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Curr. Opt. Photon. 2022; 6(6): 590-597

Published online December 25, 2022 https://doi.org/10.3807/COPP.2022.6.6.590

Copyright © Optical Society of Korea.

Incident-angle-based Selective Tunability of Resonance Frequency in Terahertz Planar Metamolecules

A Young Lim, Joong Wook Lee

Department of Physics and Optoelectronics Convergence Research Center, Chonnam National University, Gwangju 61186, Korea

Corresponding author: *leejujc@chonnam.ac.kr, ORCID 0000-0002-4624-8795

Received: August 10, 2022; Revised: November 2, 2022; Accepted: November 4, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

We carry out numerical simulations of the responses of planar metamaterials composed of metamolecules under obliquely incident terahertz waves. A Fano-like-resonant planar metamaterial, with two types of resonance modes originating from the two meta-atoms constituting the meta-molecules, exhibits high performance in terms of resonance strength, as well as the outstanding ability to manipulate the resonance frequency by varying the incident angle of the terahertz waves. In the structure, the fundamental electric dipole resonance associated with Y-shaped meta-atoms is highly tunable, whereas the inductive-capacitive resonance of C-shaped meta-atoms is relatively omnidirectional. This is attributed to the electric near-field coupling between the two types of meta-atoms. Our work provides novel opportunities for realizing terahertz devices with versatile functions, and for improving the versatility of terahertz sensing and imaging systems.

Keywords: Metamaterials, Optical devices, Terahertz

OCIS codes: (060.2630) Frequency modulation; (160.3918) Metamaterials; (230.5750) Resonators; (300.6495) Spectroscopy, terahertz

Metamaterials are artificial composites with periodic structures consisting of subwavelength geometric elements called meta-atoms. The remarkable advantage of these materials is that they exhibit unique electromagnetic characteristics, such as negative refraction, invisible cloaking, super-resolution imaging, and outstanding optical behaviors across the electromagnetic spectrum, especially from microwave to optical frequencies [16].

Various devices with desirable optical characteristics and versatile functions can be realized using metamaterials created by selecting a specific design of meta-atoms and engineering their spatial arrangement. Optical metamaterials exhibit interesting optical phenomena, such as reflective-index engineering, chirality, frequency selectivity, and high spectral tunability [710]. Furthermore, the fabricated metamolecules, composed of two or more different types of meta-atoms, provide high-level functionalities such as plasmon-induced transparency, generation and manipulation of Fano-type resonance, tunable multiple resonators, and resonance-mode engineering, owing to their strong electric near-field coupling and structural asymmetry [1117].

Many such metamaterials exhibit favorable properties in response to terahertz (THz) frequencies, which are much lower than those in the optical and infrared regions; therefore, it is easier to realize multifunctional devices based on metallic subwavelength structures [1820]. In particular, Jo et al. [21] reported that a planar THz metamaterial (denoted as a metarotamer), composed of metamolecules formed from two types of meta-atoms (C- and Y-shaped metallic rods), exhibits a tunable Fano-like resonance when the optically isotropic, inner Y-shaped meta-atoms rotate. Nevertheless, the effects of obliquely incident waves on the resonance response of THz metamaterials remain to be understood; this information can help in achieving advanced device functions, such as higher angular selectivity and wider controllability of the resonance frequency [2227].

In this paper, we report planar THz metamaterials based on metamolecules composed of two types of meta-atoms, and analyze their coupling with obliquely incident THz waves. We design metamolecules with two basic components, a C- and a Y-shaped metallic rod, exhibiting inductive-capacitive (LC) and electric dipole resonances respectively. The two resonances are separately controlled by changing the angle of incidence of the THz waves: The fundamental dipole resonance of the Y-shaped meta-atoms is relatively tunable, while the LC resonance is almost omnidirectional. The electric near-field coupling between the two types of meta-atoms further amplifies these effects. These findings provide novel opportunities for realizing THz devices that require higher angular selectivity and improved resonant-frequency tunability.

The proposed THz metamaterial is illuminated by a polarized THz electromagnetic wave along the x axis, as shown in Fig. 1(a). The angle of incidence θ is defined as the angle formed between the incident THz wavevector and the z axis. Fig. 1(b) shows a top-down image of the unit cell, which consists of a metamolecule combining a C-shaped split-ring resonator (SRR) and a Y-shaped metallic rod. The C-shaped SRR has diameter and angular gap of D = 100 μm and ϕ = 10° respectively. The length of one arm of the Y-shaped rod is L = 40 μm, and the linewidth of all metal structures is w = 5 μm. The thickness and period (along both x and y axes) of the metamolecule are set to t = 10 μm and P = 120 μm respectively. The metamolecules are designed in such a way that the end of one arm of the Y-shaped rod can be placed on the same axis as the angular gap of the C-shaped SRR.

