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Abstract
We propose an all-dielectric single-layer guided-mode resonance filter (GMRF) operating in the high-frequency terahertz (THz) region. For the fabrication of thin gratings to achieve strong resonance in the high-frequency region, the refractive index and absorption must be small, while the tensile strength must be high. Cyclic olefin copolymer (COC) films have a lower refractive index and absorption than polyethylene terephthalate (PET) films and a higher tensile yield strength than polytetrafluoroethylene (PTFE) films. Therefore, the COC film was found suitable to fabricate a GMRF operating in the high-frequency THz region. We fabricated COC-based single-layer GMRFs with a thickness of 50 µm and grating periods of 500, 400, 300, 200, and 100 µm; the resonance frequencies of the TE0,1 mode were 0.576, 0.712, 0.939, 1.329, and 2.759 THz, respectively. A shorter grating period caused a greater shift of the resonance to a higher frequency. In particular, the COC film enabled the fabrication of a 100-µm grating period with a ridge width of 32 µm and length of 2 mm, enabling the GMRF to operate up to 2.759 THz, which is very high frequency compared to the previous highest frequency of 0.7 THz. These results were in good agreement with a simulation using rigorous coupled-wave analysis.
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1. Introduction
After the first THz photoconductive antenna was developed [1,2], several wideband THz sources operating in the high-frequency region have been developed. As high-frequency filters are required to utilize these high THz frequencies, the demand for various types of high-frequency filters is increasing. Many studies have been reported on THz band-pass, notch, and high-pass filters using various materials and devices such as metamaterials, metal meshes, metal slits, and waveguides [3–6]. However, because most of these are metal devices with high reflection and absorption losses, the transmittance and Q-factor decrease rapidly as the frequency increases [7]. Recently, the transmission efficiency and Q-factor were improved by applying the Cerenkov lasing effect [8]. Although these studies reported high transmittance values and Q-factors, it is difficult to produce the nanostructured patterns used in THz filters. However, guided-mode resonance filters (GMRFs) composed of an all-dielectric material have high potential as THz notch filters because of their simple design and strong resonance in a narrow frequency range.
All-dielectric GMRFs have many advantages over other devices for implementing a notch filter that operates in a high-frequency THz region [9]. First, since dielectric materials have low absorption and dispersion compared to metals, they are suitable for a filter with low loss and high transmission efficiency [10–12]. Second, the conditions of GMR must be satisfied simultaneously with diffraction and waveguide propagation conditions [13–15]. Therefore, resonance occurs in a very narrow frequency band. Comprehensive studies have been recently conducted on the realization of GMR conditions based on materials and design parameters [16,17]. Third, the patterns in GMRFs can be easily fabricated from single-layer dielectric films with simple designs. Furthermore, since all-dielectric GMRFs are metal-free, they have the advantage of being high-power filters.
A GMRF has already been applied as a high-power filter for microwaves [18]. Since THz waves have a shorter wavelength than microwaves, it is possible to produce THz GMRFs with micrometer-scale patterns. The most important factors in designing a GMRF are the optical properties of the dielectric material and the geometric structure of the patterns. These two factors are related to diffraction and waveguide propagation conditions, which are important physical phenomena for achieving GMR. In particular, GMRFs that can operate in the low frequency (long wavelength) region with short period patterns are more suitable for band-pass filters than notch filters due to the multiple high-order diffraction modes that occur. [19–21]. Moreover, a low refractive index and low absorption are required for creating a GMRF with strong resonance in the high THz region. However, although silicon and germanium have the lowest absorption coefficients in the THz region, their reflection losses are significantly large owing to their high refractive indexes [22]. Conversely, low-refractive-index materials used in THz devices such as polytetrafluoroethylene (PTFE), high-density polyethylene (HDPE), and polypropylene are suitable for THz notch filters owing to their low refractive indexes when compared with silicon and germanium. Meanwhile, materials having low absorption increase the transmittance by reducing the absorption loss at the GMR frequency. Therefore, a GMRF operating in the high-frequency THz region requires a low refractive index and low absorption. In addition, a thinner material leads to higher single-mode resonance in the filter. Moreover, a shorter pattern period yields a higher GMR frequency. Unfortunately, owing to the lack of high-tensile-strength materials for operation in the high-frequency region, it has not been possible to fabricate a GMRF with a thin and short pattern period that operates in the high-frequency region above 0.7 THz [10–12]. However, PTFE, polyethylene terephthalate (PET), and the cyclic olefin copolymer (COC) satisfy the conditions for good GMRF operation in the high-frequency region due to their high tensile strength combined with low refractive index and absorption [23–25]. Therefore, we compared the characteristics of GMRFs consisting of PTFE, PET, and COC thin films with a thickness of 50 µm to determine high-frequency resonance. As it is difficult to develop a grating pattern on a considerably thin film with a mechanical machining method, we fabricated GMRFs using a femto-second laser machining method (prepared by L2k Co.). In this study, we compared thin single-layer GMRFs, developed based on these materials with pattern periods ranging from 100–500 µm to determine the most suitable notch filter for operation in the high-frequency THz region. The total transmittance resonance measured according to the grating period and frequency was in good agreement with the results of a simulation based on rigorous coupled-wave analysis (RCWA).
