Abstract
1. INTRODUCTION
Guiding of electromagnetic waves in a desired direction has captured the interest of researchers in both academic and engineering communities [1–4]. Metasurfaces, consisting of meticulously arranged sub-wavelength resonators, are examined to push the development of electromagnetic manipulation [2] and extensively applied to obtain unique phenomena such as anomalous reflection/refraction [5–7], vortex beam generation [8,9], beam splitting [10–12], and cloaking [13], among others, owing to their advantages of negligible thickness and high in-plane flexibility. In particular, the study of tailoring circularly polarized waves based on a metasurface platform prevents the bulky size of traditional optical devices. Thus, metasurfaces were widely utilized in the fields of polarimetry [14], circular polarizers [15], and spin-to-orbital converters [16,17]. However, because of the innate phase difference between distinct spin states, inverse phase profile flipping is acquired by shifting the polarization state of the incident waves. For example, wavefronts equivalent to convex and concave lenses can be achieved by spatial parabolic phase distribution under normal incidence of left-handed circularly polarized (LHCP)/right-handed circularly polarized (RHCP) waves and RHCP (LHCP) waves [18], respectively. With the help of the Pancharatnam–Berry phases, a large number of anisotropic and chiral metasurfaces are used to design spin-dependent meta-devices with distinct phase profiles [19–21]. Nevertheless, the manipulation of circularly polarized waves is not limited to this aspect. The immense potential in spin-selective techniques lies in chiral structures.
Chirality is a concept originating in biochemistry that is nearly omnipresent in nature and refers to a structure lacking a mirror symmetry plane [22]. In the context of microwave and optics regimes, chirality represents a series of unusual chiroptical responses that are significant in the fields of physics and material sciences [23–25], one such being circular dichroism. Owing to the characteristic of differential absorption of distinct spin states, circular dichroism provides an auxiliary degree of freedom for tailoring circularly polarized waves with designated spin states [26–28]. Unfortunately, it is not easily observed in nature owing to a mismatch between the scale of molecules and wavelength of incident light that considerably limits its practical applications in engineering [29].
Circular dichroism can be theoretically demonstrated via metasurfaces in an arbitrary span of frequency ranging from the microwave to visible domain because of the deep sub-wavelength scale of meta-atoms or unit cells [30]. The methods of applying chiral nanoantenna [31,32], achiral oriented arrays [33], and multi-layered structures [34] are studied in optics and terahertz domains. Some investigations were conducted in the microwave frequency range as well, such as asymmetric split-ring resonators [35] and double-ring unit cells [22]. However, the mechanism in these works is governed by the symmetry-breaking substrate effect; thus the resulting circular dichroism was relatively weak. It is noticed that the conspicuous circular dichroism is significant for multi-dimensional electromagnetic manipulation in spin-selective systems, but research on this issue is still in the nascent stage.
Sign up for Photonics Research TOC. Get the latest issue of Photonics Research delivered right to you!Sign up now
In this work, we propose a paradigm for exhibiting distinct circular dichroism and shaping spin-selective wavefronts to push the development on this aspect. Ohmic dissipation into the two-dimensional (2D) structures is introduced to enhance the chiroptical responses. Two lumped resistors of 200 Ω each are loaded in an N-shaped chiral resonator that serves as the meta-atom of our design. Consequently, the Pancharatnam–Berry phases are combined with the spin-selective amplitude flipping from nearly 0 and 1 for distinct circular polarization states. As a proof-of-concept, we fabricate a planar dihedral corner reflector that achieves retro-reflection and absorption for RHCP and LHCP waves, respectively. The enhancement and reduction of the radar cross section (RCS) are simultaneously achieved by flipping the circular polarization states. Numerical simulations, as well as experimental measurements, are performed to verify the feasibility of the proposed paradigm.
2. DESIGN AND RESULTS
Figure 1.Conceptual illustration of the proposed corner reflector. The functionality of retro-reflection for RCS enhancement and absorption for RCS reduction is achieved by flipping the polarization states of RHCP and LHCP waves, respectively.