Figure 1.Schematic diagrams of the THz metamolecule resonator. (a) Sample geometry and orientations of polarization and incidence angle. The THz electromagnetic wave is obliquely incident on the THz resonator, at variable angles. (b) Schematic illustration and related dimensions of a unit cell of the metamolecule composing the metamaterial.

To calculate the angle-dependent transmission spectra at THz frequencies, we carry out a frequency-domain study using the COMSOL Multiphysics software, which is a finite-element analysis, solver, and simulation package with a variety of applications in physics and engineering. Periodic boundary conditions are used in the x and y directions, to avoid boundary problems caused by finite-size effects. The incident THz wave propagates along the z axis, where port boundary conditions are applied. Transmission spectra are analyzed in steps of 0.005 THz over the frequency range of 0.1 to 1.0 THz. A free triangular mesh type is selected to optimize the simulation efficiency. Silicon (with a dielectric constant of 11.68) is used to model a lossless dielectric substrate, and the conductivity of aluminum, the material composing the resonator, is set to σ = 4.55 × 107 S/m.

The simulated THz transmission amplitude spectra of each resonator at a normal incidence angle of θ = 0° are shown in Fig. 2(a). The red and blue dashed lines indicate the resonances of the C- and Y-shaped meta-atoms before being combined into a metamolecule. In the p-polarized wave, the odd-mode LC resonances of the C-shaped meta-atom are excited; the two lowest odd-mode resonances are shown in Fig. 2(a). The lower frequency of 0.225 THz corresponds to the fundamental LC resonance, while the second-order LC resonance is located at 0.67 THz. For the Y-shaped meta-atom, the electric dipole resonance appears at a frequency of 0.73 THz.

Figure 2.THz transmission amplitude spectra and surface current distributions. (a) Simulated THz transmission amplitude spectra of meta-atoms and metamolecule, for normally incident p-polarized waves. (b) Simulated surface current distributions for each meta-atom at 0.225, 0.67, and 0.73 THz (from left to right, in order), and the corresponding z components of the electric near-field distributions at these resonant frequencies. (c) Simulated surface current distributions and z components of the electric near-field distributions of the metamolecule at 0.225, 0.635, and 0.735 THz (from left to right, in order).

The transmission spectrum of the metamolecule structure obtained by combining the two meta-atoms is shown as a black solid line in Fig. 2(a). The metamolecule is designed in such a way that the dipole resonance of the Y-shaped rod and the second-order LC resonance of the C-shaped SRR are excited together by the p-polarized wave. Thus, after combining the two components the second-order LC resonance is strongly redshifted from 0.67 to 0.635 THz, whereas the minimum of the electric dipole resonance excited by both arms of a Y-shaped meta-atom, oriented parallel to the polarization of the incident wave, remains almost unchanged near 0.73 THz. The interaction of the two meta-atomic structures with spatially overlapping resonances results in the generation of a Fano-like resonance, as shown in Fig. 2(a).

The underlying physical mechanisms of the resonance characteristics can be understood by analyzing the distributions of the surface current and electric near field, shown in Figs. 2(b) and 2(c). The fundamental LC resonance is observed at 0.225 THz, based on the fact that the surface current distribution shows a circular current flow in the whole ring. Furthermore, the surface current distribution at 0.635 THz shows a region with counterclockwise current flow, and two regions with clockwise flow. This means that the resonance at 0.635 THz is due to the typical second-order LC resonance. In contrast, at 0.735 THz the current and electric near-field on the C-shaped SRR are sufficiently restrained, but those on the Y-shaped rod are strongly excited, showing the typical pattern of an electric dipole resonance.

To understand the effects of the interaction of the two adjacent resonators, the angle of incidence θ is adjusted from 0° to 60° in the TE and TM mode directions respectively. In the TE mode the incident wave is tilted along the y axis, so that the electric field component of the incident wave remains parallel to the metasurface. On the other hand, in the TM mode the wave is tilted along the x axis, so that the magnetic field component of the incident wave remains parallel to the metasurface. Under the simulated conditions, the polarization of the incident THz wave is parallel to the x axis. Then, we quantitatively analyze the degree of change in the resonance frequency before and after coupling.

