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Abstract
Herein, we demonstrate one of the highest terahertz group delay of 42.4 ps achieved experimentally at 0.23 THz, on a flexible planar metamaterial. The unit cell of metasurface is made up of a textured closed cavity and another experimentally concentric metallic arc. By tuning the central angle of the metallic arc, its intrinsic dipolar mode is in destructive interference with the spoof localized surface plasmon (SLSP) on textured closed cavity, which results in a plasmon-induced transparency phenomenon. The measured transmittances of as-fabricated samples using terahertz-time domain spectroscopy validate numerical results using extended coupled Lorentz oscillator model. It is found that the coupling coefficient and damping ratio of SLSP relies on the radius of the ring structure of textured closed cavity. As a consequence, the slow light maximum values become manoeuverable in strength at certain frequencies of induced transparency windows. To the best of our knowledge, our experimental result is currently the highest value demonstrated so far within metasurface at terahertz band.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
An electromagnetic pulse can be manipulated to propagate at group velocity far below that of light in vacuum, a phenomenon known as the slow light effect [1–4]. This slow light effect can dramatically reduce transmission noise in telecommunication [1–4]. In light of this, a significant amount of attention is geared towards the realization of optoelectronics and photonics devices for such application [5–15]. More so, the terahertz wave occupying the 0.1 THz to 3 THz (1 THz = 1012 Hz) portion of the electromagnetic spectrum is drawing great attention due its technological importance. This frequency band is above the highest frequency used for the fifth generation telecommunication (5G), which falls between 0.03 THz and 0.3 THz. Therefore, progress in innovation of solid state terahertz slow light devices will facilitate the realization of post-5G communication network all over the world. In the past, planar metamaterials (MM) designed for plasmon-induced transparency (PIT) effect were considered as the most cost-effective approach to achieve slow-light from near-infrared region to terahertz band [5–34]. Such planar devices are known as metasurfaces which are two-dimensional (2D) analogues of metamaterial. Basically, these are engineered material composed of ultra-thin thickness and sub-wavelength resonators. As such, the wave-matter interaction length is very short, allowing little changes in the permittivity of the bulk material. It should be noted that the terahertz regime is far below the plasma frequencies of metals. At this frequency range, the behavior of metals are close to those of perfect electric conductors (PECs), which are unable to directly support localized surface plasmon (LSP) modes [35–37]. Alternatively, a periodically textured closed surface can mimic LSPs beyond PEC limit, namely spoof-LSP (SLSP) [38–43]. The SLSP exhibits very strong energy confinement on the periodically textured closed surface, which results in sharp resonance modes. Therefore, a destructive interference of SLSPs is able to induce a transparency window [43]. As predicted, a maximum group delay could be ramped up to 46 ps by tuning the destructive interference between dipole oscillator frequency and SLSP on textured closed cavity [44].
In this work, we demonstrate terahertz group delays above 40 ps based on the interaction of SLSP. The evolution of slow light with structural variation of MM is interpreted by using an extended coupled Lorentz oscillator (ECLO) model [45–47]. This model addresses questions raised concerning the methods employed for phase detuning, damping coefficient, and coupling coefficients of SLSP resonators to determine the altitude and frequency positions of localized slow light plateaus. Moreover, the figure-of-merits (FOM) of terahertz slow light can be evaluated easily from the delay-bandwidth product (DBP) [48,49]. We have not only experimentally validated our early numerical findings [44], but also provided a detailed mechanism on tuning the terahertz PIT window, as well as, an unprecedented maximum group delay.
