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Abstract
Spoof surface plasmon polariton (SSPP) is kind of sub-wavelength electromagnetic (EM) mode, which is favorable for miniaturization and thinning of EM devices. In this paper, we propose a method of designing thin planar retro-reflector that can operate under multiple incidence angles at the same frequency. The retro-reflector is composed of a transmissive phase gradient metasurface (TPGM) placed above a metallic patch array (MPA), where the former couples and decouples SSPPs while the latter supports eigen-mode propagation of SSPPs. Under oblique incident angles, the TGPM can impart 0 and π Pancharatnam–Berry (P-B) phases alternatively, producing P-B phase gradients along its surface. Incident waves can be coupled as SSPPs propagating on the MPA which will be reflected at the borders of the MPA, thus the wave-vector of SSPPs is reversed. In this way, retro-reflection can be realized under the two incidence angles θ=±45.0°. Moreover, due to mode mismatch between the TPGM and MPA under normal incidence, the retro-reflector acts like a planar metallic plate under θ=0°. To verify this method, a prototype was designed, fabricated and measured. Both the simulation and measurement results verify significant backscattering enhancement under θ=±45.0° and 0° at 10.0 GHz. This work provides an alternative method of designing planar retro-reflectors and may find applications in wireless communication, target tracking, etc.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Backscattering enhancement can be produced when the main lobe of reflected electromagnetic (EM) waves is directed backwards to the source, resulting in enhancement of backward radar cross section (RCS) [1] which is a measure of how detectable an object is by radar. Since backscattering enhancement has important applications in military and civilian fields such as radar target detection, enemy target recognition and marine rescue [2–3], the design of retro-reflectors with excellent backscattering enhancement performances has become attracted great attentions from microwave engineers and has been extensively studied [4–6]. To enhance backscattering, some traditional retro-reflectors were devised, such as corner reflectors [7] and Luneburg lens [8–10]. They usually take up large space due to their bulky volumes. Therefore, their applications to conformal scenarios, such as on the body of aircrafts, are restricted. It is desirable that planar or even conformal curved retro-reflectors be devised. Metasurfaces are 2-D counterpart of metamaterials and has provided unprecedented freedom in manipulating EM waves upon thin surfaces [11]. Recent years have witnessed the rapid progresses in manipulating EM scatterings using metasurfaces [12–16]. In particular, many planar metasurfaces have been proposed for the sake of backscattering enhancement. [17–18] Amir Arbabi et al. propose a kind of cascaded metasurface, each performing a predefined mathematical transformation, provide a new optical design framework that enables new functionalities not yet demonstrated with single metasurfaces. [19] With the increase of incident angle, Ref. 19 provides a successful case of continuous angle change. Wong et al. proposed a planar retro-reflector with only two discretized cells based on Huygens’ metasurface, which achieves retro-reflection with 94.0% power efficiency under 82.87° for TE-polarized waves [20–21]. Memarian et al. [22] designed reflective blazed surfaces using a multiple of coupled blazing resonance cells, which can achieve retro-reflection under different incident angles. Nevertheless, the multichannel retro-reflections are achieved at different frequencies, rather than at the same frequency. It is desirable to achieve multichannel retro-reflection at the same frequency.
In this paper, we propose a planar multi-incident angle retro-reflector (MRR) based on the coupling-decoupling of SSPP using metasurface, which can achieve retro-reflection at two symmetrical directions and vertical incidence, all at the same frequency. Using metasurfaces, SSPP can be excited efficiently at GHz frequencies [23–26]. Chen et al. proposed a broadband SSPP coupler based on a transmissive metasurfaces, which can enable SSPP excitation and transmission with high efficiency in 7.0-9.90 GHz. In addition, a wideband SSPP planar antenna was designed and can achieve wideband frequency scanning characteristics owning to the nonlinear dispersion relation of SSPP [27]. Therefore, metasurfaces can be used to excite and decouple SSPP efficiently, which provides a new means of manipulating EM waves on planar surfaces.
