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Abstract
Chiral metamirror is one of the recently developed metadevices which can reflect designated circularly polarized waves, mimicking the exoskeleton of iridescent green beetles. Here, an optically transparent metamirror that can absorb microwave chiral photons in a broadband spectrum is demonstrated. A coupled mode theory is adopted to reveal the underlying physics for the improved bandwidth performance. Excellent agreements have been observed between numerical and experimental results, indicating a bandwidth for chiral absorption as high as 2.37 GHz. The optical transparence of the resistive patterns and substrate make the designed metamirrors suitable as microwave coatings in front of optical devices, which may find potential applications in cascaded optical systems working for both microwave and optical signals.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Enhancing the absorption of light is of significant importance due to its wide applications in radar cross section reduction [1], photovoltaics [2,3], light detection [4,5], biosensing [6], thermal imaging [7], light emission [8,9], and so forth. The recent rise of metamaterials opens new opportunities to tailor the electric and magnetic responses in subwavelength meta-atoms, leading to ultrathin perfect absorbers from radio to optical frequencies [10,11]. Since its first demonstration [12]. metamaterial-based absorption has been realized by either metallic or dielectric resonators and harvest the incident light over a broad band [13]. Various methods have been investigated to explore wideband absorption, including multiple resonances [14,15]. stacked multilayers [16], lumped elements [17], and nanocomposite structures [18]. Polarization sensitive and insensitive absorbers can be achieved by utilizing isotropic and anisotropic inclusions, respectively.
More recently, chiral metamirror comprised of chiral meta-atoms expands the functionality of metamaterial absorber. Compared with ordinary absorbers, chiral metamirror absorbs specific chiral photons and reflect back those with an opposite handedness. The design principle for chiral absorption is simultaneously breaking the required rotational and mirror symmetries, by using twisted structures [19] or asymmetric metasurfaces [20–23]]. The spin-selective absorption of chiral metamirrors provides an extra degree of freedom to design chiroptical devices [21,24–26]. For instance, ultracompact circularly polarized light detector that distinguishes circular polarized light can be achieved, by combining chiral plasmonic nanostructures with hot electron injection [27]. By introducing gradient phase discontinuities, chiral beam deflector is capable of anomalously reflecting specific chiral photons while totally absorbing other spin states [28,29]. Independent meta-hologram for one circular polarization has also been developed based on chiral building blocks, providing multiplexing holograms with reduced polarization cross-talk [30]. So far, narrow bandwidth is the major limitation of the metamirror-based chiral absorption. Despite efforts have been spent to improve the bandwidth [31], the physical mechanism of chiral interactions is complicated and chiral absorbers with broadband performance are still urgently needed.
At the same time, optically transparent metamaterials have also attracted intense interest due to its promising electronic applications in scenarios where large light transmittance is required. The routes for optically transparent absorbers include using transparent spacer and resistive films like graphene, Indium tin oxide (ITO) or other conducting oxides [32–35]. Compared with traditional metamaterials, optically transparent metamaterials become more promising for advanced electromagnetic devices with both microwave and visible functionalities.
In this paper, we report on a strategy to design optically transparent chiral metamirrors with high-efficiency chiral absorption over a wide microwave band. ITO film with moderate surface resistance is selected as the material for chiral meta-atoms, in order to increase the dissipation rate of a chiral resonator. A coherent coupled mode theory is employed to reveal the underlying mechanism of broadband chiral absorption. By using polymethyl methacrylate (PMMA) and polyethylene glycol terephthalate (PET) substrates, the fabricated metamirror shows high transparence for visible light. Experimental measurement agrees well with the numerical calculations, showing a single resonant peak in reflection. The bandwidth of the proposed metamirror is as high as 2.37 GHz, nearly 7 times as high as that in copper-based structures.
