High-Quality-Factor Electromagnetically Induced Transparency in All-Dielectric Metasurfaces Supporting Quasi-Bound States in the Continuum

Abstract

Electromagnetically induced transparency based on bound states in the continuum (EIT-BIC) has emerged as a significant research focus in photonics due to its exceptionally high quality factor (Q-factor). This study investigates a periodic dielectric metasurface composed of silicon bar–square ring resonators, with a comparative analysis of both monolayer and bilayer configurations. Through systematic examination of transmission spectra, electric field distributions, and Q-factors, we have identified the existence of EIT-BIC and quasi-BIC phenomena in these structures. The experimental results demonstrate distinct characteristics between monolayer and bilayer systems. In the monolayer configuration, a single BIC is observed in the low-frequency region, with its quasi-BIC state generating an EIT window. In contrast, the bilayer structure exhibits dual BICs and dual EIT phenomena in the same spectral range, demonstrating enhanced spectral modulation capabilities. Notably, in the high-frequency region, both configurations maintain a single BIC, with the number remaining independent of structural layer count. The number and spectral positions of BICs can be effectively modulated through variations in incident angle and structural symmetry. In particular, the bilayer configuration demonstrates superior modulation characteristics under oblique incidence conditions, where the quasi-BIC linewidth broadens with increasing incident angle, forming a broader high-Q transparency window. This comparative study between monolayer and bilayer systems not only elucidates the influence of structural layers on BIC characteristics but also provides new insights for flexible spectral control. These findings hold significant implications for artificial linear modulation and play a crucial role in the design of future ultra-high-sensitivity sensors, particularly in optimizing performance through structural layer engineering.

1. Introduction

Bound state in the continuum (BICs) is a concept first introduced in quantum systems in 1929 by two sages of quantum physics, John von Neumann and Eugene Paul Wigner [1]. This is a universal fluctuation phenomenon whose energy exists in the form of a bound state in the continuum region of the eigenstates [2]. It has been found in water waves [3,4,5], sound waves [6,7,8] and electromagnetic waves [9]. In recent years, its new phenomena in different material media and different types of situations have been investigated through extensive experiments [10]. In the radiation continuum domain, BICs represent a special class of electromagnetic eigenstates that do not radiate. Although its sum momentum may match that in vacuum, the BIC is still completely confined inside the resonant system [11,12,13]. Based on the high quality factor (Q-factor), quasi-BICs show great promise for a variety of applications in areas such as narrowband filtering [14], high-sensitivity sensing [15,16], and molecular spectral coding for imaging and image edge detection [17].

Photonic crystals and optical metamaterials, as typical periodic optical systems, interact with light at subwavelength scales and are capable of creating a high density of electromagnetic energy localization in a very small space [18,19,20]. This property makes them a platform for studying light–matter interactions and manipulating the properties of light fields [21]. The BICs in photonic systems arise from the strong interaction between light and the material structure, where certain resonant conditions prevent radiation, and its Q-factor theoretically tends to infinity, but in practice, it is not possible to exist in an infinite periodic system, and engineering mainly applies its radiation leakage to quasi-BIC [22,23,24,25]. Researchers have successfully achieved the research transition from BIC to quasi-BIC over nearly a decade of experiments using the design of asymmetric structures, changing the geometry of the system, and choosing different dielectric materials [26,27,28]. By the above, a BIC without linewidth can be changed into a quasi-BIC containing a certain linewidth and at the same time with a high Q-factor and in the form of an EIT resonance [29].

Dielectric metasurfaces are a novel artificial two-dimensional structure that consists of subwavelength-sized scatterers arranged by subwavelength spacing, which are capable of modulating the amplitude, phase and polarization of light within the subwavelength thickness. While metallic systems have large absorption losses that make them unsuitable for use in high-efficiency devices, dielectric materials, which have only small dissipation losses and good chiral properties, have attracted a lot of attention from researchers in recent years. In 2020, Katsuya Tanaka et al. investigated a mechanism to maximize the chiral response of photonic nanostructures and declared that efficient ultrathin polarization elements can be applied to future integrated circuits. In 2023, Lijuan Wu et al. experimentally demonstrated magnetically quasi-BICs in dielectric metasurfaces while showing that magnetic dipole BICs have great potential for manipulating spontaneous emission [30,31]. Chiral properties refer to the differential response of a material to left-handed and right-handed circularly polarized light, which is essential for polarization-sensitive applications such as optical filters and sensors.

In this thesis, a periodic dielectric metasurface structure consisting of a silicon bar and a silicon square ring is explored. By scrutinizing the transmission spectra, electric field distribution, and Q-factor of the structure, we not only reveal the existence of EIT-BIC and quasi-BIC, but also find that the variation in the incident angle and the symmetry of the structure can effectively modulate the number and position of the BIC. The results show that we can achieve precise and flexible control of the spectral properties by flexing the structural parameters, changing the angle of incident light, and optimizing the combination of resonators inside the structure. This finding is of great significance for realizing the artificial linear regulation strategy and provides new ideas and research in related fields. Meanwhile, due to the high quality factor of this all-dielectric metasurface structure, its sensing sensitivity is enhanced accordingly, which lends the results of this research significant potential for application in the field of ultra-high-sensitivity sensor design. In contrast, the bilayer structure exhibits dual BICs and dual EIT phenomena in the same spectral range, demonstrating enhanced spectral modulation capabilities. Notably, in the high-frequency region, both configurations maintain a single BIC, with the number remaining independent of structural layer count. The number and spectral positions of BICs can be effectively modulated through variations in incident angle and structural symmetry. Particularly, the bilayer configuration demonstrates superior modulation characteristics under oblique incidence conditions, where the quasi-BIC linewidth broadens with increasing incident angle, forming a broader high-Q transparency window. This comparative study between monolayer and bilayer systems not only elucidates the influence of structural layers on BIC characteristics but also provides new insights for flexible spectral control. These findings hold significant implications for artificial linear modulation and play a crucial role in the design of future ultra-high-sensitivity sensors, particularly in optimizing performance through structural layer engineering. The transmission spectra and electric field distributions were computed using CST Studio Suite, a commercial electromagnetic simulation software. The finite-difference time-domain (FDTD) method was employed to simulate the optical response of the metasurface under different incident angles.