Inspired by this, we propose the planar MRR configuration as shown in Fig. 1. The incident and reflected beams in green, red and purple colors in Fig. 1 represent that the MRR can achieve backscattering enhancement under three different incident angles at the same frequency. The sub-cells in Figs. 1(b) and 1(c) represent the wave vector directions and their values provided by the MRR under different oblique incident angles. The details are elaborated in Section 2 part. The planar MRR consists of a transmissive phase gradient metasurface (TPGM) placed above a metallic patch array (MPA). To enable retro-reflection at both +θ and -θ directions, spatial symmetry of the PGM has to be maintained. Under this consideration, the alternative 0-π-0 phase profile is designed on the TPGM plane based on P-B phase. Under oblique incidence, the transmitted waves can be split into two branches of evanescent waves (EWs) with different wave-vectors by the TPGM, according to momentum conservation. A MPA is put below the TPGM. By wave-vector matching, one of the two branches can be coupled as SSPPs on the MPA whereas the other one cannot due to mode-mismatch. For the SSPP propagating on the MPA, the TPGM can also acts as a de-coupler due to reciprocity. Due to the phase gradients added by the TPGM, the decoupled waves possess an anti-parallel in-plane wave-vector with the same magnitude as that of incident waves. In this way, SSPP can be decoupled as retro-reflected waves towards the source. Since such a MRR configuration can operate only for SSPP with reversed propagation direction, parts of the incident EM energy can be retro-reflected and the retro-reflection is always accompanied by specular reflection. That is to say, to achieve retro-reflection at the two symmetrical channels at both +θ and –θ directions, the retro-reflection efficiency has to be sacrificed. As for normal incidence (θ=0°), the wave-vectors of both the two branches mismatch the MPA, all the incident waves are reflected normally. In this way, the MRR can achieve retro-reflection under +θ and -θ, together with total retro-reflection under normal incidence. Therefore, the MRR can realize retro-reflection at three incident angles at the same frequency. As an example, a prototype was designed, simulated and measured. Both simulation and measurement results show that the prototype can achieve retro-reflection at θ=+45.0°, -45.0° and 0°, all at 10.0 GHz, which convincingly verifies our method.
Fig. 1. Schematic illustration of the design principle of the MRR: (a) the MRR can achieve retro-reflection under three different incident angles at the same frequency; wave vector directions and their values provided by the MRR under incident angle (b) 45.0° and (c) -45.0°.
This paper is structured as follows. Section 2 presents the design mentality of the MRR which consists of a TPGM and an MPA. Section 3 and 4 validates results with simulation and measurement respectively. Conclusions are given in Section 5.
2. Design
The MRR consists of a TPGM and an MPA. The former acts as a transparent window that can impart large in-plane wave-vector to transmitted waves and can split transmitted waves into two branches, whereas the latter act as a mode matcher that can couple one branch of transmitted waves as SSPP mode. The MRR design includes the designs of TPGM, MPA and the combined MRR. In order to prevent confusion, the two coordinate systems (xyz and uvw) involved in this paper are shown in Fig. 1, and the -u direction is specified as the positive direction.
2.1 Design of the TPGM
When y-polarized plane waves are obliquely incident on TPGM at angle θ, the parallel wave-vector along TPGM surface should be conserved, that is,
where k0 is the free-space wave-vector, and ξ=dΦ/dx=2π/L denotes the in-plane wave-vector imparted by TPGM. The propagation direction of transmitted waves can be controlled by designing the P-B phase profile on the TPGM, and the refraction angle isThe transmitted waves “disappear” when θr≥90.0°. That is, the incident waves are coupled as EWs due to the large in-plane phase gradient imparted by the TPGM.
Figures 2(a) and 2(b) show, respectively, the perspective views and structural parameters of the TPGM sub-cell: the top and the bottom layers are two mutually orthogonal metallic gratings. The double arrow structure which is surrounded by F4B dielectric layers (dielectric constant ɛr=2.65, loss tangent tanδ=0.001, thickness h=4.0 mm), as the middle layer, is a double-head arrow structure. The two metallic gratings form a Fabry-Perot-like cavity, illustrated as in Fig. 2(f), which will improve the cross-polarization conversion of the double-head arrow structure significantly. The double-head arrow structure is adopted to improve the transmission of incident EM waves instead of obtaining cross-polarized EM waves merely, reducing the EM waves scattering and loss caused by impedance mismatch between the air and dielectric surface, so as to improve the overall retro-reflection efficiency of the MRR.