2. Methods
2.1 Design
Figure 1(a) shows the parameters of the unit cell of three types of MMs which support SLSP. The textured closed cavity of periodically corrugated surface has a ring of mean radius R, which is overlaid with inward and outward radial groove of height h = 60 µm. The total number of grooves, N = 48, and the inner radius of the open area is r = 90 µm. From left to right, the circular ring cavity is on the outer-edge, middle, and inner-edge of grooves, respectively. Thus, the three types of MM are termed as outer-ring, middle-ring, and inner-ring, respectively. Correspondingly, the ring varies at three cases: (1) The radius of outer-ring MM is R = 151 µm. (2) The radius of middle-ring MM is R = 120 µm. (3) The radius of inner-ring MM is R = 89 µm. Note that, the three radii support distinct PIT effect, as is optimised by simulation using CST Microwave Studio. For a large radius, the central frequency of terahertz PIT move below 0.2 THz, which is out of the frequency range of our THz-TDS setup. While for a shorter radius, the PIT effect are not very clear since the groove size become shorter accordingly, which cannot support the spoof surface plasmon. The thickness of the ring is 2 µm on all three types of MM. The thickness of the metal arc concentric to the circular ring, w is 5 µm, as is identical to the thickness of the periodic grooves. In simulation, we vary the angle of the arc θ, from 60 degree to 180 degree, with 3 degrees increment. For convenience, three samples for each type of MM are fabricated, that is for θ=60, 120 and 180 degree. The optical images (VHX-500, Keyence Inc.) of the unit cells of as-fabricated three types of MMs, with θ = 60 degree, are illustrated in Fig. 2(b).
Fig. 1. (a) Schematic diagram of a unit cell of proposed binary MM, in which p = 420 µm, r = 90 µm, w = 4 µm, h = 60 µm, g = 15 µm, respectively. l is the length of the metallic arc. (b) Microscopic images (VHX-500, Keyence Inc.) of unit cell of as-fabricated binary MM. (c) A schematic diagram showing terahertz transmission and group velocity delay through a periodic array of binary MM, as measured using a THz-TDS. KTHz refers to the wave vector of incident THz pulse. EX and HY refer to the electrical and magnetic component of the incident electromagnetic waves, respectively. XYZ are the coordinate axis in free space.
Fig. 2. Terahertz transmittance against frequency for different central angles, θ = 60, 120, and 180 degree for (a) outer-ring, (b) middle-ring, (c) inner-ring MM. Blue solid line: simulated (S) results. Green solid line: ECLO model based theoretical (T) results. Red solid line: experimental (E) results.
2.2 Fabrication
The fabrication procedure is as outlined below, which is similar to our previous work [50]. First, a polymethyl-methacrylate (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. The PMMA is dehydrated slightly for 5 to 10 s at 60°C, prior to attaching the polyimide sheet. Next, the polyimide/PMMA/Si wafer is cleaned properly with Isopropyl alcohol and water, and dehydrated at 120°C for 2 min. MM patterns are then transferred on AZ 1512 HS resist-coated (4000 rpm; 30 s) polyimide surface 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. 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 metalized layer overlaying it are removed by a lift-off process in acetone. The as-fabricated MM is realized by soaking the polyimide/PMMA/Si wafer in acetone for more than 2 h, to dissolve PMMA sacrificial layer.
2.3 Characterization
Figure 1(c) depicts the transmission of terahertz waves through the MM array. The transmission spectra of the MMs were 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 0.1 THz to 0.4 THz, which is in agreement to our earlier work [44]. The diameter of the incident terahertz beam is 2 mm, which covers more than 9 unit cells of each type of MM, since the period of each meta-molecule is 420 µm. The temporal window is set at 15 ps in order to avoid the etalon echoes from the polyimide substrate. 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 sample substrate serves as a reference. The terahertz radiation is in normal incidence onto the metal layer of MMs. The transmission spectrum, extracted from Fourier transforms of the measured time-domain electric fields, is defined as:
2.4 Simulation
The simulation results are obtained from a finite element method-based platform CST Microwave StudioTM. The time-domain solver is adopted with the unit-cell boundary conditions in the x-y plane of 420 µm × 420 µm square area. Since the PIT effect occurs between the super-radiant and sub-radiant resonators, the interaction of the two circular cavities between adjacent unit-cells are neglected. The distance, along the z direction, of the input and output ports is set at 30 µm from the MM. Therefore, the simulation can be executed under far-field condition, which is available for plane-wave approximation. The transmittance T(ν) as well as the phase spectrum of the MM can be calculated as a function of S-parameter, T(ν) = |S21|2. The mesh cell of simulation is 943488 at 40 lines per wavelength. The mesh line ratio limit is 20. The minimum mesh step is 0.40, and the maximum mesh step is 9.18. The permittivity of polyimide is 3.5. Gold (Au) is modelled as lossy metals with conductivity 4.56×107 S/m. The permittivity for polyimide used is 3.5 at 1 THz. The permeability of all the materials is 1.
