Metamaterials have been engineered to achieve electromagnetically induced transparency (EIT)-like behavior, analogous to those in quantum optical systems. These meta-devices are opening new paradigms in terahertz communication, ultra-sensitive sensing and EIT-like anti-reflection. The controlled coupling between a sub-radiant and a super-radiant particle in the unit cells of these metamaterial can enable multiple narrow plasmon induced transparency (PIT) windows over a broad band, with considerable group delay of electromagnetic field (slow light effect). Phase coherence between these PIT windows is highly desired for next-generation multichannel communication network. Herein, we numerically and experimentally validate a controllable frequency hopping mechanism between “slow light” windows in the terahertz (THz) regime. The effective media are composed of plasmonic “molecules” in which an asymmetric split-ring resonator (ASRR) or Fano resonator is displaced on the side of a cut-wire (Lorentz oscillator). Two metasurfaces where ASRR is on opposite side of the cut-wire are investigated. In these two cases, the proximity of the cut-wire to the gap on the ASRR having asymmetry is different. On one side, when the gap is nearer to the cut wire, displacing the ASRR along the cut-wire, produces only one narrow transparency window at 0.8 THz, corresponding to 20 ps group delay. When the ASRR is positioned on the opposite side, such that the gap is further, two transparency windows are observed when the ASRR is displaced along the cut-wire. That is, the transparency window hops from 0.8 THz to 1.2 THz. This corresponds to an increase from 20 to 30 ps in slow light effect. Numerical simulations suggest these single or multiple PIT windows occur if the couplings between the plasmonic modes in the different arrangements are either in-phase or out-of-phase, respectively.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
In photonics, coherent control is a concept to selectively manipulate the spectral and temporal response of resonating molecules [1–2]. In another words, it’s a method to control light by light through quantum interference in an atomic or molecular system. The destructive and constructive interference of plasmonic modes in these optical quantum systems can result to a narrow transparency window over a broad band, a phenomenon called electromagnetically induced transparency (EIT). Planar materials with subwavelength resonant features, called metasurface, have also been engineered to exhibit a Fano-type resonant behaviour analogous to EIT of optical quantum systems, a phenomenon called plasmon induced transparency (PIT) [3–10]. PIT devices can be integrated into solid-state circuit, as well as, free space optical systems (loss modulation, polarization, non-linearity), to slow down propagating light pulse in a broad electromagnetic frequency region [11–12]. PIT originates from a destructive interference of intrinsic mode of basic resonators inside metamaterials. If there is a high disparity between the quality (Q) factors of the coupled resonators, at the same resonance frequency [11–12]. A giant dispersion within this transparency window is created to dramatically slow down the group velocity of propagating light pulse. Conventionally, only one PIT window appears in the terahertz spectrum owing to the destructive interference between a fixed super-radiant and sub-radiant resonators of a metasurface [13–33]. However, the rush to meet requirement for high speed and high data volumes in the future, demands that the next generation of communication devices operating in the gigahertz (1 GHz = 109 Hz) to terahertz (1 THz=1012 Hz) frequency band be less lossy, multi-channel and broad bandwidth components . Very recently, multispectral PIT effect has been demonstrated either by hybridization between two dark resonators in a bright–dark–dark configuration metasurface or by a net coupling effect in a bright–bright–dark configuration metasurface [35–38]. These approaches may limit applications on miniaturized and versatile devices. An alternative method is using a binary metasurface consisting of an asymmetric double gap split-ring resonator (ASRR; Fano resonator) and a single SRR resonator (Lorentzian resonator) . A dual PIT window observed serves as a classical analog of a four-level tripod quantum system in which a double-EIT (DEIT) effect is encountered . Until today, all above multispectral PIT windows occur simultaneously in the frequency spectrum. To the best of our knowledge, there hasn’t been any discussions on how to coherently control the frequency hopping between the multispectral PIT windows.
