• Photonics Research
  • Vol. 9, Issue 5, 726 (2021)
He Wang1、2、†, Yao Jing1、†, Yongfeng Li1、3、4, Lingling Huang2、*, Maochang Feng1, Qi Yuan1, Jiafu Wang1, Jieqiu Zhang1, and Shaobo Qu1
Author Affiliations
  • 1Department of Basic Sciences, Air Force Engineering University, Xi’an 710051, China
  • 2School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China
  • 3State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China
  • 4e-mail: liyf217130@126.com
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    DOI: 10.1364/PRJ.422509 Cite this Article Set citation alerts
    He Wang, Yao Jing, Yongfeng Li, Lingling Huang, Maochang Feng, Qi Yuan, Jiafu Wang, Jieqiu Zhang, Shaobo Qu. Spin-selective corner reflector for retro-reflection and absorption by a circular dichroitic manner[J]. Photonics Research, 2021, 9(5): 726 Copy Citation Text show less

    Abstract

    Recently, we have witnessed an extraordinary spurt in attention toward manipulating electromagnetic waves by metasurfaces. Particularly, tailoring of circular polarization has attracted great amounts of interest in both microwave and optics regimes. Circular dichroism, an exotic chiroptical effect of natural molecules, has aroused discussion about this issue, yet it is still in its infancy. Herein, we initiate circular dichroism followed by controlling spin-selective wavefronts via chiral metasurfaces. An N-shaped chiral resonator loaded with two lumped resistors is proposed as the meta-atom producing an adequate phase gradient. Assisted by the ohmic dissipation of the introduced resistors, the effect of differential absorption provides an auxiliary degree of freedom for developing circularly polarized waves with a designated spin state. A planar corner reflector that can achieve retro-reflection and absorption for right- and left-handed circularly polarized incidence is theoretically simulated and experimentally observed at microwave frequency. Thus, our effort provides an alternative approach to tailoring electromagnetic waves in a circular dichroitic manner and may also find applications in multi-functional systems in optics and microwave regimes.

    1. INTRODUCTION

    Guiding of electromagnetic waves in a desired direction has captured the interest of researchers in both academic and engineering communities [14]. 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 [57], vortex beam generation [8,9], beam splitting [1012], 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 [1921]. 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 [2325], 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 [2628]. 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.

    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

    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.

    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 z 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]: Ei=E02eikzziωt(x^y^)(1±i),where “+” and “−” represent the RHCP and LHCP waves, respectively. Accordingly, the Jones matrix of the reflection fields is expressed as Er=RlinEi=(rxxrxyryxryy)Ei,where Rlin is the reflection matrix under the Cartesian base; rxx(yy) and ryx(yx) are the co- and cross-polarized reflection coefficients under the incidence of x- and y-polarized waves, respectively. Furthermore, it is concluded that the reflection matrix for circular polarization is governed by eigenvectors u=(1/2)1/2(1,i)T and v=(1/2)1/2(1,i)T. In this work, the circular dichroism for total absorption of LHCP waves is analyzed as an example. With this aim, the reflection coefficients must satisfy rLL=rLR=rRL=0 and rRR=1. Thus, the solution is expressed by Rlin=eiγ2(1ii1),where the polarization state is referred to the propagation direction of electromagnetic waves. The clockwise and counter-clockwise directions are defined as RHCP and LHCP waves when viewed along the propagation direction, γ is an arbitrary phase shift, and a time-harmonic propagation of ejwt is considered. The eigenvalue of κ=0 with the eigenvector of (1,i)T is obtained for the matrix Rlin, which indicates that total absorption of LHCP waves and reflection of RHCP waves with the handedness preserved are achieved.

    (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 rRR(LL) and rRL(LR) of the proposed meta-atom under normal incidence of circularly polarized waves, and (d) phase responses under the illumination of RHCP waves when the pivoting angle varies from 0° to 150° with an interval of 30°.

    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 rRR(LL) and rRL(LR) of the proposed meta-atom under normal incidence of circularly polarized waves, and (d) phase responses under the illumination of RHCP waves when the pivoting angle varies from 0° to 150° with an interval of 30°.

    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 x and y directions are set as the “unit cell” and two Floquet ports are fixed along the ±z 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 rRR is >0.9 at 13–27 GHz, whereas rLL was <0.2 in the same frequency band. The cross-polarization reflection coefficients rRL and rLR are both <0.2. 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 (Φ=±2α, 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 θi and azimuthal angle of φi, the direction of the reflected wave is calculated by [37] {θr=arcsin(kisinθicosφi+ϕx)2+(kisinθisinφi+ϕy)2kiφr=arctankisinθisinφi+ϕykisinθicosφi+ϕx,where ki is the wave vector of the incident wave, ϕx and ϕy are the provided phase gradients along x- and y-axes, respectively. In this design, the propagation direction of the reflected wave is opposite to that of the incident wave. Therefore, ϕx and ϕy are set to meet the following conditions: {ϕx=2kisinθicosφiϕy=2kisinθisinφi.

    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 ±22°. Hence, mono-static RCS enhancement is achieved in the angle ranges of θ=±22°. 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.

    (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 φ=0°, and (e) monitored electric field of Ex-component under the incidence of RHCP and LHCP waves at 20 GHz.

    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 φ=0°, and (e) monitored electric field of Ex-component under the incidence of RHCP and LHCP waves at 20 GHz.