3. Results and discussion
Terahertz transmittance as a function of frequency for different central angles of metallic arc is presented in Fig. 2. Here, the frequency window is from 0.1 to 0.4 THz since the high-order multipolar resonances are ignored in our works. At θ=60 degree, only one resonance mode is observed in the selected frequency range for the three types of MM, as are shown in Fig. 2(a), 2(b) and 2(c).
At θ=120 degree, two separate transmission minimum are observed on the spectrum, as shown in Fig. 2. These two minimum create a transparency window between the two side-modes. As θ increases to 180 degree, the aforementioned transparency window disappears in all three types of MM. At the same arc angle of θ=60 degree and θ=180 degree, the resonance frequency of intrinsic SLSP mode on textured closed cavity appears to be slightly blue shifted as the ring diameter reduces, as shown in Fig. 2. Likewise, the transparency windows of MM at the arc angle of θ=120 degree shifts in accordance to the shrinking of ring diameter. It can therefore be deduced that the arc length determines the frequency of electrical dipole oscillator, while the textured closed cavity determines the frequency of SLSP. The PIT windows are shaped by the coupling strength and damping ratio of above two resonators as well. Actually, a couple of mechanic Lorentz oscillator (ECLO) model can successfully mimic the behavior of PIT effect on binary MM in terahertz transmission spectrum [45–47]. This includes fitting the parameters, such as, coupling coefficient and damping coefficient of intrinsic modes of super-radiant and sub-radiant resonators accordingly. Based on our previous theoretical prediction, the metal arc plays the role of a super-radiant resonator, and the textured closed cavity with periodic grooves serves as sub-radiant resonators. The super-radiant mode is written as a(ω)eiωt, and the sub-radiant mode as b(ω)eiωt. Here, t is time and ω is the angular frequency. The incident terahertz field amplitude is termed as E0. Thus, the coupled equations can be written as
Where a and b represent the oscillation amplitude of super-radiant and sub-radiant resonators respectively. κ is the coupled coefficient in units of THz, which relates to the distance between the super-radiant and sub-radiant resonators. δ is the detuning factor between the intrinsic modes of aforementioned two resonators. γ is the damping coefficient in units of THz, which relates to damping coefficient. The eigenvalues of the coupled matrix are λ1,2=(δ±ω1,2)−1, where ω1,2=α±iΓ1,2 are the eigen-frequencies of resonators. The subscript 1,2 refers to the super-radiant and sub-radiant resonators, respectively. Here, the Γ1,2=γ±β is the damping factor of resonators. α and β can be retrieved from following terms:
With the help of diagonalization and transformation matrix, the oscillation amplitude of super-radiant resonator can be written as below:
Where χ1 and χ2 can be written as below:
Then, the normalized transmittance can be written as:
In Eq. (6), the superscript * refers to the conjugate value of χ and λ. Thanks to the ECLO model of Eq. (6), the theoretical transmission spectra of three types of MM are calculated and illustrated using data related to the green solid line in Fig. 2. Obviously, the spectral profiles of ECLO model are in good agreement with the experimental and simulated terahertz transmittance at the full frequency range. Therefore, it is worth interpreting the physical mechanism of this PIT effect using the ECLO model. The fitted parameters of resonance modes as well as PIT effect are listed on Table 1 below:
Table 1. The fitted parameters for ECLO model.
