Article Polarization-Sensitive Metamaterials with Tunable Multi-Resonance in the Terahertz Frequency Range
Xiaojie Chen and Yu-Sheng Lin * State Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Sun Yat-Sen University, Guangzhou 510275, China; [email protected] * Correspondence: [email protected]
Received: 17 June 2020; Accepted: 9 July 2020; Published: 13 July 2020
Abstract: We propose two designs of polarization-sensitive metamaterials (PSMs), which are composed of face-to-face spilt-ring resonators (SRRs) and a cut-wire resonator (CWR) sandwiched by two face-to-face SRRs. For convenient description, they are denoted as PSM_1 and PSM_2, respectively. PSM_1 and PSM_2 are fabricated by tailoring Au layers with periodic configurations on silicon-on-insulator (SOI) substrates. By changing the incident polarization light, the electromagnetic responses of PSM_1 can be manipulated between single-resonance and dual-resonance, while those of PSM_2 exhibit switching behavior between single-resonance and triple-resonance. By enlarging the distance between the gap centers of the two face-to-face SRRs along the y-axis direction, the electromagnetic responses of PSM_1 show switching characteristics from single-resonance to triple-resonance at the transverse electric (TE) mode and from dual-resonance to triple-resonance at the transverse magnetic (TM) mode. PSM_2 exhibits switching characteristics from single-resonance to triple-resonance at the TE mode and from dual-resonance to quad-resonance at the TM mode. Furthermore, by changing the width of the CWR under the condition of two face-to-face SRRs with a constant gap distance, PSM_2 exhibits stable electromagnetic responses at the TE mode and tunable resonances at the TM mode, respectively. This work paves the way to the possibility of metamaterial devices with great tunability, switchable bandwidth, and polarization-dependence characteristics.
Keywords: terahertz; metamaterial; polarization-sensitive; modulator; spilt-ring resonator
1. Introduction Metamaterials have attracted great attention by researchers due to their extraordinary electromagnetic properties spanning the entire spectra range. These unique optical properties are unavailable in natural materials [1]. Through electromagnetic waves, metamaterials exhibit surprising optical characteristics, such as a negative refraction index [2,3], a biosensor [4], an antenna [5], invisible cloaking [6], and a perfect absorber [7]. The classical design of a metamaterial is the configuration of a split-ring resonator (SRR). There has been much research presenting and demonstrating the use of diversified SRR designs [8–13], either symmetrically or asymmetrically, such as cross-shaped SRR [9], V-shaped SRR [10,11], spiral-shaped SRR [12], and multiple SRRs [13]. In view of these extraordinary optical properties of SRR-based metamaterials, there have been extensive studies reported in the different frequency ranges, from microwave, terahertz (THz), and infrared to visible spectra [14–19]. Designs utilizing THz metamaterials have attracted a great deal of interest owing to the extraordinary electromagnetic responses of metamaterials and the potential applications of their sensing and imaging characteristics in the THz frequency range [20–23]. This is a considerable method to obtain excellent transmission characteristics. In addition, metamaterials are useful for tunable THz devices, which have been presented with electrical control [24], optical control [25], thermal control [26], and magnetic control [27]. Recently, THz metamaterials hybridized with microelectromechanical
Crystals 2020, 10, 611; doi:10.3390/cryst10070611 www.mdpi.com/journal/crystals Crystals 2020, 10, 611 2 of 11 systems (MEMS) have become one of the most striking topics in this field, owing to their advantages of electrostatic tunability, enhanced electro-optic performance, and miniaturized size [10,11]. Many electromagnetic functions can be performed by using the MEMS technique to actively manipulate the metamaterial’s configuration. The MEMS technique has become a notable approach for tunable THz metamaterials, in areas such as resonant filtering, resonant switching, and electromagnetically-induced transparency [28,29]. In this study, we propose two designs of polarization-sensitive metamaterials (PSMs) composed of face-to-face SRRs and a cut-wire resonator (CWR) sandwiched by two face-to-face SRRs, which are noted as PSM_1 and PSM_2, respectively. These two designs are fabricated by tailoring Au layers with periodic configurations on silicon-on-insulator (SOI) substrates. The electromagnetic responses of the proposed PSMs are investigated in order to implement the tunable THz metamaterial with polarization-sensitive multi-resonance characteristics in the THz frequency range. These designs open an avenue by which THz metamaterials could be used in widespread applications, with high portability, flexibility, and compatibility.
