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Abstract
Metamaterials that offer optical control over multiple transparency windows have paved the way for advancements in terahertz (THz) modulation technology. In this paper, we have conducted a systematic investigation into the interaction between THz waves and “bright” split-ring resonators (SRRs). Through manipulation of the quantity and spatial arrangement of SRRs within metamaterial structures, we have successfully induced multiple transparency windows within the THz spectrum. Furthermore, we have explored the transmitted switching ratio of both the designed single transparency window and double resonance frequency bands as a function of the azimuthal angle of the THz wave. This work offers a general strategy for designing the number of electromagnetically induced transparency windows and holds the potential for realizing multichannel memories.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials are artificial structures composed of periodic arrays of subwavelength units [1–7]. Recently, owing to the significant advantage of metamaterials, many studies have focused on their versatile and remarkable effects, such as sub-diffraction focusing, sensing, and near-perfect absorption [8–12]. Among them, metamaterials-based transparency window has tremendous potential for applications [13–15]. Electromagnetically induced transparency is a quantum phenomenon that arises from the destructive interference between different excitation paths in a three-level atomic system, causing the initially opaque medium to become transparent [16,17]. In the past, achieving such induced transparency required highly stringent laboratory conditions, including low-temperature environments and high-intensity laser irradiation, making practical applications challenging. In recent years, owing to the rapid advancement of metamaterial technology [18,19], the sharp dispersion and significant group refractive index characteristics exhibited by metamaterials have enabled the realization of electromagnetically induced transparency within mild experimental conditions [20–23].
Metamaterials with transparency window characteristics have been widely found in cut wires, bilayer fish-scales, and SRRs [24–27]. Such as, Zhang et al. have achieved the phenomenon of a single transparency window for the first time by employing metamaterial resonators structured with parallel arrangements of metal strips [28]. Gu et al. demonstrated an on-to-off single transparency switch by using the destructive interference between cut wires resonator and SRRs [29]. Wang et al. realized double electromagnetic induced transparency window using metamaterials consisting of two asymmetric T-shaped resonators [30]. Subsequently, pursuing multiple windows has also attracted considerable attention [31–34]. Zhao et al. theoretically explored the possibility of triple-transparency windows. Their proposed structure was made of two vertical and two horizontal semimetal strips [35]. A few tunable plasmon-induced transparency metamaterials design with optically or electrically controlled regimes were reported as the potential solutions realization of multiple transparency windows [36–39]. Although significant effort has been devoted to various designs of cut wires and SRR metamaterials for realizing multiple transparency windows [40–45], precisely controlling the number of transparency windows is still a challenge.
In this work, we have achieved transparency windows spanning multiple terahertz frequency bands through precise manipulation of both the arrangement and quantity of SRRs incorporated within metamaterial structures. The response of the metamaterials to electromagnetic fields was analyzed through the study of couplings and resonances. The designed structures modulated multiple transparency windows owing to the phenomenon of destructive interference among resonators with varying SRRs dimensions (bright mode). Furthermore, by adjusting the azimuthal angle of the incident THz wave in relation to the metamaterial, we successfully realized transmission switching ratio modulation. By systematically varying the factors influencing resonance, we investigated the transition from single to triple transparency windows. This work introduces novel avenues for realizing multi-frequency bands THz devices and modulators.
2. Structure and design
Firstly, we achieved single transparency window by designing basic unit of Two SRRs (TSRRs) metamaterials. As shown in Fig. 1(a), the basic unit of the metamaterial is composed of the first SRR and the second SRR with different size, on a 500 µm thick SiO2. The metamaterial is made of 200 nm-thick aluminium. The size of the entire metamaterial array is 9.54 mm × 9.54 mm, which is fabricated via photolithography as shown in Figs. S2. The preparation processes are described in detail in the Supplement 1. The unit cells of the fabricated metamaterials are shown in Figs. 1(b)-(d).
