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We reported a broadband terahertz (THz) plasmon-induced transparency (PIT) phenomenon owing to asymmetric coupling in between the bright-and-dark resonators in meta-molecules (MMs). Each MM contains a cut-wire resonator and a couple of identical size and gap opposite-directed U-shaped resonators in mirror symmetry. An upside displacement of cut-wire induces an asymmetric deviation of cut-wire away from the X-axis in the MMs. Then, the PIT effect occurs due to the asymmetric coupling of dark resonators. The width of the transparency window extends monotonically with the deviation increasing. A picosecond-scale group delay of the THz wave is found at the transparent windows. The distribution of surface currents and electric energy reveals that the asymmetric coupling between cut-wire and U-shaped resonators results in an energy transfer from surface plasmon (SP) oscillations to the inductive-capacitive (LC) oscillation due to the local symmetry breaking in structures of MMs. A couple of counteract SPs cause the transparency window, while the LC resonance gives rise to the side modes in the THz frequency spectrum. Furthermore, the LC oscillations of side modes take place in between the cut-wire and the local area of the U-shaped resonators, which leads to a magnetic dipole momentum. The displacement of cut-wire leads to an asymmetric distribution of magnetic momentum in MMs, which extends the width of the transparency window. Our experimental findings present a new approach to develop broadband slow-light devices in the THz frequency range.
© 2017 Optical Society of America
1. Introduction
A destructive interference of the transition probability amplitude between atomic states results in a narrow transparent window over a broadband spectrum. Such a phenomenon is termed as electromagnetically induced transparency (EIT) [1–3]. EIT effect creates extreme large dispersion within this transparency window, which slows down the group velocity of incident optical pulse dramatically [4–6]. The induced slow light exhibits giant potential in optical switching [7], sensing [8] and quantum storage [9,10]. Although many atomic systems support EIT effect, the transparent windows are mostly limited in optical frequency range owing to the energy interval between the quantum states for transitions [1–10]. It is hard to support the EIT effect at terahertz (THz) region using a three-state atomic system. Besides, the applications of atoms-based EIT are hampered by the medium options and cumbersome experimental conditions.
Recently, a plasmonic analogue of EIT effect (PIT) can mimic the EIT behavior cost-effectively by using artificial meta-molecules (MMs) [11–13]. The MMs are made of multiple electromagnetic resonance elements, such as split-ring resonators (SRR) [14–16], cut-wires [17,18], and U-shape resonators [19,20]. These basic resonators support a destructive interference of surface plasmons (SPs), which dominates the PIT effect [11–13]. By using PIT-type devices, one can achieve slow light not only in optical frequency but also in THz region [14–19]. Up to now, the PIT spectral configuration can be tuned by controlling the coupling distance or excitation pathway in between above basic resonators in MMs [19–21]. However, it remains a challenge to extend the linewidth of transparency window over a broad THz spectrum since the broadband PIT effect will significantly slow down the THz pulse with different frequency components. The previous works focus on using multilayer MMs [22] or increasing the numbers of dark-mode resonators in one MM [23]. The former method is too complicated to implement the fabrication process, while the later one has to enlarge the metal area in MMs. Actually, the spatial symmetry of MM plays a key role in the manipulation the SPs by unidirectional excitation [24], which enable a new approach to achieve PIT effect [25]. At this point, the transparency window is possible to be extended if the local symmetry of modes interaction of MMs is under appropriate control.
In this work, we demonstrate a broadband PIT-effect owing to asymmetric coupling in between the bright-and-dark resonators inside meta-molecules (MMs). The designed MM composed of a cut-wire as bright-mode resonator and a couple of U-shaped resonators in mirror symmetry as dark-mode resonators. An upside displacement of cut-wire results in local symmetry breaking in the structures of MMs. Thus, a broadband PIT phenomenon is achieved. The evolution of broadband PIT effect is evaluated using THz time-domain spectroscopy (THz-TDS). The relationship between the asymmetric modes coupling and the linewidth of transparency window is revealed by numerically mapping the electromagnetic field and the THz-induced surface current.
