Article Controllable Fano‐Like Resonance in Terahertz Planar Meta‐Rotamers Subin Jo, Min Gyu Bae and Joong Wook Lee * Department of Physics and Optoelectronics Convergence Research Center, Chonnam National University, Gwangju 61186, Korea; email@example.com (S.J.); firstname.lastname@example.org (M.G.B.) * Correspondence: email@example.com Abstract: Meta‐molecules composed of meta‐atoms exhibit various electromagnetic phenomena owing to the interaction among the resonance modes of the meta‐atoms. In this study, we numeri‐ cally investigated Fano‐like‐resonant planar metamaterials composed of meta‐molecules at te‐ rahertz (THz) frequencies. We present meta‐rotamers based only on the difference in the spatial position of their component meta‐atoms (C‐ and Y‐shapes) that can be interconverted by rotations and have tunable Fano‐like resonance. This is because of the cooperative effects determined by the spatial coupling conditions of the nodes and antinodes of electric‐dipole and inductive–capacitive (LC) resonances of the meta‐atoms. The findings of this study provide potential options for explor‐ ing novel THz devices and for engineering high‐level functionalities in metamaterial‐based devices. Keywords: terahertz spectroscopy; metamaterials; modulators; active optics 1. Introduction The creation of metamaterials, which are artificially constructed composite materials Citation: Jo, S.; Bae, M.G.; Lee, J.W. with exceptional properties, has become an extremely interesting area of research in var‐ Controllable Fano‐Like Resonance in ious fields, such as optics, optoelectronics, electromagnetic field, acoustics, and thermol‐ Terahertz Planar Meta‐Rotamers. ogy [1–4]. Artificial atoms (called meta‐atoms) or molecules (called meta‐molecules), as Appl. Sci. 2021, 11, 9796. the basic structural elements for constructing metamaterials, are designed and fabricated https://doi.org/10.3390/app11219796 to implement a device with the desired characteristics and functionalities. In particular, the meta‐molecules created by engineering spatial arrangement or interatomic geometry Academic Editor: Mira Naftaly of different types of meta‐atoms achieve high‐level functionalities, such as plasmon‐in‐ duced transparency, multifunctional filtering, invisibility cloaking, tunable multiple res‐ Received: 22 September 2021 onators, reflective‐index engineering, and Fano resonance [5–18]. Accepted: 19 October 2021 Recently, metamaterials have promoted the inclusive development of terahertz Published: 20 October 2021 (THz) materials and devices because of their resonant electromagnetic response, which significantly improves the interaction between THz radiation and metamaterials. In par‐ Publisher’s Note: MDPI stays neu‐ tral with regard to jurisdictional ticular, developing THz devices and building a network connection in the THz frequen‐ claims in published maps and insti‐ cies have become key tasks for achieving sixth‐generation (6G) wireless communication tutional affiliations. [19,20]. This requires new techniques to manipulate the polarization, direction, amplifica‐ tion, collimation, resonance frequency, propagation, and phase of those THz waves. Thus, a THz metamaterial is the best candidate for realizing a device with such functionalities. Meta‐molecules composed of different types of meta‐atoms are fundamental ele‐ Copyright: © 2021 by the authors. Li‐ ments that control the transmission, reflection, and absorption of light and realize the censee MDPI, Basel, Switzerland. tunability of resonance wavelength at the THz frequencies. Various electromagnetically This article is an open access article induced transparency (EIT)‐analog optical systems based on THz metamaterials exhibit a distributed under the terms and con‐ narrow transmission or reflection spectral band and plasmon‐induced transparency be‐ ditions of the Creative Commons At‐ havior [21–24]. The EIT‐like effects of bright–bright mode coupling, which occur when tribution (CC BY) license (http://crea‐ two resonances of two different types of meta‐atoms are excited in close proximity in the tivecommons.org/licenses/by/4.0/). Appl. Sci. 2021, 11, 9796. https://doi.org/10.3390/app11219796 www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 9796 2 of 8 spectral domain, inevitably lead to resonance frequency detuning based on Fano‐type in‐ terference with ultrahigh quality factor (Q‐factor) [25–27]. Therefore, metamaterials com‐ posed of meta‐molecules are essential for fabricating versatile THz devices that require the ability to control resonance modes and spectral features. In this study, we numerically investigated a Fano‐like‐resonant planar THz met‐ amaterial composed of meta‐molecules consisting of two different types of meta‐atoms, C‐ and Y‐shaped metallic rods. In addition, we demonstrated that meta‐rotamers based only on the difference in the spatial position of their component meta‐atoms manifest tun‐ able Fano‐like resonance when optically isotropic, inner Y‐shaped meta‐atoms rotate. This phenomenon is caused by cooperative effects due to the spatial coupling conditions of the nodes and antinodes of the fundamental electric‐dipole resonance of Y‐shaped meta‐at‐ oms and higher‐order inductive–capacitive (LC) resonance of C‐shaped meta‐atoms. Our study highlights the importance of metamaterials for achieving novel THz devices and their high‐level functionalities. 