Fig. 1. (a) Schematic drawing of the single-window-transparency metamaterial. $\varphi $ is the azimuthal angle of the incident electric field polarization direction relative to the x-axis, the schematic of the corresponding unit cell with the relevant geometrical dimensions are: ${{P}_{x}}{ = }{{P}_{y}}{ = 106}$ µm, ${{L}_{1}}{ = 100}$µm, ${{L}_{{2}}}{ = 80}$µm, ${{w}_{1}}{ = }{{l}_{1}}{ = }{{w}_{2}}{ = 5}$µm, and ${{l}_{2}}{ = 3}$µm, ${{g}_{1}}$ =${{g}_{2}}$ = 52 µm. Unit cells of the fabricated (b) First SRR, (c) Second SRR, and (d) TSRRs. (e) The simulated spectra for the first SRR metamaterial (blue shot dash line), second SRR metamaterial (black dot line), and TSRRs metamaterial (red solid line).
CST Microwave Studio simulations show the transmission spectra and electric field distributions of these metamaterial structures. In the simulation, the relative permittivity of SiO2 substrate is set to 3.58. The linearly polarized incident wave is perpendicular to the metamaterial surface. All measurements are carried out using a transmission-type THz time-domain spectroscopy system (THz-TDS), as shown in Fig. S1. This system has a bandwidth of 0.1 THz to 2.0 THz by Fourier transform. A bare SiO2 substrate without metamaterial is used as the reference. The THz-TDS system test processes are described in the Supplement 1.
3. Results and discussion
Figure 1(e) shows the simulated transmission spectra of the first SRR metamaterial (short dash line), the second SRR metamaterial (dot line), and the TSRRs metamaterial (solid line) under xx-polarized incidences, respectively. Figure 2 presents the simulated transmission spectra of the first SRR, second SRR, TSRRs metamaterials, and the experimental transmission spectra of TSRRs metamaterial, respectively. When the polarization of the incident wave is x-orientation polarization (XOP), the first SRR gap will exhibit a transmission dip at 0.62 THz, as shown in Fig. 2(a). The coupling of the incident THz wave and the collective resonance of the free electrons in the metal surface leads to a low-Q (Q = 2.53) resonance for the first SRR metamaterial, which is called bright mode (Fig. 2(b)). For the second SRR metamaterial, the strong electric fields at 1.05 THz are localized at the two ends, corresponding to a low-Q (Q = 4.2) resonance, which is called bright mode [Fig. 2(d)]. For the TSRRs metamaterial, a sharp transparency window occurs at 0.80 THz, as shown in Fig. 2(e). A huge enhancement of the electric field was achieved as shown in Fig. 2(f). The first transmission dip (0.62 THz) and the second transmission dip (1.05 THz) stem from the resonances associated with the first SRR and second SRR, respectively. The difference between the experimental and simulated results can be attributed to defects introduced during the metamaterial manufacturing process [46], as well as errors in the parameters related to dispersion and substrate dielectric loss in the simulation.
Fig. 2. Simulated transmission spectra of (a) the first SRR metamaterial only and (c) the second SRR metamaterial only under XOP incident radiation. (e) Experimented (black solid line) and simulated (red solid line) transmission spectra of the TSRRs metamaterial under XOP incident radiation, the green dash-dot line represents the normalized theory modeled transmission using the coupled oscillator model. Electric field enhancement for the first SRR gap at (b) 0.62 THz, (d) second SRR at 1.05 THz, and (f) TSRR at 0.80 THz under the XOP incidence.
Next, A simple coupled two-oscillator model is employed to elucidate the coupling effect between the “bright” first SRR mode and the “bright” second SRR mode in the TSRRs metamaterial [11,13]. The first SRR unit is represented by oscillator a, the second SRR unit is represented by oscillator b [47].