2. Materials and Methods Figure1 shows the schematic drawings of PSM_1 (Figure1a) and PSM_2 (Figure1b) unit cells and the corresponding denotations, respectively. The configuration of PSM_1 is two face-to-face SRRs, while that of PSM_2 is a CWR sandwiched by the two face-to-face SRRs. The propagation direction of the incident THz wave is set along the negative z-axis direction, whereas the electric (E) field and magnetic (H) field are set as the xy-plane. The incident transverse electric (TE) polarized light is defined as the E-field, set along the x-axis direction, and the H-field, set along the y-axis direction, named the TE mode. The incident transverse magnetic (TM) polarized light is defined as the E-field, set along the y-axis direction, and the H-field, set along the x-axis direction, named the TM mode. The incident THz wave is set as a plane wave propagating vertically to the PSM surface; the surface plasma resonances will then be generated between two face-to-face SRRs for PSM_1 and between the CWR sandwiched by the two face-to-face SRRs for PSM_2. The proposed PSMs are tailored by the Au layer with a thickness of 300 nm (h = 300 nm) on SOI substrates. The structural periods of the PSMs are denoted as Px and Py along the x- and y-axis directions, respectively, where Px = Py = 100 µm. The lengths and widths of the PSMs are denoted as l and w, respectively, where l = 60 µm and w = 27.5 µm. The line widths of the PSMs are kept constant at 5 µm (c = 5 µm). The gaps and the distances of the gap center of the face-to-face SRRs along the y-axis direction are defined as g and s, respectively. The distances between the two face-to-face SRRs and between the SRRs and the CWR along the x-axis direction for PSM_1 and PSM_2 are defined as d. The geometrical parameters of the CWR are the metallic line width (a) and length (l). The g, s, and d parameters of PSM_1 are kept constant at g = 5 µm, s = 0 µm, and d = 5 µm, respectively. The g, s, d, and a parameters of PSM_2 are kept constant at g = 5 µm, s = 0 µm, d = 2 µm, and a = 1 µm, respectively. First, the transmission spectra of the PSMs are explored under the incident THz wave. Then, for PSM_2, the a and d variations are changed synchronously to investigate their relationships to the transmission spectra, while the g and s parameters are kept as g = 5 µm and s = 0 µm, and the sum value of a and d is kept constant. Finally, the effect of the incident polarization angles at 0 degrees (TE mode) and 90 degrees (TM mode) for both PSM_1 and PSM_2 are compared and investigated. The optical properties of the proposed devices are simulated through Lumerical Solutions’ finite difference time domain (FDTD)-based simulations. The propagation direction of incident light is set to be perpendicular to the x-y plane in the numerical simulations. Periodic boundary conditions are also adopted in the x and y directions, and perfectly matched layer (PML) boundary conditions are assumed in the z direction. The transmission of the incident THz wave is calculated by a monitor set under the bottom side of the proposed PSMs. Crystals 2020, 10, 611 3 of 11 Crystals 2020, 10, x 3 of 12
TE mode (a) TE mode (b) a x (E) x (E) y (H) y (H) s s z (k) g z (k) TM mode g TM mode d y (E) d y (E) d x (H) x (H) z (k) c z (k) c Au l l h h l w w Si Py Py Px Px
FigureFigure 1. 1.Schematic Schematic drawings drawings and and the the corresponding corresponding denotations denotations of of (a ()a PSM_1) PSM_1 and and (b ()b PSM_2) PSM_2 unit unit cells. cells. 3. Simulation Results and Discussion 3. Simulation Results and Discussion Figure2a,b show the transmission spectra of PSM_1 by changing the g value from 1 µm to 30 µm at the TEFig andures TM2a and modes, 2b show respectively, the transmission while s and spectrad are of kept PSM_1 as s =by0 changingµm, d = 5 theµm. g Thevalue electromagnetic from 1 μm responseto 30 μm exhibits at the TE single-resonance and TM modes at, respectively, TE mode and while dual-resonance s and d are kept at TM as mode.s = 0 μm These, d = 5 two μm di. Thefferent responseselectromagnetic show the response polarization exhibits dependence single-resonance of PSM_1. at TE mode At the and TE dualmode,-resonance the resonant at TM intensity mode. is almostThese kepttwo different constant, responses whereas the show resonant the polarization frequency dependence is blue-shifted of PSM_1. from 0.22 At the THz TE to mode, 0.27 THz the by increasingresonant intensity the g value. is almost The tuning kept constant, range is 50whereas GHz. Forthe resonant a resonance frequency larger thanis blue 0.40-shifted THz, from the resonant 0.22 frequencyTHz to 0.27 is blue-shiftedTHz by increasing with the the decreasing g value. The resonant tuning range intensity. is 50 When GHz. gForis largera resonance than 15largerµm, than there is 0.40 THz, the resonant frequency is blue-shifted with the decreasing resonant intensity. When g is no resonance. At the TM mode, there are two resonances blue-shifted from 0.13 THz to 0.17 THz (the larger than 15 μm, there is no resonance. At the TM mode, there are two resonances blue-shifted first resonance) and from 0.34 THz to 0.44 THz (the second resonance). In order to better interpret the from 0.13 THz to 0.17 THz (the first resonance) and from 0.34 THz to 0.44 THz (the second physical mechanism of this phenomenon, the corresponding E- and H-field distributions of PSM_1 at resonance). In order to better interpret the physical mechanism of this phenomenon, the the TE and TM modes under the condition of g = 30 µm are presented in Figure2c,d, respectively. At corresponding E- and H-field distributions of PSM_1 at the TE and TM modes under the condition the TE mode, the E-field is accumulated in the adjacent parts of the two face-to-face SRRs, and the of g = 30 μm are presented in Figures 2c and 2d, respectively. At the TE mode, the E-field is H-fieldaccumulated is distributed in the adjacent around part thesupper of the andtwo face lower-to- conductorface SRRs, and bars the of theH-field SRRs. is distributed It generates around a typical localizedthe upper surface and lower plasmon conductor (LSP) resonancebars of the atSRRs. 