Fig. 2. Electromagnetic responses of the sub-cell of the TPGM: (a) Perspective views of the sub-cell; (b) Structural parameters of the sub-cell: p=8.0 mm, w=0.20 mm, l=9.0 mm, d=6.0 mm, h=4.0 mm, g=0.20 mm, s=2.67 mm; (c) Simulated reflection and transmission of sub-cell 1; Cross-polarized transmission (d) and transmission phase (e) of sub-cell 1 and -2; (f) The Fabry-Perot-like cavity formed by the two metallic grating under oblique incidence.
The super-cell of TPGM consists of two sub-cells, i.e. n=2, therefore the phase step is Δφ=2π/n=π. The only difference between the two super-cell is the direction of the double-head arrow. That is to say, the two double-head arrows are mutually orthogonal to each other, leading to a π phase shift of P-B phase [5,16]. When y-polarized waves are incident on the TPGM at the angle θ=45.0°, plus the wave-vector imparted by the TPGM ξ=2π/np=2π/L=392.70m-1, the wave-vector of EWs is thus ksw=ξ−k0sinθi=244.6m-1 at 10.0 GHz. Numerical simulations were carried out using the frequency-domain solver in CST Microwave Studio with Unit Cell boundaries in x and y directions and Open Add Space in z direction, and the incident angle is θ=45.0°. The simulated results are plotted in Figs. 2(d) and 2(e), which show that the cross-polarization transmission near 10.0 GHz is very high, above 94.0%, and that the phase difference is |-311.62−(-131.74)|=179.88°≈180°, which is consistent with the design principle. Due to the alternative 0-π-0 P-B phase arrangements on the TPGM plane, the TPGM can impart to the incident waves two wave-vectors with the same magnitude but opposite directions. Thus, the transmitted modes are divided into two branches after passing through the TPGM, the magnitudes of in-plane wave-vectors of the two branches are, respectively,
Due to the two branches of transmitted modes are both EWs, it is necessary to design an SSPP coupler to realize impedance matching and transform evanescent waves into surface waves (SWs). The part 2.2 is going to state the design process in detail.
2.2 Design of the SSPP coupler
To couple the evanescent mode as eigenmode SSPP, we designed the SSPP coupler as illustrated in Fig. 3(d). The red solid line in Fig. 3(a) presents the dispersion diagram of the unit cell of the MPA calculated by the eigen-mode solver in CST Microwave Studio. Since the dispersion curve of one EM mode (in this paper, we choose Mode 1) coincides with the SSPP on the MPA at 10.0 GHz, the corresponding branch of the two EWs is coupled as SSPP mode on the MPA, as illustrated in Fig. 3(f). In contrast, the other branch (Mode 2) generated by the TPGM is with much larger wave-vector, which mismatches the underlying MPA and cannot be coupled as SSPP modes. The MPA couples the Mode-1 EWs generated by TPGM as eigenmode SSPP due to wave-vector matching. That is, the wave-vector ksspp on the MPA is approximately equal to the wave-vector ksw of Mode-1, i.e. ksspp≈ksw. By adjusting parameters of the MPA’s sub-cells, we can realize wave-vector matching,
By changing the side length a and the F4B thickness b, the dispersion curves of ksspp and ksw can intersect at 10.0 GHz and the corresponding wave-vector satisfy the condition ksspp≈ksw = 244.60m-1, as denoted in Fig. 3(a). In this way, incident EM waves can be coupled as SSPP mode on the MPA. On this foundation, if the SSPP can be decoupled along the incident direction, the backscattering enhancement can be realized, which is described in Section 2.3Fig. 3. Simulation results of the TPGM with and without the MPA coupler: (a) simulated dispersion curves of SSPP and the MPA; (b) unit cell of the MPA, where the geometrical parameters are: p=8.0 mm, a=5.60 mm, b=2.50 mm; Schematic diagrams of the TPGM without (c) and with (d) the MPA coupler; Simulated power flows of the TPGM without (e) and with (f) the MPA coupler at 10.0 GHz.
