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Abstract
We experimentally investigate the terahertz (THz) response of conductively coupled asymmetric split ring resonator-based meta-molecules in the layout of reflection and rotational symmetry. In the reflectional symmetry case, the horizontally polarized THz excites a couple of trapped modes: the low-order one is a coupled Fano-resonance, and the high-order one is a decoupled dipole oscillator. The vertically polarized THz excites an inductive-capacitor resonance as a low-order trapped mode below the frequency of a high-order intrinsic mode. The quality factors (Q factors) of trapped modes decrease with the displacement of top-and-bottom gap increasing. In the rotational symmetry case, the horizontally polarized THz excites a single trapped mode owing to coupled Fano-resonance. The vertically polarized THz excites a high-order trapped mode of coupled multiple dipole oscillations beyond the frequency of intrinsic low-order dipole oscillation. The Q factors of trapped modes increase with the displacement of the top-and-bottom gap increase. For the first time, our results reveal the trapped modes’ evolution owing to the interaction of Fano-resonators conductively coupled under different symmetry.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nowadays, metamaterials exhibits extraordinary capability in manipulating electromagnetic waves by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials so as to attract significant attentions throughout the world [1–6]. Such extraordinary properties derive from the resonant unit cells of metamaterials arranged in periodic patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Their precise geometric shape, size, orientation and layout dominate the capability of electromagnetic wave manipulation. Just like the molecular composition and structure determine chemical properties of materials. Herein, each resonant unit cell of metamaterial is termed as meta-molecule (MM). Split-ring resonator (SRR) is one of the most popular MM being successful for the manipulation of terahertz wave owing to its bianisotropy of permittivity and permeability [7-8]. Aforementioned SRRs can be rectangular, C-shape, or concentric geometry in structures [9–11]. These shapes are almost in mirror symmetry since a line perpendicular to the gap of SRR becomes the symmetric axis. An inductive-capacitor (LC) resonance occurs when the THz polarization perpendicular to the symmetric axis; alternatively, a dipole oscillation resonance take place when the THz polarization parallel to the symmetric axis [7]. Both types of resonance appear to be Lorentz shape in frequency spectrum, quality factors (Q factor) of which are below 10 due to the non-radiation loss. By inducing a second gap away from the symmetric axis, one can achieve asymmetric SRR (ASRR) [12–16]. Such a symmetric breaking in structure of MM results in a Fano-resonance of high Q factor (Q>10) in frequency spectrum [12–20]. Therefore, the ASRR-based metamaterials become a potential high resolution biosensor. Interestedly, above high Q mode of Fano-resonance are mostly observed in MMs of single ASRR structure [12–20]. An alternative approach to tuning the Q factor of Fano-resonance mode is changing the dielectric environment of MM using external power, but it make the device fabrication process to be much more complicated [21-22]. It is well-known that two resonators of the same mode frequency support a destructive interference of surface plasmons via near-field coupling [23–28]. Such a phenomenon is dominated by the distance between the resonators [29]. In comparison, the conductive coupling of two dark resonators will localizes the slow light effect at THz band owing to generate two trapped side-modes [30-31]. Until now, the mechanism of interaction between the two conductively coupled Fano-resonators is not sufficiently realized.
In this work, we investigate the THz response of MMs based on conductively coupled ASRR resonators in two symmetric layouts. One is in reflectional symmetry; the other is in rotational symmetry. In both layouts, the symmetry of each MM is broken as the relative displacement of top-gap and bottom-gap to the middle-point of ASRRs varies monotonically, The THz response of the asymmetric MMs is calibrated using THz time-domain spectroscopy (THz-TDS). The frequency response of MMs in above two symmetric layouts is recorded under horizontally and vertically polarized incident THz pulse respectively. With the help of surface current analysis and electromagnetic field simulation, the mechanism on the interaction of two Fano-resonators under conductive coupling is discussed.
