Active circular dichroism coding meta-mirror for flexible beam-forming and dynamic amplitude control

Weipeng Wan; Yongfeng Li; Yongfeng Li; Yongfeng Li; He Wang; Lixin Jiang; Zhibiao Zhu; Yang Cheng; Zhe Qin; Lin Zheng; Jiafu Wang; Shaobo Qu; Shaobo Qu

doi:10.1364/OE.432197

1. Introduction

Chirality, a basic attribute of nature, refers to the asymmetry of chiral objects that cannot coincide with their mirror image, widely existing in biomacromolecules, crystals and so on. The chiral characteristics contribute to various optical effects such as optical activity and circular dichroism, which have great potentials in biomolecular characterization and chemical spectroscopy [1]. Interestingly, due to the attractive characteristics of exotic properties and giant engineering potentials of metamaterial, chiral metamaterial has intrigued an accumulative interest in its excellent chiroptical effects from both research teams and engineering communities [2–4]. Furthermore, as two-dimensional counterpart of metamaterials, metasurfaces provide an alternative strategy to manipulate electromagnetic (EM) waves by arranging artificial structures on a plane to engineer the amplitude, phase, and polarization of EM waves. [5–7] Compared with metamaterial, planar metasurface exhibit low loss and deep subwavelength thickness, presenting great convenience for miniaturization and integration. The intriguing features of metasurface have opened an avenue for multidimensional EM waves manipulation simultaneously, boosting researches in lens imaging [8], holographic display [9], quantum optics [10], and so on.

Recently, chiral metasurface has aroused interest in realizing the spin-sensitive manipulation of EM waves. By properly manipulating the amplitude and phase of EM waves, a lot of interesting optical phenomena have been realized, including chirality-induced giant optical activity [11], extrinsic chirality [12], spin-selective absorbers [13], chiral lens imaging [14], asymmetric transmission/reflection [15,16], and spin-dependent holography [17]. Nevertheless, the exiting methods of achieving unique chiroptical effects are mainly focused on the passive paradigm, which limits their further dynamic applications in practice. Thus, active metasurfaces present the advancement of timely and intelligent control by manipulating operation patterns. To date, mechanical deformation [18–20], phase-change materials [21–23], and active components [24–26] are three mainstream methods to realize dynamic control of active metasurfaces. However, the time lag and complicated operation conditions of the phase-change phenomena that can be externally controlled by temperature, light, and electric or magnetic fields such as liquid crystal and chalcogenide remain a challenge for their applications. Fortunately, with the advent of the concept of coding and digital metasurface by Cui et al. [27], coding metasurfaces described in a digital manner with binary codes push a flexible and convenient avenue for active metasurface design with the help of PIN or varactor diodes [28–32]. However, the work for reconfigurable chiral coding metasurface is still in infancy, presenting promising potentials for further investigation.

In this paper, we proposed a scheme of chiral digital coding metasurface that is capable of the continuous modulation of its beam-forming via manipulating bias voltages on the chiral meta-atoms in microwave frequencies. An Archimedean spiral based meta-atom, breaks both the n-fold (n>2) rotational and mirror symmetries, is designed to introduce strong chirality for circularly polarized (CP) waves. With the help of tunable ohmic dissipation, the circular dichroism (CD) of the chiral meta-mirror can be continuously modulated by applying the bias voltages on the varistor diode. Thereafter, two types of the designed chiral meta-atoms are utilized as coding units, with 0 and π phase responses, making up the “0” and “1” coding elements of the digital coding metasurface. The scattering pattern is customized by arranging “0” and “1” coding elements with sophisticated coding sequences. Owning to the independent phase arrangement and amplitude modulation, the two-dimensional freedom of the digital coding meta-mirror is obtained to control the scattering beams dynamically. A proof-of-principle, constructed in checkerboard coding sequences, is designed and fabricated to realize flexible scattering beam-forming and dynamic amplitude control. The simulated and experimental results demonstrate the proposed metasurface is of the capability to perform continuous manipulation of scattered beams for a 10 dB scale under LHCP incidence while the EM responses keep consistent under RHCP incidence. Encouragingly, the proposed scheme of chiral digital coding metasurface paves an efficient way to achieve dynamic spin-sensitive scattering steering, presenting promising potentials for further applications in polarization-dependent antenna systems and microwave camouflage devices.