2.3 Design of the MRR
Free space waves can be coupled as eigenmode SSPPs utilizing the TPGM-MPA structure. Reversely, for SSPPs with reversed propagation direction, they can also be decoupled as spatial waves using metasurfaces [28]. Therefore, it is very important to reverse the propagation direction of SSPPs on the MPA in order to decouple SSPPs as spatial waves. Fortunately, the finite size of the MRR provides possibilities of reversing SSPPs since the MRR borders are abrupt changes both electrically and physically. Such abrupt changes on the borders will usually result in strong reflections of SSPPs on the MPA and therefore will reverse the propagation direction of SSPPs.
Since the TPGM can impart both ξ and –ξ to EM waves passing through it, two decoupling processes occurs within the MRR. In the first decoupling process, the TPGM imparts ξ to backward SSPPs reflected from the borders of the MPA. According to momentum conservation, we have
where “−” means that the propagation direction of ksspp is reversed on the MPA due to reflection on the borders, and θr represents the radiated angles of the decoupled SSPP. Substitute (4) into (5), we can obtain that the radiated angle of decoupled SSPP isThat is, the backward SSPPs reflected from the borders can be decoupled as retro-reflected waves towards the source, achieving backscattering enhancement.
In the second decoupling process, the TPGM impart -ξ to the forward SSPPs and the latter is then decoupled as reflected waves that obey conventional reflection laws. In this decoupling process, we have
and we can obtain the reflection angle asThis means that the retro-reflection is always accompanied by specular reflection and the retro-reflection efficiency cannot be perfect. Nevertheless, thanks to the symmetry, this MRR can achieve the same retro-reflection under incident angle θ=-45.0°.
As for normal incidence, both two evanescent modes passing through the TPGM mismatch the MPA and hence the EWs cannot be coupled as SSPPs. EM waves are reflected normally, along the normal direction of the MRR, just as a metallic plate does. Therefore, the MRR can achieve retro-reflection along three incident angles, that are, θ=±45.0° and 0°.
3. Simulation
To verify the design method, a finite area TPGM (288.0mm×96.0 mm) without a MPA is simulated using the time-domain solver in CST Microwave Studio, with Open Add Space boundaries in x, y and z directions. The simulated energy flows in Fig. 3(e) show that, incident waves are mostly reflected and quite few are coupled as SWs without the MPA. To give an intuitive illustration of the SSPP coupling effect, an SSPP coupler composed of a finite area TPGM (96.0mm×96.0 mm) and a finite area MPA (288.0mm×96.0 mm) are also simulated. The distance between the TPGM and MPA is hc=8.0 mm. The simulation setup is the same as the TPGM, as denoted in Fig. 3(d). The energy flow in Fig. 3(f) shows that, with the MPA, most of y-polarized incident waves are coupled as eigenmode SSPPs propagating on the MPA, and only few scatterings occur. Therefore, the above simulated results denote that the TPGM-MPA structure can efficiently couple the incident EM waves as eigenmode SWs.
The MRR is composed of a finite area (400.0mm× 400.0 mm) TPGM located hc=8.0 mm above an MPA with the same area (also 400.0mm× 400.0 mm). Besides, to reverse the propagation direction of SSPPs on the borders, two metal sheets with a width of 400.0 mm, a height of hq=hc+h + d=14.50 mm and a thickness of 0.017 mm are added to both ends of the MRR, so as to produce wave-vector-reversed SSPPs for the sake generating retro-reflection. The simulated electric field and energy flow results in Figs. 4(a-1), 4(b-1) and 4(a-2), 4(b-2) for θ=45° and -45° show that, most incident waves are coupled as eigenmode SSPPs along the MPA, and then are decoupled as spatial waves due to the phase gradients imparted by the TPGM. Simulation results under normal incidence in Figs. 4(a-3) and 4(b-3) show that EM waves pass through the TPGM and are reflected by the metal plate, obeying conventional reflection laws.
