction orders other than the 0th order. Most retroreflective metagratings (RMs) can achieve retroreflection only under one particular direction, limiting their applications. In this paper, we propose a quasi-omnidirectional RM based on wave-vector reversion for TE-polarized waves. The metagrating element is composed of four rotationally-symmetric sub-elements, which is composed of one probe and two directors on its two sides. The substrate-air-metal layer can reverse kz while directors can reverse kx. Therefore, the wave-vector k of reflected waves can be completely reversed by the sub-element, providing necessary momentum for retroreflection. The −2nd diffraction order of the metagrating is tailored to channel out waves with reversed k, leading to retroreflection. Due to the element’s four-fold rotational symmetry, retroreflection can be achieved along four directions, covering all of the four quarters of azimuth angle. We demonstrate prototypes in Ku band, and the average backscattering enhancement compared with a metal plane with the same area (SAMP) along the four directions reaches up to 31.3 dB with incident angle 50.0° at 15.0 GHz. Both simulated and measured results verify our design. This work provides another perspective on retroreflection and may find applications in retroreflective functional devices.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Retroreflections, [1,2] namely, a physical phenomenon in which reflected electromagnetic (EM) waves travel along the direction of incident source to obtain the backscatter radar cross section (RCS) enhanced. Retroreflections have a wide range of applications in both civilian [3] and military [4,5] fields, including rescues of fishing boats at sea and false targets to confuse enemies respectively. With more and more extensive uses of aircraft, the demand for retroreflectors is more stringent, including flat planes and even conformable ultra-thin and lightweight retroreflectors, leading to that traditional cat’s eye devices [6–8] or dihedral and trihedral corner reflectors [9–11] are no longer suitable for these new application scenarios due to their bulky volumes. Metasurfaces [12–15] with thin thickness and light mass, a two-dimensional (2D) form of metamaterials [16,17], have natural advantages for well manipulation of EM waves. The past decade has witnessed the rapid development of the metasurface, which can realize many functions including abnormal reflections [15,18–21], meta-polarizers [22–24], surface wave control [25,26] and meta-holograms [27–29]. The internal physical mechanism of these phase gradient metasurfaces (PGMs) [15,30,31] is to apply transverse wave-vector to incident EM waves so as to achieve direction manipulation over diffraction beams. However, the realized functions of PGMs [29] are based on various structural meta-atoms with different sizes or shapes to form a phase gradient library to obtain a specific phase profile. Besides, it needs accurate control to achieve well expected performances relying on the machining accuracy, and it can only achieve diffraction deflection at a specific angle for a given frequency at the same time.
In terms of realizing the retroreflection function for backscattering enhancement, a certain diffraction order of blazed reflection grating was utilized to enhance energy accumulations for diffraction waves along the source direction in the early stage [32]. To improve efficiency, Aul et al [33]. proposed the concept of metagrating to break the restriction of continuous phase or impedance profile and realized efficient EM wave control, and additionally, for the passive metasurfaces, the nonlocal performance can be utilized to ensure the efficient angle control of the beams through the excitation of evanescent mode [34] and the control of leaky wave modes [35]. Besides, by modulating displacements between uniformly sized meta-atoms rather than the geometrical parameters, Z. L. Deng et al. proposed a different design principle to achieve facile metagrating holograms based on extraordinary optical diffraction (EOD) which can allow the molding of arbitrary wavefronts with extreme angle tolerances (near-grazing incidence) in the visible–near-infrared regime, significantly simplifying the metasurface design and lowering fabrication demands and thereby opening new routes for flat optics with high performances and improved practicality [29,36–38].