0.27 It THz generates [30]. Figure a typical2d indicates localized the surface electromagnetic plasmon field(LSP) distributions resonance at of 0.27 these THz two [30] di. Figurefferent 2d resonances, indicates the which electromagnetic contribute tofield the distributions two LSP resonances of these at 0.17two THz different and 0.43resonan THz.ces The, which E-fields contribute are distributed to the two around LSP resonances the gap ofat each0.17 THz SRR and at 0.17 0.43 THz THz (the. The first resonance)E-fields are and distribut 0.43 THzed around (the second the gap resonance), of each SRR whereas at 0.17 the THz H-fields (the first are resonance) distributed and around 0.43 THz the left and(the right second conductor resonance), bars whereas of the structure the H-field at 0.17s are THz distributed and around around the the contours left and of right both conductor SRRs at 0.43 bars THz. of theThe structure transmission at 0.17 spectra THz and of PSM_1,around the obtained contour bys changingof both SRRs the atd value0.43 THz and. simultaneously keeping s = 0 µm and g = 5 µm at the TE and TM modes, are shown in Figure3a,b, respectively. At the TE mode, the resonances are first blue-shifted from 0.22 THz to 0.25 THz when d increases from 5 µm to 15 µm, and then the resonances are red-shifted from 0.24 THz to 0.19 THz when d increases from 15 µm to 25 µm. At the TM mode, there are two resonances at 0.14 THz and 0.36 THz, and both resonances are slight variations of the resonant frequency and intensity, obtained by changing the d value. This indicates that the proposed PSM_1 exhibits the polarization-dependence characteristic. The electromagnetic characteristics of PSM_1 can be switched from single-resonance to dual-resonance by changing the polarization mode from TE to TM. These results could be explained by the corresponding E- and H-field distributions at the TE and TM modes, as shown in Figure3c,d, respectively. It is obvious that the electromagnetic field distributions of PSM_1 with d = 25 µm are similar to those with g = 30 µm, which are shown in Figure2c,d. Therefore, the resonances of 0.19 THz at the TE mode and the resonances of 0.13 THz and 0.37 THz at the TM mode are LSP resonances. Crystals 2020, 10, 611 4 of 11 Crystals 2020, 10, x 4 of 12
FigureFigure 2.2.Transmission Transmission spectra spectra of of PSM_1 PSM_ with1 with diff differenterent g values g values at the at (athe) TE (a and) TE ( band) TM (b modes.) TM modes. Here, (Here,c) and ( (cd) )and are ( thed) are corresponding the corresponding E-field andE-field H-field and distributionsH-field distributions of PSM_1, of withPSM_g1=, with30 µ mg = at 30 TE μm and at Crystals 2020, 10, x 5 of 12 TMTE and modes, TM respectivelymodes, respectively (f is the monitored(f is the monitored frequency). frequency).
The transmission spectra of PSM_1, obtained by changing the d value and simultaneously keeping s = 0 μm and g = 5 μm at the TE and TM modes, are shown in Figures 3a and 3b, respectively. At the TE mode, the resonances are first blue-shifted from 0.22 THz to 0.25 THz when d increases from 5 μm to 15 μm, and then the resonances are red-shifted from 0.24 THz to 0.19 THz when d increases from 15 μm to 25 μm. At the TM mode, there are two resonances at 0.14 THz and 0.36 THz, and both resonances are slight variations of the resonant frequency and intensity, obtained by changing the d value. This indicates that the proposed PSM_1 exhibits the polarization-dependence characteristic. The electromagnetic characteristics of PSM_1 can be switched from single-resonance to dual-resonance by changing the polarization mode from TE to TM. These results could be explained by the corresponding E- and H-field distributions at the TE and TM modes, as shown in Figures 3c and 3d, respectively. It is obvious that the electromagnetic field distributions of PSM_1 with d = 25 μm are similar to those with g = 30 μm, which are shown in Figures 2c and 2d. Therefore, the resonances of 0.19 THz at the TE mode and the resonances of 0.13 THz and 0.37 THz at the TM mode are LSP resonances.
Figure 3. TransmissionTransmission spectraspectra of of PSM_1 PSM_ with1 with di ffdifferenterent d values d values at the at (thea) TE (a) and TE (andb) TM (b) modes. TM modes. Here, Here,(c) and (c ()d and) are (d the) are corresponding the corresponding E-field E and-field H-field and H distributions-field distributions of PSM_1 of PSM with_d1= with25 µ dm = at25 TE μm and at TETM and modes, TM modes, respectively respectively (f is the ( monitoredf is the monitored frequency). frequency). To investigate the coupling effect between the gap center distance of the face-to-face SRRs and To investigate the coupling effect between the gap center distance of the face-to-face SRRs and the incident THz wave, the transmission spectra of PSM_1 with different s values from 0 µm to the incident THz wave, the transmission spectra of PSM_1 with different s values from 0 μm