2. Experiment
The resonators 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 period of MM is 114 μm. The detailed structures of MMs are presented in Fig. 1(b). Such a MM consists of two independent resonators: a cut-wire of 86 μm length and 4 μm width as well as a couple of U-shaped resonators in mirror symmetry along the Y-axis, which has 48 μm long baselines and 28 μm short arms. The widths of U-shaped resonators are identical to 4 μm. Then, the cut-wire is inserted into the middle line of U-shaped resonators along the X-axis, which is vertical to the baselines of the U-shape resonator. The gap size between the terminal of cut-wire and U-shaped resonator is 2 μm along the X-axis. The cut-wire resonator is shifted towards the upper-arms of U-shape resonators; an asymmetric deviation δ is induced in the MMs, as shown in Fig. 1(b). Herein, one can investigate the relation between the δ and PIT effect. The THz radiation is normally incident on the surface of the samples, as shown in Fig. 1(c). In this configuration, the electric component of incident THz wave is parallel to the length of the cut-wire so that the cut-wire resonator will be excited directly by the incident THz wave owing to the localized surface plasmon (SP) oscillation [26–28]. However, the U-shaped resonators play the role as dark-mode element, which has to be excited by the bright resonators. The transmission spectra of the samples were measured by a commercial THz-TDS system (TERA K15, Menlosystem). The detected THz signals are read out into an integrated Lock-In amplifier at the time constant of 100 ms. The resonance modes are recorded in the frequency range from 0.3 THz to 2.0 THz. The diameter of focal area of incident THz wave is 2 mm, which covers hundreds of meta-molecules since the period of each meta-molecule is 114 μm. All THz measurements are conducted in nitrogen atmosphere so as to avoid water absorption in air. A bare SI-GaAs wafer identical to the sample substrate served as a reference. The THz radiation is in normal incidence onto the metal layer of MMs. The transmission spectrum is extracted from Fourier transforms of the measured time-domain electric fields, which is defined as:
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 commercial software CST Microwave Studio was used to simulate the THz transmittance as well as to map the surface currents and electromagnetic field distribution.
Fig. 1 (a) Schematic diagram of the element of metamolecule, in which l = 86 μm, a = 28 μm, d = 42 μm, w = 4 μm, s = 48 μm, L = 98 μm, g = 2 μm, respectively. (b) The microscope image of MM, in which the period(p) is 114μm. (c) The characters of I, II, III, IV, V, VI and VII refer to the unit cells of MMs with different asymmetric deviation δ of 0, 4, 6, 8, 10, 12, and 16 μm correspondingly. (d) Experimental illustration of the THz-TDS measurement of the MMs. The polarization of incident THz pulse is along the cut-wire.
3. Results and discussion
The THz transmittances of the independent cut-wire and U-shaped resonators are shown in Fig. 2(a)-2(b), which are derived from the fast Fourier transform of the measured THz time domain data. A Lorenz shape resonance occurs in THz spectrum when the THz polarization is parallel to the cut-wire along the X-axis. However, a similar resonance mode occurs to the U-shaped resonators only the THz polarization is along the Y-axis. Therefore, the cut-wire serve as bright resonator while the U-shaped resonator as dark resonators in MMs. The Q factors of resonance modes are calculated as below:
where ν is the mode frequency and Δν is the mode linewidth. Correspondingly, the details of resonance modes are listed in Table 1.Fig. 2 THz transmittance of (a) cut-wire and of (b) U-shaped resonators under THz irradiation with different polarization. Blue solid-line refers to the measured THz transmittance. Red solid-line refers to the simulated THz transmittance. The electric density at resonance modes of (c) cut-wire and of (d) U-shaped resonators, respectively. The surface current distribution at resonance mode of (e) cut-wire and of (f) U-shaped resonators, respectively.
Table 1. Resonance modes of basic resonators
It is evident that the central frequencies of both types of basic resonators are approximated respectively. It indicates that the detuning factor of resonance frequency of bright-and-dark resonators can be neglected. The damping ratios of cut-wire and U-shaped resonators are close since the linewidths of both modes are similar. The Q factor of U-shaped resonators is slightly higher than the cut-wire. The electric energy distributions of bright-and-dark modes are shown in Fig. 2(c)-2(d), both of which are accumulating at the terminals of the metal structures. To the U-shaped resonator, there is no obvious energy localization at the gap area, which differs from the SRR. Figure 2(e)-2(f) show that the mono-directional surface currents of SP oscillation dominate the bright mode of cut-wire [12,26,28], and a couple of parallel current flows along the baselines of the U-shape resonators. Unlike the SRR, there is no circulating current in the independent U-shape resonators in mirror symmetry. At this point, the dark mode of independent U-shape resonator attributes to collective oscillations of SP rather than the inductive-capacitive (LC) resonance [29,30].
