1. Introduction

Over the past decades, EIT due to quantum interference has been widely and thoroughly investigated [1–3]. The EIT phenomenon pertains to situations where a medium that would typically be opaque can generate a transparency range of narrow bandwidth due to the effects of powerful resonant coupling illumination. The coherent beam of light can traverse the atomic medium without any loss in energy. In addition, due to a potent dispersion effect, the atomic medium does not exhibit any absorption or reflection properties. Recently, attention has been increasingly shifted to the EIT effect in metamaterials, which is realized by coupling bright and dark modes [4,5]. However, achieving a high Q-factor EIT requires two resonances with minimal mismatch and significant Q contrast. BIC can be achieved by eliminating the coupling between resonant modes and radiation channels, which is considered as a resonant state with zero linewidth and infinite Q-factor [6,7]. By comparison, quasi-BIC with a finite Q factor, which showcases measurable high-Q-factor resonance in the spectrum [8], has been explored for many applications including perfect absorber [9], sensors [10], lasers [11], harmonic generation enhancement [12], and electromagnetic field enhancement [13]. Dielectric metasurfaces have gained considerable interest for BIC research due to their ability to reduce the inherent ohmic losses caused by ultra-high Q resonances, in contrast to metallic materials [14,15]. To excite high-Q quasi-BIC modes, different dielectric metasurface structures have been proposed, such as split rings [16], asymmetric nanorods [17], notch cubes [18–20], and nanodisks [21,22], which can realize single or double quasi-BIC within a given wavelength range. By contrast, multi-quasi-BIC modes attract more attention due to the advantage of having multiple resonances in a narrow spectrum and provide more possibilities for designing multifunctional sensors and modulators. In recent years, researchers have achieved triple quasi-BIC in all-dielectric metasurfaces by breaking geometric symmetries, including the periodicity, unit structure, and incidence angle [23–27]. However, there is a lack of research focusing on transitioning BIC points into quasi-BIC to excite tunable high-Q EIT effects. Huang et al. proposed an all-dielectric metasurface consisting of hollow cylinders arranged in a tetrameric configuration, which induces a distinct EIT resonance [28]. Algorri et al. designed a metasurface consisting of a square slot ring and analysed its symmetry using the symmetry adapted linear combinations approach for the unperturbed unit cell and the irreducible representations analysis for perturbation effects [29]. He et al. designed a two-layer all-dielectric metasurface to excite the high-Q factor EIT via a bright electric dipole resonance and a dark toroidal dipole resonance [30]. Abujetas et al. exploited a metasurface composed of high refractive index dielectric material and demonstrated the excitation of an ultra-narrow BIC-induced transparent band through extensive experiments [31]. However, previous studies have mostly been based on a single EIT, which cannot simultaneously excite the high Q EIT effect and quasi-BIC modes on the proposed metasurfaces, and have focused on the slow light effect or refractive index sensing application of the EIT, while neglecting its potential modulation function.

Phase change materials (PCMs) have recently been studied to explore tunable phenomena from variable dielectric constants, which can be reversibly realized through external stimuli such as lasers, electricity, and thermal control [32–34]. Liu et al. loaded graphene into an all-dielectric metasurface and achieved a high modulation depth of the EIT resonance transmission amplitude by varying the conductivity of graphene either by changing the Fermi energy level or by changing the number of layers [35]. Barreda et al. demonstrated spectral tuning effects using Sb₂Se₃. Meanwhile, Ge₂Sb₂Te₅ exhibited an on/off switching effect of quasi-BIC resonances [36]. Chen et al. proposed a dynamically tunable multi-resonance and polarization-insensitive electromagnetically induced transparency metamaterial. The EIT-like effect can be adjusted by tuning the conductivity of vanadium dioxide [37]. However, the PCMs just mentioned display little contrast in dielectric constants and limited tuning range. By contrast, epsilon-near-zero (ENZ) materials, whose real part of dielectric constant is zero or close to zero at certain wavelengths, are capable of significant optical modulation. Nano-devices incorporating ENZ materials exhibit optical coupling effects, enabling advanced optical applications. One of the most widely used materials in the field of ENZ is indium tin oxide (ITO). By taking advantage of its ENZ behaviour, many potential applications of ITO have been proposed or validated [38,39]. The ENZ wavelength of ITO closely relates to the electron density, which can be modulated by applying the gate voltage [40,41] or pump light [42], and transforms its dielectric constant from dielectric to metal [43]. The inherent absorption efficiency of the ITO material can be significantly altered when the dielectric constant approaches ENZ state. Thus, integrating ENZ ITO films with all-dielectric metasurfaces can modulate the wavelength and amplitude of the quasi-BIC. At present, few works have focused on integrating ENZ materials with BIC metasurfaces, which remains challenge. Ma et al. proposed an all-dielectric metasurface with five square holes and demonstrated active control of the position and intensity of the resonance peaks of the quasi-BIC transmission spectrum by integrating an ENZ ITO film [44]. However, the research of tuning high-Q-factor BIC-based EIT effects using ENZ materials has been limited.