2. Results

Recently, the spiral structure has been widely applied into metamaterials design for its great geometric characteristics, which is an excellent chiral structure with asymmetric optical responses [33–35]. Significantly, the Archimedean spiral has gotten plenty of attention for its profound influences in both research and engineering, which can be described in Cartesian coordinates as:

(1)$$\left\{ {\begin{array}{c} {x\textrm{ = (}a + b\theta \textrm{)cos(}c\theta \textrm{)}}\\ {y = (a + b\theta \textrm{)sin(}c\theta \textrm{)}} \end{array}} \right.$$

where a, b, and c are the decisive parameters to shape the spiral and θ is the independent variable. As shown in Fig. 1(b), there is no mirror symmetry axis or rotational symmetry center of the spiral, which presents a strong chirality. To enhance the chiroptical effect of the spiral, we perform a 180-degree rotation operation to make up a double helical structure, shown in Fig. 1. The Archimedean spiral based chiral meta-atom composes of a metallic spiral layer constructed on FR-4 (ε_r=4.3, tanδ=0.05, and thickness t₁=1 mm) substrate, a foam (ε_r = 1.05, tanδ=0.05, and thickness t₂=1 mm) spacer layer, and a metal ground in a four-layer structure. All the metal layers have a thickness of 0.017 mm. To achieve a dynamical manipulation of absorption amplitude, we have inserted a varistor diode (BAP70-02) between two spirals. In addition, two inductances are employed to introduce a radio-frequency choke, which blocks alternating current but allows direct current to pass through. After a comprehensive optimization, the geometric parameters are obtained as following: a=0, b=1, c=π, θ ranges from 0 to 3.05, p=8.5 mm, w=0.4 mm, d_x=0.5 mm, and d_y=1 mm.

Fig. 1. The geometric configuration of the proposed chiral meta-atom. (a) Perspective view. (b) Top view.

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To better understand the underlying mechanism of circular dichroism, we perform the theoretical analysis of meta-atoms based on the reflection matrix. Here, the incidence is considered to illuminate the meta-mirror of the xoy-plane vertically. The incident and reflected fields in the plane can be connected with Jones Matrix as following [36]:

(2)$$\left( \begin{array}{l} E_r^x\\ E_r^y \end{array} \right) = \left( {\begin{array}{cc} {{R_{xx}}}&{{R_{xy}}}\\ {{R_{yx}}}&{{R_{yy}}} \end{array}} \right)\left( \begin{array}{l} E_i^x\\ E_i^y \end{array} \right) = {\mathbf R}\left( \begin{array}{l} E_i^x\\ E_i^y \end{array} \right)$$

where R is the Cartesian Jones reflection matrix of the meta-atom, while $E_r^{x(y)}$ and $E_i^{x(y)}$ are the reflected and incident electric field in the x(y) direction, respectively. Through the coordinate conversion from Cartesian base to circular base, the reflection matrix of circularly polarized states is calculated by linearly polarized reflection coefficients:

(3)$$\begin{aligned} {{\mathbf R}_{cir}} &= \left( {\begin{array}{cc} {{R_{RR}}}&{{R_{RL}}}\\ {{R_{LR}}}&{{R_{LL}}} \end{array}} \right) = {{\mathbf \Lambda }^{ - 1}}{{\mathbf{R\Lambda}} }\\ &= \frac{1}{2}\left( {\begin{array}{cc} {({R_{xx}} + {R_{yy}}) + i({R_{xy}} - {R_{yx}})}&{({R_{xx}} - {R_{yy}}) - i({R_{xy}} + {R_{yx}})}\\ {({R_{xx}} - {R_{yy}}) + i({R_{xy}} + {R_{yx}})}&{({R_{xx}} + {R_{yy}}) - i({R_{xy}} - {R_{yx}})} \end{array}} \right) \end{aligned}$$