To validate the operating principle of our design and explain it in detail, the underlying mechanism of achieving circular dichroism is analyzed by the Jones matrix. We assume that a circularly polarized wave of normal incidence propagates along the direction and impinges on a desired reflective metasurface, of which the transmission amplitude can be regarded as 0. The electric field in the reflection region can be decomposed into two linearly polarized components in orthogonal directions [36]:
Figure 2.(a) Topological structure of the proposed chiral meta-atom, (b) surface current distribution under the illumination of LHCP and RHCP waves, (c) co- and cross-polarization amplitudes
To further elaborate the operating mechanism of the proposed meta-atom, the surface current is monitored by the computer simulation technology (CST) microwave studio. In the simulation, the boundary conditions along the and directions are set as the “unit cell” and two Floquet ports are fixed along the directions. The surface current distributions at 20 GHz under the illumination of LHCP and RHCP waves are shown in Fig. 2(b). When circularly polarized waves are incident, the surface current is excited along the metallic resonator structure in a spin-selective manner; it was substantially suppressed when the LHCP waves impinged on the meta-atom, whereas it was highly enhanced under the illumination of RHCP waves. Therefore, it is inferred that different resonances are achieved under distinct polarization states, and this is attributed to the spin-selective ohmic dissipation introduced by the lumped resistors (circular dichroism is presented in Appendix B). The reflection amplitude of the meta-atom [Fig. 2(c)] shows the effect of differential absorption. Under normal incidence of the circularly polarized waves, the co-polarization reflection coefficient is at 13–27 GHz, whereas was in the same frequency band. The cross-polarization reflection coefficients and are both . In addition, the reflection characteristics for oblique incidence are discussed in Appendix B. It is indicated that the spin state of the RHCP reflection is converted with high efficiency, but the reflection of the LHCP wave is suppressed. In contrast to the metal plane, the proposed meta-atom can convert the spin states and preserve the handedness of the reflected waves. Thus, it is concluded that the proposed meta-atom is governed by the Pancharatnam–Berry phase (, where “+” and “−” represent RHCP and LHCP waves, respectively). Figure 2(d) illustrates the phase responses of the proposed meta-atom under the incidence of RHCP waves. A phase difference of approximately 60° is obtained at 18–30 GHz when the pivoting angle increases from 0° to 150° with an interval of 30°. Hence, the arbitrary forms of phase distribution can be theoretically acquired by meticulously aligning the meta-atoms owing to the high flexibility of phase manipulation.
Considering the preservation of handedness of the reflected waves and Pancharatnam–Berry phase of the proposed meta-atom, we design the planar dihedral corner reflector to achieve retro-reflection/absorption followed by the enhancement/reduction of the RCS. To achieve retro-reflection, an appropriate phase gradient is required. Therefore, we implement the generalized Snell’s law [1]. When a flat metasurface is illuminated by a plane wave at an elevation angle of and azimuthal angle of , the direction of the reflected wave is calculated by [37]
In accordance with Eq. (5), a dihedral corner reflector consisting of two parts with reverse phase gradients is proposed. The operating frequency is set at 20 GHz, and phase shift of each adjacent meta-atom was fixed as 94°. Consequently, retro-reflection is achieved when RHCP waves illuminated the corner reflector at an incident angle of . Hence, mono-static RCS enhancement is achieved in the angle ranges of . Owing to the effect of differential absorption, the reflection amplitude is nearly 0 when the polarization state flips to left-handed circular polarization. Thus, the effect of the phase gradient is inconspicuous, which infers an omnidirectional RCS reduction.
Figure 3.(a) Phase distribution of the proposed planar corner reflector, (b) schematic of the arrangement of meta-atoms in the designed corner reflector, (c) 3D far-field patterns under the illumination of RHCP and LHCP waves at an incident angle of 22° at 20 GHz, (d) normalized 2D far-field patterns in the cutting-plane of
Figure 4.(a) Simulated 3D far-field patterns under normal incidence of RHCP and LHCP waves at 20 GHz, (b) monitored electric field of
Moreover, the performance of mono-static RCS is simulated. The RCS curves in the cutting-plane of the -plane with the elevation angle ranging from to 40° are presented in Fig. 4(d). In contrast to the metallic sheet of the same scale, a distinct enhancement in the RCS is achieved in a wide angular range in the regions of approximately under the incidence of RHCP waves. The maximum value of RCS enhancement is 25 dB relative to the metallic sheet. According to the analysis, the mono-static RCS of LHCP waves is sharply reduced due to the circular dichroitic effect. The simulation results show that the RCS reduction is for normal incidence. In addition, there are two small rises around the elevation angle of attributed to a slight imperfection in the absorption of the LHCP wave.