to 40 μm at the TE and TM modes are shown in Figures 4a and 4b, respectively. The g and d values are kept constant at 5 μm. The electromagnetic responses indicate that PSM_1 with different s values exhibits polarization-sensitivity. At the TE mode, the main resonance that occurs at 0.24 THz is blue-shifted, and the resonant intensity decays as a result of the increasing s value. Meanwhile, two resonances are generated around the resonant frequencies of 0.12 THz and 0.34 THz. By increasing the s value, these two resonances are red-shifted, and the corresponding resonant intensity becomes stronger. This shows a switchable behavior. At the TM mode, there are two resonances, at 0.14 THz and 0.37 THz, and there is no resonance at 0.24 THz for s = 0 μm. By increasing the s value, these two resonances are red-shifted with decreasing resonant intensities. A resonance is generated at 0.24 THz which is blue-shifted, and the resonant intensity increases when the s value is increased. This indicates the behavior of a switchable electromagnetic response. The corresponding E- and H-field distributions of PSM_1 at the TE and TM modes under the conditions of s = 0 μm, 20 μm, and 40 μm are presented in Figures 4c and 4d, respectively. The corresponding monitored frequencies are 0.23 THz, 0.24 THz, and 0.25 THz at the TE mode and 0.36 THz, 0.33 THz, and 0.33 THz at the TM mode. At the TE mode, the E-fields are gathered at the adjacent parts of the two face-to-face SRRs and the H-fields are distributed around the upper and lower conductor bars of the SRRs. This indicates that the resonances of 0.23 THz for s = 0 μm, the resonances of 0.24 THz for s = 20 μm, and the resonances of 0.25 THz for s = 40 μm are LSP resonances. Figure 4d indicates the electromagnetic fields distributions of resonances under the conditions of s = 0 μm, 20 μm, and 40 μm, which contribute to LSP resonances at 0.36 THz, 0.33 THz, and 0.33 THz at the TM mode. The E-field is distributed within the gap of the SRRs, and the H-field is distributed around the corners of the SRRs for s = 0 μm. For s = 20 μm and s = 40 μm, the H-fields are distributed around the contours of the SRRs. Meanwhile, the E-fields are restricted in the middle adjacent parts of the face-to-face SRRs for s = 20 μm and at the apexes of the adjacent parts of the SRRs for s = 40 μm. By increasing the s value, the E- and H-fields captured by PSM_1 at the TE and TM modes vanish, which indicates the correspondingly decreasing resonant intensities. Crystals 2020, 10, 611 5 of 11
40 µm at the TE and TM modes are shown in Figure4a,b, respectively. The g and d values are kept constant at 5 µm. The electromagnetic responses indicate that PSM_1 with different s values exhibits polarization-sensitivity. At the TE mode, the main resonance that occurs at 0.24 THz is blue-shifted, and the resonant intensity decays as a result of the increasing s value. Meanwhile, two resonances are generated around the resonant frequencies of 0.12 THz and 0.34 THz. By increasing the s value, these two resonances are red-shifted, and the corresponding resonant intensity becomes stronger. This shows a switchable behavior. At the TM mode, there are two resonances, at 0.14 THz and 0.37 THz, and there is no resonance at 0.24 THz for s = 0 µm. By increasing the s value, these two resonances are red-shifted with decreasing resonant intensities. A resonance is generated at 0.24 THz which is blue-shifted, and the resonant intensity increases when the s value is increased. This indicates the behavior of a switchable electromagnetic response. The corresponding E- and H-field distributions of PSM_1 at the TE and TM modes under the conditions of s = 0 µm, 20 µm, and 40 µm are presented in Figure4c,d, respectively. The corresponding monitored frequencies are 0.23 THz, 0.24 THz, and 0.25 THz at the TE mode and 0.36 THz, 0.33 THz, and 0.33 THz at the TM mode. At the TE mode, the E-fields are gathered at the adjacent parts of the two face-to-face SRRs and the H-fields are distributed around the upper and lower conductor bars of the SRRs. This indicates that the resonances of 0.23 THz for s = 0 µm, the resonances of 0.24 THz for s = 20 µm, and the resonances of 0.25 THz for s = 40 µm are LSP resonances. Figure4d indicates the electromagnetic fields distributions of resonances under the conditions of s = 0 µm, 20 µm, and 40 µm, which contribute to LSP resonances at 0.36 THz, 0.33 THz, and 0.33 THz at the TM mode. The E-field is distributed within the gap of the SRRs, and the H-field is distributed around the corners of the SRRs for s = 0 µm. For s = 20 µm and s = 40 µm, the H-fields are distributed around the contours of the SRRs. Meanwhile, the E-fields are restricted in the middle adjacent parts of the face-to-face SRRs for s = 20 µm and at the apexes of the adjacent parts of the SRRs for s = 40 µm. By increasing the s value, the E- and H-fields captured by PSM_1 at the TE and TMCrystals modes 2020 vanish,, 10, x which indicates the correspondingly decreasing resonant intensities. 6 of 12
FigureFigure 4. 4.Transmission Transmission spectra spectra of PSM_1of PSM with_1 with diff erentdifferents values s values at the at (a the) TE ( anda) TE (b and) TM (b modes.) TM modes. Here, (cHere,) and ((dc) areand the (d) corresponding are the corresponding E-field and E-field H-field and distributions H-field distributions of PSM_1 of with PSMs =_10 withµm, 20s =µ 0m, μm, and 20 40μm,µm and at TE 40 andμm TMat TE modes, and TM respectively modes, respectively (f is the monitored (f is the monitored frequency). frequency).
