An Electrically Tunable Terahertz Filter Based on Liquid-Crystal-Filled Slits with Wall Corrugations
An Electrically Tunable Terahertz Filter Based on Liquid-Crystal-Filled Slits with Wall Corrugations
Zhang, Shi-Yang;Ma, Jing;He, Hai-Ling;Tong, Cheng-Guo;Liu, Huan;Fan, Ya-Xian;Tao, Zhi-Yong
2022-11-23 00:00:00
hv photonics Communication An Electrically Tunable Terahertz Filter Based on Liquid-Crystal-Filled Slits with Wall Corrugations 1 , 2 3 1 2 1 1 , 2 Shi-Yang Zhang , Jing Ma , Hai-Ling He , Cheng-Guo Tong , Huan Liu , Ya-Xian Fan 1 , 2 , and Zhi-Yong Tao * Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing, Guilin University of Electronic Technology, Guilin 541004, China Academy of Marine Information Technology, Guilin University of Electronic Technology, Beihai 536000, China Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi’an 710127, China * Correspondence: zytao@guet.edu.cn Abstract: We propose a type of hollow planar waveguide with corrugated walls, which can realize electrically tunable terahertz (THz) filtering by filling the slit with liquid crystals. When the THz signals propagate in a planar waveguide with periodic corrugations, the transmission spectrum always exhibits many pass and stop bands. Inserting a section of defects in the middle of the periodic corrugations can excite an extremely narrow transmission peak, which would be a very good THz filter for frequency division. To achieve tunability of this narrow linewidth THz filter, we also fill the slit between the two corrugated walls with a nematic liquid crystal. The effective refractive index of liquid crystals will change with the external electric field, thus tuning the frequency of the narrow peak. The simulated results show that the center frequency of the proposed filter can be tuned linearly in the frequency range of 0.984~1.023 THz by the external electric field. Moreover, the bandwidth of the filter can be adjusted from 3.2 GHz to 0.3 GHz by increasing the number of periods in the waveguide, and a maximum Q value of 2556 can be achieved when the number of periods at both sides of the defect is 12. Citation: Zhang, S.-Y.; Ma, J.; He, H.-L.; Tong, C.-G.; Liu, H.; Fan, Y.-X.; Keywords: periodic waveguides; narrow linewidth filter; electrical tuning Tao, Z.-Y. An Electrically Tunable Terahertz Filter Based on Liquid- Crystal-Filled Slits with Wall Corrugations. Photonics 2022, 9, 894. 1. Introduction https://doi.org/10.3390/ photonics9120894 In recent years, terahertz (THz) technology has been applied in many fields, such as military [1], medical [2], communication [3], sensing [4], imaging [5], and security Received: 1 November 2022 inspection [6]. The research on THz technology revolves around three main components, Accepted: 21 November 2022 namely THz sources [7,8], detection [9], and its applications [10–12]. The THz application Published: 23 November 2022 is closely related to the promotion of functional devices. The realization of high-power Publisher’s Note: MDPI stays neutral sources [13], absorbers [14,15], sensors [16], switches [17], and filters [18] has expanded the with regard to jurisdictional claims in applications and aroused the interest of researchers. Constantly optimizing THz devices published maps and institutional affil- greatly benefits the development and promotion of THz technology, and many scholars are iations. also committed to this research. As a key device in the THz system, a THz filter can select a particular frequency band of signals to pass through or separate the frequency we need from a wideband, which greatly improves the working efficiency of the THz system [19–21]. Wilk et al. showed the Copyright: © 2022 by the authors. first electron-switchable Bragg structure for THz frequencies [22]. The structure worked as Licensee MDPI, Basel, Switzerland. a stop-band filter and a mirror. It has a 60 GHz-wide stop-band with a center frequency of This article is an open access article 300 GHz, which can be removed by reorienting the liquid crystal molecules in an external distributed under the terms and electric field. Mendis et al. demonstrated a universal filter using a parallel plate waveguide, conditions of the Creative Commons which provides low-pass, high-pass, band-pass, and band-stop filtering functions in the Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ THz frequency range [23]. Vieweg et al. proposed a switchable THz notch filter [24]. The 4.0/). filter, comprising a liquid crystal layer, exhibited a half-wave retarder and an isotropic Photonics 2022, 9, 894. https://doi.org/10.3390/photonics9120894 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 894 2 of 9 layer in different states. Yan et al. demonstrated an optically controllable narrowband THz filter and a dual-wavelength filter using square lattice photonic crystals with defects [25]. Capmany et al. incorporated graphene into integrated coupled resonator waveguides to achieve reconfigurable operations [26]. Brunetti et al. proposed an ultra-high performance rejection filter based on a silicon double-loaded Mach Zehnder interferometer (MZI), which takes advantage of the high selectivity of the ring resonator and the large rejection ratio of MZI [27]. This paper proposes an electrically tunable THz filter based on liquid crystal (LC) filled slits with periodic wall corrugations. The wall corrugation with defects provides a narrow transmission peak filter while the tunability of the LC index is employed to tune the device. Section 2 presents the mechanism of defect mode generation in planar THz waveguides filled with liquid crystals. In Section 3, we discuss the effects of external electromagnetic fields on the filling LCs. Based on the experimental data, we simulate the effective refractive index of LCs with the varying electric field by a cubic polynomial model, which enables us to mimic the electrical tuning of the proposed THz filter. In Section 4, we will describe the various filter properties. Finally, a general conclusion is given. 2. Filter Structure When a THz wave propagates through a waveguide with periodically corrugated walls, the Bragg resonance can be generated because the same modes in the waveguide interact with each other. The Bragg resonance can always result in the so-called Bragg gap in the spectrum, in which the THz radiation cannot pass through the waveguide. In our study, we truncate the periodic structure at its midpoint and insert a section of the straight waveguide, so the periodicity of the original waveguide is broken, but not its symmetry. This treatment allows THz waves to pass through the corrugated waveguide at specific frequencies in the previous Bragg gap, producing a narrow transmission peak. The transmission peak thus obtained is usually considered to be a defect mode. The electrically tunable THz filter based on liquid-crystal-filled slits with corrugations proposed in this paper is shown in Figure 1. It is a planar waveguide with a periodically undulating structure etched on the inner wall of high-density polyethylene (HDPE). Then a thin film of gold with a thickness of 1 m is coated on the upper and lower surfaces of the waveguide. The hollow part of the waveguide is filled with a nematic LC (E7) and then sealed with 10 m-thick HDPE, which connects the four boundaries of the upper and the lower plates. In Figure 1, HDPE is only drawn at the inlet and outlet ports of the waveguide to facilitate the display of the structure. Gold is chosen to be coated on the inner wall of the waveguide because gold has low loss in the THz band and can serve as a perfect electrical conductor [28]. However, HDPE has high transmittance and low loss in the THz band, which can significantly reduce the loss before the THz wave enters the waveguide [29]. The waveguide inner-wall period undulation structure has a rectangular shape, the period l = 220 m, the undulation depth a = 71.6 m, the average distance d = 214 m, the inserted defect length is w = 264 m, and the number of periods is 20. The length of the straight waveguide at the inlet and outlet of the waveguide l = 275 m. The THz source produces a horn-shaped beam, with the signal incident from the left end of the waveguide and out from the right end. The THz radiation is guided in the layer of LCs between the two gold-coated plates, and the inset in Figure 1 depicts the cross-sectional view of the guided mode. The three-dimensional Euclidean space coordinate system is also shown in the left corner of Figure 1, in which the x-axis is along the horizontal symmetry axis of the waveguide. Due to the inner wall’s gold-coated upper and lower surfaces, the THz waves will have Bragg resonance