In this paper, we design an all-dielectric metasurface, which consists of two rectangular apertures etched onto a unit and arranged in a periodic manner on a SiO₂ substrate. The proposed metasurface can simultaneously excite high-Q-factor EIT and quasi-BIC modes. The article highlights the high-Q-factor EIT effect caused by the destructive interference between quasi-BIC and magnetic dipole resonance. Our study showcases the modulating capability of this device by integrating the metasurface with an ENZ ITO film. By adjusting the carrier concentration of ITO, we successfully regulate the transmission intensity of the EIT effect. The device exhibits a high-transmission/low-transmission state at a certain wavelength, where the transmission intensity of the EIT effect modulates from 90% to 5%. This behavior results in modulation depths in the range of 1200-1250 nm from -17 to 24 dB. Our research results may facilitate the advancement of high-performance spatial light modulators.

2. Structures and method

Figure 1(a) displays the designed all-dielectric metasurface, which comprises silicon and an SiO₂ substrate. The parameters of the unit structure, as depicted in Fig. 1(b), are a nanocube with a square cross-section, with a period P of 850 nm in the x and y directions, a side length L of 700 nm for silicon, a thickness t of 200 nm and a substrate D of 200 nm. Two rectangular air holes were etched into these structures. Compared to the slotted and nanoblock structures currently available for EIT research [28,35,45], the metasurface we proposed containing two rectangular air holes, which can confine the electric field within rectangular air holes to reduce the modes affected by loss and dispersion of the dielectric material, thus improving the Q-factor [46]. As shown in Fig. 1(c), these holes have a width w of 100 nm. The first rectangle air hole has a fixed side length of ${L_1}$ = 480 nm, whereas the side length ${L_2}$ of the second rectangle air hole varies. G is the gap between the two rectangular holes. The asymmetric parameter $\alpha $ = (${L_1}$-${L_2}$)/${L_1}$ is used to stimulate BIC. The material parameters of Si and SiO₂ are referenced from the Palik refractive index database. The finite-difference time-domain (FDTD) method was employed, taking periodic boundary conditions in the x and y directions and perfectly matched layer (PML) boundary conditions in the z direction, and the mesh $dx$, $dy$ and $dz$ are set to 5 nm in the simulation. The symmetry of C₂ within the unit is broken when ${L_1} $ ≠ ${L_2}$. To excite a prominent resonance response, we used an x-polarized plane wave that propagates along the z-axis to incident perpendicularly onto the all-dielectric metasurface.

 

Fig. 1. (a) Schematic diagram of the all-dielectric metasurface. (b) Schematic diagram of the unit cells. (c) Top view of the unit cells.

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The experimental feasibility and portrays the entire process flow in preparing this nanostructure as follows [47]. First and foremost, use a low-pressure physical vapor deposition (LPCVD) method to deposit Si onto an SiO₂ substrate. Second, spin-coating the ZEP520A photoresist onto the Si plan. Subsequently, the rectangle holes were obtained through electron beam lithography (EBL) and developing techniques, followed by inductively coupled plasma (ICP) etching. The photoresist was removed in the final step and cleaned using deionized water. During the fabrication process, the size, shape and arrangement of the metasurface may deviate from the design, resulting in reduced Q-factor in the experiment compared to the simulation.