Figures 5a and 5b show the transmission spectra of PSM_2 by changing g from 1 μm to 30 μm and simultaneously keeping s = 0 μm, d = 2 μm, and a = 1 μm at the TE and TM modes, respectively. At the TE mode, the resonant frequency is blue-shifted from 0.21 THz to 0.26 THz, while the resonant intensity is almost kept constant when the g value is increased. The tuning range is 50 GHz. For the resonance larger than 0.4 THz, the resonant frequency is blue-shifted, and the resonant intensities are strong only for g = 1 μm and g = 5 μm. At the TM mode, there are three resonances that are blue-shifted, from 0.15 THz to 0.20 THz (the first resonance), from 0.29 THz to 0.36 THz (the second resonance), and from 0.37 THz to 0.44 THz (the third resonance). Compared with the transmission spectra of PSM_1 by changing g from 1 μm to 30 μm in Figures 2a and 2b, the electromagnetic characteristic of PSM_2 is the same at the TE mode but is different at the TM mode. The electromagnetic response exhibits single-resonance at the TE mode for both PSMs, while it exhibits dual-resonance for PSM_1 and triple-resonance for PSM_2 at the TM mode. The extra resonance from 0.29 THz to 0.36 THz at the TM mode is contributed by the CWR, which generates a stronger coupling effect of PSM_2 at the TM mode but is almost transparent at the TE mode. These could be explained by the corresponding E- and H-field distributions of PSM_2, with g = 30 μm at the TE and TM modes in Figures 5c and 5d. The electromagnetic field distributions of PSM_2, with g = 30 μm at the TE mode, are similar to those of PSM_1 in Figure 2c, which indicates that the LSP resonances of these two devices are almost the same at the TE mode. At the TM mode, three LSP resonances are generated, at 0.19 THz, 0.36 THz, and 0.43 THz, for g = 30 μm. The E-fields are distributed around the gaps of each SRR and the apexes of the CWR at 0.19 THz, while the H-fields are distributed around the left and right conductor bars of the structure and the contour of the CWR. At 0.36 THz, the electromagnetic fields are gathered at the contour of the CWR, while at 0.43 THz, the electromagnetic fields are distributed around the contours of the SRRs and the middle part of the CWR. Therefore, the difference in the electromagnetic response between PSM_1 and PSM_2 at the TM mode is that the CWR contributes a greater coupling effect with the two face-to-face SRRs, leading to the second resonance at around 0.30 THz and the stronger resonant intensity of the transmission spectra that are shown in Figure 5b, compared with those shown in Figure 2b. Crystals 2020, 10, 611 6 of 11
Figure5a,b show the transmission spectra of PSM_2 by changing g from 1 µm to 30 µm and simultaneously keeping s = 0 µm, d = 2 µm, and a = 1 µm at the TE and TM modes, respectively. At the TE mode, the resonant frequency is blue-shifted from 0.21 THz to 0.26 THz, while the resonant intensity is almost kept constant when the g value is increased. The tuning range is 50 GHz. For the resonance larger than 0.4 THz, the resonant frequency is blue-shifted, and the resonant intensities are strong only for g = 1 µm and g = 5 µm. At the TM mode, there are three resonances that are blue-shifted, from 0.15 THz to 0.20 THz (the first resonance), from 0.29 THz to 0.36 THz (the second resonance), and from 0.37 THz to 0.44 THz (the third resonance). Compared with the transmission spectra of PSM_1 by changing g from 1 µm to 30 µm in Figure2a,b, the electromagnetic characteristic of PSM_2 is the same at the TE mode but is different at the TM mode. The electromagnetic response exhibits single-resonance at the TE mode for both PSMs, while it exhibits dual-resonance for PSM_1 and triple-resonance for PSM_2 at the TM mode. The extra resonance from 0.29 THz to 0.36 THz at the TM mode is contributed by the CWR, which generates a stronger coupling effect of PSM_2 at the TM mode but is almost transparent at the TE mode. These could be explained by the corresponding E- and H-field distributions of PSM_2, with g = 30 µm at the TE and TM modes in Figure5c,d. The electromagnetic field distributions of PSM_2, with g = 30 µm at the TE mode, are similar to those of PSM_1 in Figure2c, which indicates that the LSP resonances of these two devices are almost the same at the TE mode. At the TM mode, three LSP resonances are generated, at 0.19 THz, 0.36 THz, and 0.43 THz, for g = 30 µm. The E-fields are distributed around the gaps of each SRR and the apexes of the CWR at 0.19 THz, while the H-fields are distributed around the left and right conductor bars of the structure and the contour of the CWR. At 0.36 THz, the electromagnetic fields are gathered at the contour of the CWR, while at 0.43 THz, the electromagnetic fields are distributed around the contours of the SRRs and the middle part of the CWR. Therefore, the difference in the electromagnetic response between PSM_1 and PSM_2 at the TM mode is that the CWR contributes a greater coupling effect with the two face-to-face SRRs, leading to the second resonance at around 0.30 THz and the stronger resonant intensity of the transmission spectra that are shown in Figure5b, compared with those shown in Figure2b. Figure6a,b show the transmission spectra of PSM_2 by changing the s value from 0 µm to 40 µm at the TE and TM modes, respectively. The g, d, and a values are kept as g = 5 µm, d = 2 µm, and a = 1 µm. Evidently, the transmission spectra of PSM_2 by changing the s value at the TE mode shown in Figure6a are similar to those of PSM_1 shown in Figure4a. It can be explained by the E- and H-field distributions of PSM_2 in Figure6c. It is obvious that the electromagnetic field distributions of PSM_2 at the TE mode are similar to those of PSM_1, shown in Figure4c. Therefore, the resonances of 0.22 THz, 0.23 THz, and 0.25 THz at the TE mode are LSP resonances. At the TM mode, there are three resonances, at 0.16 THz, 0.29 THz, and 0.39 THz, at the initial state (s = 0 µm). By increasing the s value, the PSM_2 device can be switched from triple-resonance to quad-resonance. The E- and H-field distributions of PSM_2 with s = 0 µm, 20 µm, and 40 µm at the TM mode are summarized in Figure6d. The electromagnetic fields are gathered in the CWR and are quite different from those of PSM_1, which are shown in Figure4d. This causes the di fference in the transmission spectra between PSM_1 and PSM_2 at the TM mode. It indicates that the LSP resonances of 0.29 THz for s = 0 µm, 0.30 THz for s = 20 µm, and 0.40 THz for s = 40 µm are generated by the CWR. Crystals 2020, 10, 611 7 of 11 Crystals 2020, 10, x 7 of 12
FigureFigure 5.5. TransmissionTransmission spectra spectra of of PSM_2 PSM_2 by by changing changingg valueg value at theat the (a) ( TEa) TE and and (b) ( TMb) TM modes. modes. Here, Here, (c) and(c) and (d) are(d) theare correspondingthe corresponding E-field E-field and and H-field H-field distributions distributions of PSM_2 of PSM with_2 withg = 30 g µ= m30 atμm TE at and TE TMand Crystalsmodes,TM 20 modes,20, respectively10, x respectively (f is the(f is monitored the monitored frequency). frequency). 8 of 12
Figures 6a and 6b show the transmission spectra of PSM_2 by changing the s value from 0 μm to 40 μm at the TE and TM modes, respectively. The g, d, and a values are kept as g = 5 μm, d = 2 μm, and a = 1 μm. Evidently, the transmission spectra of PSM_2 by changing the s value at the TE mode shown in Figure 6a are similar to those of PSM_1 shown in Figure 4a. It can be explained by the E- and H-field distributions of PSM_2 in Figure 6c. It is obvious that the electromagnetic field distributions of PSM_2 at the TE mode are similar to those of PSM_1, shown in Figure 4c. Therefore, the resonances of 0.22 THz, 0.23 THz, and 0.25 THz at the TE mode are LSP resonances. At the TM mode, there are three resonances, at 0.16 THz, 0.29 THz, and 0.39 THz, at the initial state (s = 0 μm). By increasing the s value, the PSM_2 device can be switched from triple-resonance to quad-resonance. The E- and H-field distributions of PSM_2 with s = 0 μm, 20 μm, and 40 μm at the TM mode are summarized in Figure 6d. The electromagnetic fields are gathered in the CWR and are quite different from those of PSM_1, which are shown in Figure 4d. This causes the difference in the transmission spectra between PSM_1 and PSM_2 at the TM mode. It indicates that the LSP resonances of 0.29 THz for s = 0 μm, 0.30 THz for s = 20 μm, and 0.40 THz for s = 40 μm are generated by the CWR.
