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Abstract
Herein, we propose an all dielectric, open-slit, U-shaped resonant arm-based metasurface that achieves three bound states in the continuum (BIC) in the high-frequency terahertz band whose quasi-BIC (QBIC) states can achieve Q factor of the magnitude order of 104. The maximum sensitivities of accidental QBIC and the figure-of-merit were respectively equal to 1717 GHz/RIU and 16670. Furthermore, the dependencies of the three QBICs on the THz incidence angle were different. Finally, the tunable sensor based on the Dirac semimetal metasurface achieves active tuning of the sensitivity and sensing range. This overcomes the shortcomings of the fixed structure without tuning capabilities, and provides a broad applicability platform for THz sensors.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Localization of strong electromagnetic fields in micro–nano structures can enhance light–matter interactions and is associated with important applications in nonlinear harmonic generation [1,2], slow-light devices [3], narrow-band filters [4,5], and sensitive sensors [6]. The magnitude of the quality factor (Q factor) is usually used to represent the relationship between the strength of the interaction. Typically, lower Q factors and wider bandwidth responses cannot easily meet the practical production needs of highly sensitive devices. Fortunately, the unique, ultra-high Q factors of the bound states in the continuum (BIC) play an extremely important role in the monochromaticity of terahertz (THz) waves and in the maximization of device dispersion, thus providing great prospects for THz devices. The first proposal of BIC was in quantum mechanics [7]; it was subsequently studied extensively in macroscopic systems. By contrast, in metasurfaces [8,9], BIC was defined as the nonradiative eigensolution of the wave equation above the light cone. Two methods are commonly used to obtain the BIC, namely symmetry protection of the structure [10,11] and the destructive interference of the mode of the resonator (accidental BIC) [12,13]. The BIC is a dark mode that cannot be directly displayed in the spectrum because of its infinite Q factor and infinitely narrow bandwidth; thus, a quasi-BIC (QBIC) with a converging Q factor response can be obtained by violating the BIC, and by introducing perturbations to the structure. In sensing applications, a QBIC with a high-Q factor can produce small frequency shifts when the analyte or the environment changes somewhat; these will be very beneficial for the sensor's sensitivity enhancement and pave the way for the development of narrowband and high-Q application devices. In recent years, the study of THz-based BICs has received increased scientific attention from researchers [14–17]. Specifically, Liu et al. [14] experimentally verified the QBIC of metallic THz metasurfaces, wherein the Q factor was not high owing to the inherent ohmic loss of the metal. In addition, research on BIC base on all dielectric metasurface (ADM) was also being conducted [15], and considerable Q-factor improvements were reported. However, the aforementioned work was conducted only for one BIC, and the application of BICs in the frequency range is somewhat limited. Therefore, the study of metasurface devices that generate multiple BICs has great potential for future applications.
Meanwhile, THz sensors [18–22] are of great interest owing to their improved sensing performance caused by high Q factors. Xie et al. [18] fabricated sensors based on metal resonators according to the use of the Fano resonance principle; however, the response was insensitive to very low concentrations of molecules, and the overall sensitivity was low. Subsequently, Wang et al. [19] enhanced the sensitivity of the sensor by using a toroidal dipole (TD) resonance based on the high-refractive index medium of LiTaO3. Once the structural parameters of the devices in the above reports were determined, their functions were also determined; these limited the applications of the devices. He et al. [20] achieved active sensitivity tuning based on a graphene metasurface [23–26] by using the electromagnetically induced transparency (EIT) resonance. However, graphene is too thin, and results in a weak interaction of light with matter. The positive news is that the tuning properties of Dirac semimetal metamaterial (DS), known as three-dimensional (3D) graphene, have recently become a hot topic of research [27,28]. Currently, there is limited concern about BIC-based sensing applications and active tuning of the sensing range used to modulate sensors; accordingly, these aspects need to be explored in depth by researchers. However, this paper has carried out in-depth pioneering research on these shortcomings.
In this study, we propose a metasurface based on an all-dielectric, open-slit, U-shaped resonant arm that achieves three BICs for the first time in the high-frequency THz band, and the Q factors of its QBIC states can reach up to the magnitude order of 104, while different types of BIC degradation can be manipulated by changing the structural parameters, thus providing an option for the development of THz wave manipulation. The QBIC generated by ADM was applied to the sensor, and the sensing sensitivities of three QBICs were obtained. Different coupling modes lead to different sensing performances, whereby the sensitivity of the accidental QBIC can be as high as 1717 GHz/RIU and the figure-of-merit (FoM) can be as high as 16670. In addition, the dependence of the QBIC on the THz incidence angle is discussed. Finally, we use the geometric configuration of ADM to design a tunable sensor based on Dirac semimetal metasurface (DSM) that can change the Fermi energy of DS by adjusting the bias voltage of the metasurface to realize the active tuning of the sensor’s sensitivity and sensing range. The cross-fusion of the BIC and sensor is violated owing to the shortcoming that the sensing performance cannot be changed after structural processing, thus providing a broad platform for THz sensors.