Figure 5.(a) Photograph of the fabricated metasurface prototype with the inset showing the meta-atoms, and (b) measured mono-static RCS under the illumination of RHCP and LHCP waves at 20 GHz. The mono-static RCS of a metallic sheet of the same size as the proposed metasurface is shown for comparison.
The measured mono-static RCSs of the proposed corner reflector at 20 GHz and a metallic sheet of the same size under the illumination of RHCP and LHCP waves are compared and shown in Fig. 5(b). For the metallic sheet, the energy is concentrated in the backward direction owing to specular reflection. The maximum value of RCS occurs at nearly 0° but is weak in the other angular domains. In sharp contrast, the RCS curve of the proposed corner reflector shows two distinct peaks at under the incidence of RHCP waves, demonstrating the considerable RCS enhancement within this range. On the other hand, no distinct peak appears on the RCS curve when illuminated by LHCP waves. Moreover, the RCS in the range of elevation angle from to 40° is , indicating that nearly omnidirectional RCS reduction is achieved. The measured results are in accordance with those obtained in the simulations, verifying the feasibility of our method. The slight deviations between the measured and simulated results can be attributed to the uncertainty in the welding of the resistors and unavoidable interference in the experimental environment.
3. CONCLUSIONS
In summary, we proposed a paradigm of tailoring circularly polarized waves in a dichroitic manner. A meta-atom that exhibits distinct circular dichroism is attained by introducing ohmic dissipation of a 2D chiral resonator through loading lumped resistors. Owing to the spin conversion characteristics of the meta-atom, a flexible manipulation of phase gradient is achieved by applying the Pancharatnam–Berry phase. The arbitrary form of the phase profile can be theoretically acquired for the designated circular polarization state. A dihedral corner reflector with symmetric phase gradients with respect to the -plane is designed as a proof-of-concept. The simulation and measurement are conducted in the microwave regime that effectively demonstrates the feasibility of our method and manifestation of mono-static RCS enhancement/reduction for RHCP/LHCP waves. Significantly, the proposed paradigm provides an alternative approach to design spin-selective meta-devices with an auxiliary dimension for tailoring electromagnetic waves that is suitable in circular polarization systems and radar/communication applications.
APPENDIX A: UNDERLYING MECHANISM OF ACHIEVING CIRCULAR DICHROISM
The cases of rotation and mirror symmetry are discussed as follows.
First, we consider the case of rotational symmetry. By rotating a chiral structure through an arbitrary angle, the new reflection matrix can be further explained by matrix transformation of rotation [
Next, suppose the mirror symmetry plane of a symmetric structure is rotated from the -plane through a rotational angle of with respect to the -axis. Accordingly, the reflection matrix is expressed as
Therefore, to achieve the circular dichroitic effect, it is necessary to simultaneously break the -fold rotational () and mirror symmetries [
APPENDIX B: CIRCULAR DICHROISM IN THE PROPOSED N-SHAPED META-ATOM
The curves of absorption of the RHCP/LHCP waves and corresponding circular dichroism are presented in Fig.?
Figure 6.(a) Curves of absorption and circular dichroism of the proposed N-shaped meta-atom, (b) curves of circular dichroism when the resistance increases from 40 Ω to 160 Ω, (c) co-polarization amplitudes
Figure?
APPENDIX C: EXPERIMENTAL SETUP
A photograph of the experimental setup for the measurement of the RCS is shown in Fig.?
Figure 7.Photograph of the experimental setup for the RCS measurement.
