Terahertz (THz) technology has shown great promise in a variety of applications such as spectroscopy, imaging, sensing and broadband wireless communications [1–3]. Over the past decades, various THz sources, detectors and systems have been intensively developed for the use of THz waves in academia and industry [4–6]. In addition, various studies have been conducted on THz devices such as THz filters, modulators, phase shifters, switches, mirrors, and so on. However, while devices and systems that operate in the microwave and light wave bands have been well developed, devices and systems that operate in the THz wave band are still insufficient. This is because the electromagnetic properties of most natural materials are not suitable for use in the THz frequency band. To overcome the limitation of the electromagnetic properties of natural materials in the THz band, many studies have been conducted on materials that can artificially control the electromagnetic properties. Artificially controllable materials, called metamaterials, can be designed to exhibit extraordinary electromagnetic properties not commonly found in natural materials [7–9]. The electromagnetic response of a metamaterial is determined by the structure and periodicity of a unit cell composed of a metal whose period is shorter than the wavelength of the incident wave. The electromagnetic properties of metamaterials, especially resonance, can be artificially engineered by controlling the period or structure of the unit cell. Metamaterials capable of artificially controlling electromagnetic resonance enable the development of new THz devices and systems for various applications [10–13].

The particular structural design of a metamaterial induces unique and desired interactions with the incident electromagnetic THz waves. Numerous studies on the design of THz metamaterials have been reported to demonstrate their potential applications such as negative refractive index, super-lensing, absorber, invisibility cloaking, and tunable devices. Among the THz metamaterials, H-shaped structures are widely used for negative refractive indices, multi-bands, tunable metamaterials, and ultra-sensitive metamaterials [14–17]. A thorough understanding of the mechanism of the interaction between THz waves and the metamaterial is essential to make the best use of THz H-shaped metamaterial in various applications. The control of the electromagnetic field distribution in the metamaterial by changing the structure of the metamaterial is of fundamental importance, not only in the design of metamaterial devices, but also in all applications that involve interactions between the electromagnetic field and metamaterials [18].

In this study, we investigate the resonance characteristics of the H-shaped metamaterial in the THz frequency range as its width is varied. The H-shaped metamaterial exhibits different electromagnetic responses depending on the polarization of the incident electric field. The H-shaped metamaterials were numerically analyzed in two modes in which the polarization of the incident THz electric field was either parallel or perpendicular to the width of the H-shaped metamaterial. The resonant frequencies of the metamaterial in both modes were changed by controlling only the width. To study the resonance characteristics, we numerically analyzed the electric field distribution and the surface current density induced in the metamaterial structure. The numerical analysis was verified by measurements using the THz-TDS (time-domain spectroscopy) system. The measured results are consistent with the simulations and clearly demonstrate the validity of the numerical analysis for H-shaped metamaterials.

The unit cell of the H-shaped metamaterial consists of two vertical metal strips connected by a horizontal metal strip, as shown in Fig. 1. Keeping the height of the structure fixed, its width was varied to determine the change in the electromagnetic properties according to variations in the structure ratio of the metamaterial. The H-shaped metamaterial has a height of 43 μm and its width ranges between 22–55 μm. The width of the metal strip and the spacing between the H-shaped structures are both 5 μm, so the height of the unit cell is 48 μm and the width changes effectively between 27 μm to 60 μm. The thickness of the Al₂O₃ substrate and gold electrode is set to 450 μm and 200 nm, respectively, the same as the fabricated device. The H-shaped metamaterials were numerically analyzed using an electromagnetic simulator HFSS (High Frequency Structure Simulator). For the exact simulations, the Advantest TAS 7400 THz-TDS system was used to measure and calculate the dielectric properties of the Al₂O₃ substrate. The permittivity and dielectric loss of the Al₂O₃ substrate were 9.3 and 0.025, respectively. The H-shaped metamaterial has different electromagnetic properties depending on the polarization of the incident electric field.

Figure 1. Schematic of the H-shaped metamaterial with different widths (a) 22 μm and (b) 55 μm.