According to our previous findings [44], the occurrence of induced transparency windows is attributed to the destructive interference between the SLSP on textured closed cavity of periodic grooves and dipole oscillator on metal arc. At θ=60 degree and θ=180 degree, the intrinsic resonance frequency of dipole is far away from the intrinsic resonance frequency of SLSP [44]. As such, the intrinsic SLSP on textured closed cavity of periodic grooves dominates the single resonance spectral profiles in Fig. 2. Thus, the coupled phase factor φ, as well as, the coupling coefficient κ, are all identical to zero on all three types of MM under investigation. The damping coefficient γ, in Table 1 indicate that the SLSP on cavity with large ring radius damps much faster than that on cavity with small ring radius. The ratio between the sub-wavelength periodic groove length, h, and outer radius, R, of circular cavity determines the dispersion relation of SLSP [38–44]. The SLSP mode exhibits stronger field strength on textured closed cavity compared with the corresponding modes in a conventional circular cavity of equal outer radius having no grooves. As such, the damping coefficients of single resonance modes, νs, as well as, the transparency windows, νT, all decrease with shrinking of the ring-size of textured closed cavity. Furthermore, the coupling coefficients, κ, of aforementioned modes, and the transparency windows decrease accordingly. Thus, we deduce that the ring-size determines not only the intrinsic resonance frequency of SLSP on textured closed cavity, but also the coupling strength between the electrical dipole on metallic arc and SLSP on cavity. As such, the windows of PIT effect can be manipulated directly by tuning the central frequency and coupling strength of SLSP. Such a mechanism is not realized in our earlier work [44].
Figure 3 maps the electromagnetic field distributions of transparency windows of three types of MMs. for θ = 120 degree, at 0.23 THz. An intrinsic electrical dipole is seen on the metallic arc and another SLSP of opposite polarity occurs at three types of textured closed cavity. Figure 3(a) shows that two SLSPs of opposite direction lead to a fake quadrupole, which repels each other in magnetic dipole momentum shown in Fig. 3(b). This phenomenon is similar to the PIT behavior of asymmetric coupled MM [51]. Here, the oscillation strength of SLSP on textured closed cavity is termed, ESLSP, and Earc is the electrical field on metallic arc. From close observation of the electromagnetic map shown in Fig. 3, the strength of two SLSPs of opposite polarity can be concluded as below: (1) Earc > ESLSP (Outer-ring), (2) Earc ≈ ESLSP (middle-ring), (3) Earc < ESLSP (inner-ring). It is evident that the destructive interference reaches a maximum at θ=120 degree on middle-ring MM.
Fig. 3. (a) Electrical field distribution and (b) magnetic field distribution of terahertz transparency window of the three types of MMs with θ = 120 degree at 0.23 THz. The color bar refers to the polarity as well as the relative strength of electromagnetic field.