Fig. 4. Simulation results of the MRR at 10.0 GHz under incident angle (a-1)-(e-1) θ=45.0°, (a-2)-(e-2) θ=-45.0° and (a-3)-(e-3) θ=0°: (a-1)-(a-3) Ey and (b-1)-(b-3) power flow distributions; (c-1)-(c-3) Backward RCS and (d-1)-(d-3) far fields polar plots of the MRR and metal plate; (e-1)-(e-3) 3D effect diagrams of far fields
To analyze the backscattering enhancement effect of the MRR quantitatively, the backward RCS was also simulated. Besides, two kinds of metal plates were also simulated for reference. One metal plate is with the same area as the MRR. The other metal plate is with the projection area (400.0×cos(45.0°)×400.0mm2) of the MRR on x-o-y plane, whose simulation results are denoted as solid black lines with triangular shape in Figs. 4(c-1) and 4(c-2). The angle between the metal plate and x-o-y plane is defined as θ. Simulation results for θ=45.0° and -45.0° are plotted in Figs. 4(c-1) and 4(c-2). It can be found that the backward RCS of MRR reaches the peak value of 17.98dBm2 and 18.01dBm2 at 10.0 GHz for θ=+45.0° and -45.0°, respectively. The backscattering enhancement is 27.57 dB and 27.60 dB, respectively compared with the metal plate with the same area under ±45.0°incident angles (RCS=-9.59dBm2). The bistatic RCS diagrams in Figs. 4(d-1) and 4(d-2) show that the RCS at the specular reflected direction of the MRR is, respectively, 13.64dBm2 and 13.54dBm2 under θ=45.0° and -45.0°, with reductions by 9.12 dB and 9.22 dB respectively compared with that of a bare metal plate (22.76dBm2). For the case of normal incidence, the simulated results in Fig. 4(c-3) and 4(d-3) show that, the backward RCS of the MRR is 25.60dBm2 at 10.0 GHz, very close to that of a bare metal plate (25.73dBm2). Figures 4(e-1)–4(e-3) show the far-field diagram of simulated RCS under incident angle 45.0°, -45.0° and vertical incidence respectively, which can more intuitively observe the effect of backscattering enhancement from MRR.
In order to further describe the backscattering enhancement effect of the MRR, the operation efficiency for the cases of θ=45.0°, -45.0°, and 0° can be calculated using the formula below [29].
For example, ζ45=10^(17.98/10)/ 10^(22.76/10) = 33.27%. The calculation method is the same in the case of -45.0° incident angle and vertical incidence. Thus, using Eq. (9), backscattering enhancement efficiencies of the MMR at 10.0 GHz for θ=45.0°, -45.0°, and 0° are ζ s 45≈33.27%, ζ s -45≈33.50%, and ζ s 0≈84.53%, respectively.
4. Experiment
To further verify the method, a finite area prototype (with an area of 400.0×400.0mm2) was fabricated and measured. The fabricated prototype denoted in Fig. 8(a) and 8(b) is fabrication by printed circuit board (PCB) technology. The measurements consist of two parts: retro-reflectivity and backward RCS, both utilizing X-band horn antennas in microwave anechoic chamber as denoted in Fig. 5 and Fig. 8(c). Besides, the horn antennas are fixed and the prototype is rotated to measure the MRR’s retro-reflectivity under oblique incident angles.
Fig. 5. Schematic illustration of the experimental setup: (a) a metal plate with the projection area utilized for the sake of normalization; (b) MRR measurement
As for the measurement of retro-reflectivity, a metal plate with the projection area of the MRR (400.0×cos(45.0°)×400.0mm2) is firstly measured for the sake of normalization as denoted in Fig. 5(a). After that, the reflectivity under different incident angles is measured by rotating the position of the MRR and keeping the horn antennas unchanged as denoted in Fig. 5(b). The measured results of retro-reflectivity under different incident angles are shown in Fig. 6, where the red lines represent reflectivity of the MRR while the blue lines represent reflectivity of the metallic plate with the same area under oblique incident angles. The measured results in Figs. 6(b) and 6(e) show that the retro-reflectivity reach a peak -8.64 dB and -8.72 dB at 10.0 GHz for θ=45.0° and -45.0°, respectively; and the backscattering enhancements are 21.20 dB and 17.27 dB respectively compared with the metal plate with the same area (-29.84dBm2 and -25.94dBm2). Besides, the bandwidths of the enhancements over 10.0 dB both exceed 1.0 GHz. To further investigate the sensitivity of the MRR to incident angles, the retro-reflectivity under nearby angles ±35.0° as denoted in Figs. 6(a) and 6(c) and ±55.0° as denoted in Figs. 6(d) and 6(f) was also measured. It can be found that when the angle deviation is ±10.0°, the enhancement effect still exists but is generally lower than that under the designed angles.