Initially, the cut-wire is inserted into the middle line of U-shaped resonators along the X-axis, the bright mode resonator and dark mode resonator are brought in close proximity in both spatial and frequency domain. A single-mode resonance is observed in the MM of number I. We address that the MM of number I has two symmetric axis: X-axis and Y-axis. When the cut-wire is displaced towards the upper-arms of U-shaped resonators, an asymmetric deviation δ is induced in our MMs from number II to VII. As shown in Fig. 3, the linewidth of single mode of MM number II become broad, but the PIT effect remains invisible in the measured and simulated THz transmittance even though a 4 μm asymmetric deviation away from the X-axis. When the δ increases from 4 μm to 6 μm, however, the single resonance mode splits into two side modes in transmission spectrum, which opens a transparency window at around 0.59 THz. Such a window becomes wider and wider over the range of transmission spectrum with the δ increasing from 6 μm to 16 μm. Herein, we define that the frequency of transparency windows as νT, the low frequency side modes as νL, while the high frequency side modes as νH, respectively. Correspondingly, the linewidth of νT, νL and νH are termed as ΔνT, ΔνL and ΔνH. As shown in Fig. 3, the transmittance of νT rises up while that of νT maintains when the δ of MMs increase. Here, we address that there is no PIT-effect observed when the polarization of incident THz wave is perpendicular to the cut-wire. A possible reason is the counter-interplay in the electric dipole oscillation on the U-shaped resonator so that the cut-wire cannot be excited simultaneously. Therefore, we focus on the discussion in the case of THz polarization parallel to the cut-wire. The accurate parameters of symmetry breaking induced broadband PIT effect are listed in Table 2.
Fig. 3 (a) The simulated THz transmittance of MMs. (b) The measured THz transmittance, respectively. ΔνT refers to the width of transparency windows; Dash-line: the central frequencies of side modes. I, II, III, IV, V, VI and VII refer to the asymmetric deviation of 0 μm, 4 μm, 6 μm, 8 μm, 10 μm, 12 μm, and 16 μm, correspondingly.
Table 2. Properties of νL, νT and νH of MMs with different displacement of cut-wiresa
When the asymmetric deviation δ increases from 6 μm to 16 μm, not only the transparent window ΔνT but also the linewidth of side modes ΔνL and ΔνH become wider in the THz transmittance spectrum. Simultaneously, Q factors of νT, νL and νH decrease with the δ increasing. The previous works indicate that the coupling coefficient decreases with the spacing between the bright and dark mode resonators increasing, which results in an increase in the Q-factor [21]. In our case, however, an increased asymmetric deviation shortens the spacing between resonators in one side but elongate it in the other side. Consequently, the transparency windows become much wider, as is totally different from the realized PIT behavior.
A significant evidence of PIT effect is a positive group delay (Δtg) at the transparency window in spectrum [15,26,27]. Here, the Δtg represent the time delay of THz wave packet instead of the group index. The Δtg can be calculated from the equation as below:
where φ and ν refer to the effective phase and frequency of THz complex transmission spectrum, respectively. To determine the φ, the phase of incident THz wave is subtracted, traveling in the free-space between input port and the metal layer of MMs, from the phase between the input and output port. As such, only the desired phase difference between free-space and the output port which is positioned 625 μm behind the MMs. From the measured spectra, however, the phase of free-space is initially subtracted from the measured phase of MMs. An additional phase delay of free-space with the thickness of 625 μm was manually added to the subtraction. The effective phase can be calculated from the equation as below:Here, φT is the measured phase spectrum of our MMs, and φref is the phase spectrum of reference; k is the wave-number of free space and D is the distance between input and output ports. Such a calculation method is the same as the retrieval of the group delay of PIT phenomenon of concentric twisted double SRRs [15].Figure 4(a) shows the measured phase spectrum of our MMs, in which a distinct phase transition is found at the νL and νH modes. Following aforementioned retrieval method of group delay, an obvious group delay occurs at the frequencies of transparency windows in MMs, which is shown in Fig. 4(b). With the asymmetric deviation δ increasing from 6 μm to 10 μm, the Δtg increases monotonically from 3.5 ps to 4.6 ps. However, a further increase of δ reduces the Δtg from 4.6 ps to 2.6 ps with the δ increasing from 10 μm to 16 μm. Such a “Λ”-type variation of group delay indicates that the dispersion reaches maximum at δ = 10 μm. It is known that the destructive interference of SPs dominate the PIT effect. The SP propagating at the metal-GaAs interface is naturally an electron density wave, which only exists as a transverse magnetic mode. Such an oscillation of electrons is driven by the electric field of incident THz wave; thus, the propagating direction of SPs must be along the wave polarization at normal incidence. Due to the coupling between the resonators, the SPs on the U-shaped resonators are excited simultaneously by the SPs oscillation on the cut-wire. The coupling effect is proposed to reach at the maximum at δ = 10 μm so that the destructive interference of SPs oscillation induced dispersion achieves maximum. The interaction of SPs oscillation in above asymmetric excited PIT effect can be approved by the surface current analysis.