In this paper, we propose a different route to design a metagrating which breaks the continuous phase or impedance profile adopted by phase gradient metasurface, achieving the −2nd EOD based on wave-vector reversions to obtain quasi-omnidirectional retroreflections in four quadrants of the azimuth zone as a flat plane reflector for the given frequency and incident angles denoted as red areas in Fig. 1. The quasi-omnidirectional retroreflective metagrating (QORM) is composed of four rotationally-symmetric structured patch antennas (SPAs) which consist of a probe with two directors on its both sides as the array element and spatial distributions can be seen in the inset of Fig. 1, enabling highly efficiency manipulation for transverse electric (TE) incident EM waves without the need of deeply subwavelength elements. The −2nd EOD in broadband and wide-angle range is achieved utilizing the receiving-radiation reciprocity of the path antenna, demanding two aspects including the control of diffraction grating period p and manipulation of the antenna radiation pattern reconfigurability. The design of grating period is based on the −2nd EOD theory illustrated later, laying a foundation for the existence of 2nd, 1st, 0th, −1st and −2nd diffractions, while the realization of antenna radiation pattern reconfigurability depends on the substrate-air-metal layer and directors on two sides of the probe to realize reversions of longitudinal and tangential wave-vectors, i.e., kz and kx simultaneously denoted by indigo and red curved arrows in the inset of Fig. 1. The QORM, achieving well performance of retroreflections relying on the judiciously design theory, also has the advantage of easy fabrication due to the SPA adopted in this paper consists of several seemingly simple metal short lines instead of complex cures meanwhile having a well efficient guiding effect on TE incident EM waves. To avoid confusion about incident and reflection angles, the pitch angle θ and azimuth angle φ are defined here. The 2D upper half space is divided into four quadrants through azimuth angle φ=0.0°, 90.0°, 180.0° and 270.0° respectively. The incident angle in each quadrant is defined as positive and the reflection angle is defined as negative, as denoted by θi and θr in Fig. 1 respectively. As an example, this paper proposed a QORM with the achievement of −2nd EOD in a broadband range from 14.0 GHz to 18.0 GHz in Ku band with wide incident angle range from 32.15° to 90.0°, and distinguishingly can obtain highly efficient retroreflections in four quadrants in the azimuth zone at a specific frequency point 15.0 GHz with incident angle 50.0° as denoted by the yellow and orange arrows in Fig. 1. The simulated and measured results are consistent with the expectation and verify the correctness of the design concept. This design method has higher design degrees of freedom (DOF) in controlling EM waves as reflective plane devices, is conducive to the miniaturization and integrated design for microwave and even optical devices, and can be easily extended to terahertz and even optical frequency.
Fig. 1. Schematic illustration of the design principle of the QORM: Specular reflections occur in the middle green area denoted as R0 when the incident angle is smaller than the critical angle, surrounded by the red areas in four quadrants of the azimuth zone where efficient −2nd EOD denoted as R−2 can be achieved when the incident angle is larger than the critical angle. The yellow and orange arrows represent the efficient retroreflections for the specific frequency and incident angles. Under the action of the SPA whose spatial distribution can be seen in the inset, the wave-vector reversions denoted by indigo and red curved arrows are obtained to achieve efficient 2nd EOD.
2. Results and discussion
2.1 Efficient −2nd EOD and scarcely any parasitic diffractions
Setting the direction along the x axis as positive, when EM waves illuminate on the metagrating under incident angle θi with azimuth angel φ=0.0°, the mathematical analytical over the incident angle θi, reflection angle θr and free space wave-vector k0 = 2π/λ where λ is the wavelength according to the frequency f can be obtained as Eq. (1) utilizing the conservation of tangential wave-vectors based on the generalized Snell's law [29,39–40].
where m = 0, ±1, ±2, ±3··· is an integer and ζ=2π/p represent the diffraction orders and grating vector respectively, and p is the element period of the metagrating. It can be seen from Eq. (1) that for a fixed incident angle and reflection angle, the diffraction order is directly proportional to the metagrating element period, that is, with the increase of diffraction order, the period of structural element also increases, so the design DOF for EM waves are increased too. The metasurface or metagrating proposed based on EOD theory basically adopt −1st diffraction [29,36–38], while in this paper the diffraction order is increased to −2nd-order, that is, m=−2. Thus, the corresponding tangential wave-vector conservation relationship is obtained as Eq. (2) from Eq. (1). The tangential wave-vector of the incident waves k0·sinθi can be replaced by kx so as to obtain Reflection Wood anomaly (RWA) lines as denoted in Fig. 2(a), relying on the equation kx+m·ζ=±k0 (see Supplement 1). To obtain the analytical expression between the grating period pm corresponding to the mth diffraction order and the incident angle θi, we consider the special case of retroreflections, i.e., the reflected waves radiate along the source direction where θr=-θi, so as to obtain Eq. (3).Fig. 2. Reflection Wood anomaly (RWA) lines and the metagrating element based on reciprocity of SPA. a Diffraction order chart composed of a series of RWA lines. b Schematic illustration and simulated results of the SPA fed by a coaxial port: (i) perspective view of the SPA with all dimension marked, where px = py = 26.11 mm, l1 = 4.90 mm, l2 = 4.50 mm, d = 10.50 mm, th1 = 0.75 mm, th2 = 5.25 mm; (ii) simulated S11 and total efficiency of the SPA; (iii) surface current on the SPA at 15.0 GHz; (iv) far-field radiation pattern at 15.0 GHz; (v) far-field radiation pattern is off-set by the grating wave-vector η=-k0sinθid/p at 15.0 GHz, and available diffraction orders of the metagrating denoted by red (m=−2), yellow (m=−1) and green (m = 0) arrows respectively; c Perspective view of (i)-(ii) 1D and (iii) 2D metagratings and their elements.