2. Results
2.1 Simulation
RCWA simulation was performed to determine the resonance frequency according to the GMRF structure. RCWA is a common method for calculating the reflectance or transmittance of periodic structures with a short calculation time and high accuracy [26,27]. We obtained a transmittance image of the resonance frequency according to the GMRF grating period. The single-layer GMRF used in the simulation was composed of a 50-µm-thick COC film with a refractive index of 1.52 [23], and absorption was negligibly small. In the simulation, a vertically polarized THz beam is incident on the GMRF in the direction parallel to the grating ridges with a filling factor (FF) of 32%, as shown in Fig. 1(a). Figure 1(b) shows the transmittance for the transverse electric (TE) mode of the single-layer GMRF operating between 0.3 and 3 THz for grating periods (Λ) in the range of 100–500 µm. The scale bar indicates the intensity of power transmittance. The area between the dashed curves indicates the range in which GMR can exist based on the following equation [13,14,28]:
Fig. 1. (a) Geometry of a single-layer GMRF. The grating period (Λ), filling factor (FF), ridge width (FF × Λ), and ridge thickness (d) of the binary grating are indicated. A vertically (y-direction) polarized THz wave is normally incident from air onto the GMRF (+z-direction). The figure at the bottom shows a cross-section in the x-direction of the GMRF. (b) 2D image of total transmittance for the TE mode with respect to the grating period and frequency, as obtained through an RCWA simulation for the GMRF with FF = 32% and d = 50 µm. The area between the dashed curves indicates the range in which GMR can occur based on Eq. (1).
In general, an infinite-period structure is modeled by simplifying it to a unit cell of a one-period structure in which the period is repeated infinitely for efficient calculation. In addition, it is considered that an ideal plane wave is incident on the unit cell for simplicity. However, there are two major differences between the experimental measurements and simulations. First, only a finite number of ridges and grooves of the grating are spanned by the incident THz beam diameter, as shown in Fig. 2(a). The number of ridges and grooves spanned by the diameter of the THz wave is determined by the grating period, which is inversely proportional to the resonant frequency and proportional to the wavelength [7,27]. Figure 2(b) presents the minimum transmittance on resonance simulated using the finite-difference time-domain (FDTD) method according to the number of ridges contained in the THz beam with a diameter of 25 mm. The number increases as the grating period decreases. The dotted lines in the figure indicate the positions corresponding to the number of ridges when the grating period is 500, 400, 300, 200, and 100 µm. When the grating period exceeded 500 µm (40 ridges), the on-resonance transmittance increased rapidly, and approached zero with a decrease in the grating period. An effective GMRF should exhibit high frequency rejection on resonance; thus, the maximum grating period to achieve a strong GMR effect is approximately 500 µm.
Fig. 2. (a) Schematic of a THz beam near the beam waist. (b) Simulated minimum transmittance on resonance as a function of the number of periods within a THz beam with a diameter of 25 mm at the beam waist. The dotted lines indicate the positions corresponding to the number of ridges when the grating period is 500, 400, 300, 200, and 100 µm. (c) Simulated transmittance image according to the number of ridges away from the beam waist. The simulation conditions are as follows: ridge number at the beam waist = 40, Λ = 510 µm, FF = 32%, d = 50 µm, and refractive index = 1.52. The inset shows the simulated transmittance for a ridge number of 48.
Second, a THz beam generated by a photoconductive antenna creates a parallel wave through a silicon lens and a parabolic mirror. However, after reflecting from the parabolic mirror, the THz beam has a beam waist at the focal point of the parabolic mirror. Thereafter, the THz beam diameter gradually increases in its propagation direction. The THz beam dispersion is more severe in the low-frequency component of the THz wave than its high-frequency component [29]. If the silicon lens and parabolic mirror located behind the transmitter (Tx) chip are aligned according to the ideal dimensions and position, the THz beam of all components passes vertically at the beam waist, as indicated by the solid lines in Fig. 2(a). However, it is difficult to experimentally implement such an ideal setup. Therefore, the THz waves at the rim of the THz beam diameter exhibited a greater angle of incidence than the central THz wave. As the angle of incidence increases, the resonance is separated [9] and side lobes are generated. Figure 2(c) shows the simulated transmittance image according to the number of ridges away from the beam waist, where we assumed that all THz frequency components (THz wavelengths) were incident perpendicular to the GMRF. The transmittance corresponding to a ridge number of 48 is shown in the inset. A side-lobe resonance exists next to the main resonance. The side lobe appears stronger as the ridge number and the incident angle increase.