Here, we demonstrate a frequency hopping effect in a Fano-Lorentzian metasurface at different asymmetric layout. Such a binary metasurfaces consists of periodic metal cut-wire (Lorentzian resonator), and an ASRR (Fano-resonator). We study the spectral response as the ASRR is gradually displaced along the cut-wire. Two metasurfaces based on the proximity of the cut-wire to the split gap on the ASRR having unequal arm, are evaluated. The metal structures of our Fano-Lorentzian metasurfaces are patterned on a polyimide thin-film. We provide an analytical and numerical insight into the evolution of the induced transparency windows as well as the variation of slow light phenomenon with displacement of ASRR along the cut-wires.
Figure 1(a) shows the layout of unit cell of two types of metasurfaces. The unit cell size is 150 µm x 150 µm. The unit cell is composed of metallic cut-wire of length 122.5 µm and an ASRR of side 60 µm, printed on a 25 µm thick polyimide film. The width of the metallic resonators is 6 um. The ASRR is placed at a fixed distance, d1=4 µm from the cut-wire, which is at about 1/100 wavelength of terahertz radiation. As such, the cut-wire is in strong coupling region to the ASRR . The lateral length of ASRR is L = 60 µm, and the gap-size is g=3 µm in both types of metasurfaces. The centre of the gap on one side of the ASRR with unequal arm lengths is displaced by a distance, d = 15 µm, from the centre axis passing through the gap on the side with asymmetry. Two types of metasurfaces are considered based on whether the ASRR is on one or opposite side of the cut-wire resonator. To paint a better picture, in one metasurface the cut-wire is near to the split on the ASRR with unequal arm (d = 20.5 µm), Fig. 1(a-i). In another metasurface, when the ASRR is on the opposite side of the cut-wire, the split on the ASRR with unequal arms is much further from the cut-wire (d = 53.5 µm), Fig. 1(a-ii). The metasurfaces would be identified as type I, Fig. 1(a-i) and type II, Fig. 1(a-ii) metasurfaces, respectively. The ASRR is translated over a distance, δ, along the cut-wire, on both types of metasurfaces. The material used for the metallic resonators is Gold (Au) with thickness 0.2 µm.
To realize a practical device, a polymethylmethacrylate (PMMA) sacrificial layer is spin-coated on a supporting 3-inch silicon (Si) wafer at 3000 rpm for 30 s (Laurell spinner 650M). A clean piece of 50×50 mm polyimide sheet is then attached onto the PMMA/Si wafer. Next, the polyimide/PMMA/Si wafer is cleaned properly with Isopropyl alcohol and water, and dehydrated at 120°C for 2 min. Resonator patterns are then transferred onto the polyimide using AZ 1512 HS resist-coated (4000 rpm; 30 s) using a maskless photolithography (MLA150 Maskless aligner – Heildberg instruments). The development process is conducted in 400 K AZ remover/H2O mixture at the ratio of 1:4. A 20 nm chromium (Cr) and 200 nm gold (Au) film layers are deposited consecutively on the patterned polyimide by electron beam deposition (PVD75, KURT J. Lesker) at a rate of 0.5 As−1 for Cr and 1 As−1 for Au. Finally, the unexposed resist and the reside metal layer are removed by lift-off process in acetone. The as fabricated metasurface is realized by soaking the polyimide/PMMA/Si wafer in acetone for more than 2 hours, to dissolve PMMA sacrificial layer. Optical images (VHX-500, Keyence Inc.) of as-fabricated cut-wire only, ASRR only, and the two types of metasurfaces are illustrated in Fig. 2(b) respectively.