As an example, to achieve retroreflections for a given design frequency f0 = 15.0 GHz, and the incident angle θi = 50.0°, the solution of Eq. (3) obtains that −2nd EOD can be realized when the grating element period p−2 = 26.11 mm and the incident angle is in the range from the critical angle θic = 32.15° to 90.0° (details in Supplement 1). It can be seen from the red area in Fig. 2(a) that there also exist 0th and −1st diffractions when the −2nd-order is obtained by the period manipulation meticulously. Equation (3) further explains that the larger the absolute value of the diffraction order is, the higher the design DOF will be for the metagrating over the same design frequency, and the more beneficial it will be for the miniaturization and integration designs for microwave devices. However, as the absolute value of order increases, the additional diffraction orders increase in the meanwhile. Obviously, it is particularly important to eliminate these parasitic diffractions. Inspired by this, in this paper, based on the design theory protected by the patch antenna reciprocity, the patch antenna reradiation pattern is reconfigured on the premise of choreographed metagrating element period p−2, so as to eliminate parasitic diffractions.
The structural patch antenna (SPA) adopted in this paper is denoted in Fig. 2(b), where a probe and two directors on both sides are attached on a F4B dielectric substrate whose thickness is th1 = 0.75 mm with permittivity εr = 2.65(1 + 0.001j), meanwhile there is an air layer with thickness th2 = 5.25 mm between the F4B and the metal ground plane, forming the substrate-air-metal layer. The feed coaxial port is connected to the end of the probe in the middle of the SPA to obtain simulated results including S11, radiation efficiency, surface current and far-field radiation distribution at 15.0 GHz which are shown in Fig. 2(b), utilizing the time-domain solver in CST Microwave Studio with “open add space” boundary condition in x, y and z directions. From the return loss S11 and radiation efficiency of the SPA in Fig. 2(b) ii, it can be seen that there is at least 2.5 GHz bandwidth around 15.0 GHz where the patch antenna can radiate efficiently. It can be seen from the radiation pattern shown in Fig. 2(b) iv that it has two main lobes symmetrical about the E plane, and their directions are θp-R = 41.0° and θp-L=−41.0° respectively. To further analyze the radiation mode and polarization direction of the SPA, it can be found that the surface current distribution denoted in Fig. 2(b) iii of the probe is dense and the radiation mode is the 1st mode, which is opposite to the surface current distribution direction of directors on both sides. The existence of directors, coupled with the 1st radiation mode of the SPA, provides an additional wave-vector η for the antenna radiation pattern analyzed as Eq. (4).
where d represents the mode distance of the SPA. Under the action of additional wave-vector η, the two main lobe directions of SPA reradiation can be obtained as θRR-L=−54.10° and θRR-R = 30.14° by Eq. (5a) and (5b) respectively. Among them, the left main lobe reradiation direction θRR-L=−54.10° is very close to the −2nd EOD −50.0°. Judiciously, the reradiation direction of the main lobe on the right side θRR-R = 30.14° is different from either −1st diffraction 0° or 0th diffraction 50.0° according to Eq. (1), which skillfully avoids the diffraction directions of these two parasitic diffraction orders, thus forming a well shape of the reradiation pattern, as shown in Fig. 2(b) v. Therefore, by the action of the substrate-air-metal layer and directors, the simultaneous reversions of the z and x direction wave-vectors are achieved, so that on the basis of the determination of the grating element period p−2, the patch antenna reradiation pattern reconfiguration manipulation is realized, so as to eliminate the 0th and −1st diffractions, and obtain the efficient −2nd EOD. Additionally, the phase conservation based on the tangential direction of the metagrating surface in Supplement 1 also verifies the correctness of the theoretical analysis.Note that the scattered waves also obey the wave-vector relation as Eq. (1) when the incident angle θi is smaller than the critical angle θic = 32.15°, and the condition |k0·sin(θr)|≤k0 allows only a propagating 0th diffraction order, i.e., m = 0. Thus, there only exists specular reflection when the incident angle below the critical angle denoted as the green area in Fig. 1. Therefore, in theory, it can be concluded that when the incident angle θi is in the range from 32.15° to 90.0°, the metagrating can achieve −2nd EOD efficiently, and when the incident angle is in the range from 0.0° to 32.15°, only the 0th diffraction exists.