in the waveguide due to the periodic corrugations, thus creating a Bragg gap. The straight waveguide we introduce in the periodic structure can excite a defect mode with a very narrow linewidth. Photonics 2022, 9, 894 3 of 9 Photonics 2022, 9, x FOR PEER REVIEW 3 of 9 Figure 1. Structure of the proposed electrically tunable THz filter. A layer of gold is coated on the Figure 1. Structure of the proposed electrically tunable THz filter. A layer of gold is coated on the corrugated HDPE substrates to form the wall of waveguides. The big blue dots denote the filled corrugated HDPE substrates to form the wall of waveguides. The big blue dots denote the filled LCs, LCs, and the THz radiation passes through the slit from left to right along x-axis. The inset depicts and the THz radiation passes through the slit from left to right along x-axis. The inset depicts the the cross-sectional view of the guided mode. cross-sectional view of the guided mode. To actively modulate the operating frequency of this defect mode, we have intro- To actively modulate the operating frequency of this defect mode, we have introduced duced nematic LCs in the waveguide cavity [30]. Liquid crystals are widely used nonlin- nematic LCs in the waveguide cavity [30]. Liquid crystals are widely used nonlinear dielec- ear dielectric materials because of their special physical, chemical, and optical properties tric materials because of their special physical, chemical, and optical properties [31–33]. In [31–33]. In the present study, the nematic LCs (E7) are selected as the material to fill the the present study, the nematic LCs (E7) are selected as the material to fill the waveguide waveguide slit because E7 has sensitive electrical tunability in the terahertz band and its slit because E7 has sensitive electrical tunability in the terahertz band and its loss is very loss is very small [34], which is ignored in the simulation. small [34], which is ignored in the simulation. LC (E7) molecules are very sensitive to the external electric field. As long as the ex- LC (E7) molecules are very sensitive to the external electric field. As long as the ternal electric field changes slightly, the arrangement of LC (E7) molecules will change. external electric field changes slightly, the arrangement of LC (E7) molecules will change. When the voltage is turned off, that is E = 0 V/mm, LCs molecules are randomly arranged, When the voltage is turned off, that is E = 0 V/mm, LCs molecules are randomly arranged, and LC is an isotropic medium. When a bias voltage is applied to LCs, the dipoles will be and LC is an isotropic medium. When a bias voltage is applied to LCs, the dipoles will be arranged along the direction of the electric field, and the LC turns to an anisotropic me- arranged along the direction of the electric field, and the LC turns to an anisotropic medium, dium, resulting in the changes of LC (E7) optical properties—that is, the effective refrac- resulting in the changes of LC (E7) optical properties—that is, the effective refractive index tive index neff will change with the varying external electric field. The phenomenon that n will change with the varying external electric field. The phenomenon that the optical eff the optical properties of LC change due to the external electric field has been called the properties of LC change due to the external electric field has been called the photoelectric photoelectric effect of LCs. Yang et al. have experimentally measured the refractive index effect of LCs. Yang et al. have experimentally measured the refractive index n of liquid eff neff of liquid crystals in the frequency range of 0.5 THz to 1.5 THz when the electric field E crystals in the frequency range of 0.5 THz to 1.5 THz when the electric field E ranges from ranges from 0 V/mm to 7 V/mm [35]. Although our proposed structure is different, our 0 V/mm to 7 V/mm [35]. Although our proposed structure is different, our design only design only depends on the change of effective refractive index neff brought by LC photo- depends on the change of effective refractive index n brought by LC photoelectric effects, eff electric effects, and its optical properties are similar. Since our filter works in the range of and its optical properties are similar. Since our filter works in the range of 0.7 THz~1.4 THz, 0.7 THz~1.4 