Figure 1(c) depicts the terahertz waves in normal incidence onto the metasurface. The transmission spectra of the metasurface are measured by a fiber-coupled terahertz-time domain spectroscopy (THz-TDS) system (TERA K15, Menlosystem GmbH). The detected terahertz signals are read onto an integrated lock-In amplifier at the time constant of 100 ms. The resonance modes are recorded in the frequency range from 0.4 THz to 1.4 THz, which is in co-relation to our earlier works [26–29]. We address that the signal-to-noise (S/N) ratio above 1.4 THz is much lower than that below 1.4 THz. Therefore, we avoid discussing anything about high order frequency mode in our work. The diameter of the incident terahertz beam is 2 mm, which covers more than 9 unit cells of each type of metasurface, since each unit cell is 150 µm×150 µm. The frequency resolution is 10 GHz. All terahertz measurements are conducted in nitrogen atmosphere to avoid water absorption in air. A bare polyimide thin film of 25 µm identical to the metasurface substrate serves as a reference. The terahertz radiation is in normal incidence onto the metal layer of metasurface. The transmission spectrum, extracted from Fourier transforms of the measured time-domain electric fields, is defined as:
The simulation results have been obtained from a FDTD algorithm-based platform CST Microwave Studio. The time-domain solver is adopted with the unit-cell boundary conditions in the x-y plane of 150 µm ×150 µm square area. The input-and-output ports along the z-direction are set 20 µm away from the front-side and back-side metasurface, respectively. The permittivity, ε, of polyimide is ε=3.5 and the permeability, µ, of polyimide is µ=1. The electric conductivity of gold is 4.6×107 S/m. The number of cells is 183708. The mesh density is 40 cells per wavelength. The excitation source is a time-domain THz pulse signal from the spectrometer, of which its temporal window is 17 ps. The temporal interval between two point is 1/3 ps correspondingly. The simulation frequency range is the same as experimental measurement (0.4 THz to 1.4 THz). The transmittance T(ν) as well as the phase spectrum of the metasurface can be calculated by the functions of S-parameters T(ν) = |S21|2. The mesh cell is hexahedral for simulation. The mesh density is 50 lines per wavelength.
The THz transmittances of a single cut-wire and an individual ASRR are shown in Figs. 2(a) and 2(b), respectively. These are derived from the fast Fourier transform of the measured THz time domain data. Fano-resonance naturally is a type of resonant scattering phenomenon that gives rise to an asymmetric lineshape. The THz polarization is parallel to the cut-wire along the Y-axis so that the Lorentzian lineshape resonance on cut-wire and asymmetric Fano-resonance mode on ASRR can be excited simultaneously. As such, one can investigate the coherent interference of above two modes when cut-wire couples with the ASRR. The Q factors of resonance modes of the two types of resonators are calculated as below [41–46]:1.
Table 1 indicates that the Q factor of Fano-resonance mode of ASRR is much higher than Lorentzian mode of the cut-wire. At this point, the cut-wire can be recognized as super-radiant bright resonators, and the ASRR plays the role as sub-radiant dark resonator. The electric energy distributions of intrinsic modes of the cut-wire and the ASRR are shown in Figs. 2(c) and 2(d), respectively at around 0.8 THz. Both are observed to be accumulating at the terminals of the metal structures. To the ASRR, there is asymmetric energy localization at the gap area. Figures 2(e) and 2(f) show that the mono-directional surface currents of surface plasmon oscillation dominate the super-radiant mode of cut-wire, and a circulating current flow along the edge of the ASRR. However, the current on side of ASRR with longer arm length and gap at the center of ASRR are larger than that on side of ASRR with shorter arm length. As such, an interference process between a localized dipole oscillation (LD) on longer-arm of ASRR and a dipole resonant on shorter-arm of ASRR produces the Fano-resonance on ASRR [41–46].
3. Results and discussion
The simulated and measured transmittance of metasurface as a function of frequency versus displacement δ is presented in Fig. 3. The δ is at 0.0, 21.0, 42.0 and 62.5 µm respectively, that is over a step size of 21 µm. In type-I metasurface, there is a medium transparent within a narrow spectral range around a transmittance minimum area in the spectrum (δ = 0.0 µm), as shown in Fig. 3(a). The central frequency of such a transparency window is termed as νT. νT is almost the same as intrinsic Fano-resonance of ASRR, as shown in Fig. 2(b). Such a window keeps its frequency without any displacement of ASRR, as shown in Fig. 3(a). In type-II metasurface, however, this transparency window closes when the displacement δ increases from 0.0 µm to 62.5 µm Alternatively, another transparency window opens at δ = 42.0 µm, and the width of the second transparency window increases monotonically with increasing δ, shown in Fig. 4(b). The central frequencies of the second transparency windows is located at around 1.2 THz. It is neither identical to the Lorentzian mode of cut-wire nor to the Fano-resonance of ASRR. A fine mapping of the transmission versus the frequency ν and displacement δ are simulated and given in Fig. 4.
