1. Introduction

Electromagnetic (EM) waves have various types, ranging from gamma rays to radiowaves. EM waves are widely used in human lives, in applications such as wireless communication, cooking, medical care, and cosmetics. In particular, because the modern age is highly dependent on electric energy, EM waves exist in all spaces involving a flow of electricity.

EM waves are widely used to realize communication. Notably, because EM waves do not require a medium to travel, they can scatter freely in space. Moreover, because EM waves travel at the speed of light, information can be transmitted at the highest speed in the observable universe.

With the advancement in communication devices, the adopted frequencies of EM waves are continually increasing as more information can be transmitted at high frequencies. Mobile communication prior to 4G used the 800 MHz to 2.6 GHz bands, and 5G mobile communication, which is currently being commercialized, uses the 3.5 GHz and 28 GHz bands. In the future sixth-generation mobile communication, the use of the sub-THz or THz range is being considered as the main frequency to transmit and receive a considerable amount of data. However, with the increase in the frequency, the transmission range of EM waves may be limited. In particular, at frequencies of 300 GHz or higher, EM waves undergo significant atmospheric absorption and path attenuation; consequently, it is necessary to develop a high-gain and high-directional antenna and a beamforming device. In addition, to enhance the frequency selectivity, it is necessary to identify the waveform to which an optimal design can be applied.

Metamaterials and metasurfaces have emerged as promising tools to manipulate EM waves in the gigahertz, terahertz (THz), and visible regions, as unlike natural materials such as plasmonics and photonics, no light confining or guiding mechanism must be used. THz metamaterials have been used to realize many valuable applications such as switching [1,2], filtering [3], sensing [4–6], and focusing devices [7]. Guided mode resonance (GMR) represents a physical mechanism that is most commonly used to develop THz filter applications. However, GMR-based filters typically exhibit an extremely narrow transmission peak owing to the intrinsically Fano-type high-Q mode [8–12], which may limit the development of THz communication systems. It has been reported that, in contrast to dielectric structures, GMR components based on metal grating achieve narrowband transmission. [13–16]. In addition, a coupling two metallic gratings in a FP-GMR coupled configuration has been studied in the near-IR frequency [17,18]. Ferraro et al. reported a study implementing FP-GMR composed of two metasurface substrates in the THz region, and confirmed the study result of separating the GMR mode by adjusting the distance between the two metasurface substrates. [19]. Recently, a meta-surface-based filter for high data rate has also been reported, and the proposed frequency selective-surfaces structure has a low bit error rates as 10⁻¹⁰ in low THz range, its advantage is a quasi-linear phase profile for next generation wireless communication [20]. In next-generation wireless communication, broadband transmission in a high frequency band must be ensured because a wide band frequency must be used to transmit and receive considerable data.

Considering these aspects, in this study, we developed a broadband transmission filter by placing two metasurfaces on the upper and lower surfaces of the dielectric slab. In addition, the transmission and reflection characteristics in the THz band were compared through a theoretical analysis and experimental verification of the metamaterials. In particular, the proposed metamaterial transmission material can help ensure a high transmission efficiency in the THz band and enhance the directivity of the antenna. A metapattern is identically prepared on the front- and back-surfaces of the dielectric substrate through a simple manufacturing method known as e-beam lithography. Notably, the proposed metamaterial is designed such that incident EM waves pass through the surface and interface through metasurface control. In addition, a THz band EM wave passing through the metasurface can exhibit nearly perfect and broadband transmission. The proposed metasurface can likely be applied to EM wave filters, long-range radar, space antenna, next-generation wireless communication and future telecom applications.

2. Experimental setup

2.1 Fabrication of sample

Samples were fabricated using e-beam lithography to prepare metallic gold patterns (thickness of 0.1 µm) on both sides of a quartz substrate with an area of 5 × 5 cm². The thickness, dielectric constant, and dielectric loss tangent of the quartz substrate were 50 µm, ɛ = 3.75, and 0.001, respectively. The lossy-metal model was used for gold with an electric conductivity of σ = 5.8 × 10⁷ S/m. First, a gold thin film was deposited on the quartz substrate through an e-beam evaporator. Considering the required structural shape based on simulation results, a suitable mask was prepared before the sample fabrication. The photomask was made of soda lime coated with chrome, and its tolerance and positioning accuracy were ±1 µm and ±2 µm, respectively. Finally, the metallic gold pattern was manufactured via e-beam lithography.