2. Experiment
Figure 1 (a) shows the schematic diagram of the MM in reflection and rotational symmetry including the parameters of geometric structure. Initially, two perfect symmetric SRRs coupled conductively with both the top and the bottom gaps exactly at the center. Then, the top and bottom gaps gradually displaced by a certain distance δ, while keep the middle-gap in the center. In the layout of refectional symmetry, the top-and-bottom gap shift in the same direction along the X-axis. In the layout of rotatioanl symmetry, the top-and-bottom gap shift in the opposite direction along the X-axis. To both type of symmetric layout, the δ increases from 0 μm to 12 μm at the step of 3 μm, as shown in Fig. 1 (b). The method of sample fabrication and characterization is the same as our previous works [30–35]. The unit cell of each MM is in the rectangular area of 50 μm × 50 μm. The sample size of MM is 1 cm × 1 cm. The patterns of MMs are fabricated on a piece of 625 μm-thick semi-insulating gallium arsenide (SI-GaAs) substrates by photolithography. A metal layer of 120 nm thick gold (Au) and 5 nm thick titanium (Ti) is deposited on the patterned substrate. The Ti acts as an adhesion layer between Au and SI-GaAs. The as-fabricated MM in rotational symmetry is shown in Fig. 1 (c), where the lattice period of MM is 50 μm. The THz transmission spectra of MM are measured by a standard THz-TDS system. A Ti: Sapphire oscillator (Mai-Tai, Spectra-Physics GmbH) is used for ultrafast optical excitation and a pair of low-temperature grown GaAs photoconductive antennas is used as THz radiation emitter and sensor. The THz emission is collimated onto the metal layer of MM by a couple of off-axis parabolic mirrors (OAPM) with a diameter of 50.8 mm. The transmitted THz wave was collimated by another couple of OAPM onto the sensor. The signal was read out into a Lock-In amplifier (SRS 272, Stanford Instruments) at the time constant of 100 ms. The whole measurement was carried out in dry nitrogen environment to avoid absorption of water vapor. The resonance mode are recorded in the frequency range from 0.1 THz to 3.0 THz with the frequency resolution of 10 GHz. A bare SI-GaAs wafer identical to the sample substrate served as a reference. The transmission spectrum is extracted from Fourier transforms of the measured time-domain electric fields, which is defined as [30–35]:
where Esample(ν) and Eref(ν) are the Fourier transformed electric fields through the sample and reference, respectively. T(ν) is the transmittance as a function of THz frequency. Finally, a finite difference time domain (FDTD) algorithm based software CST Microwave StudioTM is used to simulate the THz transmittance of MMs as well as the electromagnetic field at resonance mode correspondingly. In this context, the vertically polarized THz wave is termed as EX, while the vertically polarized THz wave is termed as EY. The FDTD simulation is using the hexahedral mesh by automatically mesh generation function. Mesh line limit is 10, and the mesh number is 132300.
Fig. 1 (a): Schematic diagram of the MM in reflection and rotational symmetry. The length of lateral l is 33 μm, the gap is 3 μm, The width of lateral w is 3 μm, the arm of single ASRR is 12 μm, respectively. (b) Microscopic images of the MM in rotational symmetry with lattice periods L of 50 μm. (c): Illustration of the symmetry broken evolution of two types MMs. (d): The diagram of THz transmittance measurement. Kz is the wave-vector of THz pulse, Ex is the polarization of electric component, Hy is the polarization of electric component.
3. Results and discussion
The measured and simulated transmittances of MMs are illustrated in Fig. 2. Initially, the conductively coupled symmetric SRR are both in reflectional symmetry and rotational symmetry (I in Fig. 2 (a) and V in Fig. 2(b)). Such a MM has no reaction to the EX incident wave, but an intrinsic single resonance mode at 1.18 THz to the EY incident wave. To the reflection symmetric MM shown in Fig. 2(a), the trapped modes occur gradually in the THz spectrum with the δ increases from 0 to 12 μm. The central frequencies of resonance mode as well as linewidths are listed in Table 1.
Fig. 2 (a) THz transmittance of MM in reflectional symmetry excited by the horizontally polarized (EX) and vertically polarized (EY) THz pulse. I, II, III, IV, V refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively. (b) THz transmittance of MM in rotational symmetry excited by the horizontally polarized (EX) and vertically polarized (EY) THz pulse. VI, VII, VIII, IX, X refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively. Blue solid-line: simulation data. Red solid-line: measurement data.