A remarkable character of PIT effect of MM is a positive group delay (Δτ) at the transparency window in frequency spectrum [23,26,27]. The Δτ can be calculated from the equation as below:
where ϕ and ν refer to the effective phase and frequency of terahertz complex transmission spectrum, respectively. The measured and simulated group delays as a function of terahertz frequency for the three types of MMs at θ=120 degree are illustrated in Fig. 4. The measured and simulated Δτ of outer-ring MM is above 20 ps. The measured Δτ of middle-ring MM, reaches a maximum up to 42 ps, beyond the simulated 40.7 ps. This value is very much close to our previous prediction [44]. For the inner-ring MM, both the measured and simulated Δτ exceeds 35 ps. To the best of our knowledge, such a large group delay exceeds those reported for other terahertz slow light on binary MM. From a careful observation of Fig. 2 and Fig. 4, it is obvious that the group delays at the transmission minima are all negative. The negative group delay refers to a phenomenon whereby an electromagnetic wave penetrates a dispersive medium in such a way that its amplitude envelope is advanced though the medium rather than undergoing delay [52]. It is found that the negative group delay overlap well with the intrinsic mode frequency of metallic arc and of the textured closed cavity correspondingly. This is the same as other PIT effect in previous reports [26,27,28]. Based on our findings, the maximum value of terahertz slow light relies on the central angle of metal arc θ. This is illustrated in Fig. 5. Here, a detailed relationship between the arc angle and terahertz transmittance as well as the slow light is revealed by numerical simulation using finite element method (FEM). In these simulations, the primitive unit-cell is excited at normal incidence, under TM-polarization (E ‖ x-axis), the same as experimental condition. Periodic boundary conditions are applied in the simulation to mimic 2D infinite structures. As a result of tuning the central angle of metallic arc, a strong coupling region has been identified in each transmittance map of inner-ring, middle-ring, and outer-ring MM, as shown in Fig. 5(a). Obviously, these strong coupling regions shift from low frequency to high frequency as the ring radius of the textured closed cavity reduces. Similarly, the coupling regions shift to a relatively smaller central angle with reducing ring radius.According to the interaction of SLSPs, the coupling reaches a maximum when the intrinsic SLSP on textured closed cavity is equal to the dipolar oscillation on metallic arc [44]. The dipole length determines the resonance frequency [49]. A shorter arc implies a higher resonance frequency. Meanwhile, a ring of larger diameter corresponds to a lower resonance frequency. As such, the coupling regions shift with the ring radius. The slow light reaches a maximum at the maximum values, where coupling occurs, as shown using white broken lines-closed paths in Fig. 5(b). It is obvious that the slow light plateaus of each type of MM overlaps at the coupling regions, also depicted with white broken lines-close paths in Fig. 5(a). This is evidence that the destructive interference of SLSPs at the coupling region results in the slow light maximum values. The maximum values of three types of MM are listed in Table 2 below.
Fig. 4. The measured (red solid line) and simulated (blue solid line) of group delay of three types of MM at 120 degree (a) outer-ring (b) middle-ring and (c) inner-ring.
Fig. 5. (a) The simulated terahertz transmittance as functions of central angle of arc and frequency of three types of MM; (b) The group delay as functions of central angle of arc and frequency of three types of MM. The white dash line enclosed area denotes the coupling region.
Table 2. The terahertz slow light maximum values of three types of MM shown in Fig. 5(b).
As shown in Table 2, the central frequency of terahertz slow light maximum value shifts to higher frequency as the ring size reduces. Accordingly, the central angle of metallic arc decreases monotonically. Therefore, the terahertz slow light plateaus become manoeuvrable by accurately tuning the ring-size of textured closed cavity. Meanwhile, the maximum values of slow light plateaus can be controlled by tuning the metallic arc length precisely. Here, the slow light maximum value of outer-ring MM is 45.7 ps, slightly smaller than we predicted 46.6 ps [44]. This is owing to the dielectric environment (n = 1.8) of 25 µm thick polyimide substrate which is higher than that of free-space (n = 1.0) [44]. It is interesting to see that the slow light maximum values of outer-ring and inner-ring MM are both higher than that of middle-ring MM. It is known that the dynamic property of SLSP relies on the ratio between inward-outward periodic grooves to the radius of the ring [39–41]. For the middle-ring MM, the periodic grooves are half inward and half outward in length. Thus the effective groove length is smaller than the outer-ring and inner-ring MM. As such, its slow light maximum value is slightly lower than those of outer-ring MM and inner-ring MM. The recent progress on terahertz slow light on MMs are listed in Table 3 below:
Table 3. The progress on measured maximum value of terahertz group delay in MM.
It is obvious that our result is currently the highest group delay demonstrated so far within planar metamaterials at terahertz band.