2.2 Measurement for terahertz spectra

The THz transmission spectra were measured at the fs-THz beamline of the Pohang accelerator laboratory through THz emission measurement [21]. A Ti : sapphire regenerative amplifier (800 nm, 120 fs, l kHz, 3.2 W) was used to produce a laser pulse. The THz radiation was collected and focused onto a 10 × 10 mm2 〈110〉 ZnTe nonlinear crystal by using parabolic mirrors. The pump pulse fluence was varied from 0.05–1.27 mJ/cm² by maintaining the pump beam size at 5 mm. We recorded the magnitude of the transmitted THz beam at different frequencies and transformed the value to the transmission through calculation based on the magnitude in free space. The measurement range is 0.6–2.2 THz. The transmission measurement results were obtained at a total of 50 points, and the resolution of measurement was 0.03235 THz per point interval.

 

Fig. 1. (a) Schematic and geometrical parameters of the adopted metasurface. The inset shows the image of the fabricated sample. ($a = 60\; \mu m,\; d = 100\; \mu m,\; h = 50\; \mu m,\; \delta = 0.1\; \mu m$) (b) Schematic of the band-structure and (c) corresponding three-level diagram, explaining the excitation, and coupling mechanism of Fabry–Perot (FP) (bright) and guided (dark) modes in the system (black line with circles). (d) Contour region: Determined band-structure for the GMR in the metasurface. The solid-circle line indicates the unperturbed guided mode (GM) in the bare quartz slab. The black and red translucent dashed lines are band structures of GMR and FP, respectively. The dotted square box region indicates the broadband transmission that occurs around the band folded GMR at ${k_x} = 0$.

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2.3 Simulation for terahertz spectra

The designed metamaterial is characterized by 3D finite-difference frequency-domain (FDFD) method using a commercial software package CST microwave solver (2022) for the angle-resolved transmission spectra of the metasurfaces. In simulations, the unit cell boundary conditions are set in the x- and z-directions and the perfect matching layers are employed in the y-direction. Moderate hexahedral mesh size is adopted to ensure the accuracy of simulation. The terahertz wave with the polarization along the x-axis is normally incident onto the metasurfaces (i.e., the plane wave is normally incident along the y-direction and the electric field is along the x-direction, corresponding to the magnetic field along the z-direction) as shown in Fig. 1(a).

3. Results and discussion

3.1 Induction of GMR in a terahertz metamaterial

We designed the metasurface transmission structure for targeting the 2 THz band. For the THz frequencies, electromagnetic wave attenuation in low loss atmospheres is mainly caused by water vapor. Accordingly, it can be advantageous for communication only by using the THz transmission window band with less absorption by the atmosphere. In particular, it has been reported that the amplitude transmission window increases by about 70% from 1.9 THz to 2 THz band [22]. The unit cell is composed of two gold disks attached on the upper and lower surfaces of the quartz slab, as shown in Fig. 1(a). The incidence of the p-polarized wave (${H_x} = {H_y} = {E_z} = 0$) and fundamental TM₀ guided mode (GM) are considered. Two modes are likely induced in the slab, namely, the Fabry–Perot (FP) mode and GMs. The right side of Fig. 1(a) is an optical image of the fabricated sample. The FP mode (red line in Fig. 1(b)) is above the light line ($\omega = c{k_x}$) in the dispersion diagram pertaining to $\omega (k )$, where ${k_x}$, $\omega $, and c denote the wavevector along the surface of the slab and frequency and speed of light in free space, respectively. The first harmonic of the resonant transmission frequency of the FP mode is ${\omega _{FP}} = \pi c/\sqrt \varepsilon h$ (${\lambda _{FP}} = 2\sqrt \varepsilon h$) under normal incidence ($\theta = {0^ \circ }$), where $\varepsilon \approx 3.75$ is the electric permittivity of the quartz slab. The spectral width of FP mode is broad (${\omega _{FP}}/\Delta {\omega _{FP}} \approx 2.27$), and thus, this mode functions as the bright mode (radiative continuum). The GM is intrinsically non-radiative (the red line below the light line in Fig. 1(b)) and thus functions as the dark mode (discrete). Dispersion of the GM can be determined by numerically calculating the transcendental equation $\tan ({\beta h/2} )- \textrm{cot}({\beta h/2} )= \varepsilon \sqrt {{\omega ^2}({\varepsilon - 1} )/{c^2}{\beta ^2} - 1} $, where ${\alpha ^2} = k_x^2 - k_0^2$, ${\beta ^2} = {k^2} - k_x^2$, ${k_0} = \omega /c$ and $k = \sqrt \varepsilon {k_o}$ [15]. This result has a good agreement with the dispersion diagram through simulation as shown in Fig. 1(d). If an array of disks, the period of which is in the subwavelength scale, is introduced, GMR is induced owing to the coupling between the bright and dark modes caused to the band-folding effect (blue dotted line in Fig. 1(b)). Therefore, the resonant frequency is determined at the band-folding position (${k_x} = 2\pi /a$) of the GM, after correcting the perturbation of band-gap formation [23–25], similar to that of surface plasmons on gratings [25]. The concept of this coupled oscillator is similar to that of classical Fano systems [26,27], and Fano-like asymmetric spectra appear at the coupling point (circle in Fig. 1(b)), as discussed in the subsequent section. This concept can also be described as a three-level diagram, as shown in Fig. 1(c). Figure 1(d) shows the band structures of GMR in this structure (contour plot above the light line) and unperturbed GM, obtained using frequency-domain and eigen-mode solvers, respectively.