Table 1. The ν and Δν of reflectional symmetry
Here, we identify the low-order mode as νL and the high-order mode as νH correspondingly. To the reflection symmetric MM excited by the EX wave, the trapped νH mode appears at 1.62 THz with the δ of 3 μm, and it occurs blueshift in frequency spectrum with the enlargement of the δ. However, the trapped mode νL becomes observable until the δ increase up to 6 μm, and it occur redshift in frequency spectrum with the enlargement of the δ. To the reflectionally symmetric MM excited by the EY THz wave, the intrinsic νH mode shifts from 1.18 THz up to 1.54 THz monotonically with the δ increase from zero to 12 μm. Meanwhile, a low-order trapped mode νL appears at 0.73 THz with the δ of 3 μm, and this mode exhibits redshift in frequency spectrum with the δ rises up to 12 μm.
The THz responses of rotationally symmetric MMs are shown in Fig. 2(b). The EX wave gives arise to a single trapped mode νs until the δ rises up to 9 μm. The oscillation strength of the trapped mode νs increases gradually with the δ increases from 9 to 12 μm. However, the EY wave results in dual resonance mode: a low-order intrinsic mode νL and a high-order trapped mode νH, which is similar to the case of reflectional symmetry. The central frequencies of resonance mode as well as linewidths are listed in Table 2.
Table 2. The ν and Δν of rotational symmetry
When the δ achieves 9 μm, the linewidth of low-order intrinsic mode νL suddenly changes from 0.40 THz to 0.14 THz, and the high-order trapped mode νH become observable in THz spectrum. Meanwhile, the linewidths of both νL and νH modes become narrower with the δ increasing. Correspondingly, the intrinsic mode νL shifts to the lower frequency while the trapped mode νH shifts to the higher frequency as is the same as the THz response of MM in reflectional symmetry. In comparison, the trapped mode νs occurs only at the δ of 9 μm. The central frequency of νs mode slightly shifts in frequency spectrum and its linewidth almost does not change.
The Q factor is a criterion to evaluate the damping ratio of a resonance mode, which is a ratio of the central frequency ν to the linewidth Δν of the resonance mode. Here, the Δν is the full width at half-maximum (FWHM) of mode spectrum [30]:
The Q factors of resonance mode of MMs in reflectional and rotational symmetry are listed in Table 3 as below:Table 3. Q factors of resonance mode of MMs in reflectional and rotational symmetry
In both symmetries, it is evident that the Q factors of resonance mode exceed 10 when the incident THz is in horizontal polarization. However, such a high Q factor degrades dramatically when the incident THz polarization turns to be vertical. In reflectional symmetry, the Q factors of trapped modes are totally beyond 10, however, the Q factors of intrinsic modes are no more than 4. In rotational symmetry, the Q factors of both νL and νH mode are below 10. The variation trend of Q factors of resonance mode of MM in above two symmetries is shown in Fig. 3.
Fig. 3 Q factors of resonance mode as a function of δ. The δ is 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively. (a) MM in reflectional symmetry excited by the horizontally polarized (EX) THz pulse. Blue solid square: νL. Red solid circle:νH. (b) MM in reflectional symmetry excited by the vertically polarized (EY) THz pulse. Blue hollow square: νL. Red hollow circle: νH. (c) MM in rotational symmetry excited by the horizontally polarized (EX) THz pulse. Black solid triangle: νs. (d) MM in rotational symmetry excited by the vertically polarized (EY) THz pulse. Blue hollow pentagon: νL. Purple hollow star: νH.
In reflectional symmetry, the Q factors of both νL and νH modes decrease monotonically with the δ increasing. In rotational symmetry, however, the Q factors of both νL and νH mode as well as the νs mode increase initially with the δ increasing. When the δ achieves 9 μm, the Q factor of νs mode achieve maximum. Our results indicate that the Q factor of trapped mode of conductively coupled Fano-resonator is higher than that of phase-changing materials based resonators but lower than that of the graphene-supported Fano-resonators [21,22].