2.2 Measurement
In previous studies, various types of GMRFs operating in the low-frequency THz region were fabricated using quartz, PTE, and PTFE [23–25]. The resonance frequencies were less than 0.7 THz. However, for operation in the high-frequency THz region, a material with a thin thickness, low absorption, and low refractive index is required [30]. Quartz is a mechanically hard material that is suitable for GMRF structures with a thickness of several hundred micrometers and periodic patterns [9,10]. However, the use of quartz involves mechanical difficulties in the fabrication of single-layer GMRFs with a thickness of tens of micrometers. Grinding or etching is performed to achieve a low thickness, but it is difficult to realize a thickness less than 200 µm. Although quartz has high stiffness, it is easily broken owing to its low tensile strength [31]. Moreover, the absorption and refractive index of quartz are high in the THz region [32]. Therefore, we compared the characteristics of GMRFs consisting of PTFE, PET, and COC thin films and excluded quartz. Table 1 lists the tensile strength, absorption, and refractive index of PTFE, PET, and COC [23,24]. Since we are targeting GMRF operation in the high-frequency range of 2 THz and above, the absorption and refractive index at 2 THz are indicated.
Table 1. Mechanical and optical properties of PTFE, PET, and COC
Although PTFE has low absorption, it has insufficient tensile strength. Therefore, the PTFE thin film is twisted or curled because of the high temperature generated in the femto-second laser machining process. The laser used in the machining method had a wavelength of 1030 nm, beam width of 230 fs, repetition rate of 30 kHz, beam diameter of 10 µm, and power of 1W. If the tensile strength is high enough and a thick film is used, there is almost no parameter error of the GMRF produced by the automated femtosecond laser processing system. However, when a single-layer GMRF is fabricated using a 50 µm thin PTFE film, the grating pattern with long ridges is not uniform, as shown in the enlarged PTFE photograph of Fig. 3(a). Meanwhile, because PET and COC have higher tensile strengths than PTFE, a single-layer GMRF with a thickness of tens of micrometers can be manufactured without deformation by using the femto-second laser machining process. The enlarged photographs of PET and COC shown in Fig. 3(a) indicate that they are relatively well cut periodically without distortion or curling errors. Since the absorption of PET increases rapidly as the THz frequency increases [30], PET is not suitable for a GMRF operating in the high-frequency THz region. However, the absorption and refractive index of COC are much lower than those of other materials in the high-frequency THz range. Moreover, COC has high mechanical strength, making it suitable for fabricating a thin single-layer GMRF. We compared the resonance properties of GMRFs consisting of PTFE, PET, and COC thin films. To compare the transmittance of GMRFs consisting of these three materials, GMRFs with a grating period of 510 µm, filling factor of 32%, and thickness of 50 µm were fabricated into a rectangle with a width of 30 mm and height of 10 mm. A metal slit with a 9-mm gap height was placed behind the GMRF to transmit the THz beam to the rectangular GMRFs, as shown in Fig. 3(b).
Fig. 3. (a) Photograph of single-layer GMRFs consisting of PTFE, PET, and COC with Λ = 510 µm, FF = 32%, and d = 50 µm. The dashed lines represent the ideal straight edge of ridges in the grating. (b) Schematic diagram of the experiment setup with a single-layer GMRF and metal slit. (c) Measured transmittance of PTFE and COC. The inset shows expanded resonances. (d) Measured transmittance of COC and PET. The yellow area indicates difference of the two in transmittances. The insert shows expanded resonances.