Furthermore, the FOM of slow-light device can be calculated from the product of the group delay time and bandwidth of transparency windows (DBP) [48]:
where, Δτ represents the time delay of THz wave packet, Δν represent the bandwidth of transparency window, which is given as: Here, νH and νL are the high and low frequency cut-off points, respectively. The cut-off frequency is the closed adjacent point of zero delays between the terahertz slow light maximum values, as shown in Fig. 4. Figure 6 shows FOM of our MMs with the central angle of metallic arc at the step of 3 degree. Since our MM is axial symmetric in structure, it is a Lorentz reciprocal system under fundamental time-bandwidth limit Δν·Δτ < 2π [48]. As shown in Fig. 6, the maxima of above FOM are close to π. Accordingly, the bandwidth Δν increases with the maximum value of group delay Δτ by tuning the arc length, as shown in Fig. 5(b). At this point, the variation of FOM as a function of arc angle θ is upside and downside, which is in agreement with the terahertz slow light plateaus of outer-ring, middle-ring, and inner-ring.4. Summary
In summary, the manipulations of terahertz slow light plateaus are demonstrated experimentally by tuning the spoof localized surface plasmon (SLSP)-induced transparency window (PIT). A binary metamaterial unit-cell composed of a metallic arc and a textured closed cavity with periodic grooves support the SLSP. The numerical mapping of electromagnetic field indicates that a destructive interference occurs between the excited and induced SLSP dipole resonances, which results in the transparency window. By tuning the diameter of the ring structure of textured closed cavity, the coupling coefficient and damping ratio of SLSP is manipulated artificially. Thus, the strength and frequency of slow light maximum values become tunable correspondingly. By tuning the central angle θ of the arc at certain range, the transparency window exhibits an open-and-close behavior. A localized terahertz slow light is presented in the transparency window. The slow light maximum value achieves 42.4 ps at 0.23 THz, which is the highest value achieved so far among planar metamaterials for terahertz slow light application.
Funding
Joint Fund of Astronomy (U1631112).
Acknowledgments
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). Zhenyu Zhao and Hui Zhao contributed equally in this work.
References
1. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301(5630), 200–202 (2003). [CrossRef]
2. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001). [CrossRef]
3. M. Soljacic, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, “Ultra low-power all-optical switching,” Appl. Phys. Lett. 86(17), 171101 (2005). [CrossRef]
4. K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on nanoscale,” Science 358(6361), eaan5196 (2017). [CrossRef]
5. N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosrirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94(21), 211902 (2009). [CrossRef]
6. K. L. Tsakmakidis, M. S. Wartak, J. J. H. Cook, J. M. Hamm, and O. Hess, “Negative-permeability electromagnetically induced transparent and magnetically active metamaterials,” Phys. Rev. B 81(19), 195128 (2010). [CrossRef]
7. S. D. Jenkins, J. Ruostekoski, N. Papasimakis, S. Savo, and N. I. Zheludev, “Many-body subradiant excitation in metamaterial array: Experiment and theory,” Phys. Rev. Lett. 119(5), 053901 (2017). [CrossRef]
8. N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101(25), 253903 (2008). [CrossRef]
9. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef]
10. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102(5), 053901 (2009). [CrossRef]