2. Design and Methods Figure 1a shows a representative unit cell of the proposed metamaterial numerically simulated in this study. The two top virtual layers have two different types of meta‐atoms, a C‐shaped metallic split‐ring resonator (SRR) with spatially varying geometric parame‐ ters and a Y‐shaped metallic rod with different rotation angles. The meta‐molecule shown in the lowest layer of Figure 1a can be considered a unit cell of composite metamaterials, produced by combining the SRR and the Y‐shaped rod. Figure 1. (a) Schematic of the THz planar meta‐rotamer consisting of the C‐shaped SRR and Y‐ shaped metal rod. The physical dimensions of the meta‐molecules in the lattice are Px = Py = 120 μm. The thicknesses of the meta‐molecules and dielectric substrate (bare silicon) are 150 nm and 200 μm, respectively. (b) Schematic of the Y‐shaped meta‐atom. The corresponding size and rotations are as follows: L = 40 μm; θy = 0°, 30°, and 60°. (c) Schematic of the C‐shaped SRR meta‐atom. The corre‐ sponding size and angular gaps are as follows: D = 100 μm; θc = 10°, 20°, and 30°. The two types of meta‐atoms are structurally combined to be an analog of rotational isomers (also called rotamers) in chemistry, in which the rotamers can be interconverted by rotations. By combining the rotating Y‐shaped meta‐atoms to the fixed SRR meta‐atom, the arrangements of meta‐atoms in a meta‐molecule that are transformed by rotation Appl. Sci. 2021, 11, 9796 3 of 8 about the central axis of bonding can be exploited to generate different conformations that provide a possible method to design promising THz devices. The basic components (C‐shaped SRR and Y‐shaped rod) display optimal character‐ istics for fabricating the composite metamaterials, which can also be called meta‐rotamers. The Y‐shaped meta‐atom is one of the simplest structures showing polarization‐insensi‐ tive transmission or absorption properties because of its higher‐order rotational sym‐ metry and folded‐slot resonators; moreover, it is available to fabricate multimode resona‐ tors and active control devices [28–33]. As shown in Figure 2a, the folded planar resonator consisting of two arms placed in the direction of polarization of the incident THz waves generates a dipole resonance with a resonant wavelength equal to twice the length of the metal rod . When the Y‐shaped meta‐atom rotates, the three arms alternately assume the function of the folded planar resonator while exhibiting polarization‐independent op‐ tical properties, as shown in the inset of Figure 2a. Here, the normalization was carried out by dividing the spectral amplitudes through the metamaterials by the spectral ampli‐ tude through bare silicon used as a substrate. Figure 2. (a) Simulated THz amplitude spectra in the arrays of Y‐shaped meta‐atoms at the rotation angles of θy = 0°, 30°, and 60°. The inset shows the values of resonance frequency. The upper image shows the near electric field distribution at the resonance frequency at the rotation angle of θy = 0°. (b) Simulated THz amplitude spectra in the arrays of C‐shaped SRR meta‐atoms at the angular gaps of θc = 10°, 20°, and 30°. The upper images show the near electric field distributions at the resonances appearing near the frequencies of 0.25 and 0.7 THz. The C‐shaped SRR meta‐atom leads to dramatic structure‐dependent features. The tunability of optical resonances can be achieved by varying the arc length of the C‐shaped, polarization‐dependent characteristics due to high structural asymmetry, and the fabrica‐ tion of composite medium with simultaneously negative values of effective permeability and permittivity. As a result, versatile and novel optical devices can be realized, such as negative refractive index devices, superlenses, multifunctional filters, polarization devices, and various types of resonators [34–38]. Figure 2b shows the simulated THz amplitude spectra in the arrays of C‐shaped SRR meta‐atoms with angular gaps of θc = 10°, 20°, and 30°. As the total arc length of the C‐shape is shorter, the two odd resonances are blue‐ shifted because the resonance wavelength depends on the arc length of the C‐shape. As in the aforementioned case, when the polarization of the incident light at normal incidence is parallel to the gap of the C‐shaped SRR, the two odd resonances appearing near the frequencies of 0.25 THz and 0.7 THz can be clearly observed. As can be inferred from the two electric near‐field images on the top, one appears at the lower frequency and corresponds to the fundamental LC resonance, whereas the other appears at the higher Appl. Sci. 