Furthermore, the dephasing time of the trapped modes at the THz band can be retrieved, as is presented in Table 4. The Cauchy–Lorentz distribution was used to define the damped harmonic oscillator [36-37]. Thus, the dephasing time for the trapped mode is given by τ = 2ħ/Δν. where ħ is the reduced Planck’s constant. In reflectional symmetry, the dephasing time is in the range from 15 to 50 ps. In rotational symmetry, the dephasing time of trapped mode excited by the vertically polarized THz beam is less than 5 ps, however, the dephasing time of trapped mode excited by the vertically polarized THz beam is less than 5 ps. As a consequence, the spatial symmetry plays a key role in the modulation of resonance mode of conductively couple Fano-resonators.
Table 4. Dephasing time of trapped modes of MMs in reflectional and rotational symmetry
A further analysis of surface currents will be helpful to reveal the origin of aforementioned phenomenon. Figure 4 shows the surface currents at the resonance modes of MM in reflectional and rotational symmetry excited by the EX and EY wave. To a symmetric SRR with two-gap in central position, the wire arms of the resonator oscillate at an identical frequency and contribute to the formation of a broad background caused by the dipole oscillation in each arms. The currents in these two arms oscillating in-phase for most part of the spectrum and interference constructively. As soon as the top/bottom gap of ASRR is off-centered, the resonance frequency on each arm differs slightly. As a consequence, the oscillation on each arms become out-of-phase, which give arise to a very sharp Fano-resonance in ASRR. However, the slightly deviated resonance frequency owing to the dipole oscillation on the arm of single ASRR is proposed to be compensated in-phase by another conductively coupled ASRR of the same geometric structure. In reflectionally symmetric MM excited by the EX wave, a couple of circulating currents flows in opposite direction: A clockwise circulating loop currents on the right halves of upper-ASRR, while an anti-clockwise circulating loop currents on the right halves of lower-ASRR. The strength of currents increases monotonically with the δ increasing. It is an evidence of constructive coupling of two Fano-resonances, which results in the trapped mode νL. To the νH mode, a couple of anti-parallel currents flow on the right arms of the upper-and-lower ASRR, and part of currents leak into the left middle-line of MM. The strength of current achieves maximum at the δ of 9 μm. In reflectionally symmetric MM excited by the EY wave, a long circulating current flows from the top-arm to the bottom-arm via the right-arm of MM; while a couple of parallel currents on left-and-right arms result in the νH mode. Such a loop of νL mode is very much like LC-resonance in a single symmetric SRR, and the loop of νH mode indicate that the dipole oscillation results in the νH mode. The current strength of νH mode is initially equal on the left-and-right arms of MM. However, the enlargement of δ transfers the current from right-arm onto the left-arm, and the currents strength become weaker and weaker correspondingly. The earlier works indicate that anti-parallel currents on top-arm and bottom-arm lead to a destructive interference of the scattered fields, which is proposed to be the origin of the νL mode redshift. To the νH mode, the currents gradually transfer from right-arm to the left-arm of MM, which indicate a decoupling behavior occurs in between two individual dipole oscillators. The oscillation length becomes shorter and shorter with the δ increasing, which is responsible for the blueshift of νH mode. In rotationally symmetric MM excited by the EX wave, however, the surface currents of mode νs exhibit reversed S-shape. When the THz polarization turns to be vertical, the surface currents of mode νL exhibit reversed S-shape, but that of νH mode become S-shape. Actually, the S-shape current is a conductive interaction of multiple dipole oscillations [38–40]. The enlargement of δ increases the strength of currents of the mode νs, νL and νH.
Fig. 4 Surface currents of resonance modes of MMs in reflectional and rotational symmetry excited by the horizontally polarized (EX) and vertically polarized (EY) THz pulse. I, II, III, IV, V refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively in reflectional symmetry. VI, VII, VIII, IX, X refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm in rotational symmetry, Color bars: The relative strength of currents.