2. Design and theory
The ADM is shown in Fig. 1(a); it consists of two U-shaped resonant arms (made of Si) and SiO2 substrate and satisfies C2 and mirror symmetry requirements. We opened a slit in the middle part of the two U-shaped resonant arms; in this way, the local electromagnetic field and the interaction with the surrounding medium can be enhanced due to the slit waveguide effect. The initial value of the slit spacing was g1 = g2 = 1 µm; the period of the metasurface structure was Px = Py = 40 µm, the spacing between the two resonant arms was g0 = 4µm, the width of the resonant arms was w = 4µm. The two resonant arms were in a square arrangement with the length equal to a = 32µm; additionally, the height of the substrate and the resonant arms are t1 = 15 µm and t2 = 5 µm, respectively, as shown in Fig. 1(b) and (c). The refractive indices of Si and SiO2 are 3.9 and 1.45, respectively. In this study, Our proposed structure model has C2 symmetry, but does not have C4V symmetry, hence its frequency response is extremely sensitive to polarized waves. By comparing the simulation process, we directly select the TE wave which can achieve the purpose as the incident wave, the electric field of the THz wave is incident vertically from + z to -z along the y polarization direction.
Fig. 1. (a) Schematic of the terahertz (THz) symmetric, periodic, all dielectric metasurface (ADM) structure. (b) Three-dimensional (3D) view of the unit cell. (c) Planar view of the unit cell (xy plane).
According to the stochastic phase approximation theory, the dynamic conductivity of DS at the low-temperature limit $T \ge {E_F}$ based on the use of the Kubo formula in 3D is expressed as [27,29],
3. Results and discussion
To obtain the QBIC, while maintaining the metasurface structure in symmetry, we explored the accidental BIC by adjusting simultaneously the sizes of the slits g1 and g2 of the left and right resonant arms, and by observing the transmission spectrum of the metasurface. First, we plot the continuous transmission spectrum of the metasurface at the incident frequency (values in the range of 6.1–6.4 THz) at various g1 and g2 values, as shown in Fig. 2(a). It can be observed that the sharp resonance of the transmission spectrum gradually blueshifts as a function of the slit widths g1 and g2, and the resonance bandwidth gradually narrows until it disappears. As the BIC cannot be shown directly in the electromagnetic spectrum, the dark state with a zero bandwidth at g1 = g2 = 4 µm is the BIC, and has infinite lifetime and zero radiation loss; these attributes are marked with green circles in Fig. 2(a). Subsequently, the resonance bandwidth starts to increase again owing to the continuous increase of g1 and g2. Meanwhile, in the color diagram in Fig. 2(a), there is a blue line in the middle of the green band which represents the resonance amplitude span (which is approximately equal to one). This phenomenon indicates that this metasurface does not transmit at the corresponding frequencies but transmits almost at 100% at other frequencies; this response increases considerably the light conversion efficiency. The slit width increases or decreases, thus resulting in a phase mismatch between the coupled modes. Therefore, the original BIC of destructive interference degenerates to QBIC, and the characteristics of QBIC are usually described quantitatively by the Q factor, as shown in Fig. 2(b), where the Q factor is defined as,
where ${\omega _0}$ is the resonant frequency, and $\Delta \omega $ is the full-width-at-half-maximum (FWHM) of the resonant intensity. Figure 2(b) shows that when g1 and g2 start to change from 4 µm to both sides, the degeneration of the BIC to QBIC starts to radiate energy into free space, and the Q factor of the divergence starts to converge and gradually decreases; even so, the QBIC still possesses an ultra-high Q factor, which can be as high as 50654 at g1 = g2 = 4.8 µm. Compared with a previous study [15], the Q factor of our proposed metasurface QBIC reaches an order of magnitude of 104, which is very beneficial for optical sensing. Based on the above analysis, the Q factor of the resonant state can converge and diverge as a function of the changes of the structural parameters of the metasurface at the high-symmetry point Γ in the two-dimensional momentum space; it is also associated with a degenerate high-intensity resonance process from BIC to QBIC. Therefore, these are parameter-tuned accidental BICs.Fig. 2. (a) Transmission amplitude as a function of the lengths of the ADM slits g1, g2 and THz wave frequency. (b) Q factor of the accidental bound states in the continuum (BIC) as a function of the slit of the ADM.
To obtain the symmetry-protected BIC (SP-BIC) and explore its properties, we break the C2 rotational symmetry ((x, y) → (-x, -y)) of the metasurface structure by moving the middle gap of the resonant arm as well as the left and right rods together by d, as shown in Fig. 3(a). Figure 3(b) shows the discrete transmission spectrum of the ADM as a function of the slit size g1, g2 and the resonant arm moving distance d. As shown, the change from the red to the yellow curve denotes the degradation of the accidental BIC to the QBIC; only one QBIC appears in the spectrum, and this QBIC corresponds to the preferred structural parameters of g1 = g2 = 5.2 µm, d = 0 µm.
Fig. 3. (a) Schematic of structure of the THz asymmetric unit cell (d indicates the displacement magnitude). (b) Discrete transmission spectrum of ADM as a function of the moving distance d pertaining to slit sizes g1, g2, and resonant arm. (c) Displacement magnitude d of the asymmetric metasurface and THz wave frequency as a function of transmission amplitude. (d) Q-factor of symmetry-protected-BIC (SP-BIC) as a function of asymmetry α.
