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Abstract
In this paper, a terahertz metamaterial structure with multiple physical features such as EIT-like resonance, Fano resonance, and terahertz wave absorption, is implemented. The device consists of a metal structure and a GaAs layer. The conductivity of GaAs can be adjusted by optical pump. When the conductivity of GaAs is 10 S/m, with the TE polarization wave incenting, the Fano resonance formed, and when the TM polarization wave was incenting, the EIT-like resonance formed. Modulation of the resonance can be achieved by adjusting the conductivity of GaAs, and a maximum modulation depth of 96.5% is obtained. When the conductivity of GaAs is 2 × 105 S/m, a double narrow-band absorption is obtained with TM polarization wave exciting. The maximum sensitivity reaches 513 GHz/RIU and the maximum FOM value reaches 39.5, which indicates that the device has excellent performance in refractive index sensing. The device also has a wide range of applications in terahertz sensors, slow-light devices, and terahertz modulators.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials are artificially designed sub-wavelength structures that have specific properties that natural cannot possess [1]. Compared to conventional materials, many applications have been proposed based on metamaterials, such as superlenses [2], perfect absorbers [3], Fano modulators [4] and EIT modulators [5]. Electromagnetically induced transparency (EIT) is a type of quantum interference in three-level atomic systems [6–8], resulting in reduced light absorption at the atomic resonance frequency [9–11]. The bright mode can be directly excited by the incident electromagnetic wave, while the dark mode cannot be directly excited. When the two resonators are cross-coupled, the dark mode will be excited by bright mode near-field coupling, while the bright mode will be offsetted and suppressed, and a transparent window obtained [12–14]. Fano resonance also the is the result of coupling between resonators originated from atomic systems, which have asymmetric spectral. [15–17]. In general, the dipolar (D) plasmon resonance with high radiative loss as the bright mode, which can be directly excited with incident electromagnetic wave. The higher order resonances such as quadrupolar(Q), octupolar(O), hexadecapolar(H) serve as the dark mode [18–22]. Metamaterials can also realize other application such as wave absorption by matching the resistance of free space [23,24].
In recent years, many researchers have proposed multiple function devices to achieve both EIT-like and Fano effects. In 2020, He et al. achieved double resonance effects of EIT-like and Fano using metal split rings [25]. In 2021, Shi et al. achieved modulation of Fano using InSb temperature-controlled materials with a modulation depth of 80% [26]. In 2021, Tan et al. achieved two functions that it possess excellent dual-band filter and switch device [27]. In 2019, Mao et al. implement broadband absorbers and polarization converters using graphene and VO2 [28].
Metamaterial narrow band absorbers can be used in a wide range of sensing applications. Metamaterial-based optical refractive index sensors have shown great potential for applications in biomedicine, disease diagnosis and drug delivery [29–31]. Compared to conventional sensing technologies, optical refractive index sensors offer the advantages of label-free biochemical detection, real-time detection and high sensing performance [32–34]. In 2022, Lai et al. proposed a triple-band terahertz absorber, which sensitivity is 125 GHz/RIU [35]. In 2022, Xiong et al. designed a terahertz sensor that sensitivity reach 208 GHz/RIU [36].
However, these metasurfaces can only achieve single or integrated two functions. Few metamaterials can realize triple-function. The work proposed a metamaterial device (GAM) with composite structure composed of metal structure and GaAs. When no optical pump incenting, the Fano resonance obtained under the incidence of TE wave and EIT-like resonance obtained under the incidence of TM wave. Fano resonances are caused by dipolar and octupolar coupling, while EIT-like resonances are originated from the coupling of bright and dark resonators. When incident optical pump energy is higher than the band gap of GaAs, the device appeared the characteristic of double narrow-band absorption. The EIT-like and Fano are modulated by light pumping, and a maximum modulation depth of 96.5% obtained. The sensitivity of the GAM device in the absorber reached a maximum of 513 GHz/RIU. The device has potential for applications in modulation, sensing, optical switching, etc.