3. Results and simulations

3.1 Multiple Quasi-BICs excited by all-dielectric metasurfaces

A symmetry-protected BIC has an infinitely high Q-factor and is an ideal state. Resonance modes that are excited by symmetry-breaking are called quasi-BIC states and have high Q-factors that can be measured. We utilized the asymmetry parameter $\alpha $ = (${L_1}$-${L_2}$)/${L_1}$ to illustrate the induced asymmetry and defined $\Delta L$ = ${L_1}$-${L_2}$. Then, symmetry breaking was introduced by fixing ${L_1}$ and altering ${L_2}$. Figure 2(a) shows the transmission spectra with different $\Delta L$ values, where the four excited resonance modes are labeled as modes I, II, III, and IV. When $\Delta L $ = 0, $\alpha $ = 0, only one magnetic dipole resonance mode I emerges. The linewidths of modes II, III, and IV are zero, which indicates that the energy of the BIC is not leaked into free space. As illustrated in Fig. 2(a), when $\Delta L$ ≠ 0, the transmission spectrum reappears with three high Q-factor resonances. This phenomenon arises from structural symmetry breaking, which creates a zero-energy radiation channel for the metasurface and ultimately results in BIC leakage and a shift toward quasi-BIC modes. When $\Delta L$ increases, a redshift in resonance peaks occurs due to the increased effective refractive index of the silicon metasurface. The transmission spectra of modes II, III, and IV were fitted using the standard Fano resonance equation [48]:

 

Fig. 2. (a) Transmission spectra with different $\Delta L $ values. (b) Simulation of the transmission spectra (solid line), where $\Delta L$ = 60 nm, using Matlab calculation; theoretical fit by Fano formula (dashed line). (c), (d), (e) Effect of the asymmetry on the Q-factor of quasi-BICs (log-log scale). The Q-factors from simulations were calculated using the Fano fit for quasi-BIC II, quasi-BIC III, and quasi-BIC IV. The solid line represents the theoretical fit by an inverse square function.

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Here, ${\omega _0} $ is the resonance frequency; ${a_1}$, ${a_2}$, and b are constant real numbers; $\gamma $ is the overall damping rate of the resonance cavity, which is directly proportional to the resonance spectrum linewidth. For the asymmetric line-shape Fano resonances in the transmission spectrum, the radiation Q calculation demands fitting the spectrum to formula (1), followed by calculating using $Q = \; {\omega _0}/2\gamma $. The radiation Q-factor is an important factor in determining the asymmetry of the resonance curve. Figure 2(b) shows the fitting results for the transmittance curve of modes II, III, and IV when $\Delta L$ = 60 nm. The resulting fitted Q-factors were 7604, 10064, and 15503 for modes II, III, and IV, respectively. Furthermore, we analyzed the relationship between array size and Q-factor and found that the Q-factor increases gradually as the array size increases.

A symmetry-protected BIC is unmeasurable due to its infinite Q-factor. However, introducing symmetry breaking enables the symmetry-protected BIC to shift to a quasi-BIC mode. In the quasi-BIC resonant state, asymmetry parameter $\alpha $ and the Q-factor satisfy $Q \propto \alpha $^-2. In this context, the resonance mode is defined by examining the correlation between asymmetry parameter $\alpha $= (${L_1}$-${L_2}$)/${L_1}$ and Q-factor, where ${L_1}$ and ${L_2}$ are the lengths of the rectangular holes on the left and right, as shown in Fig. 1(c). The radiation Q-factor can be expressed as [47]:

Here, A is the area of the periodic unit, ${p_0}$ is the dipole moment of the unit molecule, and ${k_0}$ is the wavevector along the $z$-axis. The Q-factors for quasi-BIC modes II, III, and IV, in relation to various asymmetrical parameters $\alpha $, are illustrated in Fig. 2(c)–(e). Observation shows the correlation between asymmetry parameter $\alpha $ and Q-factors of modes II, III, and IV follows a square reciprocal trend $Q\; \propto \alpha $^-2. The Q-factor increases when $\alpha $ decreases. For quasi-BIC modes, one can design the Q-factor and linewidth by modifying the structure parameter.

To understand the emergence of the quasi-BIC, we analyzed its multipole expansion. The derivation equation in the interference is examined [49,50].