THz, we read the effective refractive index neff of the LCs in this frequency we read the effective refractive index n of the LCs in this frequency band from the eff experimental band from thdata. e expW erimen e employ tal da the ta. curve-fitting We employ t algorithm he curve-fto ittin prg ocess algori the thm data to and process obtain the data and obtain the cubic polynomial fitting of the effective refractive index neff of the LCs the cubic polynomial fitting of the effective refractive index n of the LCs with a different eff electric with a field differe asnt follows: electric field as follows: 3 2 n = a f + b f + c f + d. (1) eff 3 2 neff = a × f + b × f + c × f + d. (1) 2 2 The optimal coefficients and R are shown in Table 1. It can be seen that R is close to 2 2 The optimal coefficients and R are shown in Table 1. It can be seen that R is close to 1, which means that the fitting results are in good agreement with the experimental data. 1, which means that the fitting results are in good agreement with the experimental data. Thus, we used this cubic polynomial fit in our simulations. Thus, we used this cubic polynomial fit in our simulations. Photonics 2022, 9, x FOR PEER REVIEW 4 of 9 Photonics 2022, 9, 894 4 of 9 Table 1. Optimal coefficients for the cubic polynomial fit. Table 1. Optimal coefficients for the cubic polynomial fit. E (V/mm) a b c d R 0 0.0656 −0.1801 0.1296 1.592 0.9993 E (V/mm) a b c d R 3 0.0606 −0.1859 0.1615 1.596 0.9971 0 0.0656 0.1801 0.1296 1.592 0.9993 4 0.0246 −0.0600 0.0322 1.650 0.9919 3 0.0606 0.1859 0.1615 1.596 0.9971 4 0.0246 0.0600 0.0322 1.650 0.9919 5 0.0743 −0.2360 0.2328 1.595 0.9931 5 0.0743 0.2360 0.2328 1.595 0.9931 6 0.0578 −0.1914 0.1925 1.622 0.9955 6 0.0578 0.1914 0.1925 1.622 0.9955 7 0.0733 −0.2384 0.2410 1.619 0.9945 7 0.0733 0.2384 0.2410 1.619 0.9945 3. Electrical Tuning 3. Electrical Tuning Using the finite element method (FEM) of COMSOL Multiphysics, we calculated the Using the finite element method (FEM) of COMSOL Multiphysics, we calculated the transmission of the corrugated waveguides. In the simulation, we take the refractive index transmission of the corrugated waveguides. In the simulation, we take the refractive index of HDPE as 1.5 [36], and the dielectric function of Au is given by the Drude model [37]. of HDPE as 1.5 [36], and the dielectric function of Au is given by the Drude model [37]. When the electric intensity is set to E = 0 V/mm, the blue dashed line in Figure 2 shows When the electric intensity is set to E = 0 V/mm, the blue dashed line in Figure 2 shows the transmission of the waveguide without the defect, and the solid red line denotes the the transmission of the waveguide without the defect, and the solid red line denotes transmission of the waveguide with the defect. As expected, there is a Bragg forbidden the transmission of the waveguide with the defect. As expected, there is a Bragg forbid- band in the purely periodic waveguide; the frequency range is 0.991~1.065 THz, as shown den band in the purely periodic waveguide; the frequency range is 0.991~1.065 THz, as by the blue dashed line in Figure 2. After introducing defects, the Bragg forbidden band shown by the blue dashed line in Figure 2. After introducing defects, the Bragg forbidden gets slightly wider than a purely periodic waveguide, with a frequency range of band gets slightly wider than a purely periodic waveguide, with a frequency range of 0.986~1.065 THz. A narrow transmission peak appears near 1.039 THz, as shown by the 0.986~1.065 THz. A narrow transmission peak appears near 1.039 THz, as shown by the solid red line in Figure 2. This anomalous transmission peak is extremely narrow, which solid red line in Figure 2. This anomalous transmission peak is extremely narrow, which is is a good candidate for realizing THz narrowband filters. When the waveguide is enlarged a good candidate for realizing THz narrowband filters. When the waveguide is enlarged or reduced, the transmission peak will move to the low or high frequencies, respectively, or reduced, the transmission peak will move to the low or high frequencies, respectively, but the structure of the spectral band will not change. The size influence of waveguide but the structure of the spectral band will not change. The size influence of waveguide structure on the spectral band