2. Structure and methods
Figure. 1 shows a schematic diagram of the unit structure of the proposed GAM. The structure consists of ring and rectangle made of metallic gold. The underside is a GaAs film with a thickness of 2 µm. The conductivity of gold is 4.56${\times} $107 S/m. The semiconductor GaAs with a tunable conductivity dependent on the incident optical pump [37]. When the optical pump energy is higher than the band gap of GaAs, free carriers are generated. The time of existence of these photogenerated carriers (consisting of free electrons and holes) is determined by the recombination time. GaAs is a direct bandgap semiconductor, its generation and recombination of photogenerated carrier concentrations is relatively fast. For GaAs grown by molecular beam epitaxy (MBE), the excitation time and presence time of photogenerated carriers reach sub-picosecond levels [38]. The conductivity of GaAs can be described by the following Drude model [39]:
Where $\omega _p^2 = {{n{e^2}} / {{\varepsilon _0}{m^\ast }}}$, ${\omega _p}$ is the plasma oscillation frequency, ${\varepsilon _0}$ is the permittivity of free space, n is the density of photogenerated carriers and ${m^\ast }$ is the effective carrier mass.
Fig. 1. Schematic diagram of the proposed structural unit (a) side view (b) top view, with the relevant dimensions: p = 200 µm, t1 = 2 µm, t2 = 18 µm, t3 = 20 µm, r1 = 60 µm, r2 = 90 µm, l1 = 30 µm, l2 = 80 µm.
The pump beam in the work is a near-infrared laser pulse with a central wavelength of 800 nm with repetition rate of 1KHz, and that this optical pumping can directly excite charge carriers across the 1.42 eV bandgap of GaAs [40]. In the simulations, the conductivity of GaAs can be considered to be 10 S/m when there are no optical pump illuminate on the GaAs. When the energy of optical pump reach large enough, the conductivity of GaAs increases to 2 × 105 S/m rapidly.
3. Simulation and discussion
The device is simulated by using finite element method, unit cell boundary conditions (unit cell) were adopted in X and Y directions, and open boundary conditions (add space) were used in Z direction. The results are shown in Fig. 2. When the conductivity of GaAs is 10 S/m, the EIT-like resonance was obtained under TM polarized THz wave (blue thread). And the Fano resonance was obtained under TE polarized THz wave (red thread). When the conductivity of GaAs is 2 × 105 S/m, two narrow-band absorption peaks appear under the TM polarization incident (black thread). The proposed metamaterials can achieve EIT-like or Fano resonance conversion with excitation of different polarizations terahertz wave. In addition, it also can achieve dual narrow-band absorption by adjusting the conductivity of GaAs. A multi-functional design that can make the optoelectronic device more novel and intelligent.
Fig. 2. Transmission and absorption spectrums of the GAM at different conductivities of GaAs and different polarization incidences.
In order to analyze principle of EIT-like resonance, we give transmission spectra and electric field distribution in the XOY plane as shown in Fig. 3. It can be seen in Fig. 3(a), the single ring resonator has a significant resonance at 0.764 THz, which indicates that ring is as bright resonator (red thread). The strip does not in resonance state at 0.764 THz, which act as dark resonator (blue thread). When ring and strip are combined together, a typical EIT-like phenomenon induced with a clearly transparency window at 0.77 THz (black thread). To understand the mechanism of EIT-like, the electric field distribution for the single resonator and EIT-like resonator are shown in Fig. 3(b-d). As seen from Fig. 3(c), electric field mainly concentrate on outer ring (bright resonator). The strip resonator (dark resonator) in Fig. 3(d) did not have significant electric field. However, due to near-field coupling between bright resonator and dark resonator, the electric field mainly concentrate on strip. Therefore, the transparency window of the EIT-like is a direct consequence of spectral combination of the bright resonator and the dark resonator.
Fig. 3. (a) Simulated transmission spectra for the combined EIT-like, the sole ring, and the sole strip, respectively. (b)-(d) The electric field distribution at combined EIT-like, the sole ring, and the sole strip.
The transmission spectrum, modulation depth and group time delay of the structure were calculated under different conductivities of GaAs for investigating the modulation effect of EIT-like resonance by GaAs as shown in Fig. 4. As the conductivity of GaAs increasing, the amplitude of the EIT-like resonance gradually decreases. When the conductivity of GaAs increases to 1000 S/m, the EIT-like resonance almost disappears as seen in Fig. 4(a).
Fig. 4. (a) EIT-like resonance amplitude at different conductivities of GaAs (b) Modulation depth of dip1 and dip2 at different conductivity of GaAs (c) (d) Group time delay of this device at different conductivity of GaAs.
The modulation depth for dip1 and dip2 were also calculated in order to quantify the modulation effect, the modulation depth (Md) can be defined as [41]: $Md = ({T_{MAX}} - {T_L})/{T_{MAX}}$,here ${T_L}$ is the transmission amplitude at different conductivity of GaAs, ${T_{MAX}}$ is the maximum transmittance amplitude at dip1 and dip2.
