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Abstract
In this paper, we propose a giant circular dichroism (CD) chiral metamirror that differentially absorbs circularly polarized (CP) waves with dual/multi bands. The structure is composed of two variable τ resonators with counter split opening directions and different eigenfrequencies. Even more important, these two resonators are aligned vertically, and then integrated into one periodical unit cell, which results in the high-efficiency absorptive CD. The chiral metamirror has a narrow-band absorption of the left-handed circularly polarized (LCP) wave for lower resonance, and a broadband absorption of the right-handed circularly polarized (RCP) wave in the higher-frequency range. Optical resonator designs with diversified chiral molecules combinations are further studied in detail. Through the study of different periodic arrangements, parameters scanning optimization, and power loss distributions, it is proved that the overall permutation symmetry breakdown of total combined chiral molecules is the determining factor for the absorptive CD. Based on the principle in the microwave model, two mid-infrared chiral metamirrors are further realized, which can still show good spin-dependent absorption. This multi-polarization and multifunction response advance novel photonic devices for a variety of applications including CP laser, biomolecules detection, and energy harvester.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Mirrors, which are the most important optical components in the redirection of electromagnetic radiation, have a wide range of applications in lasers, telescopes, microscopes, and everywhere else [1]. The conventional metal mirrors, also known as “electric mirrors”, have the function of reflecting linear polarized (LP) wave without changing its polarization state, while the handedness of circularly polarized (CP) waves will show the opposite polarization state after reflection [2]. The great availability of the chiral metamaterials modeling [3,4], which interacts differently with right-circularly polarized (RCP) and left-circularly polarized (LCP) lights, has in turn stimulated interest in the possibility of new generation CP optics [5]. A number of meta-devices have been proposed and demonstrated such as chiral negative refraction [6], LP/CP converter [7–9], diode-like asymmetric transmission [10], and so on. The artificially periodic electromagnetic resonator, provides a distinct platform for chiral mirrors with enhanced optical response. Recently, researchers are no longer limited to the reflection characteristics of metamirrors. Absorptive circular dichroism metamirrors [11–13], acting as a spin-dependent absorber, can perfectly selectively absorb a designated CP illumination while reflecting another polarization mode.
In 2014, an example of a CP polarization-sensitive chiral absorber was reported [14], providing absorption only for one circular polarization, which could also be used as a circular polarizer with high polarization conversion. Meanwhile, giant CD in individual single-walled carbon nanotubes (CNTs) was achieved from extrinsic chirality in which symmetry is broken by the optical wave vector [15]. Soon after, a handedness-preserving reflector for LCP/RCP wave and a coherent perfect absorber for RCP/LCP mode was proposed [2,16]. Later, two chiral models utilizing origami craft (circular/square split rings), were designed successively, whose electromagnetic responses were dynamically controllable via switching the folding state of resonators [17,18]. These works [2,15–18] are all based on external chirality, with the indispensable condition of oblique incidence. The electric/magnetic dipole resonance is excited with the limitation of designated incident angles or specific folding constructions, which are not easy to be integrated. Although both intrinsic and extrinsic chirality greatly advance the investigation of chiral mirrors [19], improving the efficiency and bandwidth of CD have always been the pursuit of researchers. Interestingly, a micro-genetic algorithm method was utilized to optimize the strong CD [20]. In 2019, inspired by circular polarization (CP) antenna theory, a matching resistor was introduced to realize a novel broadband metasurface absorber, which could achieve a wide band (8.3–18 GHz) absorption for RCP illumination [21]. Subsequently, an optically transparent metamirror with broadband chiral absorption in the microwave region was also proposed [12]. More recently, Zhang et al. proposed an actively tunable multifunctional metamirror based on a bi-layer graphene structure. Both the spin-selective absorber and the polarization converter could be actively switched between ON and OFF states [22]. Besides, most structures utilized the helices and other morphing constructions, such as three-dimensional (3D) twisted-semicircle nanowires [23–25], rotated closed rings [26], L-shaped curled wires [27], and so on.
Although the chiral structure is diverse, the design principle mainly relies on the destruction of symmetry—breaking both the n-fold rotational (n > 2) and mirror symmetries [11,28]. At present, most of the researches are focused on the intrinsic asymmetry (or extrinsic asymmetry from oblique incidence) within one periodical unit, ignoring the overall permutation asymmetry from periodic arrangement. Besides, the absorptive CD metamirrors still suffer from low efficiency, narrow band, and complex construction. It is of great significance to study the optical response from combination of variable resonators with different arrangements. It provides a unique way to achieve strong selective absorption which has important applications in circular polarizers [29], CP lasers [30], chiral molecules detection [31,32], and energy harvester [33].