Here, ${{x}_{a}}$, ${{x}_{b}}$, ${{\eta }_{a}}{ = Q/M}$ and ${{\eta }_{b}}{ = q/m}$ are their amplitudes and coupling strengths with the incident THz electric field ${E}$. (Q, q), (M, m), (${{\gamma }_{a}}$, ${{\gamma }_{b}}$) and (${{\omega }_{a}}$, ${{\omega }_{b}}$) are the effective charge, effective mass, loss factors, and resonance angular frequencies of the oscillators a and b, where ${q = Q/A}$ and ${m = M/B}$ with A and B being the dimensionless constants that dictate the relative coupling of the incident field with the “bright” first SRR mode and “bright” second SRR modes. A is the ratio of the intensity of the interaction between the two oscillators, and B is the ratio of the two oscillators mass. ${\kappa }$ is the coupling coefficient between these two bright modes. Now by expressing the displacements vectors for oscillators a and b as ${{x}_{a}}{ = }{{c}_{a}}{{e}^{{i\omega t}}}$ and ${{x}_{{b }}}{ = }{{c}_{b}}{{e}^{{i\omega t}}}$, we solve the above coupled equations (1) and (2) for ${{x}_{a}}$ and ${{x}_{b}}$:
The susceptibility χ, which relates the polarization (P) of the two oscillators to the strength of the incident electric field (${E}$), can thus be calculated as [11]
The simulated transmission in Fig. 2(e) is fitted by the imaginary part of the nonlinear susceptibility express. ${Re(\chi )}$ represents dispersion and ${Im(\chi )}$ represents the loss (absorption) within the metamaterial. In our fitting, the transmission spectra can be fitted using ${{T}_{{theory}}}{ =\ 1 -\ Im(\chi )}$ (given by the Kramers-Kronig relations) [1]. ${{\gamma }_{a}}$ and ${{\gamma }_{b}}$ are obtained from the linewidth (full width at half maximum bandwidth) of the transmission dips shown in Fig. 2(e) (red line), which are around ${1}{.54\, \times \, 1}{{0}^{{12}}}$ rad/s (0.245 THz) and ${1}{.57\, \times \, 1}{{0}^{{12}}}$ rad/s (0.25 THz), respectively [13]. Then, we use ${{\omega }_{a}}{ = }\sqrt {{\omega }_{0}^{2}{ - }{{\kappa }^{2}}} $ to get ${\kappa =\ 3}{.14\, \times \, 1}{{0}^{{12}}}$ rad/s (0.50 THz). ${{\omega }_{0}}$ is the frequency of the transparency window. ${{\omega }_{a}}$ and ${{\omega }_{b}}$ are the resonance frequencies of oscillator a and oscillator b, which are around ${3}{.89\, \times \, 1}{{0}^{{12}}}$ rad/s (0.62 THz) and ${6}{.6\, \times \, 1}{{0}^{{12}}}$ rad/s (1.05 THz), respectively. By substituting the calculated values of ${{\gamma }_{a}}$, ${{\gamma }_{b}}$, ${{\omega }_{a}}$, ${{\omega }_{b}}$, ${\kappa }$, and setting A = 0.98, B = 1.78, amplitude offset coefficient K = (Q^2ε0)/m = 0.37, we plotted the theoretical transmission spectrum in Fig. 2(e) (green dash-dot line), which exhibits good agreement with the experimental and simulated results (more details about coupled two-oscillator model are shown in Supplement 1).