2. Coupled mode analysis for chiral absorption
We start with the physical mechanism and design principle of chiral metamirror. As we know, typical reflective metamirrors are comprised of periodic meta-atoms upon a metallic substrate, separated by a dielectric spacer. The incident field is absorbed or reradiated while interacting with meta-atoms at the interface. For a planar meta-atom array as depicted in Fig. 1(a), we assume the meta-atoms are illuminated by two coherent waves, with one as the incidence the other as the reflected one from the metallic plane. An equivalent resonance model, as shown in Fig. 1(b), is capable to analyze its scattering properties together with symmetry considerations. $\vec{q} = {[{{q_x},{q_y}} ]^T}$represents the complex oscillation amplitude for different modes. Input fields are described by the amplitude $\vec{a} = {[{{a_{1x}},{a_{2x}},{a_{1y}},{a_{2y}}} ]^T}$, where ${\vec{a}_1} = {[{{a_{1x}},{a_{1y}}} ]^T}$ and ${\vec{a}_2} = {[{{a_{2x}},{a_{2y}}} ]^T}$ indicate those incident waves from the top and the bottom, respectively. The output fields are written as $\vec{b} = {[{{b_{1x}},{b_{2x}},{b_{1y}},{b_{2y}}} ]^T}$, with ${\vec{b}_1} = {[{{b_{1x}},{b_{1y}}} ]^T}$and ${\vec{b}_2} = {[{{b_{2x}},{b_{2y}}} ]^T}$for the waves propagating in + z and -z directions, respectively. The subscripts ‘x’ and ‘y’ represent two linear polarizations. The coupled mode theory (CMT) [36–38] can be adopted to describe the wave behavior of this system. The coupled equations are expressed by
Fig. 1. Coupled mode analysis of coherent illumination on a metasurface. (a) Schematic illustration of a general metasurface under coherent inputs ${\overrightarrow a _1}$ and ${\overrightarrow a _2}$, generating output waves ${\overrightarrow b _1}$ and ${\overrightarrow b _2}$. (b) The equivalent single-port resonator model with the input $\overrightarrow a $ and the output $\overrightarrow b $. $\gamma _{x,y}^s$ is radiative scattering rate, $\gamma _{x,y}^d$ is the dissipation rate, and is the near-field coupling. (c) Calculated reflection spectra for different resonant parameters. Red curves: $\gamma _x^s$ = 0.06 GHz, $\gamma _y^s$ = 3.5 GHz, $\gamma _y^d$=$2\gamma _x^d$ = 0.2 GHz, $\kappa$ = 0.4 GHz. Blue curves: $\gamma _x^s$ = 0.06 GHz, $\gamma _y^s$ = 3.5 GHz, $\gamma _x^d$=$2\gamma _y^d$ = 1 GHz, $\kappa$ = 0.4 GHz. Black curves: $\gamma _x^s$ = 0.6 GHz, $\gamma _y^s$ = 5 GHz, $\gamma _x^d$=$2\gamma _y^d$ = 1 GHz, $\kappa$ = 1.2 GHz. Solid and dashed curves represent ${R_{ +{-} }}$ and ${R_{ -{+} }}$, respect$\kappa $ively.