In this article, we propose a giant absorptive CD metamirror composed of two variable τ resonators with counter split opening directions and different eigenfrequencies. We mainly focus on the physical essence of both intrinsic (single resonator) and extrinsic structural asymmetry (different periodic arrangements). In detail, the split opening directions, sensitive parameters optimizations, power loss distributions, individual resonator rotations, vertical and horizontal arrangements are studied.
2. Simulated and experimental method
The perspective view of the double τ resonators with vertical arrangements (DTR-V) is shown in Fig. 1(a). It consists of a top metal resonant unit, an intermediate dielectric layer, and a bottom metal plate similar to a sandwich structure. Here, the metal is copper with the conductivity of $\sigma = 5.8 \times {10^7}$ S/m. The top metal unit is made up of two asymmetric resonators ${\tau _1}$ and ${\tau _2}$, which are placed vertically. These two resonators have different parameters with varied eigenfrequencies (however, this is not the principal factor of high-efficiency CD). Besides, ${\tau _1}$ and ${\tau _2}$ resonators have counter split opening directions, which are important to produce overall permutation asymmetry. The relative dielectric constant is 4.3, with the loss tangent of 0.025. Optimized parameters are as follows: a1 = 4.9 mm, a2 = 1.2 mm, a3 = 2.4 mm, a4 = 4.1 mm, a5 = 3.9 mm, a6 = 1.1 mm, a7 = 1.4 mm, a8 = 1.0 mm, a9 = 0.4 mm, r1 = 1.2 mm, b1 = 5.6 mm, b2 = 1.2 mm, b3 = 2.9 mm, b4 = 4.1 mm, b5 = 3.9 mm, b6 = 1.0 mm, b7 = 1.7 mm, b8 = 0.6 mm, r2 = 1.6 mm, h1 = 0.035 mm, h2 = 2.0 mm, T = 18.5 mm.
Fig. 1. The design of chiral metamirror: (a) the overall perspective view. (b) double τ resonators with vertical arrangements (DTR-V). (c) Photograph of the test sample.
We use the finite integration technique (FIT) method for simulation analysis. The absorption of the metamaterial A(ω) depends on the reflectance R(ω) and transmittance T(ω) of the light incident on the metamaterial:
When the reflectance and transmittance reach the minimum at a certain frequency simultaneously, the absorption will reach the maximum. Particularly, if the thickness of the bottom copper film is greater than the skin depth of the wave, the transmission can be ignored. Chiral absorption can be described as [34,35]:
Here, ${A_ - }$ and ${A_ + }$ represents the absorptions of LCP(-)/RCP(+) incident waves. ${R_{ +{-} }}$ (${R_{ -{+} }}$) represents the cross-polarized reflectance and ${R_{ -{-} }}$ (${R_{ +{+} }}$) is the co-polarized reflectance, where the first and second subscripts respectively represent the polarization state of the reflected wave and incident wave. Similarly, ${r_{ +{-} }}$ (${r_{ -{-} }}$) represents the reflection coefficient of LCP incident wave, and ${r_{ -{+} }}$ (${r_{ +{+} }}$) represents the reflection coefficient of RCP incident wave. In addition, the CP reflection matrix can be represented by LP Jones matrix [36]:
In experiments, 60 × 60 τ resonators sample (555 × 555 × 2.07 $m{m^3}$, Fig. 1(c)) are etched based on PCB technology for free space testing. Two broadband CP spiral antennas are used as transmitting and receiving antennas, which are placed in parallel on the same side of the sample. These two antennas are set at the same horizontal line as the center of sample with a height of 1.5 meter. Four edges of sample are surrounded with conical absorbing material to eliminate diffraction interferences. The CP reflection coefficients can be obtained with the antennas connected to the Agilent E8362B network analyzer.