The transmission property of the single-window-transparency TSRRs metamaterial under different azimuthal angle ${\varphi }$ of the incident THz wave is further investigated. The transmitted time-domain pulses and the corresponding normalized transmission spectra in the frequency domain are shown in Figs. 3(a) and 3(b), respectively. When the azimuthal angle is 0 deg, a pronounced subsidiary wave packet with slow group velocity is observed following the main pulse in the time domain. In the corresponding frequency domain, two resonance dips are observed at 0.62 THz and 1.05 THz. As the azimuthal angle of the incident THz wave is gradually increased from 0 deg to 90 deg, the primary wave packet at 3 ps-4.5 ps increases, and the subsidiary wave packet at 4.5 ps-6 ps decreases (inset of Fig. 3(a)). Therefore, the corresponding transmission undergoes modulation, as shown in Figs. 3(a) and (b), respectively. When the azimuthal angle is 90 deg, the time-domain subsidiary wave packet completely disappears, and the TSRRs are perpendicular to the direction of the incident THz electric field. The TSRRs unit exhibits dark mode with almost no significant effect on the transmission. No response was observed in the transmission spectra. The characterization of azimuthal angles dependence of the single-window-transparency TSRRs switching behavior is of significant practical importance for the development of corresponding metamaterials. To this end, we calculated the switching ratio at the THz frequency bands. Figure 3(c) shows the corresponding simulated transmission switching ratio of the TSRRs metamaterial with different azimuthal angles. Transmission switching ratio was calculated from the transmission spectra as $TSR = \frac{{|{{T_\varphi } - {T_0}} |}}{{{T_0}}}$, where ${T_\varphi }$ and ${T_0}$ is the transmission coefficient at different azimuthal angles $\varphi $ and x-polarized incidences ($\varphi = 0$), respectively. A strong transmission switching ratio is identified: the TSR reaches an extraordinary value of ∼ 43 when azimuthal angle was increased to 90 deg at two resonance frequencies, as shown in Fig. 4. We next study the general strategy of the THz multiple-transparency-windows metamaterials with the various combinations of SRRs.
Fig. 3. Active control of the transparency window of the TSRRs metamaterial. (a) Simulated transmitted time-domain signals and (b) corresponding normalized Fourier transformed transmission spectra. (c) Simulated results of the transmission switching ratio of the single-window-transparency TSRRs metamaterial with different azimuthal angles ${\varphi }$ of the incident THz wave. The schematic diagram in the upper right represents the azimuthal angle when terahertz are incident on the metamaterial.
Fig. 4. Azimuthal angle dependences of the maximum switching ratio at the two resonance frequencies of 0.62 THz and 1.05 THz.
Here, a factor m was employed to represent the combination of the excitation resonance in the metamaterials, where m is the number of “bright” SRR resonators. Therefore, the factor of this single-window-transparency metamaterial will be m = 2. Further adjustments of the coupling factor m, were applied for tuning the multiple -transparency-windows spectra to realize more resonators. The multiple -transparency-windows spectra of the metamaterials we will discuss next are all under the XOP polarization of the incident wave.
An extra SRR (third SRR) (${{L}_{3}}{ = 60}$ µm) is added in the single-window-transparency TSRR metamaterial, as shown in Fig. 5(a), This unit cell of the proposed metamaterial is composed of three SRR (ThSRRs). Here, the “bright” SRR factor is ${m}$ = 3. Figure 5(b) and (c) show the transmission spectra of the ThSRRs metamaterial, one can observe that three transmission dips stem from the resonances associated with each resonator (first to third SRR), and two transparency windows appear at 0.82 THz and 1.15 THz due to interaction between these SRRs. One can clearly observe that the second transmission peak of ThSRRs stems from the coupling associated with TSRRs and the extra SRR. This behavior is further analyzed by simulating the electric field intensity distributions at three transmission dips (0.62 THz, 1.02 THz, 1.38 THz), as shown in Figs. 5(d)-(f). The SRR is strongly excited by the incident wave at the first resonant frequency of 0.62 THz. Counting from outside to inside, the second SRR is excited by the incident wave at the second resonant frequency of 1.02 THz, while the electric field primarily concentrates on the third SRR at the third resonant frequency of 1.38 THz. Thus, it results in the double-windows-transparency.
Fig. 5. (a) Schematic drawing of the double-windows-transparency metamaterial (ThSRRs). (b) Simulated transmission spectra for the TSRRs metamaterial (green shot dash line), one extra SRR (third SRR) metamaterial (black dot line), and ThSRRs metamaterial (red solid line). ${{L}_{3}} $= 60 µm, ${{g}_{3}}{ = 36}$ µm, ${{w}_{3}}{ = }{{l}_{3}}{ = 5}$ µm. The inset figure represents the unit cell of the extra SRR (third SRR). (c) Experimented (black solid line) and simulated (red solid line) transmission spectra of the ThSRRs metamaterial under XOP incident radiation. (d)-(f) Electric field distribution at three resonant frequencies of the double-windows-transparency ThSRRs metamaterial.