We fabricated a conventional THz time-domain spectroscopy (TDS) system using a Ti:sapphire femtosecond laser (Mai Tai, Spectra Physics, USA) with a center wavelength of 790 nm, a duration of 60 fs at a repetition rate of 80 MHz in a beam, and an average power of 12 mW for the Tx and receiver (Rx) antennas. The Tx antenna, consisting of coplanar metal lines with a width of 10 µm and separation of 80 µm, was fabricated on a semi-insulating gallium arsenide (SI-GaAs) wafer. The laser excitation beam was focused onto the metal-semiconductor interface of the positively biased (80 V) transmission line. The Rx antenna, which consists of two stubs with a width of 20 µm and is separated by a 5-µm gap in a coplanar transmission line of two parallel 10-µm wide metal lines with a separation of 30 µm, was fabricated on a low-temperature-grown gallium arsenide (LI-GaAs) wafer. In the proposed photoconductive THz-TDS system, the GMRFs were located in between two parabolic mirrors for transmission measurement. We calculated the transmittance using the spectrum ratio of the output pulse with the GMRFs and a reference pulse without GMRFs.
Figures 3(c) and (d) compare the measured transmittances of GMRFs made with PTFE and COC and with PET and COC, respectively. Because the absorption and refractive indices of PTFE and COC are both relatively low, their transmittances are similar. However, the resonant strength (depth) of the PTFE-based GMRF is approximately 5.4% less than that of the COC-based GMRF because of the structural deformation of–the PTFE ridges. Meanwhile, the tensile strengths of both COC and PET are sufficiently high to produce GMRFs, and the grating can be manufactured uniformly without any ridge defects. Therefore, similar resonance strengths can be obtained as shown in Fig. 3(d). However, the transmittance of the PET-based GMRF is less than that of the COC-based GMRF, as indicated by the yellow area in Fig. 3(d). This difference is due to the absorption by the material because the absorption of PET is about 68 times larger than that of COC at 2.0 THz. Therefore, the PET-based GMRF is not suitable for operation in the high-frequency THz region, because the absorption by the material increases as the frequency increases to approach the high-frequency region. Therefore, we designed and fabricated five GMRFs with different grating periods using 50-µm-thick COC films to operate the GMRFs in the high and low THz regions, as shown in Table 2. The GMRF width is designed to be 30 mm, which is greater than the diameter of 25 mm of the THz beam propagating between the two parabolic mirrors of the THz-TDS system. A shorter grating period results in a length much higher than the ridge width; consequently, the fabricated grating is easily bent or deformed. Therefore, the GMRF was designed to have a ratio of height to grating period of 5:1. To measure the same reference THz pulse, a metal slit with a gap of 1.5 mm was placed, as shown in Fig. 3(b), considering that the height of the GMRF varies according to the period, as shown in Table 2. The transmittance was calculated by measuring the reference THz pulses that passed through the gap (air) of the metal slit and the output THz pulses that passed through the GMRF in front of the slit.
Table 2. Dimensions of the COC-based GMRF with FF = 32% and d = 50 µm as well as the size of the metal slit gap
Figure 4(a) shows the measured THz pulses for GMRFs with grating periods of 500, 400, 300, 200, and 100. To measure the oscillation due to the GMRFs, measurements were performed for up to 160 ps, which corresponded to a frequency of 6.25 GHz. A scan consisted of 1200 data points with 0.1332 ps time step. This was achieved with 20-µm steps between data points corresponding to a double-pass distance of 40 µm between data points. The black and red solid lines show the reference pulse that passed through only the slit gap (air) and the output pulse that passed through the GMRF from 0 to 20 ps, respectively. Since each GMRF used a different slit gap, the output pulses passing through the GMRF were compared after normalizing the measured reference pulses. The inset of Fig. 4(a) shows the oscillation from 0 to 80 ps by magnifying the measured normalized signal from -0.05 to 0.05. The oscillation of the low-frequency component generated in the GMRF with a long grating period has a small attenuation and lasts for a long time in the time domain. However, the oscillation of the high-frequency component generated in the GMRF with a short grating period has a large attenuation and disappears quickly in the time domain. In addition, the spectral display resolution was improved by performing zero padding up to 50 times the number of measured data points. Figure 4(b) shows the fast-Fourier-transformed spectrum of Fig. 4(a) with zero-padding to a total scan length of 8000 ps (corresponded to a frequency of 0.125 GHz), which demonstrates that the grating period and resonance frequency are inversely proportional.
Fig. 4. Measured transmittance according to grating period. (a) Time-domain THz pulses for different grating periods of 500, 400, 300, 200 and 100 µm. The black line represents the reference THz pulse, and the red line represents the output THz pulse after passing through the GMRF. The inset figures show an expanded window of the oscillations after the main THz pulse. (b) Corresponding amplitude spectra of the measured THz pulses. (c) Corresponding transmittance of the measured amplitude spectra.