To facilitate the comparison of the simultaneous appearance of the accidental QBIC with the SP-QBIC, we deliberately changed the observed frequency band to 5–6.5 THz. While maintaining the structural parameters g1 = g2 = 4 µm for the accidental BIC, we only disrupted the structural C2 symmetry (d = 2 µm); in response, the energy of the SP-BIC started to leak such that two sharp resonance line patterns appeared in the green curve, i.e., the SP-QBIC after SP-BIC degeneracy. As the accidental BIC diverges not only at the origin, but also at points which do possess increased symmetry, the disruption of the symmetry of the structure does not change the destructive interference of the modes of the accidental BIC. When the parameters of the structure are changed (g1 = g2 = 5.2 µm, d = 2 µm), its dark blue transmission curve exhibits three BICs. The reason is attributed to the fact that the accidental BIC degenerates into QBIC when changing g1 and g2 in the symmetric structure case, which makes the modes maintain a phase mismatch, thus being unable to accomplish destructive interference; thus, the resonance can no longer be hidden in the spectrum. In conjunction with the disrupted structural symmetry, this leads to the simultaneous appearance of the three QBICs. Comparison of the yellow and dark blue transmission curves identified two QBICs with extremely narrow bandwidths and high-Q factors in the case of the red-colored curve at 5.4501 THz and 5.7577 THz, respectively. Additionally, we can infer that the disruption of the symmetry of the structure is insensitive to the resonant frequency of the accidental QBICs, and affects slightly the transmission amplitude. At this point, three BICs corresponding to three frequency bands are realized in the same metasurface by disrupting the symmetry of the structure and by adjusting its parameters; additionally, the changes of the structural parameters can control the order of the appearance of the BICs, as shown in Fig. 3(b). If we only change g1 and g2 in the range of 5–6.5 THz, we can manipulate the degradation of the accidental BICs to QBICs; if we only change d, we can obtain only two SP-QBIC. This method provides the impetus for the development of multiband sensing in the THz band, facilitates the scientific research process and provides a powerful technical tool in manipulating THz waves.
To facilitate the discussion on SP-BIC, we selected the frequency band (5.3–5.9 THz) in which SP-BIC can be generated; we also disregarded the incidental BIC for the time being. Figure 3(c) shows the frequency and moving distance d as a function of transmission amplitude. We named the two SP-BICs as BIClow and BIChigh according to the frequency band in which they were located; BIClow is the SP-BIC at low frequencies, and BIChigh is the SP-BIC at high frequencies, as shown in the figure. As shown, the blue circle at BIClow has a larger radius than the red circle at BIChigh; this indicates that the sensitivity of BIC to the disruption of the structural symmetry is different, BIChigh is more sensitive, and a slight break in structural symmetry will degrade BIC to QBIC. When d is negative, the transmission spectrum is almost the same as the transmission of the absolute value of d because the resonant arms are almost the same irrespective of whether they move along the positive or negative X-direction, as their coupling mode and energy distribution are the same. When d > 0, the resonant frequency of QBIClow after degenerating BIClow gradually redshifts as a function of d, while the resonant frequency of QBIChigh is almost constant. The amount of energy leakage of QBIC gradually increases as a function of d and couples with the radiation channel, thus leading to the gradual increase of the bandwidth of QBIC and the gradual decrease of the Q factor. Figure 3(b) shows that QBIChigh is an asymmetric Fano line pattern. Because of its inaccurate FHWM, when calculating the Q factor of QBIChigh, we used another Q factor calculation equation, as follows,
where fpeak is the peak frequency of the QBIC, and fdip is the dip frequency of the QBIC. The Q factor of the QBIClow is still calculated by using Eq. (1). Figure 3(d) shows the dependence of the Q factors of the two BICs on the asymmetry, where the asymmetry α is defined as where d is the resonant arm moving distance, and l is the original resonant arm’s inner wall length. It can be observed that the Q factor gradually increases as α decreases. It is also noteworthy that when α = 0, the Q factors of both BICs tend to infinity, and the resonance line shape disappears in the spectrum. The Q factors of both QBICs satisfy the α-2 law [11], which proves again that they are SP-BICs.To analyze qualitatively the excitation mechanism of BICs, we performed an electromagnetic field analysis of the metasurface. First, we demonstrated that the three QBICs were generated by magnetic dipole (MD) and electric quadrupole (EQ) resonances. We preferentially selected the structural parameters of the metasurface and calculated the transmission spectra when g1 = g2 = 6, d = 2 um. QBIClow, QBIChigh, and accidental QBIC appear in the vicinity of 5.5127 THz, 5.8388 THz, and 6.1703 THz, respectively, as shown in Fig. 5(a). The periodic metasurface structures can be regarded as four types of unit cells for optical coupling, and are divided as shown in Fig. 4(a). Meanwhile, we calculated the electromagnetic field distribution at the resonant frequencies of the three BICs, where Fig. 4(b) shows the electric field distribution of the component along the z-direction of the type-3 unit cell at the resonance of QBIClow (5.5127 THz); in this figure, the induced displacement currents are indicated by the red arrows in the figure, with the behavior of electric field reverse oscillation and displacement current hedging at the ends of the four resonant arms in the xy plane observed as an EQ resonance mode. Meanwhile, Fig. 4(c) represents the electric and magnetic field distributions of the metasurface at the resonant frequency, wherein the red ring represents the electric field, the blue arrow represents the magnetic field, and the yellow solid line in the electric field distribution diagram is the meridian. Types 2 and 3 in the dark blue-dashed box in the figure are other contributions to the resonance of QBIClow, and both of their electric fields flow along the ring on the metasurface, while the magnetic field flows flat along the z-axis through the xy-plane at the same phase. This outcome is consistent with the MD distribution of the right-handed spiral rule; thus, the EQ and MD in types 2, 3, and 4 are the main cause of QBIClow. Additionally, at the resonant frequency of QBIChigh (5.8388 THz), the coupling mode of type 1 exhibits an MD resonance, as shown in the solid brown box of Fig. 4(c), with a clockwise circular flow of electric field in the xy plane, and a magnetic field flow along the negative direction of z-axis in the xz plane. When the symmetry is broken, the BIC energy leakage and radiation channels start to couple, thus exhibiting MD or EQ resonances in the metasurface. Figure 4(d) shows the electric and magnetic fields at the resonance of the accidental QBIC (6.1703 THz) as well as the electric field distribution of the component along the X-direction. We can still observe the excitation of MD by observing only the electric and magnetic field distribution. The difference with SP-QBIC is that the electric field produces a circular flow in the yz plane, and the center of the ring is close to the part of the contact with the top layer of the metasurface and the substrate. Expanding the meridian along the electric field distribution, a magnetic field distribution flowing along the negative direction of the x-axis is obtained in the xy-plane. Furthermore, observing the electric field distribution of the component along the X-direction and displacement current, we found that the accidental QBIC also yields an EQ resonance at this resonance point, whereby the accidental BIC is formed by the destructive interference of two modes. Due to the change of the slit gap, the MD resonance will be mismatched with the EQ resonance, thus resulting in the degeneration of BIC to QBIC. Meanwhile, it can be observed that in Fig. 4, except for type 3 which can excite the electric quadrupole mode, the rest of the unit cell types are magnetic dipole modes. These results suggest that the MD and EQ resonances enhance the sharp QBIC and the light–matter interaction.