Figure 4(a) shows that there is only one transparency window below 0.8 THz, which seems to be independent on the displacement of δ. Figure 4(b) shows the first transparency window at around 0.8 THz, that becomes narrower and weaker as δ increases gradually. Such a window almost closed completely at δ > 40.0 µm. However, the second transparency window at 1.2 THz appears at around δ = 40.0 µm. This window becomes increasingly broader as δ increases monotonically. Obviously, it is a frequency hopping behavior different from any other reported multispectral PIT behavior. According to our previous results, a PIT-like behavior can mimic the transparency windows of PIT by tuning the dual modes of resonators into a very close distance in frequency domain; however, the slow light is invisible in the transparency window . Therefore, the influence of slow light is a key criterion to evaluate the PIT effect, which is a positive group delay (Δτ) at the transparency window in spectrum. Here, Δτ represents the time delay of THz wave packet instead of the group index. Δτ can be calculated from the Eq. (3) as below :5(a) and 5(b). In type-I metasurface, Δτ of the 1st transparency window fluctuates at 25 ± 3 ps with the δ increasing from 0.0 to 62.5 µm, however, this value increases to 32 ± 1 ps in type-II metasurface. Interestingly, the Δτ of the 2nd transparency window in type-II metasurface achieves 21.3 ps when the δ is at 42.0 µm. When the δ increases up to 62.5 µm, the Δτ achieves 31.2 ps. These measured group delays are relatively smaller than simulation values.
In order to illustrate a more detailed variation trend of slow light, a finer map of group delay is simulated as a function of frequency and δ in Fig. 6, in which the simulation step of δ is 1 µm.
Obviously, the frequency location of positive group delay is in agreement with the induced transparency windows in terahertz frequency spectra shown in Fig. 4. The group delay of slow light at the 1st window is constant in type-I metasurface. In type-II metasurface, however, the first slow light plateau appears in the range δ=0 µm to δ=50.0 µm, where the maximum of Δτ reaches 38.4 ps at δ = 33.0 µm. The second slow light plateau appears in the range from δ=35 µm to δ=62.5 µm, where the peak of Δτ reaches 39.0 ps at δ = 45.0 µm. Furthermore, the figure-of-merit (FOM) of slow-light device can be calculated from the product of the group delay time and bandwidth of transparency windows (DBP) [47,48]:
Table 2 shows FOM of our two types of metasurface with the displacement δ of metallic ASRR at interval of 21.0 µm. Obviously, it is a Lorentz reciprocal system under fundamental time-bandwidth limit Δν·Δτ < 2π . The FOM of the 1st transparency window is larger in type-II than in type-I metasurface. Interestingly, the bandwidth Δν of transparency windows do not change very much with the displacement δ. At this point, the variation of FOM is in agreement with the terahertz slow light values of metasurface. Both PIT behaviors is dependent on the destructive interference of resonance modes between the cut-wire and ASRR. However, the mechanism of above two slow light phenomena needs to be analyzed with a deep insight at two transparency windows.
Herein, the surface currents at the frequency of transparency window are investigated in two types metasurfaces with different displacement, δ. In type-I metasurface, the asymmetric split of ASRR is near the cut-wire. The incident THz wave gives rise to a uni-directional current flow from downside to upside on the cut-wire, as an evidence of Lorentzian oscillation. Figure 7(a) shows the current loop on the longer-arm of ASRR flows from upside to downside, which is much stronger than that on shorter-arm. According to the surface at the intrinsic Fano-resonance of ASRR shown in Fig. 2(d), we could notice that the longer-arm of the ASRR acts as a dipolar resonant excitation. Meanwhile, the simulated surface current on shorter-arm of ASRR is in opposite direction to the current on longer-arm. Both of these localized resonances are dipolar excitations individually in each of the metallic arm and their coherent interferences forms the Fano-resonance. As shown in Fig. 7(a). The Lorentzian mode on cut-wire interplays coherently in-phase with the local dipolar mode on longer-arm of ASRR, which dominates the transparency windows. In the type-II metasurface, the surface current at the frequency of the 1st induced transparency window is the same as in type-I metasurface as shown in Fig. 7(b), but the coupling distance is much smaller. To the 2nd induced transparency window, it is obvious that a couple of parallel current on longer-arm and shorter-arm dominates the spectral configuration at around 1.2 THz, and the contribution of Lorentzian resonance from cut-wire is negligible due to its weak current strength. With the help of the magnetic distribution, one can have a deep understanding on the change in mechanism.