Accordance with the Ampère's right hand screw rules, the surface currents shown in Fig.5 determine the magnetic field distribution of THz resonance mode [41–43]. In reflectionally symmetric MM excited by the EX wave, the magnetic flux of νL mode is along the THz wavevector in upper-ASRR and opposite in lower-ASRR. The magnetic dipole of νH mode is opposite to that of νL mode. Therefore, the magnetic dipole momentums of νL and νH modes are both in reflectional symmetry along the horizontal middle-line of MM. The strength of these magnetic dipoles momentum varies with the enlargement of δ. In reflectionally symmetric MM excited by the EY wave, the magnetic flux of νL mode is along the THz wave-vector in upper-ASRR of MM, but opposite in lower-ASRR of MM. In space, such a magnetic dipole is in reflectional symmetry along the horizontal middle-line of MM as well. To the νH mode, however, two magnetic dipoles distribute symmetrically along the vertical central line of MM with top-and-bottom gap of MM is on-centered. An introduction of δ break the energy balance of the two the magnetic dipoles, and the one on right-arm fades faster than the other on left-arm. Thus, two identically magnetic dipoles become a single magnetic dipole localized on the left-arm of MM finally. The increase of δ enlarges the oscillation area of magnetic dipole of νL mode (right-halves of MM), which attributes to the frequency redshift of νL mode. Correspondingly, the oscillation area of magnetic dipole of νH mode (left-halves of MM) reduces with the δ increasing, which leads to the frequency blueshift of νH mode. In rotational symmetry, a relatively large magnetic dipole locates inside the MM and a smaller magnetic dipole locates outside around the MM. These two magnetic dipoles give arise to magnetic quadruple in rotational symmetry-based MM. Such a phenomenon indicate that a magnetic quadruple dominate the νs mode, νL and νH mode. Obviously, the magnetic quadruple is not on any symmetric axis (X/Y-axis). The magnetic dipole momentum distribution of νs mode is similar to that of νL mode, while that of νH mode is opposite to the magnetic dipole momentum of νL mode. The strength of above magnetic quadruple increase monotonically with the δ increasing, however, the linewidth and the Q factor of νs mode is much larger than that of νL mode as well as the νH mode. In order to realize such a linewidth difference, the dielectric loss of resonance modes needs to be revealed.
Fig. 5 Magnetic field distribution of resonance modes of MMs in reflectional and rotational symmetry excited by the horizontally polarized (EX) THz wave and vertically polarized (EY) THz pulse. I, II, III, IV, V refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively in reflectional symmetry. VI, VII, VIII, IX, X refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm in rotational symmetry, Color bars: The relative strength of currents. + : THz wavevector, -: opposite to the THz wavevector.
The complex permittivity as a function of THz frequency is present as below [44]:
The permittivity can be derived from the simulated parameters of S11 and S21 calculated by CST Microwave StudioTM software. Initially, one can achieve the effective refractive index n and impedance z following the equation below [40]: Here, the permittivity ε is directly calculated from ε = n/z. εr is the real part of permittivity, and εi is the imaginary part of permittivity. k0 is the wave-vector of incident THz wave. d is the thickness of substrate.Figure 6 shows the retrieved dielectric function of MM in reflectional symmetry. A large εr is responsible for a strong oscillation so as to result in a deep resonance tip at νL and νH modes The εi is an evidence of energy loss. Herein, a higher εi indicates a broad resonance linewidth in spectrum. It is obvious that an enlargement of δ increase the imaginary permittivity εr of νL and νH mode. In the case of MM is excited by EX THz wave, the εi of νL and νH modes are all below 20. However, in the case of MM is excited by EY THz wave, the εi of both modes achieve 45. This is the reason why the horizontally polarized THz excitation results in a higher Q factor than the vertically polarized THz exciation, as is in agreement with the data in Table 1 and Table 3. In accordance with the surface currents, the EX wave results in a constructive inference in between two Fano-resonance modes, which oscillate in-phase so that the Q factor of νL mode is very large. Since the νH mode naturally is a single dipole oscillator, its Q factor is smaller than the Fano-resonance. Comparatively, the EY wave give arise to a LC oscillation of νL mode and a decoupled dipole oscillation of νH mode. The LC oscillation exhibits a large loss in dielectric spectrum so that its linewidth is larger than the Fano-resonance. Meanwhile, the decoupled two dipole oscillation induces a relatively larger loss than a single dipole oscillator. Therefore, the corresponding Q factors of resonance modes excited by the EY wave are relatively smaller than the Q factors of resonance modes excited by the EX wave.