FigureFigure 6. 6.Transmission Transmission spectraspectra ofof PSM_2PSM_2 byby changingchangings svalue value thetheat at (a(a)) TE TE and and ( b(b)) TM TM modes. modes. Here,Here, (c(c)) and and ( d(d) are) are the the corresponding corresponding E-field E-field and and H-field H-field distributions distributions of PSM_2 of PSM with_2 withs = 0 sµ =m, 0 20μm,µ m,20 andμm, 40andµm 40 at μm TE at and TE TM and modes, TM modes, respectively respectively (f is the (f is monitored the monitored frequency). frequency).
TheThe transmission transmission spectra spectra of PSM_2 of PSM_2 obtained obtained by changing by changing the d valuethe d and value simultaneously and simultaneously keeping gkeeping= 5 µm, gs = 50 μmµm,, s and = 0 aμm= 1, andµm ata = the 1 μm TE andat the TM TE modes and TM are modes shown are in Figure shown7a,b, in Figure respectively.s 7a and The 7b, electromagneticrespectively. The responses electromagnetic indicate that responses the PSM_2 indicate with dithatfferent the dPSM_2values with shows different polarization-sensitivity. d values shows polarization-sensitivity. At the TE mode, the resonances are first blue-shifted from 0.22 THz to 0.24 THz when d increases from 2 μm to 8 μm, and they are then red-shifted from 0.24 THz to 0.19 THz when d increases from 8 μm to 12 μm. At the TM mode, there are three resonances: one is around the resonant frequency of 0.16 THz, one is blue-shifted from 0.29 THz to 0.37 THz, and the other is blue-shifted from 0.39 THz to 0.42 THz by increasing the d value. A resonance will be generated at 0.11 THz when d is 4 μm. By increasing the d value, this resonance is blue-shifted and the corresponding resonant intensity is larger. The corresponding E- and H-field distributions of PSM_2 with d = 12 μm at the TE and TM modes are shown in Figures 7c and 7d, respectively. The corresponding resonant frequencies are 0.19 THz at the TE mode and 0.37 THz at the TM mode. Compared with the electromagnetic field distributions of PSM_1 with d = 25 μm at 0.19 THz (at the TE mode) and 0.37 THz (at the TM mode) shown in Figures 3c and 3d, the E- and H-field distributions of PSM_2 with d = 12 μm indicate the influence of the CWR. It is obvious that the coupling effect generated by the CWR becomes weaker with the larger distance between the CWR and the SRRs. Therefore, the LSP resonances of 0.19 THz at the TE mode and 0.37 THz at the TM mode are generated by the SRRs. Crystals 2020, 10, 611 8 of 11
At the TE mode, the resonances are first blue-shifted from 0.22 THz to 0.24 THz when d increases from 2 µm to 8 µm, and they are then red-shifted from 0.24 THz to 0.19 THz when d increases from 8 µm to 12 µm. At the TM mode, there are three resonances: one is around the resonant frequency of 0.16 THz, one is blue-shifted from 0.29 THz to 0.37 THz, and the other is blue-shifted from 0.39 THz to 0.42 THz by increasing the d value. A resonance will be generated at 0.11 THz when d is 4 µm. By increasing the d value, this resonance is blue-shifted and the corresponding resonant intensity is larger. The corresponding E- and H-field distributions of PSM_2 with d = 12 µm at the TE and TM modes are shown in Figure7c,d, respectively. The corresponding resonant frequencies are 0.19 THz at the TE mode and 0.37 THz at the TM mode. Compared with the electromagnetic field distributions of PSM_1 with d = 25 µm at 0.19 THz (at the TE mode) and 0.37 THz (at the TM mode) shown in Figure3c,d, the E- and H-field distributions of PSM_2 with d = 12 µm indicate the influence of the CWR. It is obvious that the coupling effect generated by the CWR becomes weaker with the larger distance between the CWR and the SRRs. Therefore, the LSP resonances of 0.19 THz at the TE mode and 0.37 THz at the TM Crystalsmode 20 are20, generated10, x by the SRRs. 9 of 12
FigureFigure 7. 7. TransmissionTransmission spectra spectra of PSM PSM_2_2 by changingchanging ddvalue value at at the the ( a(a)) TE TE and and (b ()b TM) TM modes. modes. Here, Here, (c ) (cand) and (d )(d are) are the the corresponding corresponding E-field E-field and and H-field H-field distributions distributions of PSM_2of PSM with_2 withd = d12 = µ12m μm at TEat TE and and TM TMmodes, modes, respectively respectively (f is (f the is the monitored monitored frequency). frequency).