has been discussed in detail by Ma et al. [38]. structure on the spectral band has been discussed in detail by Ma et al. [38]. Figure 2. Spectra of planar THz waveguides with (the solid red line) and without (the blue dashed Figure 2. Spectra of planar THz waveguides with (the solid red line) and without (the blue dashed line) line) defects. defects. To further analyze the defect mode of the waveguide, we simulated the THz waves To further analyze the defect mode of the waveguide, we simulated the THz waves on the horizontal symmetry axis of the waveguide. Figure 3a represents the distribution on the horizontal symmetry axis of the waveguide. Figure 3a represents the distribution of the electric field component E along the x-axis. Based on the simulated electric fields, of the electric field component Ez along the x-axis. Based on the simulated electric fields, we performed the Fourier transform to obtain the dispersion curve of the defect structure, we performed the Fourier transform to obtain the dispersion curve of the defect structure, as shown in Figure 3b. It can be seen from Figure 3 that the THz waves interact with the as shown in Figure 3b. It can be seen from Figure 3 that the THz waves interact with the periodic structure, and there is a significant energy decay at the frequency corresponding periodic structure, and there is a significant energy decay at the frequency corresponding to the Bragg gap in Figure 2, while the introduction of the defect structure creates a very to the Bragg gap in Figure 2, while the introduction of the defect structure creates a very narrow transmission with energy accumulation in this gap. narrow transmission with energy accumulation in this gap. Photonics 2022, 9, x FOR PEER REVIEW 5 of 9 Photonics 2022, 9, x FOR PEER REVIEW 5 of 9 Photonics 2022, 9, 894 5 of 9 Figure 3. (a) Spectra along the x-axis for the waveguide with the defect; (b) dispersion curves de- picting a defect mode between 1 THz and 1.05 THz. Figure 3. (a) Spectra along the x-axis for the waveguide with the defect; (b) dispersion curves 4. Filter Performance Figure 3. (a) Spectra along the x-axis for the waveguide with the defect; (b) dispersion curves de- depicting a defect mode between 1 THz and 1.05 THz. picting a defect mode between 1 THz and 1.05 THz. Electrical tunability is achieved when we fill the filter cavity with LCs. We numeri- 4. Filter Performance cally simulate the propagation of the THz waves in the Bragg defect structure with the 4. Filter Performance Electrical tunability is achieved when we fill the filter cavity with LCs. We numerically FEM. We apply external electric fields of different intensities to the filter to obtain the simulate the propagation of the THz waves in the Bragg defect structure with the FEM. We operaElec tingt ric ban ald t un of abi narrow lity is -band achiev pu ed ls e when s, as shown we fill in the Fi fg ilter ure cav 4a. ity W hen wit h t he LCs. electr We ic n field umeri- E apply rises from external 3 V/ electric mm to fields 7 V/mm of dif , the fer ent narro intensities w-band pu to the lse filter moveto s fro obtain m the the hoperating igh to the band low- cally simulate the propagation of the THz waves in the Bragg defect structure with the of narrow-band pulses, as shown in Figure 4a. When the electric field E rises from 3 V/mm frequency range. The center frequency of the defect mode is 1.023 THz when the electric FEM. We apply external electric fields of different intensities to the filter to obtain the to 7 V/mm, the narrow-band pulse moves from the high to the low-frequency range. The field is 3 V/mm, and it moves to 0.984 THz when the electric field increases to 7 V/mm. operating band of narrow-band pulses, as shown in Figure 4a. When the electric field E center frequency of the defect mode is 1.023 THz when the electric field is 3 V/mm, and it Here, rises fwe rom hav 3 V/ e mm achiev toed 7 V a /seri mme , st he of t n rarro ansmission w-band pe pu aks lse when move st he fro bia m tshe vo h ltage igh to increas the low es,- moves to 0.984 THz when the electric field increases to 7 V/mm. Here, we have achieved a while frequenc a simi y ran lar ge. exp Th er eimen center tal fr ph eq enom uency enon of t he has defec been t mo observed de is 1.023 by Deng THz when et al. w th it eh ele a ctr LCic - series of