2021, 11, 9796 4 of 8 frequency and corresponds to the second‐order LC resonance (also called quadrupole‐ mode resonance) . The meta‐molecules are designed such that the electric‐dipole res‐ onance of the Y‐shaped meta‐atom can be overlapped on the quadrupole‐mode resonance of the C‐shaped SRR in frequency. All simulations were performed using COMSOL Multiphysics software, which is a frequency‐domain solver based on the finite element method (FEM), to solve the Maxwell equations. For the structure of the metamaterial unit cell, the unit element was surrounded by periodic boundary conditions on four sides, and the top and bottom of the unit element were considered as perfectly matched layers. The simulated structure was illuminated by an x‐polarized plane wave at normal incidence. Most metals can be regarded as perfect conductors at THz frequencies. Therefore, we obtained the values of permittivity, plasma frequency, and damping constant of aluminum required for the simulations using the Drude model . In addition, the silicon layer with a thickness of 200 μm was modeled as a lossless dielectric substrate with a relative permittivity of 11.68. 3. Results and Discussion Figure 3a demonstrates the simulated amplitude spectra of THz wave transmission for the meta‐rotamer displayed in Figure 1a. For the two transition states of the meta‐ rotamers with different angles of rotation of θy = 0° and 60°, the transmission spectra clearly present two resonant dips corresponding to the frequencies of f1 and f2 at θy = 0° and f’1 and f’2 at θy = 60°. f1 and f’1 represent the second‐order LC resonance of the C‐shaped SRR, whereas f2 and f’2 represent the electric‐dipole resonance of the Y‐shaped rod. To elucidate the characteristics of the resonances, we simulated the electric near‐field distributions at the four resonant frequencies shown in Figure 3a. To clearly observe the spatial shape of each resonance mode, we plotted the out‐of‐plane electric field (𝐸 ) dis‐ tributions at the distance of 8 μm above the surface of the meta‐rotamers, as shown in Figure 3b. The figures of f2 and f’2 show that the dipole resonance mode corresponding to the two arms of the Y‐shaped metal rod lying in the polarization direction of the incident THz waves is well represented for both states of the meta‐atoms. In this case, only the position of the electric near‐field pattern is changed because of the structural change of the meta‐molecules, whereas the shape of the electric near‐field pattern and the position of the resonant frequency do not change. On the contrary, in the case of the second‐order LC resonance appearing at the fre‐ quencies of f1 and f’1, a completely different aspect is observed. The resonance mode for the C‐shaped meta‐atom does not show a clear difference for the two states of meta‐rota‐ mers. However, when the angle of rotation is 0° for the Y‐shaped rod, the electric near‐ field is activated at the ends of its arms horizontal to the polarization. When the arms of the Y‐shaped rod are adjacent to the standing wave antinodes of the second‐order LC resonance, the electric near‐fields are strongly enhanced at the ends of its arms. This im‐ plies that the coherent near‐field coupling between the bright modes of two adjacent meta‐ atoms occurs when the antinodes of the two excited resonances are located close to each other with a gap of 5 μm. To generate a stronger coupling effect, the total length of the C‐shaped SRR was tuned; thus, the two resonant modes were close to each other in the spectrum. As the angular gap changed from 10° to 30°, the second‐order LC resonance f’1 approached the dipole resonance f’2 of the Y‐shaped rod, as shown by the red curves in Figure 3a,c,e. When the antinode coupling of the two excited resonances at the meta‐rotamer state with θy = 0° appeared, the second‐order LC resonance 𝑓 shifted to the longer wavelength regime. In‐ terestingly, the second‐order LC resonance changed significantly with an asymmetrical line shape, whereas the dipole resonance was almost unchanged. This implies that, when the standing wave antinodes of the two excited resonances are spatially overlapped, the two resonances strongly interfere with each other, thereby generating Fano‐like resonance. It is known that the strong red‐shift of f’1 in the spectral band is caused by the damping Appl. Sci. 2021, 11, 9796 5 of 8 phenomenon of localized surface waves, depending on the coupling strength between the two standing wave antinodes [40,41]. Figure 3. (a,c,e) Simulated THz amplitude spectra in the meta‐rotamers consisting of the C‐shaped SRR and Y‐shaped rod meta‐atoms, for the two different states of the meta‐rotamers with rotation angles of θy = 0° and 60°, as shown by the black and red solid lines, respectively. Each THz amplitude spectra were simulated in the three types of samples with different angular gaps of θc = 10°, 20°, and 30°, as shown in (a,c,e), respectively. (b,d,f) Spatial electric near‐field distributions for the