11. W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, “Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013). [CrossRef]
12. M. P. Hokmabadi, E. Philip, E. Rivera, P. Kung, and S. M. Kim, “Plasmon-induced transparency by hybridizing concentric-twisted double split ring resonators,” Sci. Rep. 5(1), 14373 (2015). [CrossRef]
13. H. Merbold, A. Bitzer, and T. Feurer, “Near-field investigation of induced transparency in similarly oriented double split-ring resonators,” Opt. Lett. 36(9), 1683–1685 (2011). [CrossRef]
14. N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing,” Nano Lett. 10(4), 1103–1107 (2010). [CrossRef]
15. R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “Coupling between a dark and a bright eigenmode in a terahertz metamaterial,” Phys. Rev. B 79(8), 085111 (2009). [CrossRef]
16. S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80(15), 153103 (2009). [CrossRef]
17. R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011). [CrossRef]
18. J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012). [CrossRef]
19. M. Manjappa, Y. K. Srivastava, and R. Singh, “Lattice-induced transparency in planar metamaterials,” Phys. Rev. B 94(16), 161103 (2016). [CrossRef]
20. R. Yahiaoui, M. Manjappa, Y. K. Srivastava, and R. Singh, “Active control and switching of broadband electromagnetically induced transparency in symmetric metadevices,” Appl. Phys. Lett. 111(2), 021101 (2017). [CrossRef]
21. M. Manjappa, Y. K. Srivastava, L. Cong, I. Al-Naib, and R. Singh, “Active photo switching of sharp Fano resonances in THz metadevices,” Adv. Mater. 29(3), 1603355 (2017). [CrossRef]
22. T. C.-W. Tan, Y. K. Srivastava, M. Manjappa, E. Plum, and R. Singh, “Lattice induced strong coupling and line narrowing of split resonances in metamaterials,” Appl. Phys. Lett. 112(20), 201111 (2018). [CrossRef]
23. Z. Zhao, Z. Song, W. Shi, and W. Peng, “Plasmon-induced transparency-like behavior at terahertz region via dipole oscillation detuning in a hybrid planar metamaterial,” Opt. Mater. Express 6(7), 2190–2200 (2016). [CrossRef]
24. M. Manjappa, S.-Y. Chiam, L. Cong, A. A. Bettiol, W. Zhang, and R. Singh, “Tailoring the slow light behavior in terahertz metasurfaces,” Appl. Phys. Lett. 106(18), 181101 (2015). [CrossRef]
25. S. D. Jenkins and J. Ruostekoski, “Metamaterial transparency induced by cooperative electromagnetic interactions,” Phys. Rev. Lett. 111(14), 147401 (2013). [CrossRef]
26. Z. Zhao, X. Zheng, W. Peng, J. Zhang, H. Zhao, Z. Luo, and W. Shi, “Localized terahertz electromagnetically-induced transparency-like phenomenon in a conductively coupled trimer metamolecule,” Opt. Express 25(20), 24410–24424 (2017). [CrossRef]
27. Z. Zhao, X. Zheng, W. Peng, H. Zhao, J. Zhang, Z. Luo, and W. Shi, “Localized slow light phenomenon in symmetry broken terahertz metamolecule made of conductively coupled dark resonators,” Opt. Mater. Express 7(6), 1950–1961 (2017). [CrossRef]
28. Z. Zhao, X. Zheng, W. Peng, J. Zhang, H. Zhao, Z. Luo, and W. Shi, “Terahertz electromagnetically-induced transparency of self-complementary meta-molecules on Croatian checkerboard,” Sci. Rep. 9(1), 6205 (2019). [CrossRef]
29. J. A. Burrow, R. Yahiaoui, A. Sarangan, J. Mathews, I. Agha, and T. A. Searles, “Eigenmode hybridization enable lattice-induced transparency in symmetric terahertz metasurfaces for slow light applications,” Opt. Lett. 44(11), 2705–2708 (2019). [CrossRef]
30. A. Alipour, A. Farmani, and A. Mir, “High sensitivity and tunable nanoscale sensor based on plasmon-induced transparency in plasmonic metasurface,” IEEE Sens. J. 18(17), 7047–7054 (2018). [CrossRef]