transmission peaks when the bias voltage increases, while a similar experimental based field is me 3 tV asu /mm rfa,c and e [15]. it An mo ves absorpt to 0.9 ion 84 p T ea Hz k ar when ound t h 100 e elec GH tric z mo fiel ve dd i ncreas from tes he to hi gh 7 V/ tomm the. phenomenon has been observed by Deng et al. with a LC-based metasurface [15]. An low frequency with a narrow band when the voltage increased to 10 V. Here, we have achieved a series of transmission peaks when the bias voltage increases, absorption peak around 100 GHz moved from the high to the low frequency with a narrow while a similar experimental phenomenon has been observed by Deng et al. with a LC- band when the voltage increased to 10 V. based metasurface [15]. An absorption peak around 100 GHz moved from the high to the low frequency with a narrow band when the voltage increased to 10 V. Figure 4. Electrically tuning of the narrow band THz filter. (a) Transmission peak shifting with the Figure 4. Electrically tuning of the narrow band THz filter. (a) Transmission peak shifting with the external electric field; (b) peak frequency shift of the filter and its best fit denoted by the blue circles external electric field; (b) peak frequency shift of the filter and its best fit denoted by the blue circles and solid red line, respectively. and solid red line, respectively. Figure 4. Electrically tuning of the narrow band THz filter. (a) Transmission peak shifting with the To investigate the sensitivity of the proposed narrowband filter to the external electric external electric field; (b) peak frequency shift of the filter and its best fit denoted by the blue circles field, and so we lid red read lin the e, respe center ctivfr elequency y. of the peak at each electric field and fit it into a cubic Photonics 2022, 9, x FOR PEER REVIEW 6 of 9 Photonics 2022, 9, 894 6 of 9 To investigate the sensitivity of the proposed narrowband filter to the external elec- tric field, we read the center frequency of the peak at each electric field and fit it into a polynomial model of the electric field E, as shown in Figure 4b. The best-fitting curve for cubic polynomial model of the electric field E, as shown in Figure 4b. The best-fitting curve the frequency shift Df from 1 THz is: for the frequency shift Δf from 1 THz is: Δf = −9.79 × E + 51.71. (2) Df = 9.79 E + 51.71. (2) R of the linear fitting is 0.9946, indicating the excellent fitting effect. The fitting re- R of the linear fitting is 0.9946, indicating the excellent fitting effect. The fitting results sults show that the pulse peak is linearly shifted to lower frequencies as the field E in- show that the pulse peak is linearly shifted to lower frequencies as the field E increasing. creasing. A 1 V/mm increase of the external electric field results in a 9.79 GHz frequency A 1 V/mm increase of the external electric field results in a 9.79 GHz frequency shift of shift of the filter. Thus, it is possible to make the filter operate in the frequency band as the filter. Thus, it is possible to make the filter operate in the frequency band as desired desired by adjusting the external electric field. In applications, the response time of the by adjusting the external electric field. In applications, the response time of the proposed proposed filter is related to the LC molecule rotation speed when the external electric field filter is related to the LC molecule rotation speed when the external electric field changes. changes. The response time of LCs to voltage has been experimentally measured, and the The response time of LCs to voltage has been experimentally measured, and the achieved achieved recovery time is about several seconds [15]. recovery time is about several seconds [15]. In the study of periodically structured waveguides, the number of periods is an im- In the study of periodically structured waveguides, the number of periods is an portant parameter. Therefore, the number of periods is also discussed in our study. The important parameter. Therefore, the number of periods is also discussed in our study. The waveguide has a total of 20 periods, that is, 10 periods at both ends after inserting the waveguide has a total of 20 periods, that is, 10 periods at both ends after inserting the defect. n is the number of periods at both ends of the defect. We use the