Fig. 4. (a) Mode types of optically coupled unit cell. (b) Electric field distribution of the Z-directional component of the type-3 unit cell at the quasi-BIClow (QBIClow) resonance. (c) Electric and magnetic field distributions at the resonance frequency on the metasurface. (d) Electric and magnetic fields at the resonance of accidental QBIC, and the electric field distribution of the component along the X-direction.
Fig. 5. (a) ADM transmission spectrum at g1 = g2 = 6, d = 2 um. (b) Normalized scattering power diagram of multipole in Cartesian coordinates. (c, d, e) Amplified normalized scattering power spectra at the three resonant frequencies of (b).
To estimate quantitatively the MD and EQ resonances generated by ADM that dominate in the QBIC, and to expose the multipole effects of the Mie resonance, we performed a multipole decomposition [32,33] in Cartesian coordinates. Owing to the minimal contribution of multipole expansions of higher order, we only calculated the expansions of five multipoles. They contained the electric dipole (ED), EQ, MD, magnetic quadrupole (MQ), and toroidal dipole (TD), as shown in Fig. 5(b), where the three color bands correspond to the color bands in Fig. 5(a); these are the frequency bands near the resonance point of the three BICs (QBIClow, QBIChigh, and accidental QBIC listed in order from low to high frequencies). These show the transmission curves and the multipole analysis versus incident wave frequency. For a clearer view of the magnitude of the multipole contribution, we enlarge the red, yellow, and blue bands in Fig. 5(b), as shown in the corresponding Figs. 5(c), 5(d), and 5(e), respectively. In these figures, the vertical coordinates are the normalized scattering powers of the multipoles. It can be observed in Fig. 5(c) that although the contribution of MQ to QBIClow is not small, QBIClow is mainly controlled by EQ, and MD plays a minor role, while other multipoles are suppressed considerably. Combined with the analysis in Fig. 4, the homophase oscillations between the coupled modes of types 2, 3, and 4 become the main contributors to QBIClow. The MQ in Fig. 5(d) partially contributes to the QBIChigh; however, the contribution is an order of magnitude different from that of the MD such that the MD dominates, and the rest of the multipoles are almost suppressed. This resonance is mainly due to the coupling between the type-1 unit cell. The accidental QBIC is due to the multipole contributions of MD and EQ, while the MD contribution is slightly higher and dominates. The MD resonance of this QBIC is also caused by the coupling of type 1; however, the electromagnetic field distribution is different from that of QBIClow, and the electric field is localized between the substrate and the metasurface, as shown in Figs. 4(c) and 4(d). It can also be observed that although they are both MD resonances, they are from different unit cell types. Therefore, each type has made its own contribution to QBIC.
As the Q factor of the QBIC generated by the metasurface in this study is very high, and the linewidth is very narrow, it is of far-reaching significance to study the sensing sensitivity based on the transmission peak of the QBIC to quantify the sensing performance. We added a layer of photoresistive material (refractive index n = 1.6) on the top layer of the ADM as the sensing analyte, and preferentially chose the structural parameters of the asymmetric metasurface, i.e., g1 = g2 = 5.2 µm and d = 2 µm, as shown in Fig. 6(a), where h is the thickness of the analyte. To investigate the sensitivity of the analyte thickness to the frequency shift, we studied first the frequency shift variation of the three QBICs by varying the thickness h, as shown in Fig. 6(b), where the frequency shift is defined as,
where f(h0) is the resonant frequency without analyte, and f(h) is the resonant frequency of QBIC when the analyte thickness is h. It can be observed from the figure that the resonant frequencies of all three QBICs are red shifted (Δf > 0) as the thickness of the analyte increases, and the curves of the frequency shifts of all three QBICs show increasing trends as functions of power (exponents greater than zero and less than 1). As the electric field of the ADM is strongly localized in its gap, the interaction between the electric field and the analyte is stronger when the thickness of the analyte is lower, thus resulting in a sharp increase in the frequency shift. The frequency shifts of all three QBICs tend to be stable, and the red shifted amplitude does not change much when the thickness h is greater than 20 µm because the analyte is in the region where the edge electric field is mainly distributed. Additionally, the edge electric field disappears at a certain height from the metasurface. The results show that the frequency shift changes of all three QBICs are more sensitive to the thin analytes due to the specific curve changes when each unit thickness is changed. Furthermore, comparison of the frequency shift amplitudes of the three QBICs shows that the frequency shift of the accidental BIC is much larger than that of the SP-BIC. The analyte thickness ranges from 0 µm (no analyte) to 20 µm, and the accidental QBIC frequency shift is approximately equal to 1074 GHz, thus indicating that the accidental QBIC is more sensitive to the change of thickness.Fig. 6. (a) Schematic of the sensor after the addition of the analyte. (b) Frequency shifts of the three QBICs as a function of the analyte thickness h. Frequency shift for three QBICs as a function of analyte refractive index with (c) h = 20 µm and (d) h = 2 µm. (e) Figure-of-merit of the accidental QBIC. (f) Dependence of the three QBICs on the angle of the incident wave.