Electron beam lithography is used to pattern the Au disk array on the upper and lower sides of the 50-um-thick quartz slab. Each disk has a diameter of $a = 60\mu m$ and thickness of approximately $\delta \approx 100nm$. The unit cell dimension is $d = 100\mu m$ in both the x- and z-directions. The transmission spectra are measured via THz time-domain spectroscopy. Figures 2(a) and 2(b) present the spectra of the samples without and with the metasurface pattern. The experimental transmission spectra are in agreement with the simulation results. The FP interference pattern on the slab can be clearly observed in Fig. 2(a). The first harmonic FP occurs at approximately 1.5 THz (${\lambda _{FP}} = 2\sqrt \varepsilon h$). Although the FP spectrum corresponds to broad transmission, the transmission peak is not abruptly degraded. Therefore, FP cannot be employed as a filter. After the metasurface is placed on both sides of the slab, the FP peak exhibits a red-shift below 1 THz as the effective propagation length of the light is increased by the disks. Subsequently, a broad GMR transmission peak appears at approximately 2 THz. The transmission values indicated by the three downward arrows in Fig. 2(b) are 0.984, 0.892, and 0.941. Therefore, this framework can be used as a broadband transmission filter, although a valley point appears to exist. The spectral width is considerably larger than that of the conventional GMR, which is based on the spectrally narrow and high-Q Fano resonant property [10,12,28]. The peak around 1.65 THz shown in Fig. 2(b) is a hollow rectangular waveguide mode that was inevitably formed due to the boundary condition of the simulation, and it is expected that the mode does not appear in the actual experiment.

 

Fig. 2. (a) and (b) shows the calculated (black solid line) and measured (hollow circles) transmission spectra of Febry-Perot and broadband transmission using multi-GMR modes respectively.

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3.2 Spectral broadening of the transmission peak by switching from ring to disk