3. Results and discussions
The reflectances of CP waves are calculated in Fig. 2(a). As we known, for a metal mirror, ${R_{ -{+} }}$ is equal to ${R_{ +{-} }}$ with total reflection. However for this model, the total values of ${R_{ -{+} }}$ and ${R_{ +{-} }}$ are both less than 0.4 over the whole frequency range with two dips around 9 GHz and 12.5 GHz. Specifically, at 8.99 GHz, the minimum value is 0.08. Around 12.5 GHz, the values less than 0.2 cover from 11.42–13.48 GHz with a much wider dip, indicating good impedance matching with the free space. On the other hand, the co-polarized reflectances ${R_{ -{-} }}$ and ${R_{ +{+} }}$ present great contrast. For the LCP wave, ${R_{ -{-} }}$ possesses a high-pass filtering response with a sharp sinking at 8.6 GHz. For the RCP wave, ${R_{ +{+} }}$ is strongly band rejected around 12.5 GHz. Taking into account both co- and cross-reflectance, CP absorption and $C{D_{ab}}$ curves have been calculated in Fig. 2(b). Obviously, the structure has an absorption of 91% at 8.98 GHz for LCP wave. For RCP wave, it produces wideband high-efficiency absorption with peak value of 97.4% at 12.22 GHz. From 12.06 GHz to 12.80 GHz, the absorption is always greater than 80%, with a relative bandwidth of 6.0%. The absorptive circular dichroism is +0.72 (LCP absorption domination) and −0.79 (RCP absorption domination) at 8.98 GHz and 12.22 GHz, respectively. The experimental results are shown in Figs. 2(c) and 2(d) which agree well with simulations. The oscillations of values mainly attribute to the non-uniform axial ratio of CP antennas, which further affect the optical response differences between LCP and RCP waves. Imperfect PCB fabrication precision and interference from the environment would also produce slight experimental errors.
Fig. 2. (a) Simulated reflectances and (b) calculated absorption and absorptive CD of DTR-V metamirror. (c) and (d) are the corresponding measured results.
The optical responses from varied combination modes of dual resonators are further studied in Fig. 3. As we known, for two-dimensional metasurface, the response for CP waves will be transformed into its orthogonal mode with its mirror image [21]. Here, the mirror image (along the y-axis) is marked with superscript “T”. Specifically, for the mirror image of DTR-V (${\tau _1}^T + {\tau _2}^T$) case, the absorption modes will be reversed to RCP domination (negative CD) and LCP domination (positive CD) for lower and higher resonances. When the ${\tau _1}$ resonator and mirror symmetrical ${\tau _1}^T$ resonator are combined vertically, the structure does not have any circular dichroism over the whole frequency range. The LCP absorption and RCP absorption play an equal role with the counter split opening directions. This permutation and combination are also suitable to the ${\tau _2}$ resonator, as shown in Figs. 3(a) and 3(b).
Fig. 3. Simulated absorption and $C{D_{ab}}$ spectra for varied combinations: (a) ${\tau _1} + {\tau _1}^T$, (b) ${\tau _2}^T + {\tau _2}$, (c) ${\tau _1} + {\tau _2}^T$, (d) ${\tau _1}^T + {\tau _2}$. $C{D_{ab}}$ spectra of (e) ${\tau _1}^R + {\tau _2}$, (f) ${\tau _1} + {\tau _2}^R$. The bottom right insert in (c) is the LCP absorption of ${\tau _1}$ and ${\tau _2}^T$ individually.
Although ${\tau _1}$ and ${\tau _2}$ resonators are equipped with different eigenfrequencies, either one of them cannot individually stimulate strong absorptive CD. Situations are similar to the cases of ${\tau _1} + {\tau _2}^T$ and ${\tau _1}^T + {\tau _2}$ variants. Optical activities with two resonances (around 12 GHz and 13 GHz) result from the superposition of individual eigenfrequencies. As shown in the bottom right insert of Fig. 3(c), the LCP absorption of ${\tau _1}$ and ${\tau _2}^T$ resonators are +0.82 at 14.69 GHz and +0.64 at 13.68 GHz, respectively. Resonant frequencies shifts mainly come from the differences of overall permutation of final combined chiral molecules. Later, we discuss the responses with individual resonator rotated round central axis. Here, the rotation variant (along the z-axis) is marked with superscript “R”. The $C{D_{ab}}$ is very similar in the $^{\prime}{\tau _1}^{\prime}$ rotated (Fig. 3(e)) and ${\tau _2}$ rotated (Fig. 3(f)) cases. The differential absorptive performance is significantly affected when the individual resonator are rotated with 90°/270°. Both the lower and higher resonances are very weak compared with initial prototype. The surface currents accompanied with magnetic coupling between two metallic layers are seriously destroyed, which makes the design don’t work. For the cases of 180° rotation, although the higher resonant intensity is weakened, strong $C{D_{ab}}$ at lower frequencies is preserved. This deterioration of CD around 12.5 GHz is attributed to the approximate symmetry along the mirror axis along the x-coordinate.