ToTo investigate investigate the the coupling coupling effect effect betweenbetween thethe distancedistance ofof thethe SRRs SRRs and and the the CWR CWR and and the the width width of ofthe the CWR CWR and and the the incident incident THz THz wave, wave the, the transmission transmission spectra spectra of PSM_2, of PSM_2 obtained, obtained by changing by changing the d theand d aandvalues a values at the at TE the mode TE mode and the and TM the mode, TM mode are shown, are shown in Figure in8 Figurea,b, respectively.s 8a and 8b, The respectively. distance of Thethe distance two SRRs of is the kept two constant SRRs is at kept 5 µm. constant By increasing at 5 μm the. Bya increasingvalue from the 0.5 aµ valuem to 2.5fromµm 0.5 at μm the stepto 2.5 of μm0.5 atµm, the the stepd value of 0.5 will μm, decrease the d value accordingly will decrease from 2.25accordinglyµm to 1.25 fromµm. 2.25 At theμm TEto 1.25 mode, μm. there At arethe twoTE mode,resonances, there are at 0.22 two THz resonances and 0.43, THz,at 0.22 which THz bothand 0. show43 THz, minor which variations both show in resonant minor frequencyvariations andin resonantintensity frequency by simultaneously and intensity changing by simultaneously the a and d values. changing This the indicates a and d thevalues. high This stability indicates obtained the highat the stability TE mode obtained by changing at the the TEa and moded values; by changing the electromagnetic the a and d responses values; the ofPSM_2 electromagnetic are almost responsesthe same. of In PSM_2 other words, are almost the optical the same. behavior In other of PSM_2 words, under the optical the incident behavior THz of wavePSM_2 are under identical the incidentwhen a andTHz dwaveare changed. are identical At thewhen TM a mode,and d theare electromagneticchanged. At the characteristicsTM mode, the showelectromagnetic switchable characteristicselectromagnetic show behavior switchable that can electromagnetic be switched from behavior dual-resonance that can be to switched quad-resonance from dual by-resonance decreasing to quad-resonance by decreasing the a value. There are four resonances, at 0.11 THz, 0.18 THz, 0.34 THz, and 0.45 THz, for a = 0.5 μm and d = 2.25 μm, while three resonances are generated at 0.16 THz, 0.29 THz, and 0.38 THz under the conditions of a = 1.0 μm, d = 2.00 μm and a = 1.5 μm, d = 1.75 μm, and two resonances at 0.22 THz and 0.33 THz under the condition of a = 2.0 μm, d = 1.50 μm and a = 2.5 μm, d = 1.25 μm. The corresponding E- and H-field distributions of PSM_2 with a = 1.5 μm, d = 1.75 μm at the TE and TM modes are summarized in Figures 8c and 8d, respectively. At the TE mode, the E-field is distributed within the middle part of the CWR, except for the areas related to the gaps in the SRRs, and the H-field is distributed around the upper and lower conductor bars of the SRRs, as well as the apexes of the CWR. At the TM mode, the electromagnetic fields are restricted to the contour of the CWR. The electromagnetic field distributions of PSM_2 indicate that the resonances at 0.22 THz at the TE mode and 0.29 THz at the TM mode are LSP resonances. This clarifies that the CWR contributes more at the TM mode. Crystals 2020, 10, 611 9 of 11 the a value. There are four resonances, at 0.11 THz, 0.18 THz, 0.34 THz, and 0.45 THz, for a = 0.5 µm and d = 2.25 µm, while three resonances are generated at 0.16 THz, 0.29 THz, and 0.38 THz under the conditions of a = 1.0 µm, d = 2.00 µm and a = 1.5 µm, d = 1.75 µm, and two resonances at 0.22 THz and 0.33 THz under the condition of a = 2.0 µm, d = 1.50 µm and a = 2.5 µm, d = 1.25 µm. The corresponding E- and H-field distributions of PSM_2 with a = 1.5 µm, d = 1.75 µm at the TE and TM modes are summarized in Figure8c,d, respectively. At the TE mode, the E-field is distributed within the middle part of the CWR, except for the areas related to the gaps in the SRRs, and the H-field is distributed around the upper and lower conductor bars of the SRRs, as well as the apexes of the CWR. At the TM mode, the electromagnetic fields are restricted to the contour of the CWR. The electromagnetic field distributions of PSM_2 indicate that the resonances at 0.22 THz at the TE mode and 0.29 THz at the TM mode are LSP resonances. This clarifies that the CWR contributes more at the TM mode. Crystals 2020, 10, x 10 of 12
FigureFigure 8. 8. TransmissionTransmission spectra spectra of of PSM PSM_2_2 by by changing changing aa andand dd valuevaluess at at the the ( (aa)) TE TE and and ( (bb)) TM TM modes. modes. Here,Here, ( (cc)) and and (d (d) )are are the the corresponding corresponding E- E-fieldfield and and H- H-fieldfield distributions distributions of PSM of PSM_2_2 with with a = a1.5= μm,1.5 µ dm, = 1.75d = 1.75μm atµm TE at and TE andTM TMmodes, modes, respectively respectively (f is (thef is monitored the monitored frequency) frequency)..
