Chiral metamaterial absorber with high selectivity for terahertz circular polarization waves

Yongzhi Cheng; Haoran Chen; Jingcheng Zhao; Xuesong Mao; Zhengze Cheng

doi:10.1364/OME.8.001399

1. Introduction

Electromagnetic (EM) metamaterials (MMs) as artificial materials made from sub-wavelength metal/dielectric structures possesses exotic properties and capability for the manipulations of the lights that are unavailable in nature [1]. The MM absorber (MMA) as a particular research branch of MMs has been paid a great attention increasingly due to its potential application in stealth, energy harvester, sensing and so on [2–9]. Design and realization of the high performance and multi-functional MMAs for various applications are always the important goals pursued by researchers. Up to now, various MMAs have been proposed and demonstrated to be able to near perfectly absorb EM waves across the whole spectrum from microwave to visible region [10–19]. However, the majority of the designed MMAs are operated only for the linear polarization (LP) waves, and seldom for circular polarization (CP) waves. The CP wave could be widely used in optoelectronic techniques and devices, such as optical communication, liquid crystal displays, remote sensors and circular dichroism (CD) spectroscopy [20–23]. It is highly desirable to design high performance devices, especial the absorber for CP wave.

Recently, chiral MMs (CMMs) have been attracted great interest since they cannot only manipulate the LP waves but also CP waves [24]. CMMs as a sub-class of the MMs lacks any planes of mirror symmetry and cannot be brought to coincide with themselves, where the right circular polarization (RCP, + ) and left circular polarization (LCP, -) waves of two eigenmodes are excited for the normal incident arbitrary plane EM wave. Generally, CMMs have different responses for LCP and RCP waves, thus resulting in a CD effect and other exotic EM properties by special chiral-geometric design [24–32], such as optical activity, negative refraction, asymmetric transmission (AT) effect, and polarization conversion. Various designs of CMMs including conjugated gammadion structure [24], spiral wire structure [25], split-ring structure [26–28], cut-wire structure [29], three-dimensional helix structure [30], L-shaped structure [31,32], and other novel structures [33–36] have been proposed and demonstrated to enable chiral-selective field enhancement for special CP waves. However, in the above mentioned designs of the CMMs, the emphasis for the CP waves is mainly put on the transmission rather than reflection. From the viewpoint of absorber design, both the transmission and reflection of the CP waves should be taken into account. Therefore, it is expected that the CMMs would play a key role in constructing novel absorbers for the CP waves. Li et al proposed an ultra-thin CMMA based on the L-shaped folded metallic wires $LCP$ , which can only absorb the LCP wave with the absorbance of 93.2% [37]. Then, Tang et al proposed a chiral-selective plasmonic absorber based on ŋ-shaped-resonators [38], which can achieve the selective absorption for LCP and RCP waves, respectively. However, the absorbance for LCP and RCP waves is less than 90%. To my best knowledge, there are no relative reports of the high performance CMMA for LCP and RCP waves, especially in terahertz region. The development of MMs with unusual properties at terahertz region is especially important since devices for manipulating the terahertz wave is considerably limited. Thus, the effective design of the CMMA with the high chiral-selectivity and perfect absorption performance waves is highly desirable in terahertz range.

In this work, we demonstrate numerically a novel CMM absorber (CMMA) with high chiral-selective absorption for LCP and RCP waves in terahertz region. The unit-cell of the proposed CMMA consists of a bi-layered fourfold twisted Via-T-shaped (VTs) structure printed on both sides of a dielectric substrate. The CMMA could selectively achieve high absorption level of over 90% for different CP waves depending on the chirality. Due to the strong selective absorption of the proposed CMMA, a high CD value of over 34 dB can be achieved. The physical mechanism behind chiral-selective absorption is analyzed in detail. This selective absorption property of the proposed CMMA can be applied as a homogeneous circular polarizer and a negative refractive index medium. Such proposed CMMA designs suggest applications in frequency selective absorption filters, terahertz spectroscopic, detecting, and terahertz communications.