Fig. 6. Measured results of retro-reflectivity under different incident angles (a) θ=+35.0°, (b) θ=+45.0°, (c) θ=+55.0°, (d) θ=-35.0°, (e) θ=-45.0°, (f) θ=-55.0°, (g) θ=+10.0°, (h) θ=+0.0°, and (i) θ=-10.0° respectively
As for normal incidence, a metal plate with an area of 400.0×400.0mm2 was measured for normalization. The results in Fig. 6(h) show that the retro-reflectivity of the MRR is very close to that of the metal plate. Similarly, the retro-reflectivity under two more incident angles was also measured. The results indicate that the MRR is not so sensitive to incident angles when the angle deviation is ±10.0° as denoted in Fig. 6(g) and 6(i).
Both simulation and measured results show that the MRR proposed in this paper can enhance the backscattering relative to the metal plate with the same area under incident angle θ=±45.0° and normal incidence, while the MRR could not exceed the backscattering intensity of the metal plate with the projected area of the MRR’s under normal incidence forever. Thus, to compare the simulation results with the measured results, the backscattering reduction of the MRR relative to the projected area metal plate is taken as the judgment index. Specifically, the backscattering reduction of the simulation result is the reduction of the MRR relative to the projected area of the metal plate. As for measured results, du to a metal plate with the projection area of the MRR (400.0×cos(45.0°)×400.0mm2) is firstly measured for the sake of normalization, thus, the measured results in Fig. 6 are the backscattering reduction of the MRR relative to the projected area metal plate. The simulation and measured backscattering reduction results of the MRR relative to the metal plate with the projection area of the MRR under different incident angle are denoted in Fig. 7. The comparison between the simulation and measured results show that the two profiles have good consistency, no matter in the case of incident angle 45.0°, -45.0° or vertical incidence. Therefore, the theoretical analysis is convincing.
Fig. 7. The simulation and measured backscattering reduction results of the MRR relative to the metal plate with the projection area of the MRR under different incident angle (a) θ=45.0°, (b) θ=-45.0° and (c) θ=0°
As for RCS measurement, the RCS results under continuous angle are obtained by rotating the sample with fixed positions of two horn antennas as denoted in Fig. 8(c). The measured backward RCS results in Fig. 8(d) indicate that the three incident angles for backward RCS enhancement peaks are 43.40°, -43.0° and 0°, and that the backscattering enhancement is 25.37 dB and 28.76 dB under the two oblique incidence angles respectively, compared with theoretically calculated values of a metal plate with the same area. Besides, the maximum RCS of the MRR is very close to the theoretical calculation and the difference between them is only 1.50 dB. The backward RCS enhancements of the MRR demonstrate the consistency between simulation and measurement results, which convincingly verifies the design method of MRR.
Fig. 8. (a) the prototype, (b) specific dimensions of the prototype, (c) schematic illustration of the backward RCS measurement setup and (d) the result
5. Conclusion
In conclusion, we propose and verify an alternative method of designing a thin planar retro-reflector that can operate under multiple incidence angles at the same frequency. A TPGM based on P-B phase is adopted to couple incident waves as evanescent modes with large wave-vectors imparted by the TPGM and an MPA layer is utilized to couple the matched evanescent mode as SSPP modes propagating on the surface of MPA. To enable retro-reflection at two symmetrical oblique incidence angles, the 0-π phase arrangement is adopted on the TPGM plane, which can impart anti-parallel wave-vectors with the same amplitude while opposite directions to EM waves passing through the TPGM. To reverse the wave-vector of SSPP modes on the MPA, two metallic sheets are added on borders of the MRR. In the way, the reversed SSPPs can be decoupled as retro-reflected waves. Therefore, the MRR can achieve retro-reflection at two symmetrical oblique incidence angles. Moreover, due to mode mismatch, the MRR can also achieve retro-reflection under normal incidence. In all, the MRR can realize retro-reflection in three incident angles. This work provides an alternative method for designing multi-incident angle retro-reflectors and can be extended to the design of retro-reflectors with higher performances such as wide-angle and wideband.
Funding
National Key Research and Development Program of China (SQ2017YFA0700201); National Natural Science Foundation of China (61601507, 61671466, 61671467, 61801509, 61901508, 61971435, 61971437).
Disclosures
The authors declare no conflicts of interest.
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