Fig. 4 (a) The measured phase spectra and (b) the group delay of MMs. I, II, III, IV, V, VI and VII refer to the asymmetric deviation of 0 μm, 4 μm, 6 μm, 8 μm, 10 μm, 12 μm, and 16 μm, correspondingly.
The surface currents of νL, νT, and νH mode are shown respectively in Fig. 5. In our case, the cut-wire is deviated from the symmetric X-axis of the MMs. It is obvious that the incident THz wave generated the surface current decreases with the asymmetric deviation increasing at the transparency window νT mode. However, the U-shaped resonators experience a strong coupling so that its surface current increases monotonically owing to the deviation of cut-wire. It indicates that asymmetric deviation give arise to an energy transfer from the cut-wire onto the U-shaped resonators. Most of the surface current accumulates at the baseline of the U-shaped resonators and its direction is anti-parallel between the left and right halves of the MMs. Along the X-axis, the direction of surface currents on the upper and lower halves of arms of U-shaped resonators are anti-parallel as well. Actually, the anti-parallel current flow will results in resonance energy dissipation, which is in accordance with the destructive interference of SPs oscillation [28]. To the νL modes, clockwise circulating currents are produced in between the lower halves of baseline of U-shaped resonators and cut-wire. To the νH modes, counter-clockwise circulating currents are produced in between the higher halves of baseline of U-shaped resonators and cut-wire. Since the circulating current is the evidence of the LC resonance, we proposed that the two localized LC resonance give arise to the side modes of νL and νH. One criterion to evaluate the LC resonance is to calculate the complex permittivity as a function of THz frequency as below [31]:
The permittivity can be derived from the parameters of S11 and S21 calculated by CST Microwave Studio software. Initially, one can achieve the effective refractive index n and impedance z following the equation below [31]: Here, the permittivity ε is directly calculated from ε = n/z.Fig. 5 Surface currents of MMs: I, II, III, IV, V, VI and VII refer to the asymmetric deviation of 0 μm, 4 μm, 6 μm, 8 μm, 10 μm, 12 μm, and 16 μm, correspondingly. The νT, νL and νH refer to the transparent window, low-frequency mode and high frequency mode respectively. The symbols of black-arrows refer to the equivalent surface currents circulating loops. The color bar refers to the relative strength of surface currents.
Figure 6 shows the retrieved complex permittivity of the MMs with different deviation respectively. To the modes of νL and νH, the real part of the function of complex permittivity εr shows a large negative value, while the imaginary part εi shows large positive values, describing a lossy medium at these frequencies. Since the dielectric function is flat the frequency of νT modes, it is evidence that the νT originates from the interaction of coupled SPs oscillations rather than the LC resonance in between the U-shaped resonators. Comparing the Q factors of side modes in Table 2 and the dielectric functions in Fig. 6, it is evident that the imaginary parts of permittivity of νL modes are always smaller than those of νH modes. In principle, the larger positive εi corresponds to a stronger energy loss of resonance mode. Therefore, it approves that the Q factors of νL modes are always smaller than those of νH modes in our MMs under the same enviroment. How does the SP dipole oscillation transfers to the LC oscillation in side modes? Such a question can be extracted from mapping the electromagnetic field distribution of MMs.
Fig. 6 The frequency-dependent dielectric functions of MMs. The red lines refer to the real permittivity εr. The blue curves refer to the imaginary permittivity εi. I, II, III, IV, V, VI and VII refer to the asymmetric deviation of 0 μm, 4 μm, 6 μm, 8 μm, 10 μm, 12 μm, and 16 μm, correspondingly.
As shown in Fig. 7, the incident THz wave excited a SP dipole so that the electric energy accumulates on the terminals of cut-wire when the asymmetric deviation δ is 0. With the increase of δ, electric energy transfer to the terminals of arms of U-shaped resonators. To the νT modes, the strength of SPs interaction between cut-wire and U-shaped resonators achieves maximum at δ = 10 μm, which maximize the dispersion coefficient so that the group delay reach 4.6 ps, as shown in Fig. 4(b). In optical metamaterials, it is found that the intensity of central nanorod decreases in corresponding to the increase of intensity in the side-nanorod [32]. Such a plasmonic breathing behavior is in agreement with the mapping of electric density at the transparent window νT. To the νL and νH modes, the increase of asymmetric devication δ induces the electric energy concentrating gradually at the gap area between the upper-arms of U-shape resonators and cut-wire. Such an area plays the role as capacitor so as to support the LC oscillation. An intense energy accumulation in the gap area enhances the LC resonance, as shown in Fig. 3. In contrast, there is no accumulation of electrical energy density in such a gap area at νT modes. These results are in good agreement with above interpretation that the LC oscillation cause the νL and νH modes.