2. Structure design and simulations

Figure 1 shows schematic diagram of the unit-cell structure of the proposed CMMA, which is composed of bi-layered fourfold twisted VTs separated by a dielectric substrate. The fourfold T-shaped structure on each side of the dielectric substrate is positioned so that each one rotated by 90^◦ with respect to its neighbor. In this physical model, the front fourfold T-shaped structure is connected with the bottom one by a copper cylinder, and the diameter of copper cylinder is the same with the wire width of the T-shaped structure. Thus, the overall unit-cell structure has uniaxial fourfold rotational (C₄) symmetry for plane wave propagation direction, not any mirror plane and center of inversion, thus leading to the strong chirality. In numerical simulation, the polydimethylsiloxane (PDMS) with permittivity and loss tangent of 2.35 and 0.06 is selected as a dielectric substrate [39]. The metallic patterned layers were modeled as a gold film, and the material parameters are explained by the surface impedance model with Drude parameters [40]. The optimized geometric parameters of the unit-cell structure are given as: p = 80 μm, l = 48 μm, l₀ = 22 μm, w = 6 μm, t_s = 21 μm, g = 12 μm, t_m = 0.6 μm. The CMMA structure is periodic along the x- and y-axis with the periods of 80 μm to avoid diffraction at the normal incidence for frequencies up to 3.75 THz.

Fig. 1 Schematic of the designed CMMA: (a-c) the front, lateral and perspective view of the unit-cell structure, respectively.

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To explore the chiral-selective absorption properties of the proposed CMMA, the numerical simulation was carried out by the frequency domain finite element method using the CST Microwave Studio. In numerical simulation, the unit-cell boundary condition was applied and the two CP (LCP and RCP) eigenwaves were used directly. In simulation process, a broadband CP wave is employed as the excitation source and is normally through the unit-cell structure of the proposed CMMA from the + z to -z direction. For the normal incident CP waves, both transmission and reflection coefficients can be recorded in numerical simulation. Thus, the absorbance of the proposed CMMA for LCP and RCP waves can be calculated using the following equations:

A_{-} = 1 - R_{+ -} - R_{- -} - T_{- -} - T_{+ -} = 1 - {| r_{+ -} |}^{2} - {| r_{- -} |}^{2} - {| t_{- -} |}^{2} - {| t_{+ -} |}^{2}

A_{+} = 1 - R_{- +} - R_{+ +} - T_{+ +} - T_{- +} = 1 - {| r_{- +} |}^{2} - {| r_{+ +} |}^{2} - {| t_{+ +} |}^{2} - {| t_{- +} |}^{2}

Where t_– and t₊₊ are the LCP and RCP transmission coefficients, respectively; r_– and r₊₊ are the LCP and RCP reflection coefficients, respectively; t_+-, t_-+, r_+- and r_-+ are the cross-polarization reflection and transmission coefficients, respectively. The A_- (A₊) presents the absorbance of the LCP(RCP) waves. Owing to the C₄ symmetry of the unit-cell structure of the designed CMMA, the cross-polarization reflection and transmission coefficients (t_+-, t_-+, r_+- and r_-+) are very small (<0.01), thus negligible. Therefore, in this study, we just need to consider co-polarization reflection and transmission coefficients (t_–, t₊₊, r_– and r₊₊) for normal incident CP waves. The calculation equations of absorbance of the proposed CMMA can be rewritten as:

A_{-} = 1 - R_{- -} - T_{- -} = 1 - {| r_{- -} |}^{2} - {| t_{- -} |}^{2}

A_{+} = 1 - R_{+ +} - T_{+ +} = 1 - {| r_{+ +} |}^{2} - {| t_{+ +} |}^{2}

For the designed CMMA, besides the absorbance, the other chiral optical properties also should be considered. The important one is CD parameter (△), referring to the absorptivity difference between the RCP and LCP waves, which is expressed by the following equation:

Δ = lg | T_{+ +} | - lg | T_{- -} |

Another one is ellipticity angle η, which characterizes the polarization state of transmitted waves, and expressed as:

η = arc \tan [(| t_{+ +} | - | t_{- -} |) / (| t_{+ +} | + | t_{- -} |)]

It should be noticed that the ellipticity angle η also can be used to measure the CD effect.