Here, c is the speed of light in vacuum, $\mathrm{\alpha }$ and $\mathrm{\beta }$ are the Cartesian coordinate components x, y, and z in formula (3), and the current density is:

The radiated power of the multipole moment is calculated as follows:

At the wavelength of 1251.9 nm, as illustrated in Fig. 3(b), mode III exhibits an outward displacement current from the center of the rectangular aperture, which is perpendicular to the incident plane. This current subsequently diffuses toward the four vertices from the center of aperture and forms an electric quadrupole (EQ) on the $x$-$y$ plane. The current finally flows toward the four vertices that are perpendicular to the incident plane. Figure 3(c) portrays the magnetic field vector in the form of a ring in the $x$-$y$ plane, which results in a toroidal dipole (TD) oriented along the $z$-direction. The interaction among multiple dipole moments influences the far-field distribution (as depicted in the inset in Fig. 3(a)). Non-radiative BIC modes are induced by the EQ and TD interference, which lead to directional radiation in the $x$-direction. As shown in Fig. 3(e), mode IV at λ = 1299.6 nm creates an EQ feature on the x-y plane due to the displacement current. Meanwhile, Fig. 3(f) displays a magnetic quadrupole (MQ) feature on the $x$-$y$ plane due to the magnetic vector. Therefore, the radiation pattern in the far-field region (as depicted in the inset in Fig. 3(d)) is a typical quadrupole pattern with four petals visible on the $x$-$y$ plane. In addition, any leakage in the $z$-direction can be disregarded due to its insignificance.

 

Fig. 3. (a), (d) Scattered power of the electric dipole (ED), magnetic dipole (MD), toroidal dipole (TD), electric quadrupole (EQ), and magnetic quadrupole (MQ) for quasi-BIC III and quasi-BIC IV at $\Delta L $ = 60 nm. The inset is the far-filed radiation pattern. (b) $x$-$y$ field electric and (c) $x$-$y$ field magnetic distributions at $\lambda $ = 1251.9 nm. The black arrows denote the displacement current vector and magnetic field vector, respectively. (e) $x$-$y$ field electric and (f) $x$-$y$ field magnetic distribution at $\lambda $ = 1299.6 nm. The black arrows denote the displacement current vector and magnetic field vector, respectively.

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We analyzed the structure using a multipole decomposition. Based on the results in Fig. 3(a), when the difference in length $\Delta L$ is 60 nm, the far-field scattering power of the nanostructure at the resonant wavelength is mainly influenced by toroidal dipoles (TD) in the z-direction and electric quadrupoles (EQ) on the $x$-$y$ plane. Furthermore, the magnetic dipoles (MD) make a minor contribution. Mode IV, which is illustrated in Fig. 3(d), is primarily dominated by quadrupoles EQ and MQ, with secondary contributions from the MD. The multipole decomposition results are consistent with the near-field analysis.

We examine the EIT effect in Fig. 4. An observation of the electric field distribution in the $x$-$y$ plane at the transparency window when $\lambda $ = 1224.3 nm and $\Delta L $ = 60 nm, where black arrows represent displacement current vectors, indicates an electric quadrupole (EQ) response proximate to the rectangular air hole in the $x$-$y$ plane. In addition, a toroidal dipole (TD) response around the unit cell is evident, which implies that the EQ dominates the EIT resonance. We further conduct a multipole decomposition of this structure, as depicted in Fig. 4(a). The numerical results are consistent with the distribution of the electromagnetic field.

 

Fig. 4. (a) Scattered power of the electric dipole (ED), magnetic dipole (MD), toroidal dipole (TD), electric quadrupole (EQ), and magnetic quadrupole (MQ) for EIT. (b) $x$-$y$ field electric distribution at λ = 1224.3 nm. The black arrows denote the displacement current vector.

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To investigate the underlying cause of the EIT effect, we computed the transmission spectrum for the transparency window at $\Delta L$ = 60 nm using various G parameters, as depicted in Fig. 5(a). When $G$ = 70 nm, a transformation of the EIT effect can be observed and result in two distinct resonances: mode II at $\lambda $ = 1194.74 nm and mode I at $\lambda $ = 1222 nm.