References
[1] N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, Z. Gaburro. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science, 334, 333-337(2011).
[2] N. Yu, F. Capasso. Flat optics with designer metasurfaces. Nat. Mater., 13, 139-150(2014).
[3] S. Chen, Z. Li, W. Liu, H. Cheng, J. Tian. From single-dimensional to multidimensional manipulation of optical waves with metasurfaces. Adv. Mater., 31, 1802458(2019).
[4] Q. Ma, T. J. Cui. Information metamaterials: bridging the physical world and digital world. PhotoniX, 1, 1(2020).
[5] S. Sun, K. Yang, C. Wang, T. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. Kung, G. Guo, L. Zhou, D. P. Tsai. High-efficiency broadband anomalous reflection by gradient meta-surfaces. Nano Lett., 12, 6223-6229(2012).
[6] Z. Li, E. Palacios, S. Butun, K. Aydin. Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting. Nano Lett., 15, 1615-1621(2015).
[7] N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, H. Chen. Terahertz metamaterials for linear polarization conversion and anomalous refraction. Science, 340, 1304-1307(2013).
[8] S. Yu, L. Li, G. Shi, C. Zhu, Y. Shi. Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain. Appl. Phys. Lett., 108, 241901(2016).
[9] Y. Bao, J. Ni, C. Qiu. A minimalist single-layer metasurface for arbitrary and full control of vector vortex beams. Adv. Mater., 32, 1905659(2019).
[10] T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, Q. Cheng. Coding metamaterials, digital metamaterials and programmable metamaterials. Light Sci. Appl., 3, e218(2014).
[11] T. Cui, S. Liu, L. Li. Information entropy of coding metasurface. Light Sci. Appl., 5, e16172(2016).
[12] H. Xu, L. Zhang, Y. Kim, G. Wang, X. Zhang, Y. Sun, X. Ling, H. Liu, Z. Chen, C. Qiu. Wavenumber-splitting metasurfaces achieve multichannel diffusive invisibility. Adv. Opt. Mater., 6, 1800010(2018).
[13] Z. H. Jiang, P. E. Sieber, L. Kang, D. H. Werner. Restoring intrinsic properties of electromagnetic radiators using ultralightweight integrated metasurface cloaks. Adv. Funct. Mater., 25, 4708-4716(2015).
[14] A. Ehsan, K. S. Mahsa, A. Amir, F. Andrei. Full stokes imaging polarimetry using dielectric metasurfaces. ACS Photon., 5, 3132-3140(2018).
[15] J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, F. G. Von, S. Linden, M. Wegener. Gold helix photonic metamaterial as broadband circular polarizer. Science, 325, 1513-1515(2009).
[16] Y. Guo, M. Pu, Z. Zhao, Y. Wang, J. Jin, P. Gao, X. Li, X. Ma, X. Luo. Merging geometric phase and plasmon retardation phase in continuously shaped metasurfaces for arbitrary orbital angular momentum generation. ACS Photon., 3, 2022-2029(2016).
[17] H. Wang, Y. Li, H. Chen, Y. Shen, J. Wang, J. Zhang, A. Zhang, T. Cui, S. Qu. Spin-to-orbital angular momentum conversion with quasi-continuous spatial phase response. Adv. Opt. Mater., 7, 1901188(2019).
[18] L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, S. Zhang. Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity. Light Sci. Appl., 2, e70(2013).
[19] T. Cai, G. Wang, H. Xu, S. Tang, H. Li, J. Liang, Y. Zhuang. Bifunctional Pancharatnam–Berry metasurface with high-efficiency helicity-dependent transmissions and reflections. Ann. Phys., 530, 1700321(2017).
[20] H. Wang, J. Du, H. Wang, Y. Lu, P. Wang. Generation of spin-dependent accelerating beam with geometric metasurface. Adv. Opt. Mater., 7, 1900552(2019).
[21] W. Guo, G. Wang, X. Luo, H. Hou, K. Chen, Y. Feng. Ultrawideband spin-decoupled coding metasurface for independent dual-channel wavefront tailoring. Ann. Phys., 532, 1900472(2020).