where $\gamma _\mu ^s$ ($\mu \in \{{x,y} \}$) is the radiative scattering rate, $\gamma _\mu ^d$ the dissipation rate, ${\delta _\mu } = f - {f_\mu }$ the frequency detuning, ${f_\mu }$ the resonant frequency, and $\kappa$ the near-field coupling for each mode. K describes the coupling between the input (output) fields and the resonant system, C indicates the direct coupling between the input and output fields. From Eq. (1), we can derive the scattering matrix (defined by $\textbf{S}\overrightarrow a = \overrightarrow b $) that relates the input and output fields
To enhance the interaction between input fields and meta-atoms, we introduce identical phases for the forward and backward inputs by setting ${\overrightarrow a _1} = {\overrightarrow a _2}$. Such a condition will guarantee the antinode of the standing wave at the meta-atom plane, and thus results in a maximum coupling. Consequently, the output fields propagating in the + z direction can be calculated byFrom above equations, we can find that a large frequency detuning can be achieved by increasing $\gamma _\mu ^d$, $\gamma _\mu ^s$ and $\kappa$, so as to improve the bandwidth performance of chiral absorption. To validate this concept, we investigate several parameter combinations, as demonstrated in Fig. 1(c). The resonant frequency is set to fx = fy = 10 GHz. In the first case (red curves), the CMT parameters are selected as $[{\gamma_x^s,\gamma_y^s,\gamma_x^d,\gamma_y^d,\kappa } ]$= [0.06, 3.5, 0.1, 0.2, 0.4] GHz. The corresponding metamirror shows a narrowband chiral absorption mode because of the low dissipation rates. In the second case (blue curves), the dissipation rates are increased to $[{\gamma_x^d,\gamma_y^d} ]$ = [1,0.5] GHz while keeping other parameters unchanged. At this point, the bandwidth of the resonant mode becomes large yet the efficiency of the chiral absorption declines. In the third case (black curves), larger radiative scattering rates and stronger coupling effect are adopted, with the new values of $[{\gamma_x^s,\gamma_y^s} ]$ as [0.6, 5.0] GHz and $\kappa$as 1.2 GHz. Consequently, the circular dichroism grows again over a broadband frequency range. Therefore, significant increase on the radiative scattering rates, the dissipation rates, and the coupling strength is greatly helpful for building broadband and highly efficient chiral metamirrors.
3. Designer broadband chiral metamirror
Following the theoretical analysis presented above, we next design a broadband chiral metamirror. Since the key point is to design meta-atoms with large dissipation rates, we choose a highly lossy conductive material, such as ITO, instead of copper. Compared with copper, ITO film has larger resistance and shows transparency to the visible light, serving as an ideal platform for broadband and optically transparent metamirrors. Two optimized devices and their electromagnetic performance are illustrated in Fig. 2. The first metamirror is comprised of copper-based meta-atoms, as shown in Fig. 2(a). Each unit cell is a cubic with the lattice constant of 8.8 mm and its total thickness is 2.9 mm. The dimensions of the asymmetric split-ring resonator are l = 5.5 mm, k = 2.91 mm, w = 1 mm, g = 1 mm. Copper is selected as the conductive material with the conductivity of 5×107 S/m and its thickness dCu = 0.105 mm. The thickness of FR4 spacer is 2.7 mm, with the relative permittivity of 4.2 and the loss tangent of 0.025, copper background is located at the bottom.
Fig. 2. Designer chiral metamirrors. (a) A unit cell of the copper-based metamirror. (b,c) The corresponding absorption and reflection spectra. (d) The designer ITO metamirror. (e,f) The corresponding absorption and reflection spectra.
The second metamirror is designed with ITO resonators, as shown in Fig. 2(d). Compared with copper, ITO not only has bigger impedance but also has excellent optical transparency. The lattice constant is 9.4 mm and the total thickness H = 3.9 mm. It consists of two ITO-PET film layers and a PMMA layer between them. The surface impedance of ITO-PET film layers is 5Ω/sq and the permittivity of PET is 3, the thickness of ITO-PET layer dPET = 0.175mm. The thickness of the PMMA spacer dPMMA = 3.6 mm and its permeability is 2.25. The geometry parameters of the ITO resonator are l1=8.4 mm, k1 = 4.7 mm, w1 = 1.0 mm, g1 = 2.0 mm.