Usually, the THz band is more suitable for the detection of biomolecules who have a strong response in the THz range [34,35]. In addition, the refractive index of biomolecules usually varies between 1.4 and 2.0. To achieve the sensing effect of detecting the refractive index of the analyte, we calculated and observed the frequency shifts of three QBICs by varying the refractive index of the analyte, as shown in Fig. 6(c) (analyte thickness h = 20 µm) and Fig. 6(d) (analyte thickness h = 2 µm); moreover, the red, pink, and green lines in the figure are linear fits of the frequency shifts of the accidental QBIC, QBIChigh, and QBIClow, respectively. The sensitivity of the sensor is defined as:
Where, $\delta f$ represents the variation of the resonance frequency, $\delta n$ is the variation of the refractive index of the analyte. The analyte [36], which is greatly affected by temperature, is essentially that the temperature changes the refractive index or permittivity of the analyte. Since our proposed BIC sensor has a high Q factor, as long as the solid or liquid with refractive index change in the corresponding frequency range can be detected, in general, we only consider the performance of the sensor changing with the refractive index.We found that the frequency shifts of the incidental QBIC, QBIChigh, and QBIClow with refractive indices from 1 to 2 were 1718.5 GHz, 1509.2 GHz, and 1262.9 GHz when h = 20µm, and their corresponding sensitivities were 1717 GHz/RIU, 1598 GHz/RIU, and 1308 GHz/RIU, respectively. Meanwhile, it can be calculated that the average sensitivity of the accidental QBIC is approximately equal to 86 GHz/RIU per micron analyte thickness, which is still a high-sensitivity value for the sensor. When h = 2 µm, the frequency shifts of accidental QBIC, QBIChigh, and QBIClow when the refractive index changes from one to two, are 386.2 GHz, 288.8 GHz, and 313.2 GHz, respectively, and their corresponding sensitivities are 375 GHz/RIU, 291 GHz/RIU, and 318 GHz/RIU, respectively. The sensitivity of the accidental QBIC is the highest and approximately equal to 4.6 times higher at h = 20 µm than that at h = 2 µm. Compared with h = 20 µm, the sensitivity of QBIClow at h = 2 µm is higher than that of QBIChigh such that different QBICs can be selected to detect the refractive index of analytes in different environments.In addition, for sensing applications, the Q factor also constitutes an important variable affecting the sensing performance. We evaluated the performance of ultrasensitive sensors by using the FoM, which is defined as [37],
where S is the sensitivity of the accidental QBIC, and f(n) is the resonant frequency of the accidental QBIC for an analyte with a refractive index equal to n. Given that the sensitivity of the accidental QBIC is typically higher than that of the SP-QBIC, we considered the FoM of the accidental QBIC for an analyte thickness equal to 20 µm, as shown in Fig. 6(e). During the change of the refractive index of the analyte from one to two, the FoM exhibits an exponentially increasing trend. Accordingly, as the refractive index of the analyte increases, the interaction between the analyte and the interaction of the electric field is enhanced. When the refractive index value is equal to two, the FoM can reach a value which is approximately equal to 16670. Therefore, due to its ultra-high sensitivity and FoM, our proposed metasurface structure is suitable for ultra-sensitive sensing applications at the THz band. Meanwhile, we list in Table 1 the performance comparison between our proposed ADM-based THz sensor and other, recently developed sensors. It can be observed that in the study by Chen and Fan [38], a high sensitivity but a smaller FoM was achieved, whereas in the study by Wang et al. [19], a small sensitivity and a high FoM was achieved, while our proposed method has both high sensitivity and FoM, unlike all the other reports.
Table 1. Comparison of sensor performance in recent years
To investigate the dependence between the QBIC after the ADM degradation and the THz incident wave, we obtained the QBIC as a function of the incident wave angle by incident y-polarized light at different angles after the selection of the metasurface structural parameters (g1 = g2 = 5.2 µm, d = 2µm), as shown in Fig. 6(f). The positions of QBIClow, QBIChigh, and accidental QBIC have been marked in the figure. It can be found that with the slow increase of the incident angle, QBIClow is slightly red shifted, and the bandwidth increases slightly, while the QBIChigh bandwidth increases; however, the resonant frequency is gradually blue-shifted. When the symmetry of the structure is disrupted and the asymmetry of the incident light is added, the coupling strength between the radiation channel and the bound state is enhanced, and the resonance bandwidth gradually increases, thus forcing the Q factor to decrease. This shows that SP-QBIC is very dependent on the angle of incidence of the THz wave and the symmetry of the structure is very demanding. In contrast, the accidental QBIC changes insignificantly, and exhibits no dependence on the incidence angle of THz waves. Therefore, the incident, angle-sensitive QBIC can adjust the sensing range by changing the angle of incident THz waves, thus completing the tuning of the sensing range without changing the metasurface structure, which is a very flexible and practical technical attribute for THz devices.