2.2 Realization of 1D and quasi-omnidirectional metagratings
So far, the feasibility of achieving high-efficiency −2nd EOD protected by the patch antenna reciprocity has been theoretically analyzed through choreographing the array element period p and manipulating the patch antenna reradiation pattern simultaneously. To verify this concept, three types of metagratings are designed as follows, two of which are 1D metagratings capable of realizing high-efficiency −2nd EOD in x-z plane, and one is a quasi-omnidirectional metagrating capable of extending the same functionality to the x-z and y-z planes simultaneously.
These three metagrating arrangement forms are shown in Fig. 2(c), two kinds of which are 1D metagrating elements including vertical sequential and longitudinal cross arrangements denoted as insets in Fig. 2(c) i and ii respectively, and the 2D metagrating element is composed of four rotationally-symmetric SPAs as denoted in Fig. 2(c) iii. The three kinds of metagratings are simulated under different incident angles θi = 0.0°, 25.0°, 50.0° and 65.0° respectively with azimuth angle φ=0.0° firstly, utilizing the time-domain solver in CST and boundary conditions in x, y and z directions are set as “open add space”. Their sizes are consistent, all of which are 261.1mm×261.1 mm, and a metal plane with the same area (SAMP) is simulated under the same conditions as comparative data.
Far-field simulated results at 15.0 GHz of the 1D metagrating with vertical sequential arrangement are shown in Fig. 3(a), of which the top panels are curve distributions including the metagrating and SAMP where we can analyze that specific numerical and angle value, and the bottom panels are far-field 3D scatterings which can be intuitive to clearly analyze the status of the diffractions. It can be seen from the simulated results that when the incident angle is smaller than the critical angle θic = 32.15° (incident angles are 0.0°and 25.0° respectively with azimuth angle φ=0.0°), the reflected waves follow specular reflections, and main lobe directions are consistent with the SAMP’s. When the incident angle is larger than the critical angle, it has obvious highly efficiency −2nd EOD. Under the given incident angles of 50.0° and 65.0° with azimuth angle φ=0.0°, the diffraction angles are −49.0° and −38.0° respectively with azimuth angle φ=0.0° from Fig. 3(a) iii and iv, which are very close to the theoretical angles of −50.0° and −38.74° with azimuth angle φ=0.0° calculated according to Eq. (2). In particular, when the incident angle is 50.0° with azimuth angle φ=0°, the retroreflection occurs for the 1D metagrating with vertical sequential arrangement, and the backscattering enhancement value is 29.5 dB relative to the SAMP. The diffraction efficiency can be calculated as Eq. (6) [35].