As shown in Fig. 1, in mode 1 the polarization of the incident electric field is parallel to the width of the structure, whereas as in mode 2, the polarization is perpendicular to the width.

The transmittances of an H-shaped metamaterial for varying widths are shown in Figs. 2(a), 2(b) for mode 1 and mode 2, respectively. The resonance of a metamaterial is usually determined by the extent of the coincidence of the incident electromagnetic wave with the metamaterial structure. In mode 1, the electric field of the incident wave is polarized along the width of the H-shaped metamaterial. Therefore, as shown in Fig. 2(a), the resonant frequency of the metamaterial operating in mode 1 is directly affected by variations in the width of the metamaterial. The resonant frequency of the H-shaped metamaterial is observed to decrease as the width increases. An increase in the width of the H-shaped metamaterial affects the resonant frequency of the metamaterial operating in mode 2 as well, even though the structural changes are in the direction perpendicular to the polarization of the electric field. The resonant frequency of the metamaterial operating in mode 2 decreases with increasing width, as shown in Fig. 2(b).

Figure 2. Simulated transmittances of the H-shaped metamaterial with varying widths operating in (a) mode 1 and (b) mode 2.

Figure 3 shows the change in resonant frequency and variation in transmittance at the resonant frequencies for each mode as the width of the H-shaped metamaterial varies. As the width of the H-shaped metamaterial increases from 22 µm to 55 µm, the resonant frequencies of the H-shaped metamaterial operating in modes 1 and 2 decrease from 1.015 THz to 0.61 THz, and from 2.02 THz to 1.345 THz, respectively. The resonant frequency shifting ratios of the metamaterial operating in modes 1 and 2 are 39% and 33%, respectively, at the highest frequency reference. At the resonance frequency of each mode, mode 2 exhibits a lower transmittance than mode 1. As the width increases, the resonant frequency decreases in both modes, but the transmittance at the resonant frequency decreases in mode 1 and remains low in mode 2. This indicates that as the width increases, the strength of the resonance of the metamaterial increases in mode 1 and remains stable in mode 2. To analyze the resonance characteristics of the metamaterial, the electric field distribution and surface current density were simulated for each mode for varying widths of the structure.

Figure 3. Changes in THz transmission characteristics according to width of the metamaterial (a) the resonant frequency, and (b) the transmittance at the resonant frequency.

Figure 4 shows the changes in the electric field distribution of the metamaterial at resonant frequency with varying width. The same color bar, as shown in the inset of Fig. 4, was used for all electric field distributions to compare the change in the strength of the electric field strength change according to the change in width. The electric field in mode 1 is mostly formed on both sides of the H shape, while the electric field in mode 2 is mostly formed above and below the H shape. The strength of the electric field in the metamaterial is stronger in mode 1 than mode 2. As the width increases, the maximum strength of the electric field does not change significantly in mode 1, while it increases in mode 2. This means that as the width of the H-shaped metamaterial increases, the effective length of the vertical strip responding to the incident electric field increases, even though the actual length of the strip remains unchanged in mode 2. To confirm this, the surface current density of the H-shaped metamaterial was calculated and the results are shown in Fig. 5.

Figure 4. Changes in the electric field distribution of the H-shaped metamaterial at resonant frequency as its width is varied.

Figure 5. Changes in the surface current density of the H-shaped metamaterial as its width is varied.

The arrow color indicates the magnitude of the induced current, but the arrow color displayed on each device does not represent the same value. For all metamaterial devices in Fig. 5, the maximum and minimum current values were individually adjusted to express the overall current distribution through each device clearly. As the width of the H-shaped metamaterial increased, the magnitude of the surface current induced in the metamaterial decreased in mode 1 but increased in mode 2. In particular, in mode 2, the current distribution range induced in the vertical strip of the H-shaped metamaterial was widened. Therefore, as the width of the H-shaped metamaterial increases, the operating frequency of the metamaterial decreases, regardless of the polarization of the incident electromagnetic wave.