meta‐ molecules at the resonances of 𝑓 , 𝑓 , 𝑓 , and 𝑓 . For the three types of samples with different an‐ gular gaps of θc = 10°, 20°, and 30°, 𝑓 = 0.63, 0.65, and 0.66 THz, 𝑓 = 0.74, 0.74, and 0.74 THz, 𝑓 = 0.66, 0.68, and 0.70 THz, and 𝑓 = 0.73, 0.73, and 0.73 THz, respectively. To quantitatively understand the dependence of coupling strength on the state of meta‐rotamer, we plotted the values of resonant frequency extracted from the simulations versus the angular gap θc, for the structure with only C‐shaped SRR meta‐atoms and the meta‐rotamers with two different states, which are determined by different angular gaps, as shown by the black squares, red circles, and blue triangles in Figure 4a, respectively. When the two standing wave antinodes were not aligned, the combined effect of the C‐ and Y‐shaped meta‐atoms appeared as a simple summation of each resonance without a Appl. Sci. 2021, 11, 9796 6 of 8 significant change in the resonant frequency, as shown by the red circles in Figure 4a. On the contrary, the clear red‐shift of the second‐order LC resonance was visible because of the strong coupling when the standing wave antinodes were placed opposite to each other, as quantitatively compared in Figure 4b, which shows the values of resonant fre‐ quency shift, Δ𝑓 = f’1 − 𝑓 and Δ𝑓 = f’2 − 𝑓 . The coupling strength is important in achieving resonance characteristics such as a high Q‐factor. As shown in Figure 4c, the Q‐factor exhibits an interesting growth behavior with the increase of the angular gap showing higher coupling strength between the two resonances. Here, if the coupling strength is increased by approximating the two reso‐ nances in the spectrum, a larger Q‐factor can be expected. Although we expected to max‐ imize the Q‐factor and the resonance strength, there was a tradeoff between these factors, which is a typical characteristic of the resonance phenomenon, as shown in the values of resonance depth (blue squares). On the contrary, the Q‐factor and resonance depth ex‐ tracted from the dipole resonance of the Y‐shaped rods exhibited a slight difference by varying the angular gap. Thus, the asymmetric feature of the Fano‐like resonance caused by the strong coupling between each resonance of two different types of meta‐atoms sug‐ gests a method to control the resonant frequency and the Q‐factor. Figure 4. (a) Resonant frequencies of the second‐order LC resonance obtained at three samples of the C‐shaped meta‐atoms and two states of meta‐rotamers. (b) Frequency shift of the second‐order LC resonance (Δ𝑓 ) and dipole resonance (Δ𝑓 ) as a function of angular gap θc. (c) Q‐factor (red squares and circles, left scale) and resonance depth (blue squares and circles, right scale) for the two resonances, 𝑓 (blue and red squares) and 𝑓 (red and blue circles), respectively. 4. Conclusions In conclusion, we have demonstrated meta‐rotamers with Fano‐like resonance. The meta‐rotamers based only on the difference in the spatial position of their component meta‐atoms, the C‐shaped SRR and Y‐shaped metal rod, can be interconverted by the ro‐ tation of the Y‐shaped meta‐atom. The resonant frequency and the Q‐factor can be con‐ trolled by asymmetric characteristics of Fano‐like resonance. This is because of the coop‐ erative effects determined by the spatial coupling conditions of nodes and antinodes of the second‐order LC resonance by the C‐shaped SRR meta‐atoms and the dipole reso‐ Appl. Sci. 2021, 11, 9796 7 of 8 nance by the Y‐shaped meta‐atoms. The higher Q‐factor observed in the antinode–anti‐ node combination is due to the strong electric near‐field coupling between two resonant modes located spectrally very close together. In addition, the red‐shift of the LC resonance may be caused by the increase of effective inductance value in the condition of the anti‐ node–antinode coupling. We believe that the findings provide possibilities for exploring metamaterial‐based THz devices, such as modulators, sensors, antennas, and switches, requiring high sensitivity and multifunctions of spectral tunability and selectivity. Author Contributions: Conceptualization and methodology, J.W.L.; writing—original draft prepa‐ ration, S.J.; writing—review and editing, J.W.L. and M.G.B.; data acquisition and analysis, S.J. and M.G.B.; supervision, project administration, and funding acquisition, J.W.L. All authors have read and agreed to the published version of the manuscript. Funding: National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant Number: NRF‐ 2019R1F1A1058851). Institutional Review Board Statement: Not applicable Informed Consent Statement: Not applicable Data Availability Statement: Data are contained within the article. Conflicts of Interest: The authors declare no conflicts of interest. References 1. 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Applied Sciences – Multidisciplinary Digital Publishing Institute
Published: Oct 20, 2021
Keywords: terahertz spectroscopy; metamaterials; modulators; active optics