3. Results and discussions

Figure 2(a) shows the simulated reflection and transmission coefficients as a function of frequency for normal incident CP waves. It can be observed that the magnitudes of the reflection coefficients r_– and r₊₊ for LCP and RCP waves are equal; both of them are less 0.3 around resonance frequencies of 1.91 THz and 2.91 THz. It means that the relative impedance of the CMMA is nearly matched to free space at resonances. It also can be observed that the transmission of RCP and LCP waves are different significantly at resonances due to the chiral nature of the proposed CMMA structure. At the lower frequency of 1.91 THz, the magnitude of transmission coefficient for the RCP wave is about 0.88, which is higher than that for the LCP waves, and the one for the LCP is about 0.16. While the magnitude of transmission coefficient for the RCP wave is about 0.042 at the higher frequency of 2.91 THz, which is lower than that for the LCP waves, and the one for the LCP is about 0.86. It means that only the RCP waves can be selected to pass through the CMMA while the LCP waves are forbidden to transmit mostly at the lower frequency. At the higher resonance frequency of 2.91 THz, the case is on the contrary, only the LCP waves can be selected to pass through the CMMA while the RCP waves are forbidden mostly to transmit. This will cause the different distortion and absorption of the two CP waves going through the CMMA slab, implying a giant CD effect at resonances.

Fig. 2 (a) Simulated reflection and transmission coefficients for CP waves, (b) the corresponding absorbance for LCP and RCP waves.

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As shown in Fig. 2(b), we present the absorbance spectra for both LCP and RCP wave incidences. It can be observed that the absorbance for LCP wave is 91% and 24%, while the one for RCP is 15% and 97% at 1.91 THz and 2.91 THz, respectively. Obviously, our CMMA has significant absorption for an LCP wave whereas no considerable absorption for RCP wave at the lower frequency of 1.91 THz. On the other hand, at the higher frequency of 2.91 THz, the CMMA becomes strongly absorptive for RCP wave while quite weak absorption for LCP wave. It means that a selective absorption for CP wave with particular handedness while reflecting the other one at different resonance frequency can be realized. Obviously, the CMMA has the two strong chiral-selective absorption frequency band just using a single chiral structure, which is much superiority compared with the previously reported chiral absorbers required different chiral structures for each polarization [33,37]. Thus, our designed structure can act as a perfect LCP wave absorber at the lower resonance frequency while reflecting nearly 90% of the RCP wave, and perfect RCP wave absorber while reflecting LCP wave with reflectance of nearly 90% at the higher resonance frequency. The characteristic of high chiral-selective absorption for LCP and RCP waves will result in a giant CD effect.

The absorbance difference between the LCP and RCP waves can be characterized by CD parameter Δ. As shown in Fig. 3(a), we present the simulated CD spectrum of the CMMA, where the CD amplitude of about 34.6 dB and −42.2 dB at two selective resonance frequency regimes, which could construct a relative pure circular polarizer. To study CMMA applied as a circular polarizer, we give the ellipticity angle η as shown in Fig. 3(b). It can be observed that the value of the η is about −21.8^◦ and 32.5^◦ at the lower and higher resonance frequencies, respectively. It means that, for normal incident waves passing through the CMMA slab, the transmitted wave exhibits prominent RCP and LCP characteristics at the lower and higher resonance frequencies, respectively. It should be noticed that the circular polarizer is valid for any arbitrarily polarized incident waves due to its C₄ symmetry of the unit-cell structure. Thus, the homogenous RCP and LCP polarizer is realized with our proposed CMMA.

Fig. 3 (a) The calculated CD parameter Δ, (b) ellipticity angle η.

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Fig. 4 The retrieved refractive index for (a) LCP and (b) RCP waves.

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It is well known that besides the impedance-matched characteristic, relative large imaginary part of the refractive index is also required for a perfect absorber. Obviously, we can conjectured our designed CMMA is near impedance-matched for LCP and RCP waves at the lower and higher resonance frequencies, respectively. To further characterize the chiral-selective absorptive of the CMMA, we retrieved the refractive index of the LCP and RCP waves using a standard retrieval procedure with the simulation data of the transmission and reflection [41,42]. As shown in Figs. 4(a,b), it can be observed that the real part of the refractive index of LCP and RCP waves is negative, with minimal values of −3.65 and −2.5 around the absorptive peak frequencies, respectively. In addition, the corresponding imaginary part of the refractive index for the LCP and RCP waves are up to the maximal values of about 2.12 and 2.46, respectively. Thus, it can be imagined that the near perfect absorption of the LCP wave at the lower frequency and the one of the RCP wave at the higher frequency are associated with the relative large imaginary part of the refractive index for the LCP and RCP waves, respectively.