In order to understand the loss mechanism of the DTR-V metamirror, the power loss density distribution (The z-coordinate of the cutting plane is located as z = 1 mm) under the CP wave is analyzed in Fig. 4. Closely linked with the power loss, the influences on $C{D_{ab}}$ caused by certain sensitive geometric parameters are also investigated in Fig. 5. In Fig. 4(a), there is almost no power loss in this chiral device for the incident RCP wave at 8.98 GHz. On the contrary, LCP incident wave interact intensely with the chiral molecules. Part of the loss is mainly concentrated at the position a5 and r1 of the ${\tau _1}$ resonator, and the other part is at the position b5 and r2 of the ${\tau _2}$ resonator, as shown in Fig. 4(b). This is convincingly demonstrated by a5 and b5 parameters sweep in Figs. 5(a) and 5(b). At low resonant frequencies, the $C{D_{ab}}$ values drastically fluctuate with the change of these two parameters. At the same time, a5 is more sensitive than b5, which accords well with the power loss distributions in Fig. 4(b). Both the ends of upper right and bottom left arcs immediately impact the rotational and mirror symmetries with relatively homogeneous power loss distributing on both ${\tau _1}$ and ${\tau _2}$ resonators. Thus strong absorptive CD can be stimulated only when the ${\tau _1}$ and ${\tau _2}$ resonators are integrated with high degree of asymmetry.
Fig. 4. Cross section of power loss in the dielectric layer on the x-y plane: (a) and (b) are for RCP and LCP illumination at 8.98 GHz. (c) and (d) are for RCP and LCP illumination at 12.22 GHz. (e) The z-coordinate position of the cut plane.
Fig. 5. The absorptive CD spectra of the designed DTR-V metamirror with different geometric parameters: (a) a5, (b) b5, (c) a3, (d) b3, (e) a7, (f) b7. (unit: mm)
Interestingly, at the high resonant frequency of 12.22 GHz, the situation is similar with the case of ${\tau _1}^T + {\tau _2}$ in Fig. 3(d). However, the RCP absorption is greatly enhanced. The energy loss mainly concentrates on ${\tau _2}$ resonator, with additional dissipation area at a3 of $^{\prime}{\tau _1}^{\prime}$ resonator. From Figs. 5(c)-(f), it can be seen that the influences of parameters b3 and b7 on $C{D_{ab}}$ are more sensitive than parameters a3 and a7, all of which have little impact on the lower resonance. It is worth noting that a3 and b3 will show positive $C{D_{ab}}$ with certain parameters, indicating LCP absorption dominations. Phase difference between ${E_x}$ and ${E_y}$ can be produced by this anisotropy chiral molecules. Sufficient phase accumulation can be obtained by the change of certain parameters, which will reverse the LCP/RCP absorption dominations [37]. After all, $C{D_{ab}}$ is intensely influenced by the change of the geometric parameters, which is directly linked with the symmetry degree of the total combined chiral molecules. They play an indispensable role in the realization of spin-dependent absorption of the DTR-V metamirror.
Further, the simulated results of $C{D_{ab}}$ spectra with different loss tangents are shown in Fig. 6. As the loss tangent of the dielectric decreases continuously, $C{D_{ab}}$ degrades correspondingly, without the change of both the lower and higher center resonant frequencies. For lossless dielectric medium, $C{D_{ab}}$ is reduced to zero without both the LCP and RCP absorptions. However, even if a small value (0.005) is taken, the peak values are still above 0.5. Strong magnetic coupling between two metallic layers are achieved, which yields intense normal component electric field (${E_\textrm{z}}$) in the middle dielectric [35,38]. Together with the constructive/destructive interference within multi-layer reflections [39], the combined chiral molecules produce different phase shifts for LCP/RCP modes, transforming most incident electromagnetic wave energy to thermal energy (dielectric loss).
The sensitivity of the metamirror to incident angle is one of the key factors which affects its application in practice. As shown in Fig. 7(a), with the increase of incident angles, the lower resonance is blue-shifted and the amplitude reduces gradually. It is still greater than 0.54 when the incident angle is up to 60°. Different incident angles will bring different phase shifts for counter handedness states, and further weaken the constructive/destructive interference within multi-layer reflections. For higher resonance, although the bandwidth is seriously deteriorated, the peak values around 12.22 GHz keep unity. The experimental results match well with the simulated results.
Fig. 7. (a) simulated and (b) experimental $C{D_{ab}}$ spectra at different oblique incidence angles.