From Fig. 4(b), as the conductivity of GaAs increasing, the depth of its modulation of the EIT-like resonance gradually increases, reaching a maximum value of 94.6%. It is well known that EIT-like resonance is accompanied by a slow light effect. The slow light effect of metamaterials can be described by the group time delay (${t_g}$) [42,43]: ${t_g} = {{ - d\varphi (\omega )} / {d\omega }}$, where $\varphi (\omega )$ is the phase at different frequencies. As seen in Fig. 4(c), the group time delay reaches maximum value when the conductivity of GaAs is 10 S/m, reaching 2.03 ps. In Fig. 4(d), the group time delay decreases as the conductivity of GaAs increases, the group delay close to 0 ps when the conductivity of GaAs increases to 1000 S/m.
In order to investigate the influence of GaAs conductivity on the EIT-like resonance, the coupling model was used to fit the EIT-like resonance theory. The interference and coupling of EIT-like resonances in metamaterials can be analyzed by means of the coupled differential equations [44,45]:
where ${x_1}$ and ${x_2}$ represent the amplitudes of the two resonators, ${\gamma _1}$ and ${\gamma _2}$ represent the losses of the two oscillators, respectively. $\delta $ is the detuning between the resonators, and $\kappa $ is the coupling factor between the two resonators. By solving Eqs. (2) and (3), the susceptibility $\chi $ is obtained as:Since the energy loss is related to the imaginary part of the $\chi $, the transmittance amplitude can be expressed as:
Where $\textrm{g}$ represents the coupling strength of the proposed metamaterial device to the incident terahertz wave.The above equations can be fitted to obtain the loss and coupling strength of the EIT-like resonance under different GaAs conductivities. From Fig. 5 it can be seen that the loss of ${\gamma _1}$ increases from 1.2 to 9.2 as the conductivity increasing, but $\kappa $ and ${\gamma _2}$ remain almost unchanged. In practical applications, the increase of loss is due to the increasing in concentration of photogenerated carriers as the luminous flux increases, which leads to an increase in conductivity and ultimately to a decrease in resonant transmission amplitude, which is consistent with the change in Fig. 4(a).
The transmission spectra under the excitation of TE-polarized wave is show in Fig. 6(a). It can be seen that the transmission spectra possess clearly asymmetrical line. To analyze the mechanism of the higher order Fano resonances under the excitation of TE-polarized waves, the electric field distribution of the z-component are shown in Fig. 6(b)-(c). As seen in Fig. 6(b), the electric field is mainly concentrated on the upper and lower sides of the ring, forming a pair of dipolar. And we can observe octupolar from Fig. 6(c). The Fano resonance is formed by dipolar and octupolar coupling.
Fig. 6. (a) The simulated transmission spectra for the TE-polarized incidence wave. (b)-(c) The electric distribution at 0.738THz and 1.276THz.
Similarly, we modulated the Fano resonance by adjusting the conductivity of GaAs. As seen in Fig. 7(a), the Fano resonance amplitude gradually becomes smaller as increasing of GaAs conductivity, and the Fano resonance disappears when the conductivity of GaAs increases to 1000 S/m. The modulation depths of dip1 and dip2 for Fano resonance under different conductivities are shown in Fig. 7(b). It can be seen that as the conductivity of GaAs increases the modulation amplitude of dip1 gradually increases to a maximum modulation depth of 96.5%. However, the modulation depth of dip 2 increases first and then decreases with the increasing of conductivity, and the maximum modulation depth is 63.8%. The Fano resonance is also accompanied with slow light effect. Figure. 7(c) and (d) describes the group delay for different GaAs conductivities. It can be seen that the group delay decreases as the GaAs conductivity increases. The maximum group delay is 1.71 ps. When the conductivity of GaAs increases to 1000 S/m, the group delay close to 0 ps.
Fig. 7. (a) Fano resonance amplitude at different conductivities of GaAs (b) Modulation depth of dip1 and dip2 at different conductivities of GaAs (c) (d) Group delay of GAM device at different conductivities of GaAs.
To investigate the effect of GaAs conductivity variations on the GAM, a theoretical fit to the Fano resonance was carried out using a coupled model. The variation of the fitted parameters for different GaAs conductivities is shown in Fig. 8. It is seen from the figure that as the GaAs conductivity increases, ${\gamma _1}$ hardly changes, while ${\gamma _2}$ increases from 1.2 to 9.18 THz. The increase in loss leads to a decrease in transmission, which is exactly in line with the change in transmission amplitude in Fig. 7(a).