To illustrate the resonance mechanism of the chiral-selective absorption associated with the giant CD effect of the proposed CMMA, we studied the surface current and power loss density distributions of the unit-cell structure at 1.9 THz and 2.9 THz, respectively, as shown in Figs. 5 and 6.

Fig. 5 The surface current distributions of the unit-cell structure of the proposed CMMA is drived by the (a,c) LCP and (b,d) RCP waves at (a,b) f₁ = 1.9 THz and (c,d) f₂ = 2.9 THz. The solid (dashed) line arrows represent the front (back) surface current distributions and induced electric field direction.

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Fig. 6 The power loss density distributions of unit-cell structure of the proposed CMMA is induced by the (a,c) LCP and (b,d) RCP waves at (a,b) f₁ = 1.9 THz and (c,d) f₂ = 2.9 THz.

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Figure 5 show the surface current distributions of the proposed CMMA drived by different CP waves at different resonance frequencies. It can be observed that the surface currents on the front and back layer of the unit-cell structure are in the cross direction, which contribute to the weaker virtual magnetic response as well as electric response [24,25,27,43–45]. In addition, the induced surface current liked as parallel and antiparallel distributions in unit-cell structure are projected onto two perpendicular directions in x-y plane, which can form magnetic and electric dipoles along specific directions [43,45]. The chirality is enhanced by the strong cross coupling between electric and magnetic field, which are associated with the giant CD effect [43]. In other words, the enchaned chirality and chiral-selective absorption is originated from the stronger EM coupling for the normal incident CP waves. In our chiral structure, each resonance can be regarded as the superposition of these electric and magnetic response modes. As shown in Fig. 5(a), for the normal incident LCP waves, in x-axis direction, the induced surface current distributions are parallel, revealing an electric response mode. While in y-axis direction, the induced surface current distributions are antiparallel, implying a magnetic response mode. Thus, in this case, the normal incident LCP wave can be absorbed significantly. On the contrary, as shown in Fig. 5(d), for the normal incident RCP wave, in x- and y-axis directions, magnetic and electric response modes are revealed, respectively, thus resulting in perfect absorption. As shown in Figs. 5(b,c), the cases are complex, for the normal incident RCP or LCP wave, both magnetic and electric response modes are excited in y-axis direction, while only the magnetic response mode in x-axis direction. Thus, only the very little RCP or LCP wave energy can be absorbed.

To obtain more insights of the underlying physical mechanism of chiral-selective resonant absorption of the proposed CMMA, we simulated the power loss density distributions of unit-cell structure induced by the different CP waves at different resonance frequencies, as shwon in Fig. 6. It can be observed that the THz wave absorption takes place in different parts of the chiral structure at different resonance frequencies. It exhibits that the different interactions of CP waves with chiral structures can induce different chiral currents inside unit-cell structure, which directly results in the different resonant absorptions. For the case of LCP wave, as shown in Fig. 6(a), it can be seen that a strong resonant absorption occurs at 1.9 THz, and vice versus, for the case of RCP, there is a high resonant absorption at 2.9 THz as shown in Fig. 6(d). As shown in Figs. 6(b,c), for the normal incident RCP wave at 1.9 THz and LCP wave at 2.9 THz, only the little and weak power loss densities are distributed in chiral structure.

Furthermore, the geometric parameters of the unit-cell structure have strong impacts on the chiral-selective absorption characteristics of the proposed CMMA. As shown in Figs. 1(a,b), for the unit-cell structure of the designed CMMA, the chiral-selective absorption properties are mainly determined by four geometric parameters: thickness of dielectric substrate (t_s), the VTs wire length (l) and width (w), and the gap width (g) between two VTs wire. Figure 7 shows the simulated absorbance for the LCP and RCP waves with different values of these geometric parameters (t_s, l, w, and g) of the unit-cell structure.

Fig. 7 Absorbance spectra of the (a1-d1) LCP and (a2-d2) RCP waves of proposed CMMA with different geometric parameters: (a1,a2) thickness of dielectric substrate (t_s), (b1,b2) the VTs wire length (l), (c1,c2) the VTs wire width (w), and (d1,d2) gap width (g) between two VTs wire.