Since the grating is positioned parallel to the polarization direction of the THz field, the TEm,n mode is generated. The first subscript (m = 0, 1, 2, …) indicates the waveguide mode in the GMR structure. When the GMRF used has a structure consisting of only a grating layer without a substrate, the waveguide mode is zero at a low thickness [33]. The second subscript (n = 1, 2, 3, …) indicates the diffraction mode generated by the GMR structure. For grating periods of 500, 400, and 300 µm, the higher-order mode, TE0,2, appears after the TE0,1 mode, but for grating periods of 200 and 100 µm, the higher-order mode does not appear, because it is out of the range of the measurement spectrum. These results agree well with the simulation results shown in Fig. 1(b). The side-lobe resonance appears next to the resonance as shown in the simulation results in Fig. 2(c). Figure 4(c) shows the measured transmittance. When the grating period is 500, 400, 300, 200, and 100 µm, the measured resonance frequency is 0.576, 0.712, 0.939, 1.329, and 2.759 THz, respectively. Although the GMRF with a grating period of 100 µm showed small resonance due to the small spectral amplitude in the high-frequency region, strong transmittance resonance was obtained at 2.756 THz.
Figure 5 compares the simulated and measured total transmittance resonance according to the grating period and frequency. A shorter grating period leads to a higher measured resonant frequency, and the grating period and resonance are inversely proportional. The dashed line represents the fitting lines for the measured data of the TE0,1 mode. The resonance frequencies obtained from the simulation and measurement are located within the resonance-frequency range indicated in the light-red area determined from Eq. (1). The TE0,1 and TE0,2 modes showed good agreement between the measurement and simulation. Since the measured bandwidth was approximately 3 THz, the resonance of the TE0,2 mode occurring above 2 THz could not be measured. However, because the TE0,1 mode is the dominant mode, the resonance of the TE0,2 mode is very small. By adjusting the grating period, the resonant frequency of the TE0,1 mode can be changed from 0.576 THz up to 2.756 THz.
Fig. 5. Comparison of simulated and measured resonance according to the grating period and resonance frequency. The black circles and red dots represent simulated and measured data, respectively. The dashed line is fitting lines for the measured data. The light-red area indicates the range in which GMR can exist, based on Eq. (1).
3. Discussion and conclusions
Notch filters in the THz range, that use metamaterials and waveguides operating in the high-frequency region, have been reported [3,6]. A powerful notch filter operating in the THz region was recently implemented using quartz, PTFE, and PET [10–12,30]. However, because these materials are thick with high absorption or low tensile strength characteristics, strong notch filters operating above 0.7 THz have not been developed. The major difficulty in fabricating a GMRF operating in the high-frequency THz region is the absorption loss of the material and its low tensile strength, which prevents the formation of a uniform grating period. Since the THz absorption by the material decreases as the thickness decreases, a single-layer GMRF without a substrate was applied in this study to reduce the thickness. Therefore, this structure has the advantage of not only small absorption but also ease of manufacture. We fabricated and measured GMRFs using PTFE, PET, and COC dielectric films, which can be made into thin films. PTFE has very low absorption in the THz region, but it is difficult to manufacture a uniform PTFE grating because its tensile strength is lower than that of COC. PET has better tensile strength than COC and PTFE, but it is not suitable because of its high THz absorption. However, COC is suitable for developing a GMRF operating at high THz frequencies, because its absorption is smaller than that of PTFE by a factor of 3.40. Moreover, although the tensile strength of COC is smaller than that of PET by a factor of 3.39, it is greater than that of PTFE by a factor of 2.08, which is sufficient for the fabrication of thin GMRFs. Therefore, we used 50-µm-thick COC films to fabricate five GMRF samples with grating periods ranging from 500 to 100 µm in 100-µm intervals. Resonance frequencies from 0.579 to 2.759 THz were successfully measured in the broadband THz spectrum. The measured resonance frequency agreed well with a simulation based on the RCWA method. GMRFs using COC films can be easily produced by laser processing with a grating period of at least 100 µm.
In conclusion, materials with low absorption, low refractive index, and high tensile strength are essential characteristics for the fabrication of GMRFs operating in the THz high frequency region. In addition, with a decrease in thickness of the single-layer GMRF, the absorption by the material decreases. Therefore, a thin film with no deformation was used to fabricate the GMRF with the smallest grating period. Moreover, we selected the smallest filling factor that can be fabricated with a uniform grating pattern, which minimized absorption losses caused by the structure. In this study, we fabricated and characterized GMRFs operating in the high-frequency THz region for the first time. Because the proposed GMR filter has a high resonance frequency, it has potential for future THz applications in broadband THz communication, spectroscopy, and image sensors.
Funding
Ministry of Science and ICT, South Korea (524420-22); Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government (MOTIE) (P0008763); National Research Foundation of Korea (2019R1A2B5B01070261).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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