The THz transmission amplitude spectra for each meta-atom, simulated at different incidence angles of θ = 0°, 30°, and 60° in TE mode, are shown in Figs. 3(a) and 3(b), while Figs. 3(c) and 3(d) display the simulated spectra in TM mode. In the case of the C-shaped SRR in TE mode, despite the decreased amplitude of the transmitted signals, both the fundamental and second-order resonance positions (at 0.225 and 0.67 THz respectively) remain almost unchanged with increasing incidence angle, compared to the signals at normal incidence, as shown in Fig. 3(a). For the Y-shaped rod, in Fig. 3(b) it is observed that the resonance position at 0.73 THz is slightly blueshifted, although this change is not considered significant. Overall, in TE mode the transmission spectrum maintains its initial shape, with only minor changes.

Figure 3.Simulated THz transmission amplitude spectra of both meta-atoms, at several angles of incidence. (a) and (b), C- and Y-shaped meta-atoms in TE mode respectively. (c) and (d), C- and Y-shaped meta-atoms in TM mode respectively.

On the other hand, Figs. 3(c) and 3(d) reveal that the simulated spectra in TM mode exhibit more pronounced changes with varying angle of incidence than those in TE mode. The position of the fundamental LC resonance at 0.225 THz does not change, as in the case of the TE mode. As shown in Fig. 3(c), the only difference with respect to the TM mode is that two small resonant peaks appear near 0.66 and 0.9 THz. The former is due to weak electromagnetically induced transparency (EIT), while the latter corresponds to magnetic-resonance-like behavior. These properties originate from the oblique incident wave that induces asymmetrical currents and asymmetrical electromagnetic field distributions on the metasurface [24, 27]. In addition, under an oblique wave the magnetic component interacts with the metasurface.

The resonance exhibits a larger blueshift in TM than in TE mode, due to the decrease in the electric field component parallel to the surface when the incident wave is tilted, although the difference was not significant [28]. Despite the difference in the overall shape of the spectra plotted in the two figures, the degree of change of the resonance position does not seem large enough to be meaningful.

To analyze the coupling effects on the above characteristics, the transmission amplitude spectra of the metamolecule resonator are simulated for both TE and TM modes, as shown in Fig. 4. No particular effect is observed in TE mode, as seen in Fig. 4(a). The resonance position corresponding to the C shape is still independent of the angle of incidence, and the degree of blueshift corresponding to the Y shape is similar to that observed for the individual meta-atom resonator. Apart from the shift of the resonance frequency position of each metamolecular resonator due to the Fano effect (shown in Fig. 2), no other angle-dependent coupling effects are not observed in TE mode.

Figure 4.Simulated THz transmission amplitude spectra of the metamolecule as a function of frequency and incidence angle, for (a) TE and (b) TM modes. The angle of incidence ranges from 0 to 60° in 10° increments.

In TM mode, the position of the second-order LC resonant frequency shows almost no change and remains fixed at 0.635 THz. The EIT-like effect, which influence the secondary resonance position of the C-shaped meta-atom resonator, does not affect the LC resonance position after combining the two structures; however, it has a slight impact at 0.67 THz, which is the resonance position of the meta-atom before coupling. In addition, the magnetic resonance at 0.9 THz is slightly weakened.

The most noteworthy effect observed in TM mode is associated with the resonance of the Y-shaped rod appearing near 0.735 THz. The blueshift of the resonant frequency shows a completely different trend, compared to the results obtained before combining the meta-atoms, and also those observed in TE mode. The strong blueshift is due to the electric near-field coupling effect, and particularly to its asymmetric distribution on one side of the C-shaped SRR. The resonance depth, which is greatly reduced in the meta-atomic structures, remains similar to that observed in the normal-incidence case, due to the electric field coupling effect of the two meta-atoms.

To elucidate the properties of the resonances, we simulate the electric near-field distributions at the incidence angles of θ = 0, 30, and 60° for a TM-mode oblique wave. Figures 5(a)5(c) display the electric field distributions on the surfaces of the C-shaped SRR, Y-shaped meta-atom, and their combined metamolecule structure respectively. As the angle of incidence increases, the shape of the near-field distribution of the meta-atoms becomes asymmetric. However, in the case of the meta-molecule, the shape of the electric field of the Y-shaped rod remains almost symmetric, as a result of the coupling effect with the C-shaped SRR.