To further investigate the influence of periodical arrangements on chiral response, double τ resonators with horizontal arrangements metamirror (DTR-H) are introduced to compare with DTR-V. Here, all parameters of ${\tau _1}$ and ${\tau _2}$ resonators remain unchanged, and the horizontal periodic length of side is also consistent with the vertical periodic length of side in DTR-V (parameter T). The diagram is shown in the insert in Fig. 8(a). In addition, ${\tau _1}$ and ${\tau _2}$ resonators still keep counter split opening directions. It is not difficult to find that the DTR-H still has a strong absorption (91.7%) for the LCP incident wave at 9.14 GHz and a much weaker absorption of 20.9% for RCP incident wave. As shown in Fig. 8(b), the power loss mainly accumulates at a5, b5, center arcs of ${\tau _1}$ and ${\tau _2}$ resonator (r1 and r2), which perfectly accord with the situation in Fig. 4(b). While the absorption of the RCP incident wave is much weaker. For higher frequency resonance around 12 GHz, the absorption of the two CP modes are almost the same. This vanish of CD is attributed to the approximate symmetry along the mirror axis (as the dotted line of the insert) along the y-coordinate, which is similar with the situations in Fig. 3(e) and Fig. 3(f) (With the individual resonator rotated with 180°).. In essence, this resonance of DTR-H at 12 GHz, is a linearly polarized absorption (x-polarized absorber), with the most power loss dissipated around the top horizontal metallic bars (Fig. 8(c)). A weak optical response around 13 GHz is because of the imperfect mirror symmetry arising from the geometric parameters differences between the ${\tau _1}$ and ${\tau _2}$ resonators.
Our proposed metamirrors also have similar absorption characteristics in the mid-infrared band. Parameters of the structure are modified appropriately as the wavelength is reduced. The model construction also uses a metal-dielectric-metal sandwich structure, where the metal is replaced by lossy metal Ag and described using the Drude model (the dielectric constant is 6.0, plasma frequency is $1.37 \times {10^{16}}rad\cdot {s^{ - 1}}$, and collision frequency is $8.5 \times {10^{13}}rad\cdot {s^{ - 1}}$) [40]. The middle dielectric layer is silicon dioxide with the relative dielectric constant of 2.25. Other optimized sizes are: a1 = 960 nm, a2 = 240 nm, a3 = 500 nm, a4 = 822 nm, a5 = 680 nm, a6 = 178 nm, a7 = 282 nm, a8 = 196 nm, a9 = 80 nm, r1 = 246 nm, b1 = 1140 nm, b2 = 240 nm, b3 = 560 nm, b4 = 822 nm, b5 = 660 nm, b6 = 240 nm, b7 = 340 nm, b8 = 110 nm, r2 = 325 nm, h1 = 40 nm, h2 = 480 nm, T = 3700 nm. As shown in Fig. 9, both the DTR-V and DTR-H metamirrors have similar chiral characteristics as the microwave models. It is worth noting that, the LCP/RCP dominative absorption is enhanced because of the localized or unlocalized surface plasmon (SP) coupling for mid-infrared [41].
Fig. 8. (a) Absorption and absorptive CD of DTR-H metamirror. Cross section of the power loss in the dielectric layer on the x-y plane: (b) is for LCP illumination at 9.10 GHz. (c) is for x polarized illumination at 11.95 GHz. (d) The z-coordinate position of the cut plane.
A comparison between our work and other previously reported CD metamirrors is provided in Table 1. We find that the majority of CD metamirrors are suited to single band in GHz. Compared with the dual-band design in [37], our structure yields remarkable CD intensity enhancement. Although the metamirror in [21] has the widest bandwidth, it occupies five layers with air spacer which is difficult to get practical applications. In addition, this design is determined by lumped resistor, which is hard to be realized in higher frequencies. In summary, our proposed metamirror is equipped with both strong absorptive CD and minimum thickness. There is still room for CD optimization in the future work. Variants with diversified chiral molecules combinations are capable of realizing dual/multi operating bands which also enhance the optical response greatly. Besides, this design strategy is also effective and applicable for higher frequencies, including GHz, THz, and IR.
Table 1. Comparison With Some Previously Reported CD Metamirrorsa
4. Conclusion
We have numerically and experimentally demonstrated an absorptive circular dichroism metamirror that differentially absorbs circularly polarized waves with dual/multi bands. The simulated results demonstrate this DTR-V metamirror can achieve high-Q resonance of LCP absorption domination at 8.98 GHz and wideband resonance of RCP response at around 12.5 GHz. Diversified chiral molecules combinations, including different structural units, co/counter split opening directions, individual resonator rotations, and vertical/ horizontal periodical arrangements are investigated to reveal the switchable optical response. The underlying mechanism is confirmed by detailed analyses of power loss distributions and parameters scanning. It is proved that the overall permutation symmetry breakdown of total combined chiral molecules is the determining factor for the absorptive CD. This design strategy is also effective and applicable for higher frequencies, which could provide alternate approaches to lightweight and reconfigurable metadevices.
Funding
K.C. Wong Magna Fund in Ningbo University; National Natural Science Foundation of China (61771268, 61871242).
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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