An H-shaped metamaterial was fabricated on a 450 μm thick single-crystal Al₂O₃ substrate. A gold electrode (200 nm) with a Ti adhesion layer (20 nm) was deposited on the Al₂O₃ substrate using the dc sputtering method. H-shaped metamaterials of various widths were patterned using photolithography and a lift-off process. The fabricated metamaterials were measured using the Advantest TAS 7400 THz-TDS system.

Dry air was purged in the THz spectroscopy chamber to maintain the humidity below 1%. Figure 6(a) shows the THz time-domain waveforms of the H-shaped metamaterial with mode and width changes. The blue and red lines indicate operation in modes 1 and 2, respectively, while the solid and dotted lines indicate widths of 55 μm and 22 μm, respectively. The peak time position of the THz pulse wave is more affected by the mode than the structure of the H-shaped metamaterial. THz pulse waves appear faster in mode 1 than in mode 2 and slightly faster in shorter-width structures. Figure 6(b) shows the THz frequency domain waveforms obtained using a fast Fourier transform. The green line indicates the result obtained by measuring only the Al₂O₃ substrate. Using the Al₂O₃ substrate as a reference value for measuring the electromagnetic properties of metamaterials, the bandwidth of the THz-TDS system is found to lie between 0.1 THz to 4 THz, while the dynamic range exceeds 50 dB. The maximum THz power of our system is concentrated in the 0.6 THz band. The resonant frequencies of the H-shaped metamaterial operating in modes 1 and 2 changed from 0.97 THz to 0.58 THz and from 1.89 THz to 1.28 THz, respectively, as the width changed from 22 μm to 55 μm. The measured resonant frequency shifting ratio of the metamaterial operating in modes 1 and 2 were 40% and 32%, respectively. The measured resonant frequencies were slightly lower than the simulation results, although the resonant frequency shifting ratios were very similar to each other. Additionally, the H-shaped metamaterial with a width of 55 μm operating in mode 1 showed the smallest power in the time domain data, as shown in Fig. 6(a) because the resonant frequency is in the maximum output frequency band of the system, as shown in Fig. 6(b). The transmittances of the metamaterial with mode and width changes are shown in Fig. 7.

Figure 6. THz measurement data of the H-shaped metamaterial according to operation mode and width change (a) time domain, (b) frequency domain.

Figure 7. Measured THz transmittances of the H-shaped metamaterial as its operating mode and width are changed.

As the width of the H-shaped metamaterial increases, the transmittance at the resonant frequency decreases from 0.83 to 0.13 in mode 1, and remains low (under 0.5) in mode 2. The measured results matched very well with the simulation results and demonstrated the meaningfulness of the numerical analysis using the electromagnetic simulator. These analytical studies, which provide an in-depth understanding of the working of the H-shaped metamaterial, can be used to design THz-tunable metamaterials and improve the sensitivity of THz sensing.

We investigated the THz resonance characteristics of an H-shaped metamaterial for varying widths. The electromagnetic response of the H-shaped metamaterial varies depending on the polarization of the incident THz electric field. The H-shaped metamaterials were numerically analyzed in two modes in which the polarization of the incident THz electric field was either parallel or perpendicular to the width of the H shape. The resonant frequency of the metamaterial was changed consistently in both modes, even if only the width of the H shape was varied. An increase in the width of the H-shaped metamaterial resulted in an increase in the resonant frequency of the metamaterial operating in the two modes without significant difference, regardless of the polarization of the incident electromagnetic wave. For the analysis of the resonance characteristics, the electric field distribution and the surface current density induced in the metamaterial in two modes were numerically analyzed by varying the structure ratio of the metamaterial. The numerical analysis revealed the cause of the change in resonance characteristics of the H-shaped metamaterial as the width changed. The efficacy of the numerical analysis was experimentally verified using the THz-TDS system. The measured results were consistent with the simulation results and clearly demonstrated the significance of the numerical analysis of the H-shaped metamaterial. These analytical studies, which provide a thorough understanding of the working of the H-shaped metamaterial, can be used to design THz-tunable metamaterials and improve the sensitivity of THz sensing.

This study was supported by the Fund of Sahmyook University in 2019.