Fig. 7 Electric density distribution of MMs: I, II, III, IV, V, VI and VII refer to the asymmetric deviation of 0 μm, 4 μm, 6 μm, 8 μm, 10 μm, 12 μm, and 16 μm, correspondingly. The νT, νL and νH refer to the transparent window, low-frequency mode and high frequency mode respectively. The color bar refers to the relative strength of electric density.
Figure 8 shows the simulated THz magnetic field strengths of MMs along the incident THz wave-vector, respectively. In accordance with the Ampère's right hand screw rules [26], the direction of circulating surface current at νL modes is clockwise in the lower half of MM, which induces a magnetic flux out-of-plane. As shown in Fig. 7, the magnetic flux opposite to the direction of incident THz wave-vector is larger than that along the direction of incident THz wave-vector. It indicates that the net magnetic dipole of νL modes is positive in our MMs. At νL modes, however, the magnetic flux along to the direction of incident THz wave-vector is larger than that opposite to the direction of incident THz wave-vector owing to the counter-clockwise currents. It indicates that the net magnetic dipole of νH mode is negative in our MMs. To the transparent window νT modes, the magnetic dipole moment transfers gradually from the cut-wire to the U-shaped resonators with the asymmetric deviation increasing. When the δ increases from 0 μm to 6 μm, the magnetic flux is around the cut-wire which induces a single magnetic dipole. When the δ increases from 6 μm to 16 μm, the magnetic dipole is strongly coupled to the U-shaped resonators. Thus, the magnetic dipole around cut-wire transfers to be a couple of magnetic dipoles with opposite momentums around the U-shaped resonators. Such a process seems like a plasmonic switching, which converts the SP to magnetic plasmons. As a consequence, the net magnetic dipole momentums are always zero, which cause a transparency window in the frequency spectrum. Our result is in accordance with earlier theoretical predictions [33–36]. Figure 8 shows that the distribution of magnetic field flux of νT modes is in mirror symmetry along the Y-axis. The destructive interference of magnetic dipoles is suggested to be the origin of transparency window. Meanwhile, the strength of magnetic dipole on the U-shaped resonators becomes stronger when the δ increases from 6 μm to 16 μm. Therefore, such a destructive interference of magnetic dipoles occurs on the adjacent frequency components of the νT mode as well. Therefore, the linewidth of the transparency window is extended. In practice, our experimental findings manifest a new approach to develop broadband slow-light devices at THz frequency range.
Fig. 8 The simulated magnetic field along the THz wave-vector. The characters I, II, III, IV, V, VI and VII refer to the asymmetric deviation of 0 μm, 4 μm, 6 μm, 8 μm, 10 μm, 12 μm, and 16 μm, correspondingly. The νT, νL and νH refer to the transparent window, low-frequency mode and high frequency mode respectively. The red color and blue color refer to the strength and the direction of magnetic fields along ( + ) or opposite (-) to the direction of incident THz wave-vector, correspondingly.
4. Conclusion
In summary, a broadband terahertz (THz) plasmon-induced transparency (PIT) phenomenon owing to asymmetric coupling in between the bright-and-dark resonators inside meta-molecules (MMs) is investigated experimentally at THz region. Both resonators manifest surface plasmons (SP) dipole oscillation of the same resonant frequencies when being excited by the incident THz radiation. Initially, the hybridization of bright-and-dark resonators do not results in the foreseen PIT effect when the MM is in X-and-Y axis symmetry. An upside displacement of cut-wire induce an asymmetric deviation of cut-wire away from X-axis in the MMs, which give arise to a PIT effect. Furthermore, the width of transparency window extends monotonically with the deviation increasing. The surface currents and electric energy distribution reveal an evolution process from SP oscillation to inductive-capacitive (LC). A couple of counteract SPs cause the transparency window while the LC resonance gives arise to the side modes in THz frequency spectrum. The counteract SPs enhance the destructive interference of magnetic dipole momentum, which is responsible for the extension of transparency window.
Funding
This work is supported by the National Natural Science Foundation of China (Grant No. 61307130) and the Joint Research Fund in Astronomy (Grant No. U1631112) under cooperative agreement between the National Natural Science Foundation of China (NSFC) and Chinese Academy of Sciences (CAS). 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 (Grant No. 14YZ077). W.P. acknowledges the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB04030000).
Acknowledgments
Z.Z and X. Z contributed equally in this work.
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