[22] L. Jing, Z. Wang, Y. Yang, B. Zheng, Y. Liu, H. Chen. Chiral metamirrors for broadband spin-selective absorption. Appl. Phys. Lett., 110, 231103(2017).
[23] M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, F. Capasso. Multispectral chiral imaging with a metalens. Nano Lett., 16, 4595-4600(2016).
[24] S. Zhang, J. Zhou, Y. Park, J. Rho, R. Singh, S. Nam, A. K. Azad, H. Chen, X. Yin, A. J. Taylor, X. Zhang. Photoinduced handedness switching in terahertz chiral metamolecules. Nat. Commun., 3, 942(2012).
[25] Y. Chen, X. Yang, J. Gao. Spin-controlled wavefront shaping with plasmonic chiral geometric metasurfaces. Light Sci. Appl., 7, 84(2018).
[26] H. Xu, G. Hu, Y. Li, L. Han, J. Zhao, Y. Sun, F. Yuan, G. Wang, Z. H. Jiang, X. Ling, T. J. Cui, C. Qiu. Interference-assisted kaleidoscopic meta-plexer for arbitrary spin-wavefront manipulation. Light Sci. Appl., 8, 3(2019).
[27] S. Yang, Z. Liu, S. Hu, A. Jin, H. Yang, S. Zhang, J. Li, C. Gu. Spin-selective transmission in chiral folded metasurfaces. Nano Lett., 19, 3432-3439(2019).
[28] Q. Wang, E. Plum, Q. Yang, X. Zhang, Q. Xu, Y. Xu, J. Han, W. Zhang. Reflective chiral meta-holography: multiplexing holograms for circularly polarized waves. Light Sci. Appl., 7, 25(2018).
[29] L. Jing, Z. Wang, R. Maturi, B. Zheng, H. Wang, Y. Yang, L. Shen, R. Hao, W. Yin, E. Li, H. Chen. Gradient chiral metamirrors for spin-selective anomalous reflection. Laser Photon. Rev., 11, 1700115(2017).
[30] M. Feng, X. Chen, Y. Li, Q. Zheng, Y. Han, J. Zhang, J. Wang, Y. Hou, Z. Liu, X. Li, C. Wang, J. Jing, H. Ma, S. Qu. Circularly polarized spin-selectivity absorbing coding phase gradient metasurface for RCS reduction. Adv. Theor. Simul., 3, 1900217(2020).
[31] M. Hentschel, M. Schäferling, B. Metzger, H. Giessen. Plasmonic diastereomers: adding up chiral centers. Nano Lett., 13, 600-606(2013).
[32] T. Fu, Y. Qu, T. Wang, G. Wang, Y. Wang, H. Li, J. Li, L. Wang, Z. Zhang. Tunable chiroptical response of chiral plasmonic nanostructures fabricated with chiral templates through oblique angle deposition. J. Phys. Chem. C, 121, 1299-1304(2017).
[33] B. M. Maoz, A. B. Moshe, D. Vestler, O. Bar-Elli, G. Markovich. Chiroptical effects in planar achiral plasmonic oriented nanohole arrays. Nano Lett., 12, 2357-2361(2012).
[34] Y. Svirko, N. Zheludev, M. Osipov. Layered chiral metallic microstructures with inductive coupling. Appl. Phys. Lett., 78, 498-500(2001).
[35] E. Plum, N. I. Zheludev. Chiral mirrors. Appl. Phys. Lett., 106, 221901(2015).
[36] C. Menzel, C. Rockstuhl, F. Lederer. Advanced Jones calculus for the classification of periodic metamaterials. Phys. Rev. A, 82, 053811(2010).
[37] M. Feng, Y. Li, J. Zhang, Y. Han, J. Wang, H. Ma, S. Qu. Wide-angle flat metasurface corner reflector. Appl. Phys. Lett., 113, 143504(2018).
[38] Z. Wang, H. Jia, K. Yao, W. Cai, H. Chen, Y. Liu. Circular dichroism metamirror with near-perfect extinction. ACS Photon., 3, 2096-2101(2016).
Set citation alerts for the article
Please enter your email address