where ${\mathbf \Lambda } = \frac{1}{{\sqrt 2 }}\left( {\begin{array}{cc} 1&1\\ i&{ - i} \end{array}} \right)$ is the coordinate transformation matrix, while “R” and “L” refer to the clockwise and counter-clockwise circularly polarized waves and “x” and “y” refer to x- and y-polarized components. Here, clockwise and counter-clockwise circularly polarized waves are defined as right-handed circularly polarized (RHCP) and left-handed circularly polarized (LHCP) waves when viewed along the + z axis. R_RR and R_LR are co-polarized and cross-polarized reflection coefficients of RHCP waves, meanwhile R_xx and R_yx are co-polarized and cross-polarized reflection coefficients of x-polarized waves.

To achieve the spin-selective absorption with perfect circular dichroism of LHCP incidence, the circularly polarized reflection amplitudes (r_RR, r_LR, r_LL, r_RL) have to meet the requirement of r_RR=r_LR=r_LL=0 and r_RL=1. The unique solution of the reflection matrix can be calculated:

(4)$${\mathbf R} = \frac{{{e^{i\alpha }}}}{2}\left( {\begin{array}{cc} 1&i\\ i&{ - 1} \end{array}} \right)$$

where α is an arbitrary phase shift, and a time-harmonic propagation of e^-jωt is considered. To better understand the EM response behavior, we calculate the eigenstates of the polarization. By solving the eigenvalue problem of Eq. (4), the eigenvalue к=0 with the eigenvector (1, i)^T is obtained. In this case, no incident LHCP waves are reflected while incident RHCP waves are completely reflected with the handedness converted.

To verify the capability of spin-selective absorption of our proposed meta-mirror, we perform the structural symmetry analysis to find out the relation between geometry with the desired reflection matrix Eq. (4). When rotating the structure by an arbitrary angle concerning the z-axis, the new reflection matrix can be accomplished by rotation matrix operation mathematically:

(5)$${{\mathbf R}_{new}} = {\mathbf D}_\gamma ^{ - 1}{\mathbf R}{{\mathbf D}_\gamma }, \textrm{with}\, {{\mathbf D}_\gamma } = \left( {\begin{array}{cc} {\cos (\gamma )}&{\sin (\gamma )}\\ { - \sin (\gamma )}&{\cos (\gamma )} \end{array}} \right)$$

where R_new is the new reflection matrix of the rotated structure and γ is the rotation angle. According to the invariance of the reflection matrix, the rotational symmetry structure has to satisfy R_new=R. Therefore, the solution to the rotational symmetry can be given as:

(6)$$\sin (\gamma )\left( {\begin{array}{cc} {{R_{xy}} + {R_{yx}}}&{{R_{yy}} - {R_{xx}}}\\ {{R_{yy}} - {R_{xx}}}&{ - {R_{xy}} - {R_{yx}}} \end{array}} \right) = {\mathbf 0}$$

To satisfy both the reflection matrix in Eq. (4) and the rotational symmetry condition in Eq. (6), the solution for the rotation angle is γ=mπ, m=0, ±1, ±2, …. Obviously, only the C₂ symmetric group can meet the requirement of the ideal spin-selective meta-atom. The above analysis has demonstrated that the proposed Archimedean spiral based double-helical structure has satisfied the rotational symmetry for circular dichroism.

In order to better understand the physical origin of the spin-selective absorption of our proposed chiral resonator, further investigation on the surface current distributions at the operation frequencies is performed. Here, we take the performance of 13.5 GHz as an example. Due to the chirality of the double-helical structure, the distinct surface current distributions are aroused on the spiral under LHCP and RHCP incidence, shown in Fig. 2. It can be clearly observed that LHCP illuminations have induced strong surface currents around the center of the spiral, while surface currents are produced outside the structure under RHCP incident waves. The inserted resistive component can consume the surface currents around the center, thus the ohmic dissipation is induced under the LHCP incidence. On the other side, the induced surface currents under RHCP can hardly introduce dissipation. The above results indicate that the chiral meta-atom presents the capability to achieve spin-selective absorption of CP waves for its asymmetric EM properties. Furthermore, the active varistor diode can continuously manipulate the energy loss of LHCP incidence by controlling the bias voltages on it.