FEM to numeri- defect. n is the number of periods at both ends of the defect. We use the FEM to numerically cally simulate the waveguide structure with n = 8~12 periods at both ends of the middle simulate the waveguide structure with n = 8~12 periods at both ends of the middle defect defect and obtain the transmission spectrum of the narrowband peaks, as shown in Figure and obtain the transmission spectrum of the narrowband peaks, as shown in Figure 5. It 5. It can be seen from the figure that with the increasing number of waveguide periods, can be seen from the figure that with the increasing number of waveguide periods, the the peak value of the narrowband is almost the same, as well as the almost total transmis- peak value of the narrowband is almost the same, as well as the almost total transmission. sion. The position of the peak value hardly moves, but the bandwidth narrows. The position of the peak value hardly moves, but the bandwidth narrows. Figure 5. Transmission peaks of the filters with a different number of periods. Figure 5. Transmission peaks of the filters with a different number of periods. To further explore the effect of the variation in the number of periods on the filter To further explore the effect of the variation in the number of periods on the filter performance, the bandwidth of the filter and the magnitude of the Q-factor have also been performance, the bandwidth of the filter and the magnitude of the Q-factor have also been investigated. Here, the Q-factor is defined as the ratio of the peak frequency to its full investigated. Here, the Q-factor is defined as the ratio of the peak frequency to its full width at half height, which is an important index of the filter performance. The larger the width at half height, which is an important index of the filter performance. The larger the Q-factor, the better the filter performance. The obtained bandwidth and the variation trend Q-factor, the better the filter performance. The obtained bandwidth and the variation of the Q-factor are shown in Figure 6. As the number of waveguide periods increases, the trend of the Q-factor are shown in Figure 6. As the number of waveguide periods in- bandwidth of the peak decreases sharply, and the Q-factor increases gradually. It can be creases, the bandwidth of the peak decreases sharply, and the Q-factor increases gradu- predicted that if we continue to increase the number of periods, it will result in a higher Q ally. It can be predicted that if we continue to increase the number of periods, it will result factor. However, the more periods, the larger the structure, which would limit applications. in a higher Q factor. However, the more periods, the larger the structure, which would So, only the maximum n = 12 is considered in our simulation, and there will be a trade-off limit applications. So, only the maximum n = 12 is considered in our simulation, and there between the high Q factor and the large size device in applications. In our calculations, the will be a trade-off between the high Q factor and the large size device in applications. In bandwidth decreases from 3.2 GHz to 0.3 GHz, indicating that this filter structure has a our calculations, the bandwidth decreases from 3.2 GHz to 0.3 GHz, indicating that this narrowband filtering function with adjustable bandwidth. The filter reaches a maximum Q-factor of 2556 when the number of periods at both ends of the defect is 12. Photonics 2022, 9, x FOR PEER REVIEW 7 of 9 filter structure has a narrowband filtering function with adjustable bandwidth. The filter Photonics 2022, 9, 894 7 of 9 reaches a maximum Q-factor of 2556 when the number of periods at both ends of the de- fect is 12. Figure Figure 6. 6. Filte Filter r bandwid bandwidth th (the (the so solid lid blue blue li line) ne) and and the the Q Q-factor -factor (the (the do dotted tted red red li line) ne) for for the the filters filters with different periods. with different periods. 