Figure 5.Simulated electric near-field distributions in TM mode at incidence angles of θ = 0° (left column), 30° (middle column), and 60° (right column), at (a) the second-order LC resonance of the C-shaped split-ring resonator (SRR) at 0.67, 0.665, and 0.65 THz (from left to right, in order), (b) the electric dipole resonance of the Y-shaped meta-atom at 0.73, 0.755, and 0.76 THz (from left to right, in order), and (c) the coupled electric dipole resonance of the metamolecule at 0.735, 0.8, and 0.815 THz (from left to right, in order).

To quantify the coupling effects, we obtain the rate of change of the resonant frequencies for various types of metastructures. Except for the electric dipole resonance of the metamolecule, M-Y(TE), all results were obtained in TM mode. The corresponding frequency shifts are plotted in Fig. 6. The values of the fundamental LC resonance of the C-shaped meta-atom and the metamolecule (C1 and M-C1) remain almost constant. Slight changes are observed for the second LC resonance of the C-shaped meta-atom and the metamolecule (C2 and M-C2). The rate of change of the secondary LC resonance frequency at 60° is 2.2% in the meta-atom structure, but decreases to less than 0.8% in the metamolecule structure. The electric dipole resonance of the meta-atom structure in TM mode and the metamolecule structure in TE mode showed the maximum frequency-change rates of 4.1% and 2.7% respectively. In contrast, the electric dipole resonance of the metamolecule in TM mode shows a high tunability of about 11%. The degree of these changes depends on the angle of incidence. Even though the resonances appear in the same metastructure and geometry, the LC resonances originating from the C-shaped SRR are omnidirectional, whereas the electric dipole resonance due to the Y-shaped rod is highly tunable.

Figure 6.Rate of change of each resonance frequency, as a function of the angle of incidence. C1 and C2 denote the fundamental and second-order resonances of the C-shaped meta-atom; Y represents the resonance of the Y-shaped meta-atom in TM mode; and M-C1, M-C2, and M-Y denote the C1, C2, and Y resonances of the metamolecule after combining the two resonators.

In conclusion, we have shown that metamolecule resonators in the THz region exhibit resonance frequencies that are tunable according to the angle of incidence. Each resonance mode of the two meta-atoms constituting the metamolecule can be independently controlled by varying the angle of incidence. The frequencies of the LC resonances due to the C-shaped SRR show little change, whereas the electric dipole resonance related to the Y-shaped rod exhibits a high frequency tunability. The electric near-field coupling between the two different types of meta-atoms further amplifies this effect. We believe that these findings may support the design of new types of metamaterials, and the development of THz devices with high angular selectivity and functionality, such as tunable frequency-selective surfaces with angular stability and sensitivity, bendable THz devices, and devices enabling directionality control of resonant modes.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

The authors thank the funding agencies for supporting our research work. In addition, the authors would like to thank the Editor in Chief, the Associate Editor, and the anonymous referees for their insightful suggestions.

National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant Number: NRF- 2022R1F1A1071757).

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Article

Article

Curr. Opt. Photon. 2022; 6(6): 590-597

Published online December 25, 2022 https://doi.org/10.3807/COPP.2022.6.6.590

Copyright © Optical Society of Korea.

Incident-angle-based Selective Tunability of Resonance Frequency in Terahertz Planar Metamolecules

A Young Lim, Joong Wook Lee

Department of Physics and Optoelectronics Convergence Research Center, Chonnam National University, Gwangju 61186, Korea

Correspondence to:*leejujc@chonnam.ac.kr, ORCID 0000-0002-4624-8795

Received: August 10, 2022; Revised: November 2, 2022; Accepted: November 4, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We carry out numerical simulations of the responses of planar metamaterials composed of metamolecules under obliquely incident terahertz waves. A Fano-like-resonant planar metamaterial, with two types of resonance modes originating from the two meta-atoms constituting the meta-molecules, exhibits high performance in terms of resonance strength, as well as the outstanding ability to manipulate the resonance frequency by varying the incident angle of the terahertz waves. In the structure, the fundamental electric dipole resonance associated with Y-shaped meta-atoms is highly tunable, whereas the inductive-capacitive resonance of C-shaped meta-atoms is relatively omnidirectional. This is attributed to the electric near-field coupling between the two types of meta-atoms. Our work provides novel opportunities for realizing terahertz devices with versatile functions, and for improving the versatility of terahertz sensing and imaging systems.