Sensors should have high sensitivity, wide frequency-response range, and reliable performance characteristics. We usually changed the structural parameters to pick the sensing range and fabricate the sensors; however, in practical production and applications, refixing the parameters increases the cost and integration difficulty, thus severely limiting their applications. Therefore, active tuning of detected wave is of great practical value.
To realize the function of active regulation of QBIC, we will continue to use this structural shape based on the design inspiration of ADM. The difference from ADM is that the thickness t2 of the top layer of the structure is adjusted to 0.5 µm, and the silicon material is replaced with DS. Additionally, a bias voltage Vg was added to the DSM with an initial Fermi energy level Ef = 100 meV. In order to achieve better sensor performance, through a comprehensive analysis of the data of multiple sets of simulation experiments, we prefer the Fermi energy in the range of 100-300meV, this range of frequency response is more obvious, as shown in Fig. 7. Furthermore, to increase the coupling strength between the resonant arms, g0 is adjusted to 2 µm, as shown in Fig. 7(a). We demonstrate by using simulation experiments and the method of analyzing the ADM discussed above that the DSM-based floating dark-state BIC is near 6.5 THz, while the shape of the metasurface remains unchanged. Therefore, the coupling mode remains essentially the same, which is still an accidental BIC controlled by the parameters g1 and g2 simultaneously, as shown in the black circle in Fig. 7(b). As the sensitivity of the episodic QBIC of the ADM-based sensor is higher than that of the SP-QBIC, we chose to analyze the tuning function of the QBIC with a symmetric structure (d = 0 µm). By optimizing the DSM structure and the spectral distribution of the QBIC, the structural parameters of the metasurface were set to g1 = g2 = 1 µm. The Fermi energy of the material was changed by varying the bias voltage of the external circuit to the DSM, which in turn regulated the material conductivity. Figures 7(c) and 7(d) show the variation of the real and imaginary parts of the complex permittivity with incident wave frequency for DSM at different Fermi energies, respectively. For the same Fermi energy, the real part of the permittivity increased as a function of frequency, while the imaginary part decreased. When the frequency was kept constant, the real part of the permittivity increased as a slow rate as a function of the Fermi energy. Conversely, the imaginary part decreased slowly when the Fermi energy increased uniformly. We consider the change of Fermi energy as a perturbation of DS, and the shift of the resonant frequency δf of QBIC can be estimated [39,40] as,
Fig. 7. (a) Unit cell based on Dirac semimetal metasurface (DSM). (b) Accidental BIC for the appearance of DSM. (c) The real and (d) imaginary parts of the permittivity curves with Fermi energies for Dirac semimetal metamaterial (DS) in the THz range. (e) DSM transmission spectrum without analyte as a function of frequency and Fermi energy. (f) DSM transmission spectrum with analyte as a function of frequency and Fermi energy (the pink curve is the reference transmission spectrum without analyte and with Ef = 0.3 eV). (g) Frequency differences between the same Fermi energies before and after the addition of analyte, and the frequency shifts of different Fermi energies for the reference transmission spectrum after the addition of analyte.
Figure 7(e) shows the transmission spectrum as a function of Fermi energy for the metasurface in the absence of an analyte. By varying the bias voltage Vg, the QBIC resonance gradually blueshifts at increasing Fermi energies, and the resonance amplitude is essentially constant, thus ensuring that the signal response can be detected in a noisy environment. The DSM-based sensor is still well-tuned when the analyte (n = 1.6, h = 20 µm) is added above the metasurface, as shown in Fig. 7(f); the pink curve is the reference transmission spectrum when no analyte is added and when Ef = 300 meV. We can observe that the QBIC is red shifted after the addition of the analyte. Subsequently, the analytes which have the same refractive index achieve larger frequency shifts as the Fermi energy level decreases. To analyze quantitatively the dynamic variation of frequency after the addition of analytes, in combination with Figs. 7(e) and 7(f), we plot the variation curve of the frequency shift of QBIC compared with the reference transmission spectrum (pink curve) as a function of Fermi energy, as shown by the yellow line in Fig. 7(g). As indicated, when the Fermi energy decreases from 0.3 eV to 0.1 eV, and the corresponding frequency shift changes from 48 GHz to 132 GHz, a compensation of 84 GHz can be obtained by changing the Fermi energy (variation of 0.2 eV). We also analyzed the frequency differences of QBIC before and after the addition of analytes at each corresponding Fermi energy, as shown by the blue line in Fig. 7(g). It can be found that the frequency shift is maximized at Ef = 0.1 eV up to 76 GHz, and the frequency shift of QBIC before and after adding analytes gradually decreases as a function of the Fermi energy. Moreover, the sensitivities of all Fermi energies corresponding to the sensor are different. Accordingly, in practical applications, we can choose different Fermi energies to alter the target sensitivity. It is worth mentioning that the sensitivity of the DSM-based sensor is about 117 GHz/RIU at Ef = 0.1 eV. The results presented above show that the sensitivity and sensing range of our proposed DSM-based sensor can be actively tuned, and the sensing range can be extended, which is beneficial for applications of narrow-band filters, switches, lasers, and other devices. We have completed the theoretical description of the tunable sensor that provides options for the development of manipulation of THz waves and that has a catalytic effect on the development of sensor devices.