5. Conclusions 5. Conclusions We have proposed an electrically tunable THz filter based on the corrugated planar We have proposed an electrically tunable THz filter based on the corrugated planar THz waveguide filled by LCs. The periodic corrugations create the Bragg gap in the fre- THz waveguide filled by LCs. The periodic corrugations create the Bragg gap in the fre- quency spectrum, while the inserted defect results in the narrow transmission peak, which quency spectrum, while the inserted defect results in the narrow transmission peak, which can be employed in the THz filtering applications. The filled LCs can be affected by the ex- can be employed in the THz filtering applications. The filled LCs can be affected by the ternal electric field, which can change the effective refractive index of LCs. Considering the external electric field, which can change the effective refractive index of LCs. Considering experimentally measured index of LCs, we can realize an electrically tunable narrow-band the experimentally measured index of LCs, we can realize an electrically tunable narrow- THz filter by varying the external electric field. The proposed filter transmission is very band THz filter by varying the external electric field. The proposed filter transmission is close to 1, and the narrowest bandwidth reaches 0.3 GHz with a maximum Q-factor of 2556. very close to 1, and the narrowest bandwidth reaches 0.3 GHz with a maximum Q-factor Its center frequency tunable band range is 0.984~1.023 THz, which can also be changed by of 2556. Its center frequency tunable band range is 0.984~1.023 THz, which can also be enlarging or reducing the structure size of the filter. Due to its impressive performance, this changed by enlarging or reducing the structure size of the filter. Due to its impressive electrically tunable filter could find applications in various THz systems, especially for the performance, this electrically tunable filter could find applications in various THz sys- frequency division multiplexing in further THz communication. tems, especially for the frequency division multiplexing in further THz communication. Author Contributions: Conceptualization, Y.-X.F. and Z.-Y.T.; methodology, S.-Y.Z. and J.M.; val- Author Contributions: Conceptualization, Y.-X.F. and Z.-Y.T.; methodology, S.-Y.Z. and J.M.; vali- idation, J.M.; formal analysis, S.-Y.Z., J.M., C.-G.T. and H.L.; investigation, S.-Y.Z. and H.-L.H.; dation, J.M.; formal analysis, S.-Y.Z., J.M., C.-G.T., and H.L.; investigation, S.-Y.Z. and H.-L.H.; writ- writing—original draft preparation, S.-Y.Z.; writing—review and editing, Y.-X.F. and Z.-Y.T.; visual- ing—original draft preparation, S.-Y.Z.; writing—review and editing, Y.-X.F. and Z.-Y.T.; visualiza- ization, S.-Y.Z.; supervision, Y.-X.F. and Z.-Y.T. All authors have read and agreed to the published tion, S.-Y.Z.; supervision, Y.-X.F. and Z.-Y.T. All authors have read and agreed to the published version of the manuscript. version of the manuscript. Funding: This research was supported by the Guangxi Natural Science Foundation (2020GXNSFBA15 Funding: This research was supported by the Guangxi Natural Science Foundation 9047, 2021GXNSFAA220073, 2021GXNSFAA220086, and 2021GXNSFDA075006), the National Natural (2020GXNSFBA159047, 2021GXNSFAA220073, 2021GXNSFAA220086, and 2021GXNSFDA075006), Science Foundation of China (12064005 and 62001132), the Innovation Project of GUET Graduate the National Natural Science Foundation of China (12064005 and 62001132), the Innovation Project Education (2022YCXS033 and 2022YCXS041), and the Double First-Class University Construction of GUET Graduate Education (2022YCXS033 and 2022YCXS041), and the Double First-Class Uni- Project of Northwest University. versity Construction Project of Northwest University. Institutional Review Board Statement: Not applicable. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the Data Availability Statement: The data presented in this study are available on request from the corresponding author. corresponding author. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflicts of interest. References 1. Huang, Y.-W.; Tseng, T.-F.; Kuo, C.-C.; Hwang, Y.-J.; Sun, C.-K. Fiber-Based Swept-Source Terahertz Radar. Opt. Lett. 2010, 35, 1344–1346. [CrossRef] [PubMed] 2. Siegel, P.H. Terahertz Technology in Biology and Medicine. IEEE Trans. Microw. Theory Tech. 2004, 52, 2438–2447. [CrossRef] Photonics 2022, 9, 894 8 of 9 3. Ibraheem, I.A.; Krumbholz, N.; Mittleman, D.; Koch, M. Low-Dispersive Dielectric Mirrors for Future Wireless Terahertz Communication Systems. IEEE Microw. Wirel. Compon. Lett. 2008, 18, 67–69. [CrossRef] 4. 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