Keywords: Metamaterials, Optical devices, Terahertz

I. INTRODUCTION

Metamaterials are artificial composites with periodic structures consisting of subwavelength geometric elements called meta-atoms. The remarkable advantage of these materials is that they exhibit unique electromagnetic characteristics, such as negative refraction, invisible cloaking, super-resolution imaging, and outstanding optical behaviors across the electromagnetic spectrum, especially from microwave to optical frequencies [16].

Various devices with desirable optical characteristics and versatile functions can be realized using metamaterials created by selecting a specific design of meta-atoms and engineering their spatial arrangement. Optical metamaterials exhibit interesting optical phenomena, such as reflective-index engineering, chirality, frequency selectivity, and high spectral tunability [710]. Furthermore, the fabricated metamolecules, composed of two or more different types of meta-atoms, provide high-level functionalities such as plasmon-induced transparency, generation and manipulation of Fano-type resonance, tunable multiple resonators, and resonance-mode engineering, owing to their strong electric near-field coupling and structural asymmetry [1117].

Many such metamaterials exhibit favorable properties in response to terahertz (THz) frequencies, which are much lower than those in the optical and infrared regions; therefore, it is easier to realize multifunctional devices based on metallic subwavelength structures [1820]. In particular, Jo et al. [21] reported that a planar THz metamaterial (denoted as a metarotamer), composed of metamolecules formed from two types of meta-atoms (C- and Y-shaped metallic rods), exhibits a tunable Fano-like resonance when the optically isotropic, inner Y-shaped meta-atoms rotate. Nevertheless, the effects of obliquely incident waves on the resonance response of THz metamaterials remain to be understood; this information can help in achieving advanced device functions, such as higher angular selectivity and wider controllability of the resonance frequency [2227].

In this paper, we report planar THz metamaterials based on metamolecules composed of two types of meta-atoms, and analyze their coupling with obliquely incident THz waves. We design metamolecules with two basic components, a C- and a Y-shaped metallic rod, exhibiting inductive-capacitive (LC) and electric dipole resonances respectively. The two resonances are separately controlled by changing the angle of incidence of the THz waves: The fundamental dipole resonance of the Y-shaped meta-atoms is relatively tunable, while the LC resonance is almost omnidirectional. The electric near-field coupling between the two types of meta-atoms further amplifies these effects. These findings provide novel opportunities for realizing THz devices that require higher angular selectivity and improved resonant-frequency tunability.

II. DESIGN AND METHODS

The proposed THz metamaterial is illuminated by a polarized THz electromagnetic wave along the x axis, as shown in Fig. 1(a). The angle of incidence θ is defined as the angle formed between the incident THz wavevector and the z axis. Fig. 1(b) shows a top-down image of the unit cell, which consists of a metamolecule combining a C-shaped split-ring resonator (SRR) and a Y-shaped metallic rod. The C-shaped SRR has diameter and angular gap of D = 100 μm and ϕ = 10° respectively. The length of one arm of the Y-shaped rod is L = 40 μm, and the linewidth of all metal structures is w = 5 μm. The thickness and period (along both x and y axes) of the metamolecule are set to t = 10 μm and P = 120 μm respectively. The metamolecules are designed in such a way that the end of one arm of the Y-shaped rod can be placed on the same axis as the angular gap of the C-shaped SRR.

Figure 1. Schematic diagrams of the THz metamolecule resonator. (a) Sample geometry and orientations of polarization and incidence angle. The THz electromagnetic wave is obliquely incident on the THz resonator, at variable angles. (b) Schematic illustration and related dimensions of a unit cell of the metamolecule composing the metamaterial.

To calculate the angle-dependent transmission spectra at THz frequencies, we carry out a frequency-domain study using the COMSOL Multiphysics software, which is a finite-element analysis, solver, and simulation package with a variety of applications in physics and engineering. Periodic boundary conditions are used in the x and y directions, to avoid boundary problems caused by finite-size effects. The incident THz wave propagates along the z axis, where port boundary conditions are applied. Transmission spectra are analyzed in steps of 0.005 THz over the frequency range of 0.1 to 1.0 THz. A free triangular mesh type is selected to optimize the simulation efficiency. Silicon (with a dielectric constant of 11.68) is used to model a lossless dielectric substrate, and the conductivity of aluminum, the material composing the resonator, is set to σ = 4.55 × 107 S/m.