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As shown in Figs. 7(a1,a2), when increases t_s, the resonant frequencies for both LCP and RCP waves decrease gradually while the absorbance at the lower frequency increase and that at the higher frequency decrease slightly, which can be interpreted by the LC resonance circuit theory [46,47]. The resonance frequencies for both LCP and RCP waves can be expressed as $f = 1 / (2 π \sqrt{L C})$ , where C and L are mainly determined by the geometric parameters of the unit-cell structure of the proposed CMMA. The L will increase with the increasing of the t_s, thus resulting in the decrease of the resonant frequencies. For the influence of the t_s on the absorbance, the EM coupling of the RCP wave will be weaken when increases t_s, while the EM coupling effect seldom on the LCP absorption property. Thus, to achieve the perfect absorption for both LCP and RCP waves simultaneously, the appropriate selection of the t_s is very important.

As shown in Figs. 7(b1,b2), there are similar cases when increasing l, the resonant frequencies decrease while the absorbance firstly increases and then decreases at the lower and higher frequency. Obviously, the decrease of the resonant frequencies is mainly due to the increase of the C. In addition, the maximal absorbance of the LCP wave is up to 92.5% when l = 46 μm, and the one of the RCP wave is up to 97% when l = 48 μm. It means that the EM coupling for the LCP and RCP wave is up to the maximum when l = 46 μm and l = 48 μm, respectively. On the contrary, as shown in Figs. 7(c1,c2), the resonant frequencies increase when increases w, the absorbance at the lower frequency increased slightly, and the one firstly increases and then decreases at the higher frequency. In this case, the L will decrease with the increasing of the w, thus resulting in the increase of the resonant frequencies. In addition, the EM coupling for the LCP and RCP wave is up to the maximum when w = 9 μm and w = 7 μm, respectively. And the corresponding maximal absorbance of the LCP wave is up to 91.8% and the one of the RCP wave is up to 97.2%. As shown in Figs. 7(d1,d2), when increases g, the resonant frequencies will increase slightly, and the absorbance will decrease slightly at both the lower and higher frequency. In this case, the C will decrease when increasing g, thus resulting in the increase of the resonant frequencies. In addition, the EM coupling for both the LCP and RCP wave will weaken with the increase of the g. It can be concluded that the resonant frequencies and absorption level of the proposed CMMA for both RCP and LCP waves are sensitive to the geometric parameters of the unit-cell structure. Thus, the chiral-selective absorption properties can be adjusted dynamically by changing geometric parameters of the unit-cell structure.

4. Conclusions

In conclusion, we present a CMMA based on a bi-layered fourfold twisted VTs structure, which can achieve a high chiral-selective absorption for RCP and LCP waves in terahertz region. The simulation results confirm that the absorbance for both RCP and LCP waves are more than 90% at different resonance frequencies, and the corresponding CD amplitude is up to maximal value of 42.2 dB, which is associated with a giant effect. The surface current and power loss density distributions indicate that the chiral-selective absorption properties of the CMMA are mainly originated from electric and magnetic resonance couping effect. Furthermore, the resonance frequencies and absorption level can be flexible controlled by varying the size of the unit-cell structure. The practical realizations of the proposed THz CMMA in experiments can be achieved easily. In terahertz region, The designed CMMA can be fabricated using microfabrication and polymer processing techniques based on the conventional photolithography methods [35,40,47]. Then, the fabricated THz CMMA can be characterized and measured by terahertz-time-domain spectroscopy (THz-TDS) [35]. In addition, owing to the geometry scalability of the CMMA, operation frequency can also be scaled to other EM spectrums. The design of CMMA offers excellent flexibility for investigation of their novel EM properties and important device, such as circular polarizer and absorber across terahertz and other regions of the EM spectrum, which can be potential applicable in imaging, detecting, and communications.

Funding

National Natural Science Foundation of China (Grant Nos. U1435209 and 61605147); Natural Science Foundation of Hubei province (Grant No. 2017CFB588).

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Chiral metamaterial absorber with high selectivity for terahertz circular polarization waves

Abstract

1. Introduction

2. Structure design and simulations

3. Results and discussions

4. Conclusions

Funding

References and links

Cited By

Figures (7)

Equations (6)

Optical Materials Express