 

Fig. 5. (a) Transmission spectra with different G. (b), (c) Scattered power of the electric dipole (ED), magnetic dipole (MD), toroidal dipole (TD), electric quadrupole (EQ), and magnetic quadrupole (MQ) for quasi-BIC I and quasi-BIC II at $G $ = 70 nm. The inset is the far-filed radiation pattern.

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These resonances diverge from one another when the G increases, which illustrates the change in wavelength and the value of G. For quasi-BIC mode II, in Fig. 6(a), the schematic of the electric field distribution indicates that the vectors of displacement current are primarily concentrated inside the rectangular hole and gap, which manifests as EQ resonance on the $x$-$y$ plane. In addition, the displacement current forms a ring around the unit cell. Figure 6(b) illustrates the magnetic field distribution on the $y$-$z$ plane, which indicates that the magnetic field does not form a ring on the $y$-$z$ plane and fails to excite magnetic TD resonances along the $x$-direction. Consequently, electric TD resonances along the $z$-direction are excited by ring currents around the unit cell. Figure 5(c) displays the results of the multipole decomposition results for mode II, and the numerical findings demonstrate good consistency with the electromagnetic field distribution. The inset in Fig. 5(c) showcases the far-field radiation pattern, which illustrates that mode II is primarily governed by the quadrupole (EQ) and results in four petals on the $x$-$y$ plane. The leakage in the $z$-direction is negligible. Here, we believe that mode II is mainly influenced by the electric quadrupole EQ, toroidal dipole TD, and electric dipole ED destructive interference, so only the radiation pattern of the quadrupole is displayed in the far field.

 

Fig. 6. (a) $x$-$y$ field electric distribution and (b) $y$-$z$ field magnetic distribution for quasi-BIC II at $G$ = 70 $ nm$. The black arrows denote the displacement current vector and the magnetic field vector, respectively. (c) $x$-$y$ field magnetic distribution and (d) $x$-$z$ field electric distribution for mode I at $G$ = 70 nm. The black arrows denote the magnetic field vector and the displacement current vector, respectively.

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For mode I, Fig. 6(c) and Fig. 6(d) show the magnetic field diagram on the $x$-$y$ plane and the electric field diagram on the $x$-$z $ plane, respectively. The black arrows in the figures indicate the direction of the magnetic field and displacement current vectors. On the $x$-$z$ plane, there is an EQ resonance, and along the y direction, an MD resonance is observed. The multipole decomposition in Fig. 5(b) demonstrates that mode I primarily consists of a superposition of EQ and MD. Hence, the lateral directional radiation in the x direction is derived from the interaction of both resonances and results in the far-field distribution (as depicted in the inset in Fig. 5(b)). In our research, we identify the bright mode as the magnetic dipole mode and the dark mode as the EQ quasi-BIC mode, which exhibit interference effect, resulting in the EIT window. Therefore, we believe that the EIT effect at $\lambda $ = 1224.3 nm is due to the destructive interference caused by mode I and quasi-BIC mode II.

Further, to ensure the stability and reliability of the structure, the geometric parameters of the metamaterial, including thickness t, period P and substrate thickness D, are tuned. The asymmetric parameter $\Delta L$ = 60 nm was chosen based on the above analysis. Plane waves are incident vertically in the $z$-negative direction and polarized in the $ x$-direction. As expected, the results show highly tunability of the proposed metamaterial. Figure 7 clearly shows the respective transmission spectra at different geometric parameters. The analysis shows that the wavelength and intensity of the resonance are affected by different surface thicknesses, substrate thicknesses and periods. Changing these parameters affects the coupling efficiency and effective optical path length of the localized resonance modes on the metasurface, which in turn affects the resonance intensity and wavelength position. When $P$ = 850 nm, $L$ = 700 nm, $D$ = $t$ = 200 nm and $\Delta L$ = 60 nm, this configuration can be optimal in terms of Q-factor and spectral contrast.

 

Fig. 7. Corresponding transmission curves of the proposed metamaterials at different structural geometries. (a) substrate thickness D of the metamaterials from 180 nm to 220 nm. (b) The period p of the meta-molecule from 840 nm to 860 nm. (c) Thickness t of the metasurface from 190 nm to 210 nm.