The simulated THz transmission amplitude spectra of each resonator at a normal incidence angle of θ = 0° are shown in Fig. 2(a). The red and blue dashed lines indicate the resonances of the C- and Y-shaped meta-atoms before being combined into a metamolecule. In the p-polarized wave, the odd-mode LC resonances of the C-shaped meta-atom are excited; the two lowest odd-mode resonances are shown in Fig. 2(a). The lower frequency of 0.225 THz corresponds to the fundamental LC resonance, while the second-order LC resonance is located at 0.67 THz. For the Y-shaped meta-atom, the electric dipole resonance appears at a frequency of 0.73 THz.

Figure 2. THz transmission amplitude spectra and surface current distributions. (a) Simulated THz transmission amplitude spectra of meta-atoms and metamolecule, for normally incident p-polarized waves. (b) Simulated surface current distributions for each meta-atom at 0.225, 0.67, and 0.73 THz (from left to right, in order), and the corresponding z components of the electric near-field distributions at these resonant frequencies. (c) Simulated surface current distributions and z components of the electric near-field distributions of the metamolecule at 0.225, 0.635, and 0.735 THz (from left to right, in order).

The transmission spectrum of the metamolecule structure obtained by combining the two meta-atoms is shown as a black solid line in Fig. 2(a). The metamolecule is designed in such a way that the dipole resonance of the Y-shaped rod and the second-order LC resonance of the C-shaped SRR are excited together by the p-polarized wave. Thus, after combining the two components the second-order LC resonance is strongly redshifted from 0.67 to 0.635 THz, whereas the minimum of the electric dipole resonance excited by both arms of a Y-shaped meta-atom, oriented parallel to the polarization of the incident wave, remains almost unchanged near 0.73 THz. The interaction of the two meta-atomic structures with spatially overlapping resonances results in the generation of a Fano-like resonance, as shown in Fig. 2(a).

The underlying physical mechanisms of the resonance characteristics can be understood by analyzing the distributions of the surface current and electric near field, shown in Figs. 2(b) and 2(c). The fundamental LC resonance is observed at 0.225 THz, based on the fact that the surface current distribution shows a circular current flow in the whole ring. Furthermore, the surface current distribution at 0.635 THz shows a region with counterclockwise current flow, and two regions with clockwise flow. This means that the resonance at 0.635 THz is due to the typical second-order LC resonance. In contrast, at 0.735 THz the current and electric near-field on the C-shaped SRR are sufficiently restrained, but those on the Y-shaped rod are strongly excited, showing the typical pattern of an electric dipole resonance.

To understand the effects of the interaction of the two adjacent resonators, the angle of incidence θ is adjusted from 0° to 60° in the TE and TM mode directions respectively. In the TE mode the incident wave is tilted along the y axis, so that the electric field component of the incident wave remains parallel to the metasurface. On the other hand, in the TM mode the wave is tilted along the x axis, so that the magnetic field component of the incident wave remains parallel to the metasurface. Under the simulated conditions, the polarization of the incident THz wave is parallel to the x axis. Then, we quantitatively analyze the degree of change in the resonance frequency before and after coupling.

III. RESULTS AND DISCUSSION

The THz transmission amplitude spectra for each meta-atom, simulated at different incidence angles of θ = 0°, 30°, and 60° in TE mode, are shown in Figs. 3(a) and 3(b), while Figs. 3(c) and 3(d) display the simulated spectra in TM mode. In the case of the C-shaped SRR in TE mode, despite the decreased amplitude of the transmitted signals, both the fundamental and second-order resonance positions (at 0.225 and 0.67 THz respectively) remain almost unchanged with increasing incidence angle, compared to the signals at normal incidence, as shown in Fig. 3(a). For the Y-shaped rod, in Fig. 3(b) it is observed that the resonance position at 0.73 THz is slightly blueshifted, although this change is not considered significant. Overall, in TE mode the transmission spectrum maintains its initial shape, with only minor changes.

Figure 3. Simulated THz transmission amplitude spectra of both meta-atoms, at several angles of incidence. (a) and (b), C- and Y-shaped meta-atoms in TE mode respectively. (c) and (d), C- and Y-shaped meta-atoms in TM mode respectively.

On the other hand, Figs. 3(c) and 3(d) reveal that the simulated spectra in TM mode exhibit more pronounced changes with varying angle of incidence than those in TE mode. The position of the fundamental LC resonance at 0.225 THz does not change, as in the case of the TE mode. As shown in Fig. 3(c), the only difference with respect to the TM mode is that two small resonant peaks appear near 0.66 and 0.9 THz. The former is due to weak electromagnetically induced transparency (EIT), while the latter corresponds to magnetic-resonance-like behavior. These properties originate from the oblique incident wave that induces asymmetrical currents and asymmetrical electromagnetic field distributions on the metasurface [24, 27]. In addition, under an oblique wave the magnetic component interacts with the metasurface.