According to the Ampère's right-hand grip rule, a cylindrical magnetic field that wraps round the cut-wire is generated. Biot-Savart law can be used to extract the magnetic field :50]. rd is the full displacement vector from the wire element (dl) to the point at which the field is being computed (r). Such an induced cylindrical magnetic field passes through the enclosed area of ASRR. Simultaneously, the anti-parallel current on longer-arm of ASRR generates a magnetic field with the same polarity takes place inside the ASRR enclosed area. The Lorentzian resonance on cut-wire constructively interferences in-phase with the LD mode on longer-arm of ASRR, which induces the transparency windows in type-I metasurface. In type-II metasurface, there are two induced transparency windows. The Lenz’s raw indicate that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field. In the 1st window, the magnetic field surrounding the cut-wire has the opposite polarity to the generated magnetic field passing through the enclosed area of ASRR. As is shown in Fig. 7(b), a strong magnetic field pass through the enclosed area of ASRR resulting in anti-parallel current on the ASRR. Thus, we can conclude that the Lorentzian resonance destructively interfere with the LD mode so as to create the 1st windows. In relation to type-I metasurface, the coupling distance between longer-arm of ASRR and cut-wire is much shorter in type-II metasurface. As a consequence, the central frequency of the 1st transparency window in type-II metasurface is slightly higher than in type-I metasurface. In the 2nd transparency window, the surface current on shorter-arm is parallel to that on longer-arm, as shown in Fig. 7(b). As a result, the magnetic field surround both arms of ASRR have the same polarity shown in Fig. 8(b). The Lorentzian oscillation on cut-wire can be neglected. Thus, the intrinsic Fano-resonance on ASRR attributes to the induced transparency window. Since the left-and-right arms are smaller than cut-wire, the 2nd transparency windows has a higher frequency than the 1st transparency windows in type-II metasurface.
A dual plasmon-induced transparency (PIT) window is observed in a type of Fano-Lorentzian metasurface composed of a cut-wire and asymmetric split ring resonator (ASRR). A change of position of the ASRR along the cut-wire (while keeping the distance between them constant), causes the transparency window to exhibit a frequency hopping behavior. Two metasurfaces based on which side the ASRR is placed next to the cut-wire, are investigated. In the first case, where the ASRR is placed on one side, such that the gap at the side on the ASRR with asymmetry, is near the cut-wire, only one PIT window located at 0.8 THz, is observed. The slow light is at around 25 ± 3 ps. In the second case, where the ASRR is placed on the opposite side of the cut-wire such that the gap at the asymmetric side is further from the cut-wire, two PIT windows are observed. The frequency of PIT windows hops from 0.8 THz up to 1.2 THz at certain displacement. The maximum value of slow light at the two PIT windows are above 30.0 ps. The numerical mapping of electromagnetic field indicates that the electrical dipole on metallic cut-wire results in a Lorentzian mode, while two coupled LD oscillation of ASRR results in Fano-resonance. In the first case, one LD on longer-arm of ASRR couples in-phase with the Lorentzian dipole, which constructs the PIT windows. In the second case, however, LD oscillation of on longer-arm of ASRR coherently coupled out-of-phase with the Lorentz dipole to create the first PIT window at 0.8 THz; Both LD mode destructively interfere to produce a second PIT windows at 1.2 THz. With increase in displacement along the cut-wire, the second LD oscillation competitively exceeds the first LD oscillation and leads to a controllable frequency hopping between the terahertz (THz) slow light windows. Our result will be beneficial for the high-speed device working at terahertz band in the future.
National Natural Science Foundation of China (U1631112).
This work was performed in part at the Micro Nano Research Facility at RMIT University in the Victorian Node of the Australian National Fabrication Facility (ANFF).
The authors declare no conflicts of interest.
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