To clarify the influence of the double-disk on the broadband transmission peak, we investigated the changes of transmission spectra according to the pattern change in the substrate. Figures 3(a) and 3(b) show the case of changing from a ring pattern to a disk pattern only on the upper-side and both on the upper- and lower-sides, respectively. The bottom transmission of Fig. 3(b) is the same as Fig. 2(b) when it is formed in a disk pattern on the upper- and lower-sides. Gradual transition from a ring to a disk is achieved by varying the inner radius of the ring from $a > r > 0$ (ring) to $r = 0$ (disk), where a and r denote the outer radius and inner radius of ring, respectively, as shown in Fig. 3. The FP background spectrum is shown with $r = a$. As r gradually decreases, sharp and asymmetric Fano line-shapes arise and broaden. The spectral broadening of the Fano peak can be attributed to the increase in the radiative damping of the dark (guided) mode caused by the dipole scattering of the dark modes from the rings or disks [23,29–31]. In this broadening process, two nearly perfect transmission peaks arise at approximately 1.8 THz and 1.94 THz ($a/2 \ge r = 0$ in Fig. 3(a)). The two peaks originate from two different types of GMR with different resonant frequencies. In the case of the unperturbed guided mode (GM) existing in the bare quartz slab, the mode frequency ($\omega $) of the two GM modes running in the + x and -x directions are the same. Since the subwavelength metasurface pattern exists in the slab, at the same time, the perturbation occurs in both GM modes. Due to the perturbation in the two modes, the degeneracy is broken and the resonance frequency of each is changed to $\omega \pm \Delta\omega $. Subsequently, an additional ring or disk is attached to the lower slab, as shown in Fig. 3(b). For the ring with $a/2 < r < a$, the broadening of the Fano peak is similar to that in the case of a single ring. When $r < a/2$, the two transmission peaks merge and the dip between the two peaks disappears, thereby forming a broad transmission peak. This phenomenon can be explained by the constructive interference between the GMR peaks. Because the incoming p-polarized wave has an electric field in the x-direction, electric dipoles are excited on the surface of the disks. As shown in Fig. 3(c), the transmission window accompanies with a sharply phase dispersion. Two sudden phase shifts are caused by EGMR and OGMR, which form a wideband transmission filter. This phenomenon shows a characteristic similar to having a quasi-linear phase profile [20].

 

Fig. 3. Transmission spectra with different values of the inner radius of the ring ($r = 0$ for the disk). Each curve is shifted by +1 with respect to the previous one. (a) The spectra with the rings or disks on the upper side of the quartz slab. (b) The spectra with the rings or disks on both upper and lower sides of the slab. (c) Normal incident transmission spectrum and phase shift as a function of frequency.

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3.3 Analysis of the role of GMR in realizing broadband transmission

Figures 4(a) and 4(b) show the current flow on the disks at the spectral positions indicated by the two downward arrows in Fig. 3(b). As shown in Fig. 4(c), the opposite direction of the current on the two disks leads to the generation of an H-field in a constructive manner at the center of the slab. After a temporal phase shift of $\pi /2$ (i.e., $exp ({i\omega t} )$ with $\omega t = \pi /2$), positive and negative charges accumulate at the edge of the disks. These charges induce a nearly uniform electric field over the slab in the y-direction. The corresponding equivalent circuit diagram is shown in Fig. 4(c). The other mode is analyzed in a similar manner, as shown in Figs. 4(b) and (d). Both modes exhibit a series RLC network, explaining the perfect transmission through the metamaterial at the resonant frequencies. Based on the analysis, the two modes are categorized as even (EGMR) and odd (OGMR) GMR, respectively.

 

Fig. 4. (a) and (b) show the surface current on the metallic disks at the spectral positions indicated by the two downward arrows in the Fig. 3(b). (c) and (d) shows field distributions (${{\boldsymbol H}_{\boldsymbol z}}$ at 0 phase and ${{\boldsymbol E}_{\boldsymbol y}}$ at ${\boldsymbol \pi }/2$ phase) and the corresponding equivalent circuit diagrams of the (c) even-mode GMR and (d) odd-mode GMR at the two spectral positions.

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The band-structure and field distributions are further analyzed at a slightly oblique angle of incidence ($\theta = {2^ \circ }$) to understand the mode behavior for broadband transmission. Four possible modes exist for oblique incidence. In the first mode, GMR occurs at approximately 1.8 THz, and this mode is completely degraded as ${k_x} \to 0$. Therefore, the GMR does not contribute to broadband transmission. The EGMR mode is split into two modes under an oblique incidence:

EGMR + ($\partial \omega /\partial {k_x} > 0$) and EGMR- ($\partial \omega /\partial {k_x} < 0$), as shown in Fig. 5(a). In particular, in the case of EGMR mode, both EGMR + and EGMR- appear to contribute to transparency independently. As soon as two EGMR modes split at oblique incidence, it is expected that the two modes will no longer be the same mode. Based on these results, it is expected that each of the two modes will independently contribute to the transmission. In the OGMR mode, the group velocity is nearly zero even under oblique incidence, and the mode exhibits a flat band-structure. Figure 5(b) shows the temporal phase shift of the four guided modes (from $\omega t = 0$ to $\omega t = \pi $). The three GMRs with slightly different resonant frequencies (approximately 1.9, 1.95, and 2 THz) contribute to the broadband transmission, as explained by the series RLC network. All the transmission peaks of the GMRs are sharp, and therefore, the transmission generated by the three GMRs is not only broad but also abruptly degraded at the spectral edge. This interplay among the GMRs can enable the development of a broadband transmission filter.