where $|{{\zeta_{\textrm{MG}}}{\theta_r}} |$ and $|{{\zeta_{\textrm{SAMP}}}{\theta_r}} |$ represent the linear RCSs of the metagrating and SAMP with the same diffraction angle, respectively, under the incident angle θi. From Eq. (6), we can obtain that the −2nd diffraction efficiencies of the 1D metagrating under θi = 50.0° with azimuth angle φ=0.0° are $\zeta _{50}^{1D} = 10\exp (15.7/10)/10\exp (18.2/10) = 56.23\%$. As for another 1D metagrating whose element arranged with longitudinal cross sub-elements, from the simulated results in Fig. 3(b), the diffraction angles under different incident angles θi = 0.0°, 25.0°, 50.0° and 65.0° with azimuth angle φ=0° are θr=−0.0° and −25.0° with azimuth angle φ=180.0°, and −43.0° and −33.0° with azimuth angle φ=0.0°, respectively. It is confirmed that for this metagrating when the incident angle is smaller than the critical angle the diffracted waves will be specular reflected, and when the incident angle is larger than the critical angle it will achieve efficient −2nd diffraction. Similarly, it has an efficient backscattering enhancement effect under the incident angle 50.0°, which is 29.2 dB relative to the metal plane, and the diffraction efficiency is 52.5% calculated by Eq. (6). Due to the 1D metagrating array elements are composed of exactly the same structural units, the −2nd EOD phenomenon has mirror symmetry, that is, when the incident angle is in the quadrant of azimuth angle φ=180.0°, the function is completely consistent with that in the quadrant of azimuth angle φ=0.0°. The 2D metagrating array and its element which consists of four rotationally-symmetric sub-elements are denoted in Fig. 2(c) iii. Theoretically, there is no resonance between metal short lines constituting the element after the rotation due to that they are perpendicular to the incident electric field, resulting in that the 2D metagrating can realize efficient −2nd EOD in the x-z and y-z plane at the same time. Firstly, its 1D performance in x-z plane is verified from the simulated results in Fig. 3(c), from which can be seen that the diffraction angles of the 2D metagrating under the incident angles 0.0°, 25.0°, 50.0° and 65.0° with azimuth angle φ=0.0° are −0.0° and −25.0° with azimuth angle φ=180.0°, and −50.0° and −38.0° with azimuth angle φ=0.0° respectively following the −2nd EOD. Secondly, to further verify its 2D characteristics, the other three incident angles θi = 50.0° with azimuth angle φ=90.0°, 180.0° and 270.0° are simulated, and the results are shown in Fig. 3(e) from which the main lobe diffracted directions are −50.0° with azimuth angle φ=90.0°, 180.0° and 270.0° respectively, varying the highly efficient backscattering enhancement whose average value are 31.4 dB compared with the SAMP in the four quadrants of azimuth zone. Thus, the 2D metagrating expands the efficient −2nd EOD to 2D space, further improves its ability to regulate the reflected EM waves, acting as an extension of the 1D metagrating.Fig. 3. Simulated results at 15.0 GHz. Simulated results of the 1D metagrating with a vertical sequential arrangement, b longitudinal cross arrangement and c 2D RRMG: bistatic RCS curves (top panels) and corresponding far-fields (bottom panels) under incident angle (i) 0.0°, (ii) 25.0°, (iii) 50.0° and (iv) 65.0° respectively with azimuth angle φ=0.0°. d. 3D waterfall diagram of diffraction angles under different incident angles with varies of frequencies. e. Bistatic RCS of the 2D RRMG under incident angle θi = 50.0° with azimuth angles φ= (i) 90.0°, (ii) 180.0° and (iii) 270.0°.
Besides wide-angle domain, being able to achieve an effective role in a broadband is also an important index to judge the performance of a microwave device. In order to more intuitively analyze the change trend of abnormal diffraction angles under different incident angles with varies of frequencies, a 3D waterfall diagram is obtained according to the Eq. (2), as shown in Fig. 3(d), demonstrating that the abnormal diffraction angle decreases with the increase of incident angle or frequency. Selecting another frequency point 15.8 GHz to investigate the EM waves scattering regulation performance of these three designed metagratings, it is instrumental in proving the broadband effect of metagratings. On the other hand, selecting a frequency where abnormal diffraction angles are not exactly consistent with the incident angle is helpful to demonstrate the theoretical method in the experimental measurements. At this time, according to the Eq. (2), abnormal diffraction angles are −43.5° and −33.2° with azimuth angle φ=0.0° respectively under incident angles 50.0° and 65.0° with azimuth angle φ=0.0° which are greater than the critical angle. It can be seen from the far-field simulated results at 15.8 GHz of the 1D metagrating with vertical sequential arrangement, with longitudinal cross sub-elements and 2D metagrating denoted in Fig. 4(a, b) and c respectively where the top panels are curve distributions and the bottom panels are far-field 3D scatterings that when the incident angle is smaller than the critical angle, the reflected waves follow specular reflections. When the incident angle is larger than the critical angle, these three designed metagratings have obvious highly efficiency −2nd EOD and their effects are surprisingly consistent. Under the given incident angles of 50.0° and 65.0° with azimuth angle φ=0.0°, the diffraction angles are −43.0° and −33.0° with azimuth angle φ=0.0° respectively as denoted in iii and iv parts of Fig. 4(a, b) and c respectively, which are very close to the theoretical angles of −43.5° and −33.2° with azimuth angle φ=0.0° calculated according to Eq. (2). According to Eq. (6), the abnormal diffraction efficiencies of the 1D metagrating with vertical sequential arrangement, with longitudinal cross arrangement and 2D metagrating at 15.8 GHz under the incident angle 50.0° with azimuth angle φ=0.0° are 87.1%, 79.4% and 63.1% respectively. To further verify its 2D characteristics of the 2D metagrating at 15.8 GHz, the other three incident angles θi = 50.0° with azimuth angle φ=90.0°, 180.0° and 270.0° are simulated, and the results are shown in Fig. 5(a) from which the main lobe diffracted directions are −43.0° with azimuth angle φ=90.0°, 180.0° and 270.0° respectively, varying the highly efficient backscattering enhancement whose average value are 30.2 dB compared with the SAMP in the four quadrants of azimuth zone.