Fig. 2. Surface current distributions on the chiral meta-atom under (a) LHCP and (b) RHCP incidences at 13.5 GHz.

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The absorptive performances of the meta-mirror under the full-wave simulation are presented in Fig. 3. Here, the solid and dashed lines are representing the results under LHCP and RHCP incidence in Fig. 3(a), respectively. When applying different bias voltages on the diode with the resistances R of 150, 300, 600 Ω, and 200 MΩ (no voltage), the resorption amplitude of LHCP waves can be manipulated from 0.95 to 0.16 with a wide adjustable scale of 0.79. An over 90% absorption from 11.9 to 15.3 GHz and an over 80% absorption from 11.1 to 17 GHz for LHCP waves are achieved with R=150 Ω. On the other hand, the amplitude is always under 0.2 for RHCP waves from 12 to 18 GHz, which is insensitive to R. Besides, the CD value can reach the peak of 0.82 at 13.5 GHz (R=150 Ω), as shown in Fig. 3(b). Here, CD is calculated by CD=| A_LCP |²- | A_RCP |² (A_LCP and A_RCP are absorption coefficients of LHCP and RHCP waves). An above 0.7 CD value from 11.8 to 16 GHz. As the resistance increases, the CD value decreases to almost 0 gradually. The simulated results have shown the dynamical control of the circular dichroism of the chiral meta-atom with the help of tunable ohmic dissipation, which are consistent with the analysis of the surface currents.

Fig. 3. Absorptive characteristics of the proposed chiral meta-mirror. (a) Absorption amplitude. (b) Circular dichroism.

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Furthermore, it is of significance for us to consider the reflection amplitude and phase to achieve scattering patterns modulation by phase gradient coding metasurface. As depicted in Fig. 4(a)-(d), in 12-16 GHz, the cross-polarized reflection amplitudes (r_RL) of LHCP waves range from below -10 dB to within -2 dB, while the co-polarized reflection amplitudes (r_LL) of LHCP waves are below -10 dB. When resistance increses, r_RL increses gradually and r_LL keep a low amplitude. Combined with the absorption performance, as the absorption of LHCP waves decreses, the left waves are converted to RHCP waves. On the other hand, the cross-polarized reflection amplitudes (r_LR) of RHCP waves are at a high value, and the co-polarized reflection amplitudes (r_RR) are below -10 dB. The incident RHCP waves are almost reflected with the polarization converted, which is insensitive to the resistance. Based on the above results, it can be concluded that the reflectivity of LHCP incidence can be dynamically manipulated by applying different resistances to the diode. Besides, the polarization of reflected LHCP and RHCP waves has been changed.

Fig. 4. The reflection amplitudes of the chiral meta-mirror with different resistance R. (a) R=150 Ω. (b) R=300 Ω. (c) R=600 Ω. (d) R=200 MΩ.

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To verify the ability to employ Pancharatnam-Berry (PB) phase to construct digital coding metasurface, we perform the proving process of PB phase principle of the meta-atom. In the Cartesian coordinate system, the new reflection matrix of the chiral atom rotated by β degree can be calculated:

(7)$${\mathbf R}_{new}^{XY} = {\mathbf C}_\beta ^{ - 1}{{\mathbf R}^{XY}}{{\mathbf C}_\beta },{{\mathbf C}_\beta } = \left( {\begin{array}{cc} {\cos \beta }&{\sin \beta }\\ {\textrm{ - }\sin \beta }&{\cos \beta } \end{array}} \right)$$

where X and Y are the polarization states of the incident waves. By transferring Cartesian base to circular base, the reflection matrix (R^LR) for circularly polarized waves can be calculated in the following equation:

(8)$${\mathbf R}_{new}^{LR}\textrm{ = }{\Lambda ^{ - 1}}{\mathbf R}_{new}^{XY}\Lambda $$

The reflection matrix under CP incidence can be derived by substituting Eq. (8) into (7) as following:

(9)$$\begin{aligned} {\mathbf R}_{new}^{LR}&=\frac{\textrm{1}}{\textrm{2}}\left( {\begin{array}{cc} {({\textrm{R}_{xx}} + {R_{yy}}) + i({R_{xy}} - {R_{yx}})}&{(({R_{xx}} - {R_{yy}}) - i({R_{xy}} + {R_{yx}})){e^{ - i2\beta }}}\\ {(({R_{xx}} - {R_{yy}}) + i({R_{xy}} + {R_{yx}})){e^{i2\beta }}}&{({R_{xx}} + {R_{yy}}) - i({R_{xy}} - {R_{yx}})} \end{array}} \right)\\ &= \frac{\textrm{1}}{\textrm{2}}\left( {\begin{array}{cc} {{R_{LL}}}&{{R_{LR}}{e^{ - i2\beta }}}\\ {{R_{RL}}{e^{i2\beta }}}&{{R_{RR}}} \end{array}} \right) \end{aligned}$$

Equation (9) indicates that only two components R_RL and R_LR can carry the PB phase information that the phase change is double the rotation angle. Therefore, the rotated unit has to satisfy the condition of R_LL=R_RR=0 under CP incidence to introduce PB phase. Due to the high-efficiency polarization conversion of the Archimedean spiral based meta-atom, PB phase can be induced by rotating the meta-atom.

The cross-polarized reflection phases of the chiral meta-atom (“0” unit) and the rotated meta-atom by 90° (“1” unit) under LHCP and RHCP incidences are simulated for further demonstration. The results are presented in Fig. 5, where the dash curves and solid curves are the performance of “0” and “1” unit respectively. Besides, the curves with different colors are results with different resistances. As shown in Fig. 5, the cross-polarized reflection phase differences between “0” unit and “1” unit maintain around 180° for both LHCP and RHCP waves in the working band. The phase differences remain stable under variable resistances of 150, 300, 600 Ω, and 200 MΩ. In addition, the slight phase shifts of R_RL is resulted from the changed EM conditions for different R in Fig. 5(a), while the varistor diode has little influence on the RHCP incidence. The simulated results are consistant with the analysis of the surface current. Consequently, the chiral meta-mirror is capable of introducing steady phase difference of π between “0” unit and “1” unit under various R.

Fig. 5. The cross-polarized reflection phases of “0” unit and “1” unit with different R under (a) LHCP and (b) RHCP incidences.

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Given the reflection properties of the chiral meta-mirror, “0” unit and “1” unit can be utilized to construct digital phase gradient coding metasurface. Here, an M*N array of coding elements with L*L array coding units in a checkerboard coding sequence is considered as an example. Under EM waves illumination, the coding metasurface can be seen as a passive antenna, meanwhile a coding element is a sub-array antenna. According to the far-field distribution relations, the far-field function can be expressed as:

(10)$$\textrm{F}(\theta ,\varphi ) = {f_{m,n}}(\theta ,\varphi ){S_\alpha }(\theta ,\varphi )$$

where θ and φ are elevation and azimuth angles of reflected waves. f_m,n(θ, φ) is the primary pattern and S_α(θ, φ) is the array pattern. Therein, S_α(θ, φ) can be calculated by:

(11)$$\begin{aligned} {S_\alpha }(\theta ,\varphi ) &= \sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {\textrm{exp} \{ j[{\varphi _{m,n}} + {k_0}{D_x}(m - 1/2)(\sin \theta \cos \varphi - \sin {\theta _i}\cos {\varphi _i})} } \\ &\quad+ {k_0}{D_y}(n - 1/2)(\sin \theta \cos \varphi - \sin {\theta _i}\sin {\varphi _i})]\} \end{aligned}$$

where k₀ is the propagation constant of the incident waves in free space, φ_m,n is the reflection phase of coding elements, D_x and D_y are the size of the coding element along the x-axis and y-axis, θ_i and φ_i are the elevation and azimuth angles of incidence, respectively. Accordingly, the reflection of the checkerboard coding metasurface with π phase gradient can be scattered into four equal-sized beams. To realize the continuous control on scattering patterns, a 6*6 array of “0” and “1” coding elements with 6*6 array of “0” and “1” units is proposed, shown in Fig. 6.