 

Fig. 5. (a) Closed view of the band-structure around the broadband transmission region (the dotted square box region in Fig. 1(d)). The blue dotted lines are the possible four GMRs formed by the band-folding effect of GM. The black solid line is the light line of the incoming p-polarized wave with ${\boldsymbol \theta } = \mathbf{2}^\circ $. The blue dots are the phase matching positions for the excitation of the GMRs. (b) Electric field distributions (E_y) of the four GMRs with different time phases (from ${\boldsymbol \omega t} = \mathbf{0}$ to ${\boldsymbol \omega t} = {\boldsymbol \pi }$), indicating the propagation directions (arrow shapes) of the GMRs along the quartz slab.

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To understand the phenomenon of transmission for each mode, we analyze the electric field distributions of the three frequencies under different time phases (x-axis). As shown in Fig. 6(a), the peak of 0.95 THz pertains to the transmission peak generated by the FP mode, and the wavelength of the incident EM wave matches the thickness of the dielectric substrate. This finding shows that the incident EM wave naturally penetrates the metasurface without generating resonance. The transmission peak of 1.914 THz, pertaining to the EGMR, indicates that resonance occurs when an incident EM wave meets the metasurface. This finding confirms that the generated resonance passes through the metamaterial and flows out while moving to the right. The transmission peak at 1.94 THz, corresponding to EGMR+, has characteristics different from those of EGMR- and confirms that resonance is generated when the incident EM wave meets the metasurface while passing through the metamaterial and flows out while moving to the left. The 2.03 THz transmission peak pertaining to OGMR, similar to the cases of EGMR- and EGMR+, induces resonance as the incident EM wave meets the metasurface. However, the generated resonance passes through the metasurface and metastructure without being biased in either direction, as shown in Fig. 6(d). This GM occurs because the metasurface and incident EM wave are coupled and function like a slab waveguide. At all the GM transmission peaks, the incident EM waves pass through the metasurface, which means that not only the FP mode but also all GMs move along the metasurface, and the maximum transmission occurs, corresponding to the passage through the metamaterial. The detailed analysis of the EM wave passing through the metasurface by guided mode in the transmission peak band will be covered in Visualization 1, Visualization 2, Visualization 3 and Visualization 4. In particular, the transmission peaks induced by EGMR + and OGMR lead to high transmission without affecting each other, which indicates that a very wide transmission band is realized.

 

Fig. 6. Electric field (E_x) distributions for three frequencies under different time phases (from $\omega t = 0$ to $\omega t = \pi $) at an incident angle of $\theta = 2^\circ $ show that the incident electromagnetic wave passes through the metasurfaces for the (a) FP (0.95 THz), (b) EGMR - (1.914 THz), (c) EGMR + (1.94 THz), and (d) OGMR (2.03 THz) modes.

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4. Conclusions

We demonstrated the development of abroad transmission filter by using gold disk array metasurfaces on a 50µm thick quartz slab. GMR transmission peaks are formed by the band-folding of the GM supported by the quartz slab. The interplay among the GMR peaks, the resonant frequencies of which are slightly different, is responsible for the broadband transmission. The mechanism of this broad transmission examined through several techniques, involving a comparison between the use of rings and disks and consideration of the surface current, series-RLC network, and band-structure of the GMR. Furthermore, the transmission peaks pertaining to EGMR and OGMR do not affect each other and have a high transmission of more than 90%, with an ultra-wide transmission band generated in the overall spectrum. This ultra-wide transmission band is a meaningful result that cannot be realized using the existing metamaterials. The proposed metasurface can pass incident EM waves at specific frequencies and can thus be applied in EM wave filters, long-distance radars, space radars, and next-generation mobile communication fields.