In recent years, the performance comparison between different modulators is shown in Table 1.
Table 1. Comparison between different modulators
The GAM device shows two absorption peaks above 93% at 1.61 THz and 1.74 THz as conductivity of GaAs is 2 × 105 S/m as shown in Fig. 9(a). Narrowband absorbers have potential applications for sensing in the terahertz field. Therefore, we investigate the sensing characteristics of the GAM by varying the thickness and refractive index of the surrounding medium. In the simulation, the refractive index of the material to be measured is fixed at 1.3 and the transmission spectra of different thicknesses of the material to be measured are simulated as shown in Fig. 9(b). Commonly, the thickness of the object to be measured is within 20 $\mathrm{\mu} m$, and the thickness of the object to be measured in the simulation is set to 0-20 $\mathrm{\mu} m$. It can be seen from the graph, as the thickness of the object to be measured increasing, the resonant frequency shift also increases. The maximum resonance shift reached when the thickness of the object to be measured is 20 $\mathrm{\mu} m$, and therefore 20 $\mathrm{\mu} m$ is chosen in the subsequent analysis. Figure. 9(c) shows the frequency shift of peaks 1 and 2 relative to the refractive index. It was clearly observed that the frequency shift increases linearly with refractive index. Thus, the GAM device demonstrated a promising application for refractive index sensing. The main parameters for assessing the performance of a high quality sensor are the sensitivity (S) and the FOM value, which are defined as [49]: $S = {{\Delta f} / {\Delta n}}$, $FOM = {S / {FWHM}}$. Where $\Delta f$ is the frequency shift for substances with different refractive indices, FWHM is Half-wave width. With Fig. 9(c), the refractive index sensitivities of peak1 and peak2 can be calculated, S(peak1) = 513 GHz/RIU, S(peak2) = 494 GHz/RIU. FOM value also can be calculated, FOM(peak1) = 12.1, FOM(peak2) = 39.5. This shows that the sensor has a good sensing performance. For a wider range of application field, the absorption properties of different polarization angles are worth investigating. The absorption properties at different polarization angles are shown in Fig. 9(d). It can be seen that the two absorption peaks can still maintain high absorption at different polarization angles, which means that the dual narrowband absorber proposed in this paper is polarization insensitive.
Fig. 9. (a) Absorption spectra of the GMA device (b) Frequency shifts for different refractive indices (c) Sensitivity of the device peak1 and peak2 (d) Absorption spectra of the device at different polarization angles
The performance comparison between different absorption sensors is shown in Table 2.
Table 2. Comparison of the performance in different absorption sensors
4. Conclusion
In summary, a novel GaAs-based tunable multifunctional device is proposed. When the conductivity of GaAs is 10S/m, EIT-like resonance is formed under TM polarization wave excitation, while Fano resonance is formed under TE polarization wave excitation. When conductivity of GaAs increases to 2 × 105S/m, a double narrow band absorber obtained under TM wave excitation. EIT-like and Fano can be modulated by adjusting the conductivity of GaAs, and the maximum modulation depth of 96.5% for Fano and 94.6% for EIT-like obtained. The modulation effect of slow light for EIT-like and Fano resonances is accompanied with the conductivity of GaAs. The Maximum group delay is 2.03 ps, and as conductivity of GaAs increasing, the group delay reduce to a small value.
The GAM device also has well sensing performance with a maximum sensitivity of 513 GHz/RIU and a FOM of 39.5. From these results it is clear that the proposed GAM device may be a terahertz modulator, a slow light device and a refractive index sensor, and that this multifunctional device integration provides a research idea.
Funding
The Research Foundation of the Institute of Environment-friendly Mate-rials, and the Occupational Health of Anhui University of Science and Technology (Wuhu) (ALW2020YF18); The Key Research and Development Plan of Anhui Province (202104g01020012); The Qingchuang Science and Technology Plan of Shandong Universities (2019KJN001); National Key Research and Development Program of China (2017YFA0700202, 2017YFB1401203); Natural Science Foundation of Shandong Province (ZR2020FK008, ZR202102180769, ZR2021MF014, ZR2022QF054); The Special Funding of the Taishan Scholar Project (tsqn201909150); National Natural Science Foundation of China (61675147, 61701434, 61735010); The Science and Technology Foundation of Housing and Urban Rural Construction of Anhui Province (2021-YF61).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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