In order to show the different absorption and reflection spectra of the two chiral metamirrors, we have performed a full-band simulation by using CST Microwave Studio. Chiral metamirror has different responses to left-handed (LCP) and right-handed circularly polarized (RCP) waves. Circular dichroism (CD) has been calculated to describe the chiral performance (CD = ALCP – ARCP), where ALCP(RCP) refers the absorption of LCP (RCP) waves. Usually, metamirrors can have a good performance of manipulating polarized wave when CD is larger than 0.5, so we define the bandwidth (BW) as the frequency range where CD is larger than 0.5. As shown in Fig. 2(b), the BW of the copper-based chiral metamirror is about 0.327 GHz, with the maximum absorption reaching 99.7%. Meanwhile, the absorption of RCP waves is pretty low, and it is suppressed lower than 20% in a fairly wide band. In the Fig. 2(c), we can see that for the RCP incidence, the metallic metamirror has a good reflection ability and the ratio of polarization conversion is high. As shown in Fig. 2(e), the BW of the ITO chiral metamirror is about 2.37 GHz, which is much larger than that of the metallic one. The maximum absorption of LCP waves approaches nearly 100%. Meanwhile, the absorption of RCP waves is kept less than 30% over a wide frequency range. In Fig. 2(f), we can see that under RCP incidence, the ITO metamirror has low absorption, reflecting back the waves without changing the handedness. Compared with the copper-based metamirror, ITO metamirror has a broader chiral band 7 times as large as that of a copper-based one. It means that the utilization of high impedance materials is capable of increasing the bandwidth of metamirrors.
We have employed a particle swarm optimization to fit the coupled mode parameters. As shown in Fig. 3, the fitted curves match well with the simulation results. According to the CMT model, we calculated the parameters of two metamirrors, as shown in the Table 1. From the table, we can find that ITO metamirror has larger radiative scattering rates, dissipation rates and near-field coupling, in consistence with previous prediction. In our design, copper is selected as the conductive material with the conductivity of 5×107 S/m and the thickness 0.105 mm. The square resistance of copper sheet is thus 1.64×10−4 Ω/sq. As a comparison, ITO has a large square resistance of 5 Ω/sq. This is the main reason why ITO chiral metamirror has a wider bandwidth than the copper-based one. It indicates that CMT model provides a promising way to improve the bandwidth of the metamirror. Furthermore, ITO film also could provide good optical transparency. In Fig. 4, we have plotted the time-dependent Ez field distributions of two metamirrors at the plane 0.01 mm below the top layer of each metamirror. The monitor frequency is 10.096 GHz, T is one period of time. For the copper metamirror, the Ez field strength under LCP incidence is stronger than that under RCP incidence. This mode behavior is consistent with the chiral absorption performance, that is, LCP waves are dissipated more efficiently by the induced conducting current in the meta-atoms. Interestingly, the ASRR creates an asymmetric electric dipolar resonance and an asymmetric quadrupole resonance under RCP and LCP incidences, respectively. For the ITO metamirror, the Ez fields of two resonant modes have smaller magnitude discrepancies, indicating smaller CD maximum yet broader bandwidth performance. The LCP mode still behaves as an asymmetric quadrupole resonance.
Fig. 3. Comparison between coupled mode predictions and simulation results. (a) reflection spectra for copper-based metamirror. (b) reflection spectra for ITO metamirror.
Fig. 4. Time-dependent Ez field distributions of two metamirrors under circular polarization illuminations. (a) Copper-based metamirror. (b) ITO-based metamirror. The frequency is 10.096 GHz, the electric field is calculated at the plane 0.01 mm below the top layer of each metamirror.
Table 1. CMT parameters of two kinds of metamirror (unit: GHz)
In order to verify our results experimentally, based on the laser etching process, we made an ITO chiral metamirror with the dimension of 200 mm × 200 mm, consisting of 400 cells. The experimental setup includes an Agilent vector network analyzer and two broadband microwave antennas. Microwave absorbing foams were placed around the sample to reduce the scattering at the edge of the measuring platform. As shown in Fig. 5(a), our antennas are linearly polarized one, so we need change the experimental results into circular basis and obtain the cicular reflection matrix. The photograph of a fabricated sample in Fig. 5(b) shows that the metamirror is highly transparent to the visible light. We have used a UV-2450 spectrophotometer to measure the visible transmission spectra of two homogeneous samples: one PMMA slab with a single-layer ITO film and another PMMA slab with ITO films on both sides. The measured results of these two samples can describe the optical transparency performance of two regions of the metamirror: the region without meta-atoms and the region with meta-atoms. The results are plotted as the red and blue curves in Fig. 5(c). Then the transmission spectrum of the ITO metamirror is calculated by considering the filling ratio of two structures. The black curve in Fig. 5(c) shows that the transmittance of the ITO metamirror is more than 50% in the wavelength range of 400 nm -700 nm. It implies that the ITO metamirror can be used not only in the microwave range, but also compatible with optical devices.