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3.2 Modulation and application of EIT by ENZ materials

After examining the EIT excited on the metasurface, we shifted our attention to the modulation of active light, which is vital aspect in creating high-performance, reconfigurable nanophotonic devices. The electroabsorption mechanism controls the concentration of free electrons and holes in a semiconductor material, regulating both the real and imaginary parts of the dielectric constant. ENZ materials can effectively change the carrier concentration by applying a voltage. ITO is a commonly used material with ENZ properties [51–53]. Our objective is to investigate the electrophotonic modulation functionalities of the metasurface, and we introduced an ITO film in the rectangular air hole at $\Delta L$ = 60 nm. The length and width of the ITO film were adjusted to match those of two adjacent rectangular holes; the film thickness was 10 nm. Precise control of temperature humidity and time is required during the experiment, where the ITO solution is spin-coated inside the circular air holes and then fading. The structure was designed such that the electric field of the resonant modes is mostly concentrated in the airholes. Therefore, we will not consider graphene, as it is typically loaded on the metasurface rather than the holes and cannot achieve a significant modulation effect. Secondly, it is acknowledged that ENZ materials have a wider tuning width and deeper tuning depth compared to other phase change materials, such as VO₂ and GST, due to their near-zero properties. Therefore, to achieve the modulation of the EIT effect, ITO is integrated onto the proposed metasurface. The metasurface is electrically modulated by applying a gate voltage between two metal electrodes on each side. Qian Li et al. have experimentally demonstrated that the ENZ wavelength in the near-infrared band can be approached by the ENZ material at approximately 8.825 voltage [54].

We can use the Drude model to describe the dielectric constant of the ITO [54,55]:

In the formula (6) and (7), ${\omega _p}$ is the plasma frequency, $\varepsilon $ is the dielectric constant, $\tau $ is the Drude damping rate and $\omega $ is the angular frequency of the incident light. The plasma frequency ${\omega _p}$ is a function of carrier density N, and $\tau $ = 0.0468${\omega _p}$. The effective mass of the electron is described as ${M^\mathrm{\ast }}_e$, e is the electron’s charge, ${\varepsilon _0}$ is the dielectric constant of vacuum, and ${\varepsilon _\infty }$= 3.8055. Figure 8 calculates the real and imaginary parts of the ITO dielectric constant at different ${N_{ITO}} $ values. At $\Delta L$ = 60 nm, the transmission spectra of the nanostructure are calculated under different carrier density ${N_{ITO}}$ values, as shown in Fig. 8(c). With the ITO film, when the carrier density ${N_{ITO}}$ increases, the transmitted spectrum exhibits a mild shift, whereas the changes in electric field distribution are not very prominent, and the intensity weakens.

 

Fig. 8. (a), (b) Changes in the real and imaginary parts of the dielectric constant of ITO with the current density ${N_{ITO}}$ and wavelength. (c) Transmission spectrum with different ${N_{ITO}}$ and wavelength values.

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To investigate the tunability contribution of ITO to the EIT effect, we observed the electric field distribution in the $y$-$z$ plane of the rectangular air hole on the left side at carrier densities of 1.56 × 10¹⁹cm^-3, 9.80 × 10²⁰cm^-3 and 1.23 × 10²¹cm^-3 in Fig. 9. As shown in Fig. 9(a), at ${N_{ITO}}$ = 1.56 × 10¹⁹cm^-3, we observed that the electric field is mainly localized within the air holes, which is similar to the electric field distribution of the non-integrated ITO film. When ${N_{ITO}}$ is equal to 9.80 × 10²⁰cm^-3, the electric field localization point tends to be closer to the ITO film, resulting in a decrease in electric field intensity and realization of intensity modulation. For ${N_{ITO}}$ equal to 1.23 × 10²¹cm^-3, the electric field is almost entirely localized inside the ITO layer, with no air holes, which can be attributed to energy leakage into the ITO layer. Moreover, due to the introduction of losses, the extinction ratio demonstrates varying degrees of reduction.

 

Fig. 9. Electric field distribution in the y-z plane of rectangular air holes for different N_ITO. (a) N_ITO= 1.56 × 10¹⁹cm^-3. (b) N_ITO= 9.80 × 10²⁰cm^-3. (c) N_ITO= 1.23 × 10²¹cm^-3.