The resonance exhibits a larger blueshift in TM than in TE mode, due to the decrease in the electric field component parallel to the surface when the incident wave is tilted, although the difference was not significant [28]. Despite the difference in the overall shape of the spectra plotted in the two figures, the degree of change of the resonance position does not seem large enough to be meaningful.

To analyze the coupling effects on the above characteristics, the transmission amplitude spectra of the metamolecule resonator are simulated for both TE and TM modes, as shown in Fig. 4. No particular effect is observed in TE mode, as seen in Fig. 4(a). The resonance position corresponding to the C shape is still independent of the angle of incidence, and the degree of blueshift corresponding to the Y shape is similar to that observed for the individual meta-atom resonator. Apart from the shift of the resonance frequency position of each metamolecular resonator due to the Fano effect (shown in Fig. 2), no other angle-dependent coupling effects are not observed in TE mode.

Figure 4. Simulated THz transmission amplitude spectra of the metamolecule as a function of frequency and incidence angle, for (a) TE and (b) TM modes. The angle of incidence ranges from 0 to 60° in 10° increments.

In TM mode, the position of the second-order LC resonant frequency shows almost no change and remains fixed at 0.635 THz. The EIT-like effect, which influence the secondary resonance position of the C-shaped meta-atom resonator, does not affect the LC resonance position after combining the two structures; however, it has a slight impact at 0.67 THz, which is the resonance position of the meta-atom before coupling. In addition, the magnetic resonance at 0.9 THz is slightly weakened.

The most noteworthy effect observed in TM mode is associated with the resonance of the Y-shaped rod appearing near 0.735 THz. The blueshift of the resonant frequency shows a completely different trend, compared to the results obtained before combining the meta-atoms, and also those observed in TE mode. The strong blueshift is due to the electric near-field coupling effect, and particularly to its asymmetric distribution on one side of the C-shaped SRR. The resonance depth, which is greatly reduced in the meta-atomic structures, remains similar to that observed in the normal-incidence case, due to the electric field coupling effect of the two meta-atoms.

To elucidate the properties of the resonances, we simulate the electric near-field distributions at the incidence angles of θ = 0, 30, and 60° for a TM-mode oblique wave. Figures 5(a)5(c) display the electric field distributions on the surfaces of the C-shaped SRR, Y-shaped meta-atom, and their combined metamolecule structure respectively. As the angle of incidence increases, the shape of the near-field distribution of the meta-atoms becomes asymmetric. However, in the case of the meta-molecule, the shape of the electric field of the Y-shaped rod remains almost symmetric, as a result of the coupling effect with the C-shaped SRR.

Figure 5. Simulated electric near-field distributions in TM mode at incidence angles of θ = 0° (left column), 30° (middle column), and 60° (right column), at (a) the second-order LC resonance of the C-shaped split-ring resonator (SRR) at 0.67, 0.665, and 0.65 THz (from left to right, in order), (b) the electric dipole resonance of the Y-shaped meta-atom at 0.73, 0.755, and 0.76 THz (from left to right, in order), and (c) the coupled electric dipole resonance of the metamolecule at 0.735, 0.8, and 0.815 THz (from left to right, in order).

To quantify the coupling effects, we obtain the rate of change of the resonant frequencies for various types of metastructures. Except for the electric dipole resonance of the metamolecule, M-Y(TE), all results were obtained in TM mode. The corresponding frequency shifts are plotted in Fig. 6. The values of the fundamental LC resonance of the C-shaped meta-atom and the metamolecule (C1 and M-C1) remain almost constant. Slight changes are observed for the second LC resonance of the C-shaped meta-atom and the metamolecule (C2 and M-C2). The rate of change of the secondary LC resonance frequency at 60° is 2.2% in the meta-atom structure, but decreases to less than 0.8% in the metamolecule structure. The electric dipole resonance of the meta-atom structure in TM mode and the metamolecule structure in TE mode showed the maximum frequency-change rates of 4.1% and 2.7% respectively. In contrast, the electric dipole resonance of the metamolecule in TM mode shows a high tunability of about 11%. The degree of these changes depends on the angle of incidence. Even though the resonances appear in the same metastructure and geometry, the LC resonances originating from the C-shaped SRR are omnidirectional, whereas the electric dipole resonance due to the Y-shaped rod is highly tunable.