Fig. 5. Experimental verification. (a) Schematic of the measurement setup with linear antennas. (b) The photograph of the fabricated sample with high optical transparency and its partial enlarged detail (the inset), with a logo of Shandong University located at the bottom. (c) The transmittance spectra from 400 nm to 700 nm of three ITO structures. Red curve: a homogeneous ITO/PET/PMMA slab. Blue curve: a homogenous ITO/PET/PMMA/PET/ITO slab. Black curve: the ITO metamirror. (d) Measured absorption spectra. (e) Measured reflection coefficients.
The measured absorption and reflection spectra are illustrated in Fig. 5(d) and 5(e). The bandwidth of circular dichorism is about 2.51 GHz. For LCP waves, the absorption is higher than 70% from 8 GHz to 11 GHz. For RCP waves, however, the absorption rate is kept less than 30%, and the metamirror provides a large ratio of reflected RCP to LCP waves over a wide bandwidth. At specific frequencies, the absorption of the sample to LCP waves is slightly smaller than the simulation. However, the experimental results are still in good agreement with the simulation.
In practical applications, angular sensitivity is an important feature. We further investigate the performance of the metamirror at different angles. Figure 6(a) shows the absorption spectra of the chiral metamirror at the 20° incidence. Here, the red curves represent the absorption spectra for LCP waves, while the blue curves correspond to the RCP counterparts. The BW of the metamirror is still quite wide when the angle of incidence is 20°, which is about 2.47 GHz, with the maximum absorption reaching 99.5%. As shown in Fig. 6(b), when the angle of incidence increases from 20° to 40°, the BW is narrower than before, which is about 1.5 GHz. but the contrast between LCP waves and RCP waves still remains high with the maximum absorption is 93%. We can see that it still has a broadband characteristic when the incidence angle is 40°. The measured results are shown in Fig. 6(c) and Fig. 6(d) respectively, due to the inaccurate fabrication of the sample, there are some differences between the measured absorption spectra and the simulation one, but it shows that the ITO metamirror still has a good circular polarization control effect when the waves income at oblique angles.
Fig. 6. Optical responses of the chiral metamirror at oblique incidences. Simulated absorption spectra at (a) θ = 20°, and (b) θ = 40°. Measured results for (c) θ = 20°, and (d) θ = 40°.
4. Conclusion
In summary, we have proposed a coherent coupled mode theory to study the chiral absorption of metamirrors. The established model reveals the underlying mechanism for the bandwidth performance and provides a guidance in the design of broadband chiral metamirrors. As an experimental verification, a chiral metamirror composed of ITO meta-atoms, PMMA and PET spacers has been demonstrated in the microwave region, with much boarder bandwidth of chiral absorption. Furthermore, the designer metamirror is highly transparent to visible light and could be suitable in cascading with optical devices. Our study may provide a theoretical guidance to the design of broadband metamirrors, and open up an alternative way towards microwave chiral devices with optical transparency.
Funding
National Key Research and Development Program of China (2018YFB2200703); National Natural Science Foundation of China (61801267, 61801268); Natural Science Foundation of Shandong Province (ZR2018QF001); Fundamental Research Fund of Shandong University (2017TB0014); Young Scholars Program of Shandong University.
Disclosures
The authors declare no conflicts of interest.
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