4. Conclusions
In this study, we proposed a metasurface based on an all-dielectric, open-slit, U-shaped resonant arm which yielded three BICs in the high-frequency THz band with the Q factors of the QBIC states ranging up to the magnitude orders of 104, while different types of BIC degradation can be manipulated by changing the structural parameters. These features provide unique capabilities for spatially varying optical properties and optical responses. Based on the ADM-generated QBIC applied to the sensor, the sensing sensitivities of three QBICs were obtained. The different coupling modes lead to different sensing performance, whereby the sensitivity of the accidental QBIC can be as high as 1717 GHz/RIU, and the three BICs used for sensing can be manipulated flexibly. Furthermore, the FoM also reflects the performance of the sensor, and the FoM can be as high as 16670. In addition, we quantified the dependence of QBIC on the THz incidence angle. Finally, we used the geometric configuration of ADM to design a tunable sensor based on DSM and changed the Fermi energy of DS by adjusting the bias voltage of the metasurface to realize the active tuning of the sensitivity and sensing range of the sensor. The cross-fusion of BIC and sensor breaks through the defect showed that the sensing performance cannot be changed after structural processing, thus indicating the development prospect of THz sensors and the provision of a broad application platform.
Funding
National Natural Science Foundation of China (61875106, 62105187); Natural Science Foundation of Shandong Province (ZR2021QF010).
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.
References
1. Z. Liu, Y. Xu, Y. Lin, J. Xiang, T. Feng, Q. Cao, J. Li, S. Lan, and J. Liu, “High-Q quasibound states in the continuum for nonlinear metasurfaces,” Phys. Rev. Lett. 123(25), 253901 (2019). [CrossRef]
2. X. Zhang, Q.-T. Cao, Z. Wang, Y. Liu, C.-W. Qiu, L. Yang, Q. Gong, and Y.-F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019). [CrossRef]
3. M. C. Schaafsma, A. Bhattacharya, and J. G. Rivas, “Diffraction enhanced transparency and slow THz light in periodic arrays of detuned and displaced dipoles,” ACS Photonics 3(9), 1596–1603 (2016). [CrossRef]
4. B. Reinhard, O. Paul, and M. Rahm, “Metamaterial-based photonic devices for terahertz technology,” IEEE J. Sel. Top. Quantum Electron. 19(1), 8500912 (2013). [CrossRef]
5. C.-C. Chang, L. Huang, J. Nogan, and H.-T. Chen, “Narrowband terahertz bandpass filters employing stacked bilayer metasurface antireflection structures,” APL Photonics 3(5), 051602 (2018). [CrossRef]
6. J. Yang and Y.-S. Lin, “Design of tunable terahertz metamaterial sensor with single- and dual-resonance characteristic,” Nanomaterials 11(9), 2212 (2021). [CrossRef]
7. J. von Neumann and E. P. Wigner, “Über das Verhalten von Eigenwerten bei adiabatischen Prozessen,” in The Collected Works of Eugene Paul Wigner, A. S. Wightman, ed. (Springer Berlin Heidelberg, 1993), pp. 294–297.
8. M. A. Baqir, A. Farmani, M. Raza, M. N. Akhtar, and A. Hussain, “Engineering of metallic nanorod-based hyperbolic metamaterials for broadband applications operating in the infrared regime,” Appl. Nanosci. 11(1), 229–240 (2021). [CrossRef]
9. J. Li, J. Li, C. Zheng, S. Wang, M. Li, H. Zhao, J. Li, Y. Zhang, and J. Yao, “Dynamic control of reflective chiral terahertz metasurface with a new application developing in full grayscale near field imaging,” Carbon 172, 189–199 (2021). [CrossRef]
10. Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107(18), 183901 (2011). [CrossRef]
11. K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018). [CrossRef]
12. H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum,” Phys. Rev. A 32(6), 3231–3242 (1985). [CrossRef]
13. C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499(7457), 188–191 (2013). [CrossRef]
14. X. Zhao, C. Chen, K. Kaj, I. Hammock, Y. Huang, R. D. Averitt, and X. Zhang, “Terahertz investigation of bound states in the continuum of metallic metasurfaces,” Optica 7(11), 1548 (2020). [CrossRef]
15. S. Han, P. Pitchappa, W. Wang, Y. K. Srivastava, M. V. Rybin, and R. Singh, “Extended bound states in the continuum with symmetry-broken terahertz dielectric metasurfaces,” Adv. Opt. Mater. 9(7), 2002001 (2021). [CrossRef]
16. D. Liu, X. Yu, F. Wu, S. Xiao, F. Itoigawa, and S. Ono, “Terahertz high-Q quasi-bound states in the continuum in laser-fabricated metallic double-slit arrays,” Opt. Express 29(16), 24779 (2021). [CrossRef]
17. J. Li, J. Li, C. Zheng, Z. Yue, D. Yang, S. Wang, M. Li, Y. Zhang, and J. Yao, “Spectral amplitude modulation and dynamic near-field displaying of all-silicon terahertz metasurfaces supporting bound states in the continuum,” Appl. Phys. Lett. 119(24), 241105 (2021). [CrossRef]