Figure 6. Rate of change of each resonance frequency, as a function of the angle of incidence. C1 and C2 denote the fundamental and second-order resonances of the C-shaped meta-atom; Y represents the resonance of the Y-shaped meta-atom in TM mode; and M-C1, M-C2, and M-Y denote the C1, C2, and Y resonances of the metamolecule after combining the two resonators.

IV. CONCLUSION

In conclusion, we have shown that metamolecule resonators in the THz region exhibit resonance frequencies that are tunable according to the angle of incidence. Each resonance mode of the two meta-atoms constituting the metamolecule can be independently controlled by varying the angle of incidence. The frequencies of the LC resonances due to the C-shaped SRR show little change, whereas the electric dipole resonance related to the Y-shaped rod exhibits a high frequency tunability. The electric near-field coupling between the two different types of meta-atoms further amplifies this effect. We believe that these findings may support the design of new types of metamaterials, and the development of THz devices with high angular selectivity and functionality, such as tunable frequency-selective surfaces with angular stability and sensitivity, bendable THz devices, and devices enabling directionality control of resonant modes.

DISCLOSURES

The authors declare no conflicts of interest.

DATA AVAILABILITY

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

ACKNOWLEDGMENT

The authors thank the funding agencies for supporting our research work. In addition, the authors would like to thank the Editor in Chief, the Associate Editor, and the anonymous referees for their insightful suggestions.

FUNDING

National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant Number: NRF- 2022R1F1A1071757).

Fig 1.

Figure 1.Schematic diagrams of the THz metamolecule resonator. (a) Sample geometry and orientations of polarization and incidence angle. The THz electromagnetic wave is obliquely incident on the THz resonator, at variable angles. (b) Schematic illustration and related dimensions of a unit cell of the metamolecule composing the metamaterial.
Current Optics and Photonics 2022; 6: 590-597https://doi.org/10.3807/COPP.2022.6.6.590

Fig 2.

Figure 2.THz transmission amplitude spectra and surface current distributions. (a) Simulated THz transmission amplitude spectra of meta-atoms and metamolecule, for normally incident p-polarized waves. (b) Simulated surface current distributions for each meta-atom at 0.225, 0.67, and 0.73 THz (from left to right, in order), and the corresponding z components of the electric near-field distributions at these resonant frequencies. (c) Simulated surface current distributions and z components of the electric near-field distributions of the metamolecule at 0.225, 0.635, and 0.735 THz (from left to right, in order).
Current Optics and Photonics 2022; 6: 590-597https://doi.org/10.3807/COPP.2022.6.6.590

Fig 3.

Figure 3.Simulated THz transmission amplitude spectra of both meta-atoms, at several angles of incidence. (a) and (b), C- and Y-shaped meta-atoms in TE mode respectively. (c) and (d), C- and Y-shaped meta-atoms in TM mode respectively.
Current Optics and Photonics 2022; 6: 590-597https://doi.org/10.3807/COPP.2022.6.6.590

Fig 4.

Figure 4.Simulated THz transmission amplitude spectra of the metamolecule as a function of frequency and incidence angle, for (a) TE and (b) TM modes. The angle of incidence ranges from 0 to 60° in 10° increments.
Current Optics and Photonics 2022; 6: 590-597https://doi.org/10.3807/COPP.2022.6.6.590

Fig 5.

Figure 5.Simulated electric near-field distributions in TM mode at incidence angles of θ = 0° (left column), 30° (middle column), and 60° (right column), at (a) the second-order LC resonance of the C-shaped split-ring resonator (SRR) at 0.67, 0.665, and 0.65 THz (from left to right, in order), (b) the electric dipole resonance of the Y-shaped meta-atom at 0.73, 0.755, and 0.76 THz (from left to right, in order), and (c) the coupled electric dipole resonance of the metamolecule at 0.735, 0.8, and 0.815 THz (from left to right, in order).
Current Optics and Photonics 2022; 6: 590-597https://doi.org/10.3807/COPP.2022.6.6.590

Fig 6.

Figure 6.Rate of change of each resonance frequency, as a function of the angle of incidence. C1 and C2 denote the fundamental and second-order resonances of the C-shaped meta-atom; Y represents the resonance of the Y-shaped meta-atom in TM mode; and M-C1, M-C2, and M-Y denote the C1, C2, and Y resonances of the metamolecule after combining the two resonators.
Current Optics and Photonics 2022; 6: 590-597https://doi.org/10.3807/COPP.2022.6.6.590

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