Fig. 4. Simulated results of 1D and 2D metagratings at 15.8 GHz. Simulated results of the 1D metagrating a with vertical sequential arrangement, b with longitudinal cross arrangement, and c 2D RRMG: bistatic RCS curves (top panels) and corresponding far-fields (bottom panels) under incident angle (i) 0.0°, (ii) 25.0°, (iii) 50.0° and (iv) 65.0° respectively with azimuth angle φ=0.0°.
Fig. 5. Simulated results of the QORM at 15.8 GHz and photos of 1D and 2D metagrating prototypes. a. Bistatic RCS curves (top panels) and corresponding far-fields (bottom panels) for azimuth angles φ= (i) 90.0°, (ii) 180.0° and (iii) 270.0° under incident angle θi = 50.0°. b. Simulated broadband retroreflection results of 1D metagrating with (i) vertical sequential arrangement, (ii) longitudinal cross arrangement, (iii) 2D metagrating and (iv) SAMP under incident angle θi = 50.0° with azimuth angle φ=0.0°. c. Front sides of the protype photos for (i) 1D metagrating with longitudinal cross arrangement and (ii) 2D metagrating, respectively, together with zoom view of the details.
To further analyze the broadband performance of these three designed metagratings in the whole Ku band, the simulated analyses are carried out and the EM effect of the SAMP is also taken as a blank control. From the simulated results under incident angle θi = 50.0° with azimuth angle φ=0.0° in Fig. 5(b), it can be seen that both 1D and 2D metagratings have obvious −2nd EOD effect relative to the metal plane, and they have at least 4.0 GHz bandwidth in Ku band whose relative bandwidth reaches 25.0%. Through the analyses of simulation data, the design concept is verified. The proposed metagratings have well EM waves control abilities, and at the same time the 2D metagrating can realize quasi-omnidirectional efficient −2nd EOD in the 2D space.
3. Experiment
To further verify the correctness of the design concept, as an example, two test samples including the 1D metagrating with longitudinal cross arrangement and 2D metagrating are processed by printed circuit board (PCB) technology, consisting of 10×10 structural elements and the sizes are both 261.1mm×261.1 mm. The processed metagrating samples are made up of a F4B dielectric substrate with a thickness of th1 = 0.75 mm above on a PMI foam mimicking an air layer with thickness th2 = 5.25 mm. In addition to the F4B dielectric substrate and PMI foam, a metal plane with equal area is located at the bottom as a metal ground. The whole measurement process of the reflection coefficient S21 over the measured samples is carried out in the microwave anechoic chamber. The sample and transmitting horn (TA) are fixed on the rotating turntable, and their relative position determines the incident angle θi and azimuth angle φ, while the receiving horn (RA) is placed outside the turntable as shown in Fig. 6(c) iv. With the rotation of the turntable, the distribution of scattered field under different incident angles can be obtained, all measured results are normalized with the data of SAMP. If we choose 15.0 GHz frequency point for test, the diffraction angular distributions of the scattering field at −50.0° with azimuth angle φ=90.0° cannot be precisely measured due to the axial overlapping between the TA and RA. Therefore, we measure the far-field distributions of reflection coefficient S21 at 15.8 GHz to indirectly demonstrate our design, which matches well with the expected results.