18. Q. Xie, G.-X. Dong, B.-X. Wang, and W.-Q. Huang, “High-Q fano resonance in terahertz frequency based on an asymmetric metamaterial resonator,” Nanoscale Res. Lett. 13(1), 294 (2018). [CrossRef]
19. Y. Wang, Z. Han, Y. Du, and J. Qin, “Ultrasensitive terahertz sensing with high- Q toroidal dipole resonance governed by bound states in the continuum in all-dielectric metasurface,” Nanophotonics 10(4), 1295–1307 (2021). [CrossRef]
20. X. He, Q. Zhang, G. Lu, G. Ying, F. Wu, and J. Jiang, “Tunable ultrasensitive terahertz sensor based on complementary graphene metamaterials,” RSC Adv. 6(57), 52212–52218 (2016). [CrossRef]
21. M.-R. Nickpay, M. Danaie, and A. Shahzadi, “Highly sensitive THz refractive index sensor based on folded split-ring metamaterial graphene resonators,” Plasmonics 17(1), 237–248 (2022). [CrossRef]
22. Z. Hamzavi-Zarghani, A. Yahaghi, L. Matekovits, and A. Farmani, “Tunable mantle cloaking utilizing graphene metasurface for terahertz sensing applications,” Opt. Express 27(24), 34824 (2019). [CrossRef]
23. M. A. Baqir, P. K. Choudhury, A. Farmani, T. Younas, J. Arshad, A. Mir, and S. Karimi, “Tunable plasmon induced transparency in graphene and hyperbolic metamaterial-based structure,” IEEE Photonics J. 11(4), 1–10 (2019). [CrossRef]
24. A. Khajeh, Z. Hamzavi-Zarghani, A. Yahaghi, and A. Farmani, “Tunable broadband polarization converters based on coded graphene metasurfaces,” Sci. Rep. 11(1), 1296 (2021). [CrossRef]
25. A. Farmani, M. Miri, and M. H. Sheikhi, “Design of a high extinction ratio tunable graphene on white graphene polarizer,” IEEE Photonics Technol. Lett. 30(2), 153–156 (2018). [CrossRef]
26. J. Li, J. Li, C. Zheng, Z. Yue, S. Wang, M. Li, H. Zhao, Y. Zhang, and J. Yao, “Free switch between bound states in the continuum (BIC) and quasi-BIC supported by graphene-metal terahertz metasurfaces,” Carbon 182, 506–515 (2021). [CrossRef]
27. G.-D. Liu, X. Zhai, H.-Y. Meng, Q. Lin, Y. Huang, C.-J. Zhao, and L.-L. Wang, “Dirac semimetals based tunable narrowband absorber at terahertz frequencies,” Opt. Express 26(9), 11471 (2018). [CrossRef]
28. L. Dai, Y. Zhang, J. F. O’Hara, and H. Zhang, “Controllable broadband asymmetric transmission of terahertz wave based on Dirac semimetals,” Opt. Express 27(24), 35784 (2019). [CrossRef]
29. O. V. Kotov and Y. E. Lozovik, “Dielectric response and novel electromagnetic modes in three-dimensional Dirac semimetal films,” Phys. Rev. B 93(23), 235417 (2016). [CrossRef]
30. H. Chen, H. Zhang, M. Liu, Y. Zhao, X. Guo, and Y. Zhang, “Realization of tunable plasmon-induced transparency by bright-bright mode coupling in Dirac semimetals,” Opt. Mater. Express 7(9), 3397 (2017). [CrossRef]
31. J. Luo, Q. Lin, L. Wang, S. Xia, H. Meng, and X. Zhai, “Ultrasensitive tunable terahertz sensor based on five-band perfect absorber with Dirac semimetal,” Opt. Express 27(15), 20165 (2019). [CrossRef]
32. E. E. Radescu and G. Vaman, “Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles,” Phys. Rev. E 65(4), 046609 (2002). [CrossRef]
33. Z. Li, T. Wu, and X. Zhang, “Tailoring toroidal and magnetic dipole excitations with the same dielectric structure,” Opt. Lett. 44(1), 57 (2019). [CrossRef]
34. M. Brucherseifer, M. Nagel, P. H. Bolivar, H. Kurz, A. Bosserhoff, and R. Büttner, “Label-free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77(24), 4049–4051 (2000). [CrossRef]
35. L. Ho, M. Pepper, and P. Taday, “Signatures and fingerprints,” Nat. Photonics 2(9), 541–543 (2008). [CrossRef]
36. H. Emaminejad, A. Mir, and A. Farmani, “Design and simulation of a novel tunable terahertz biosensor based on metamaterials for simultaneous monitoring of blood and urine components,” Plasmonics 16(5), 1537–1548 (2021). [CrossRef]
37. L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5(10), 2034–2038 (2005). [CrossRef]
38. X. Chen and W. Fan, “Ultrasensitive terahertz metamaterial sensor based on spoof surface plasmon,” Sci. Rep. 7(1), 2092 (2017). [CrossRef]
39. Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013). [CrossRef]
40. J. Hwang and J. W. Roh, “Electrically tunable two-dimensional metasurfaces at near-infrared wavelengths,” Opt. Express 25(21), 25071 (2017). [CrossRef]
41. M. Gupta, Y. K. Srivastava, M. Manjappa, and R. Singh, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017). [CrossRef]
42. Y. Zhong, L. Du, Q. Liu, L. Zhu, K. Meng, Y. Zou, and B. Zhang, “Ultrasensitive specific sensor based on all-dielectric metasurfaces in the terahertz range,” RSC Adv. 10(55), 33018–33025 (2020). [CrossRef]
43. T. Ma, Q. Huang, H. He, Y. Zhao, X. Lin, and Y. Lu, “All-dielectric metamaterial analogue of electromagnetically induced transparency and its sensing application in terahertz range,” Opt. Express 27(12), 16624 (2019). [CrossRef]