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The device’s modulation function is obtained by modifying the density of ${N_{ITO}}$ carriers in ITO via bias voltage application. As a result, the optical response is changed with the change in plasma frequency ${\omega _p}$ in formula (6). To explore the modulation capability of the device, as shown in Fig. 9(a), we extracted the transmittance schematic as a function of the wavelength for structures with ${N_{ITO}}$ values of 1.56 × 10¹⁹, 9.80 × 10²⁰, and 1.23 × 10²¹$cm$⁻³ from Fig. 8(c). In Fig. 9, the intensity notably changes in the transparency window of the EIT effect when ${N_{ITO}}$ decreases, which enables a transition between high-transmission and low-transmission states for the optical modulator by changing ${N_{ITO}}$. When ${N_{ITO}}$= 1.56 × 10¹⁹cm, the light passes through the transparency window, which corresponds to the high-transmission state. However, when ${N_{ITO}}$=1.23 × 10²¹cm⁻³, the transparency window disappears, which corresponds to the low-transmission state. This phenomenon occurs because changes in the concentration of ${N_{ITO}}$ significantly impact the resonance intensity of quasi-BIC mode II but hardly impact mode I. Furthermore, the modulation depth can be calculated as follows [56]:

In the formula (8), ${T_0}$ represent the original transmittance spectrum, and ${T_1}$ express the modulated transmittance spectrum. Figure 10(b) shows the calculated extinction ratio. Applying a bias voltage enables the modulator to achieve a modulation depth of -17∼24 dB at 1200-1250 nm. For active optical modulation, epsilon-near-zero (ENZ) materials are more likely to attain dielectric constants close to zero or even less than zero compared with other commonly used active materials, including vanadium dioxide (VO₂) and chalcogenide GST [36,37], two-dimensional material graphene [35]. When modifying the carrier density, ENZ materials display a substantial dielectric constant contrast, which enables more extensive and pronounced optical modulator.

 

Fig. 10. (a) Transmission spectrum with different ${N_{ITO}}$ values at the EIT window. (b) Modulation depths of EIT under different $ {N_{ITO}}$ values.

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Accompanied with the active control of the EIT resonance, the dispersion behavior as well as the resulted ability to slow down light propagation show dynamic modulation in the transparent window. The group delay can be used to describe the slow light effect, ${\tau _g} = d\varphi /d\omega $, where $\varphi $ is the transmission shift. Transmission phase shift and group delay variation with ${N_{ITO}}$ for metasurface were calculated after ITO integration in Fig. 11. After integrating of the ITO film, the group delay gradually decreases as the carrier concentration increases. The group delay is 0.1 ps at ${N_{ITO}}$ = 1.56 × 10¹⁹cm^-3 and the group delay is only 0.01 ps at ${N_{ITO}}$ = 1.23 × 10²¹cm^-3. As a result, the slow light capability also decreases with the increase of ITO carrier density.

 

Fig. 11. Transmission phase shift and group delay of the proposed dielectric-ITO metasurface at different N_ITO value.

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4. Conclusion

In summary, we analyzed EIT and various BIC modes in all-dielectric metasurface and examined the spectral modulation through the EIT transmission of ENZ (ITO) materials. We have found that by altering the length proportion of unilateral rectangular holes in highly symmetrical composite air hole nanostructures, metasurface can activate a high-Q-factor EIT and double BICs. A sharp quasi-BIC resonance and a magnetic dipole resonance destructively interfere to cause an electromagnetic induction transparency effect within the optical communication range. We comprehensively explained the physical properties and excitation mechanisms of EIT and quasi-BICs using far-field multipole decomposition, near-field electromagnetic field distribution, and far-field radiation contributions. To investigate the modulation function of the device, we introduced an ENZ material (ITO) system. By implementing a bias voltage, we achieved modulation depths of -17 to 24 dB in the 1200-1250 nm range, whereas the high-transmission/low-transmission status of the modulator can be toggled through various carrier densities. The design permits precision control over the perturbation parameters of these quasi-BICs to achieve ultra-high Q-factors. Our study findings provide a robust basis for the advancement of high-performance optical modulation devices and optoelectronic switching devices.