    (a) Simulated 3D far-field patterns under normal incidence of RHCP and LHCP waves at 20 GHz, (b) monitored electric field of Ex-component under the incidence of RHCP and LHCP waves at 20 GHz, (c) normalized 2D far-field patterns under normal incidence of RHCP and LHCP waves at the cutting-plane of the xoz-plane, and (d) simulated mono-static RCS with the elevation angle ranging from −40° to 40°.

    Figure 4.(a) Simulated 3D far-field patterns under normal incidence of RHCP and LHCP waves at 20 GHz, (b) monitored electric field of Ex-component under the incidence of RHCP and LHCP waves at 20 GHz, (c) normalized 2D far-field patterns under normal incidence of RHCP and LHCP waves at the cutting-plane of the xoz-plane, and (d) simulated mono-static RCS with the elevation angle ranging from 40°  to  40°.

    Moreover, the performance of mono-static RCS is simulated. The RCS curves in the cutting-plane of the xoz-plane with the elevation angle ranging from 40° 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 ±22° 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 >20  dB for normal incidence. In addition, there are two small rises around the elevation angle of θ=±22° attributed to a slight imperfection in the absorption of the LHCP wave.

    (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.

    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 ±22° 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 40° to 40° is <10  dB, 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 yoz-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 [38]: R=Dα?1RlinDα,withDα=(cosαsinα?sinαcosα),where α stands for the rotation angle of the new reflection matrix of R. As the chiral structure possesses the rotational symmetry properties of α, the matrix transformation leads to R=Rlin. Thus, the general condition for rotational symmetry is obtained as sinα(rxy+ryxryy?rxxryy?rxx?rxy?ryx)=0,and the solutions to simultaneously satisfy Eqs.?(3) and (A2) are α=kπ, k=0,±1,±2, Hence, it is concluded that only the C2 symmetric group can provide circular dichroism.

    Next, suppose the mirror symmetry plane of a symmetric structure is rotated from the xoz-plane through a rotational angle of α with respect to the z-axis. Accordingly, the reflection matrix is expressed as R=Ax?1D?α?1RlinD?αAx,withAx=(100?1),where Ax is the mirror matrix with respect to the x-axis. According to the symmetry condition of R=Rlin, the solution is obtained as sin(2α)(rxx?ryy)+2?cos(2α)rxy=0,where (rxx?ryy)/rxy is a pure imaginary number so that the mirror symmetry structure has no solution for the corresponding matrix transformation. Therefore, circular dichroism cannot be attained in structures that exhibit mirror symmetry with respect to the incidence plane.

    Therefore, to achieve the circular dichroitic effect, it is necessary to simultaneously break the n-fold rotational (n>2) and mirror symmetries [37]. Based on this principle, we propose an N-shaped resonator as the meta-atom of our design.

    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.?6(a). It is observed that the incident LHCP waves are absorbed to a great extent in the 12–30?GHz range; whereas the absorption of RHCP waves is <0.1 within the same frequency band. The circular dichroism is calculated by using CD=ALHCP?ARHCP; therefore, it is >0.6 in the 12–30?GHz range. Moreover, it is seen that circular dichroism >0.9 can be achieved in a wide frequency band from 14?GHz to 27?GHz, which indicates the distinctive performance of differential absorption and wideband characteristics. However, the variation of circular dichroism changes with the introduction of ohmic dissipation. As can be seen from Fig.?6(b), the circular dichroism of the proposed meta-atom increases with the enhancement of resistance in the operating frequency range. In this design, the resistance is optimized at 200?Ω to adapt the appropriate ohmic dissipation and thereafter exhibit a strong circular dichroitic effect for reflection of LHCP waves and absorption of RHCP waves.

    (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 rRR and rLL under oblique incidence from 0° to 30°, and (d) reflection curves under oblique incidence at an angle of 22°.

    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 rRR and rLL under oblique incidence from 0° to 30°, and (d) reflection curves under oblique incidence at an angle of 22°.

    Figure?6(c) shows the co-polarization amplitudes rRR and rLL for oblique incidence from 0° to 30°. Both rRR and rLL are stable at different angles of incidence. It is seen that the curves of rRR are >0.90 and rLL are <0.25, which indicates the circular dichroism of the proposed meta-atom under illumination by circularly polarized waves at different incident angles. In this work, an angle of incidence of θ=±22° is applied. The reflection characteristics are shown in Fig.?6(d).

    APPENDIX C: EXPERIMENTAL SETUP

    A photograph of the experimental setup for the measurement of the RCS is shown in Fig.?7. The measurement was carried out in an anechoic chamber to reduce the electromagnetic uncertainty in the environment. The prototype was fixed on a turntable that could rotate through 360° in a horizontal plane. Two standard circularly polarized horn antennas were placed far enough from the prototype: one served as a transmitter and the other as a receiver. The two antennas were connected to the two ports of an Agilent N5224A vector network analyzer. During the measurement, the turntable rotated from ?40° to 40° to obtain the RCS performance in this angle range.

    Photograph of the experimental setup for the RCS measurement.

    Figure 7.Photograph of the experimental setup for the RCS measurement.

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    He Wang, Yao Jing, Yongfeng Li, Lingling Huang, Maochang Feng, Qi Yuan, Jiafu Wang, Jieqiu Zhang, Shaobo Qu. Spin-selective corner reflector for retro-reflection and absorption by a circular dichroitic manner[J]. Photonics Research, 2021, 9(5): 726
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