Next, the same analysis has been conducted on the triple-windows-transparency metamaterial. The fourth SRR (${{L}_{4}}{ = 40}$ µm) is added in the double-window-transparency ThSRR metamaterial, as shown in Fig. 6(a), This unit cell of the proposed metamaterial is composed of four SRR (FSRRs). Here, the “bright” SRR factor is ${m}$ = 4. Figure 6(b) and (c) show the transmission spectra of the FSRRs metamaterial, one can observe that the four transmission dips stem from the resonances associated with each resonator, and three transparency windows appear at 0.81 THz, 1.13 THz, and 1.46 THz due to interaction between four SRRs. The black dot line green shot dash line in Fig. 6(b) shows that the fourth SRR exhibits a transmission dip at 1.5 THz. The green shot dash line in Fig. 6(b) shows that the metamaterial composed of three SRRs exhibits two transmission dips, and the foutth transmission dip is at 1.64 THz. One can clearly observe that the first and fourth transmission dips of FSRRs stem from the resonances associated with four SRRs, and three transparency window appears. This behavior is further analyzed by simulating the electric field intensity distributions at four transmission dips (0.62 THz, 1.01 THz, 1.35 THz, and 1.64 THz), as shown in Figs. 6(d)-(g). The first SRR exhibits a transmission dip at around 0.62 THz, which arises from the excitation of the SR mode resonance, as shown in Fig. 6(d). At the second resonant frequency of 1.01 THz [Fig. 6(e)], one can observe that the transmission dip stems from the resonance associated with the second SRR. At the third and fourth resonant frequencies of 1.35 THz and 1.64 THz (Figs. 6(f) and (g)), the transmission dips arise from the excitation of the third and fourth SRRs, respectively. Thus, it results in triple-windows transparency.
Fig. 6. (a) Schematic drawing of the triple-windows-transparency metamaterial (FSRRs). (b) Simulated transmission spectra for the ThSRRs metamaterial (green shot dash line), the fourth SRR metamaterial (black dot line), and FSRRs metamaterial (red solid line). ${{L}_{4}} $= 40 µm, ${{g}_{4}}{ = 6}$ µm, ${{w}_{4}}{ = }{{l}_{4}}{ = 5}$ µm. The inset figure represents the unit cell of the extra SRR (fourth SRR). (c) Experimented (black solid line) and simulated (red solid line) transmission spectra of the FSRRs metamaterial under XOP incident radiation. (d)-(g) Electric field distribution at four resonant frequencies of the triple-windows-transparency FSRRs metamaterial.
Further adjustments of the number of bright modes were applied for tuning the multiple-windows-transparency spectra to realize more resonators. The multiple-windows-transparency spectra of the metamaterials we will discuss next are all under the XOP polarization of the incident wave.
4. Conclusion
In summary, our research is focused on the investigation of multi transparency windows achieved through the manipulation of THz bands using metamaterials. We first examined the metamaterial with a single transparency window, utilizing the bright mode of the SRR. And the transmission switching ratio of the single transparency window and two resonance dips is demonstrated by tuning the azimuthal angle of the incident THz wave. Through adjusting the introduced resonance mode factor, we explored the evolution of metamaterial from single to triple transparency windows or the so-called multiple transparency windows. This work shows the controllability of the number of multiple transparency windows by coupling multiple “bright” SRR modes in the THz regime and the availability of the proposed general strategy for effectively designing multiple-transparency-windows.
Acknowledgments
The authors would like to acknowledge the support from the failure analysis team at the Shanghai Institute of Precision Measurement and Testing for providing experimental equipment and offering technical assistance.
Disclosures
The authors declare no conflicts 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.
Supplemental document
See Supplement 1 for supporting content.
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