Fig. 6 Retrieved dielectric function of resonance mode of MM in reflectional symmetry excited by the horizontally polarized (EX) and vertically polarized (EY) THz pulse. I, II, III, IV, V refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively in reflectional symmetry. Red solid-line: The real part of permittivity. Blue solid-line: The imaginary part of permittivity.
Figure 7 shows the retrieved dielectric function of MM in rotational symmetry. In the case of MM excited by the EX wave, the εi of mode νs varies from 5 to 15. However, In the case of MM excited by the EY wave, the maximum of εi of νL mode exceeds 45, as is triple to that of νH mode. The relatively small εi is an evidence of Fano-resonance, and it is able to be excited by the THz wave of polarization perpendicular to the off-center gap of MM. Therefore, the mode νs is attributed to an inference of Fano-resonance from upper-ASRR as well as lower-ASRR of MM. However, the Fano-resonance is insensitive to the THz polarization parallel to the three-gap of MM. Therefore, the νL mode is naturally different from the νS mode even though the surface current route is very similar. With the δ increasing, the εr and εi of νL mode decrease but that of νH mode increase monotonically. Such a behavior is very much like teeter-torter effect of complementary C-shaped SRR, in which a coupling of multiple dipole oscillation dominate high-order mode [10]. Similarly, one can deduce the mechanism of the Q factor difference from the surface currents route shown in Fig. 4. The inversed S-shaped currents of νL mode only pass through the middle-gap of MM, while the S-shaped currents of νH mode pass through the top-gap, middle-gap, and the bottom-gap. Here, the gap cut off surface current so as to limit the oscillation length of a local dipole. The top-arm and bottem-arm play the role as two independent dipole oscillators. Meanwhile, the up-left-arm and the left-middle-arms, down-right-arm and the right middle-arms works like two L-shaped dipole oscillators. The S-shape oscillation consists of two localized L-shaped dipole oscillators as well as the two individual dipole oscillators on top-arm and bottom-arm, respectively. The enlargement of δ increases the coupling between above dipole oscillators, which leads to a monotonic increase of Q factors.
Fig. 7 Retrieved dielectric function of resonance mode of MM in rotational symmetry excited by the horizontally polarized (EX) and vertically polarized (EY) THz pulse. VI, VII, VIII, IX, X refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm respectively in rotational symmetry. Red solid-line: The real part of permittivity. Blue solid-line: The imaginary part of permittivity.
4. Summary
In summary, we demonstrate a Q factor tuning method by changing the geometric symmetry of two conductively coupled ASRRs. In reflectional symmetry, the horizontally polarized THz incidence give arise to two modes of high Q factor beyond 10, while the vertically polarized THz incidence only results in one high Q factor mode beyond 10. The discrepancy between the gaps reduces the Q factors monotonically. The magnetic dipole momentum of resonance mode is in reflectional symmetry along the middle-line parallel to the gap. In rotational symmetry, the horizontally polarized THz incidence give arise to a single high Q factor mode beyond 10, while the vertically polarized THz incidence results in two modes with the Q factor below 10. The discrepancy between the gaps increases the Q factors of resonance mode. The magnetic quadruple momentum of resonance modes are in rotational symmetry along the middle- gap of MM. The Q factor of trapped modes of conductively coupled Fano-resonators relies on the systematical symmetry of metamolecule.
Funding
National Natural Science Foundation of China (NSFC) (61307130); Joint Research Fund in Astronomy (U1631112) under cooperative agreement between the NSFC and Chinese Academy of Sciences (CAS).
Acknowledgments
Zhenyu Zhao and Xiaobo Zheng contribute equally in this work.
Z.Z. acknowledges the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry as well as Innovation Program of Shanghai Municipal Education Commission (14YZ077). W.P. acknowledges the Strategic Priority Research Program (B) of the CAS (XDB04030000).
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