31. M. A. Baqir, A. Farmani, T. Fatima, M. R. Raza, S. F. Shaukat, and A. Mir, “Nanoscale, tunable, and highly sensitive biosensor utilizing hyperbolic metamaterials in the near-infrared range,” Appl. Opt. 57(31), 9447–9454 (2018). [CrossRef]
32. A. Farmani, “Three-dimensional FDTD analysis of a nanostructured plasmonic sensor in the near-infrared range,” J. Opt. Soc. Am. B 36(2), 401–407 (2019). [CrossRef]
33. A. L. F. Armani, M. E. M. Iri, and M. O. H. S. Heikhi, “Tunable resonant Goos–Hänchen and Imbert–Fedorov shifts in total reflection of terahertz beams from graphene plasmonic metasurfaces,” J. Opt. Soc. Am. B 34(6), 1097–1106 (2017). [CrossRef]
34. A. Farmani, A. Mir, and Z. Sharifpour, “Broadly tunable and bidirectional terahertz graphene plasmonic switch based on enhanced Goos-Hänchen effect,” Appl. Surf. Sci. 453, 358–364 (2018). [CrossRef]
35. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef]
36. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005). [CrossRef]
37. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]
38. Z. Liao, Y. Luo, A. I. Fernandez-Domínguez, X. Shen, S. A. Maier, and T.-J. Cui, “High-order localized spoof surface plasmon resonances and experimental verifications,” Sci. Rep. 5(1), 9590 (2015). [CrossRef]
39. Y. J. Zhou, Q. X. Xiao, and B. J. Yang, “Spoof localized surface plasmons on ultrathin textured MIM ring resonator with enhanced resonances,” Sci. Rep. 5(1), 14819 (2015). [CrossRef]
40. L. Chen, Y. M. Wei, X.-F. Zang, Y. M. Zhu, and S. L. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016). [CrossRef]
41. Z. Gao, F. Gao, and B. Zhang, “High-order spoof localized surface plasmons supported on a complementary metallic spiral structure,” Sci. Rep. 6(1), 24447 (2016). [CrossRef]
42. Z. Li, B. Xu, L. Liu, J. Xu, C. Chen, C. Gu, and Y. Zhou, “Localized spoof surface plasmons based on closed subwavelength high contrast gratings: concept and microwave-regime realizations,” Sci. Rep. 6(1), 27158 (2016). [CrossRef]
43. Z. Liao, S. Liu, H. F. Ma, C. Li, B. Jin, and T.-J. Cui, “Electromagnetically induced transparency metamaterial based on spoof localized surface plasmons at terahertz frequencies,” Sci. Rep. 6(1), 27596 (2016). [CrossRef]
44. Z. Zhao, Y. Chen, Z. Gu, and W. Shi, “Maximization of terahertz slow light by tuning the spoof localized surface plasmon induced transparency,” Opt. Mater. Express 8(8), 2345–2354 (2018). [CrossRef]
45. R. D. Kekatpure, E. S. Barnard, W. S. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys. Rev. Lett. 104(24), 243902 (2010). [CrossRef]
46. R. Taubert, M. Hentschel, J. Kästel, and H. Giessen, “Classical analog of electromagnetically induced absorption in plasmonics,” Nano Lett. 12(3), 1367–1371 (2012). [CrossRef]
47. J. Zhang, Y. Xu, J. Zhang, P. Ma, M. Zheng, and Y. Li, “Extended coupled Lorentz oscillator model and analogue of electromagnetically induced transparency in coupled plasmonic structures,” J. Opt. Soc. Am. B 35(8), 1854–1860 (2018). [CrossRef]
48. K. L. Tsakmakidis, L. Shen, S. A. Schultz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017). [CrossRef]
49. F. Ulaby, Fundamentals of applied electromagnetics (Prentice Hall, 2007).
50. S. Walia, C. M. Shah, P. Gutruf, H. Nili, D. R. Chowdhury, W. Withayachumnankul, M. Bhaskaran, and S. Sriram, “Flexible metasurfaces and metamaterials: A review of materials and fabrication processes at micro- and nano-scales,” Appl. Phys. Express 2(1), 011303 (2015). [CrossRef]
51. X. Zheng, Z. Zhao, W. Shi, and W. Peng, “Broadband terahertz plasmon-induced transparency via asymmetric coupling inside meta-molecules,” Opt. Mater. Express 7(3), 1035–1057 (2017). [CrossRef]
52. L. Brillouin, Wave propagation and group velocity (Academic, USA, 1960).