Fig. 6. Measured results of 1D and 2D RRMGs. a 1D RRMG and b 2D RRMG bistatic reflection coefficients under incident angle (i) 0.0°, (ii) 25.0°, (iii) 50.0° and (iv) 65.0° with azimuth angle φ=0.0°. c 2D RRMG bistatic reflection coefficients for azimuth angles (i) 90.0°, (ii) 180.0° and (iii) 270.0° under incident angle 50.0°, and (iv) measurement environment in microwave anechoic chamber.
Based on this measurement method, the 1D and 2D metagrating samples are measured under incident angles θi = 0.0°, 25.0°, 50.0° and 65.0° with azimuth angle φ=0.0°. It can be seen from the measured results at 16.0 GHz denoted in Fig. 6(a) that when the incident angle is smaller than the critical angle of θcr = 32.15°, the bistatic reflection coefficient S21 of 1D metagrating is very similar to that of the SAMP. While when the incident angle is in the range of 32.15° to 90.0°, main lobe directions of the diffracted EM waves are −43.0° and −37.0° with azimuth angle φ=0.0° corresponding to the incident angle θi = 50.0° and 65.0° with azimuth angle φ=0.0° respectively, which follows the −2nd EOD diffraction law according to the Eq. (2). In particular, when the incident angle is 50.0° with azimuth angle φ=0.0°, the retroreflection occurs, and the backscattering enhancement is 35.1 dB relative to the metal plane. Utilizing the same method, the measured data of the 2D metagrating at 16.0 GHz are obtained as shown in Fig. 6(b), from which it can be seen that the diffraction angles are −0.0° and −25.0° with azimuth angle φ=180.0°, and −39.0° and −35.0° with azimuth angle φ=0.0° respectively under the incident angle θi = 0.0°, 25.0°, 50.0° and 65.0° with azimuth angle φ=0.0°. Specifically, the backscattering enhancement is 22.1 dB for the 2D metagrating under the incident angle θi = 50.0° with azimuth angle φ=0.0° relative to the SAMP. To further verify the 2D effect of the 2D metagrating, the measured results at 16.0 GHz are obtained under different incident angles θi = 50.0° with azimuth angle φ=90.0°, 180.0° and 270.0° respectively as denoted in Fig. 6(c). It can be clearly concluded that the 2D metagrating has a well −2nd EOD effect in the 2D space of four quadrants in the azimuth domain, and the average backscattering enhancement reaches 27.5 dB compared with the SAMP.
Of course, strictly, there is still a deviation of 0.2 GHz between 16.0 GHz with the best measured effect and expected inspection point 15.8 GHz, which may result from sample error including the permittivity tolerance of the utilized F4B material and the air gap between substrate material and PMI foam and the incident source error. However, this does not fundamentally affect the consistency of our measured data with theoretical analysis and simulation verification.
4. Conclusion
Being able to control EM waves in multi-dimensional within the scope of a broadband and wide incident angle range is pursued by scientists and engineers constantly, this paper proposes a quasi-omnidirectional metagrating which expend the ability to control EM waves in 1D half space of traditional metasurfaces to the 2D half space, implementing efficient −2nd EOD within the wide incident angle domain meanwhile in a broadband. The design process of the QORM mainly includes the control of grating period and the manipulation of SPA reradiation pattern. On the one hand, the structural element period corresponding to the higher diffraction order is designed based on EOD theory; On the other hand, based on the reciprocity of receiving and transmitting EM waves of the patch antenna, the reradiation pattern of the SPA is reconfigured, so that the parasitic diffractions including 0th and −1th orders can be eliminated while realizing efficient −2nd diffraction, so as to improve the efficiency. As an example, we design two kinds of 1D metagratings and one kind of 2D metagrating, and select one kind of 1D and 2D metagratings for processing and measurement verification. On the whole, the simulated and measured results are highly consistent with the theoretical analysis, which well verify the design concept. The design idea we put forward can also be extended to the field of higher frequency, and has potential application value in the miniaturization and integration of THz and even optical frequency devices.
Funding
National Natural Science Foundation of China (51802349, 61801509, 61901508, 61971435, 62101588, 62101589); National Key Research and Development Program of China (2017YFA0700201); Young Talent Support Program of Shaanxi Province University (2021JQ-363); Air Force Engineering University (KGD080920016).
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.
Supplemental document
See Supplement 1 for supporting content.
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