Fig. 6. The coding metasurface with checkerboard sequence.

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The simulated 3D far-field patterns under normal incident CP waves are presented in Fig. 7. Similarly, the reflection is scattered into four main beams with same amplitude. When the resistance of the varistor diode is manipulated from 150 to 200 MΩ, the scattering patterns of LHCP waves are continuously controlled, while the scattering beams of RHCP waves keep constant with a peak value of 15.3 dB. The main reflected beams of LHCP incidence increase from 4.7 to 15.2 dB with an over 10.5 dB increase. The above phenomena indicate that the far-field patterns of LHCP can be modulated with the help of the dynamical control of R, presenting an asymmetric manipulation of scattering patterns for the incident CP waves.

Fig. 7. The far-field patterns of the proposed digital coding metasurface under normal incident CP waves with various R.

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To experimentally demonstrate the feasibility of our proposed approach, a prototype with a size of 306 mm*306 mm is fabricated. The metal layers are made of copper and covered with tin, fabricated by printed circular board technology. As shown in Fig. 8(a), the fabricated metasurface is composed of coding elements, and the bias voltage is fed by a series circuit. Thereby, the resistance of the diode can be continuously manipulated by applying different bias voltages. The utilized inductance (LQW18AN27NGOOD) is 27 nH. Figure 8(b) shows the measurement setup. In the experiment, the prototype and the transmitting antenna are fixed on a turntable, rotating with arbitrary angles. The prototype is connected with a direct current source and the voltage can be applied from 0 to 60 V. The transmitter and receiver are employing two identical standard gain horn antennas connected with a vector network analyzer (Agilent N5224A). The horn antennas are employed to transmit and receive signals from the vector network analyzer. By rotating the turntable, the 2-D far-field distribution along θ=45° and 135° plane can be measured.

Fig. 8. (a) Photograph of the fabricated meta-mirror. (b) The measurement setup.

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The normalized simulated and measured 2D scattering patterns at 13.5 GHz along θ=45° plane under normal incident CP waves are presented and compared in Fig. 9. Here, we utilize soild and dash curves with different colors to distinguish different results under LHCP and RHCP waves. When applying bias voltage as 0.67, 0.63, 0.58 and 0 V, four representative values 150, 300, 600 and 200 MΩ of the diode are obtained, respectively. Consequently, the simulation and measurement are in good agreement, which presents tunable scattering patterns of LHCP waves. The relative amplitude of main scattered beam can be continuously controlled from 0.9 to 0.1. Besides, the slight differences between the simulation and measurement mainly result from the influence of feed network and varistor diode.

Fig. 9. The simulated and measured 2-D far-field distribution along θ=45° with different R at 13.5 GHz under (a) LHCP and (b) RHCP incidence.

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3. Conclusion

In summary, we have proposed a strategy to design a chiral digital coding meta-mirror for the modulation of spin-sensitive scattering patterns via the independent manipulation of amplitude and phase. Bases on Archimedean spiral structure, the reflection amplitude of the chiral meta-atom can be dynamically controlled by adjusting bias voltages. Besides, the reflection phase can be tailored by arranging PB phase for its excellent reflection properties. A proof-of-prototype is simulated and measured for further demonstration of the feasibility. We have validated in both simulations and experiments that the scattering patterns can be manipulated from mostly absorbed to scattered. Our findings can advance the spin-selective scattering modulation and chiral digital coding metasurface and thus promote emerging applications in adaptive microwave camouflage devices and polarization-dependent systems.

Funding

National Natural Science Foundation of China (61971435, 61971437); China Postdoctoral Science Foundation (2019M651644).

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Active circular dichroism coding meta-mirror for flexible beam-forming and dynamic amplitude control

Abstract

1. Introduction

2. Results

3. Conclusion

Funding

Disclosures

Data Availability

References

Data Availability

Cited By

Figures (9)

Equations (11)

Optics Express