4.4. Conclusion Conclusionss InIn conclusion, conclusion, we we have have demonstrated demonstrate twod designstwo designs of PSM devices of PSM by devicesmodifying by the modifying corresponding the correspondingparameters to investigate parameters their to investigate superior electromagnetic their superior propertieselectromagnetic in the THzproperties wave. in The the resonances THz wave of. Theboth resonances devices could of bbeoth tuned devices to be could blue-shifted be tuned or red-shifted to be blue- byshifted changing or red the-shift geometricaled by changing parameters. the geometricalBy changing parameters. the g values, By the changing tuning ranges the g ofvalues, both PSMsthe tuning at the range TE modes of both were PSMs 50 GHz at fromthe TE 0.22 mode THz wereto 0.27 50 THz. GHz The from tuning 0.22 THz ranges to of0.27 PSM_1 THz. were The tuning 40 GHz range froms 0.13 of PSM_1 THz to were 0.17 THz40 G (theHz from first resonance) 0.13 THz toand 0.17 100 THz GHz (the from first 0.34 resonance) THz to 0.44 and THz 100 (the GHz second from 0.34 resonance) THz to at 0.44 the THz TM mode,(the second and those resonance) of PSM_2 at thewere TM 50 mode GHz, fromand th 0.15ose THzof PSM_2 to 0.20 were THz 50 (the GHz first from resonance), 0.15 THz 70to 0.20 GHz THz from (the 0.29 first THz resonance), to 0.36 THz 70 G(theHz secondfrom 0.29 resonance), THz to 0.36 and THz 70 GHz(the second from 0.37 resonance) THz to, 0.44 and THz 70 G (theHz from third 0.37 resonance). THz to 0.44 By changingTHz (the thirdthe polarization resonance). angle By changing between the 0 degrees polarization (TE mode) angle to between 90 degrees 0 degree (TM mode),s (TE mode) the electromagnetic to 90 degrees (TMresponses mode), exhibited the electromagnetic by PSM_1 could responses be manipulated exhibited from by PSM_1 single-resonance could be (atmanipulated the TE mode) from to singledual-resonance-resonance (at (at the the TM TE mode), mode) whileto dual the-resonance electromagnetic (at the responsesTM mode), exhibited while the by electromagnetic PSM_2 could be responsesswitched fromexhibited single-resonance by PSM_2(at could the TE be mode) switched to triple-resonance from single-resonance (at the TM (at mode). the TE This mode) indicates to triplethat both-resonance PSM devices (at the show TM polarization mode). This switching indicates characteristics. that both ByPSM changing devices the shows value polarization from 0 µm switchingto 40 µm, the characteristics. electromagnetic By responses changing of the PSM_1 s value show from a switch 0 μm characteristic to 40 μm that, the can electromagnetic be manipulated responses of PSM_1 show a switch characteristic that can be manipulated from single-resonance to triple-resonance at the TE mode and from dual-resonance to triple-resonance at the TM mode, and PSM_2 exhibits a switch characteristic that can be switched from single-resonance to triple-resonance at the TE mode and from dual-resonance to quad-resonance at the TM mode. Furthermore, PSM_2 shows stability at the TE mode and exhibits a switchable characteristic that can be manipulated between dual-resonance, triple-resonance, and quad-resonance at the TM mode by simultaneously changing the a and d values. The proposed PSM devices exhibit polarization-sensitive characteristics, which can be made more controllable and exhibit better optical performance. Such designs with multiband resonance are desirable for THz-wave applications, such as tunable polarizers, high-sensitive sensors, multispectral imagers, polarization-sensitive devices, multifunctional switches, and so on.
Author Contributions: Conceptualization, X.C. and Y.-S.L.; methodology, X.C. and Y.-S.L.; software, X.C.; validation, X.C. and Y.-S.L.; formal analysis, X.C. and Y.-S.L.; investigation, X.C. and Y.-S.L.; resources, X.C. and Y.-S.L.; data curation, X.C. and Y.-S.L.; writing—original draft preparation, X.C. and Y.-S.L.; writing—review Crystals 2020, 10, 611 10 of 11 from single-resonance to triple-resonance at the TE mode and from dual-resonance to triple-resonance at the TM mode, and PSM_2 exhibits a switch characteristic that can be switched from single-resonance to triple-resonance at the TE mode and from dual-resonance to quad-resonance at the TM mode. Furthermore, PSM_2 shows stability at the TE mode and exhibits a switchable characteristic that can be manipulated between dual-resonance, triple-resonance, and quad-resonance at the TM mode by simultaneously changing the a and d values. The proposed PSM devices exhibit polarization-sensitive characteristics, which can be made more controllable and exhibit better optical performance. Such designs with multiband resonance are desirable for THz-wave applications, such as tunable polarizers, high-sensitive sensors, multispectral imagers, polarization-sensitive devices, multifunctional switches, and so on.
Author Contributions: Conceptualization, X.C. and Y.-S.L.; methodology, X.C. and Y.-S.L.; software, X.C.; validation, X.C. and Y.-S.L.; formal analysis, X.C. and Y.-S.L.; investigation, X.C. and Y.-S.L.; resources, X.C. and Y.-S.L.; data curation, X.C. and Y.-S.L.; writing—original draft preparation, X.C. and Y.-S.L.; writing—review and editing, X.C. and Y.-S.L.; visualization, X.C. and Y.-S.L.; supervision, Y.-S.L.; project administration, Y.-S.L.; funding acquisition, Y.-S.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the financial support from the National Key Research and Development Program of China (2019YFA0705000). Conflicts of Interest: The authors declare no conflict of interest.
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