2. Discussion of the Experimental Process and Results

In order to study the modulation of EIT-BIC and its sensing characteristics, we designed a coupled resonators consisting of a bar and a square ring within a cycle. The resonator is made of silicon with a refractive index of 3.7 and uses silicon dioxide with a refractive index of 1.48 as a substrate. The working principle is shown in Figure 1a. For the EIT transparent window centered on dipole resonance, the geometrical parameters are optimized as follows: the length and width of the bar are L₃ = 210 μm and W₃ = 37.695 μm, respectively, and the dimensions of the square ring are L₁ = 115.5 μm, W₁ = 68.25 μm, and L₂ = 102.375 μm, W₂ = 55.125 μm, respectively. The thickness of the silica substrate is fixed at 25.41 μm. To ensure sufficient coupling strength, the set period P_x is taken as 210 μm and P_y is taken as 210 μm so that the spacing between the resonators is D = 17.9025 μm. Transmission spectra, Q-factor, and electric field distributions are systematically computed by varying the parameters such as the angle of incident light (θ).

In order to study the symmetry-protected BIC, the incident light is used as a P-polarized plane wave, polarized along the x-direction and propagating along the z-direction, and we have investigated the phenomena arising from the spectra under bar, square ring, and bar–square ring metasurface geometries, respectively. The design of the proposed metasurface is inspired by previous work on dielectric metasurfaces, particularly the studies by [31], which demonstrated the potential of chiral metasurfaces for polarization control. From Figure 2a, it can be seen that in the case of metasurface with only periodic bars in it, and leaky modes are shown clearly. The unit cell size remains consistent across all configurations, including the system without rings in Figure 2a. However, as the angle of incidence of the excitation light increases, the leaky modes of the bar undergo a significant redshift. While only the rings exist in the metasurface, it is clear that two symmetry-protected BICs appear in Figure 2b. Both individual resonators have intrinsic modes and specific angle-dependent dispersion in the spectral range of interest, providing a solid foundation for the study of BICs when two resonators are coupled to each other. Then, the structure is changed to a bar–square ring, as shown in Figure 2c. As can be seen in Figure 2c, in the first Brillouin zone near 0.803 THz at an incident angle of 0°, under the effect of structural symmetry protection, an at-Γ BIC occurs with no decay in energy, and the width of the peak is zero. This phenomenon is due to the collective oscillation of the column resonator, as the bright one can effectively couple with the incident wave. Also from Figure 2d, it can be seen that the bar–square ring metasurface shows a transparent window with a half-height width of 0.803 THz at an incident angle of 0.35° in the range of 0.771 THz to 0.828 THz, which is reduced to 0.799 THz when the incident angle is increased to 2.1°, and will be reduced to 0.793 THz if it continues to increase to 4.2°. Figure 2e shows a quasi-BIC with an increase in the oblique incident angle, but no transparent window appears, when the incident light deviates slightly from the vertical direction. The full width at half maximum is 0 at this time when the incident angle is 0°, the half-height width increases to 0.935 THz when the incident angle increases to 3.15°, and the half-height width increases to 0.94 THz when the incident angle increases to 7°.

According to the above spectrum, when the incident light deviates from the vertical, symmetry protection is broken, and as the oblique angle of incidence increases, there will be a leakage mode; the width of the mode line is directly proportional to the size of the angle of incidence, and the width of the line reflects the Q-factor of the system and the radiation loss. Generally, for dielectric structures with geometric symmetry, as the incident angle is increasing, the original symmetry may be broken, resulting in the BIC changing to quasi-BIC and the leakage of the film appearing as a phenomenon of energy attenuation. The formation of BICs can be observed in Figure 2 through the sharp resonance peaks in the transmission spectra. These peaks correspond to the bound states in the continuum, which are characterized by their high quality factor (Q-factor) and minimal radiation loss.

BIC mainly refers to a state that lies in the continuous domain but is perfectly confined without any far-field radiation and cannot be excited by an incident wave. This state has an infinitely narrow resonance peak and an infinitely large Q. Quasi-BIC, on the other hand, is a degenerate form of BIC in which the Q is degenerated to a finite value but remains high due to the weak radiation loss. Figure 3a,b represent the Q values when BIC1 at 0.803 THz and BIC2 at 0.933 THz appear on the bar–square ring metasurface. In the case of vertical irradiation, the Q values are infinite, and when the angle of incidence deviates from the zero-degree angle or the structure deviates from the symmetry, the Q value decreases significantly; this phenomenon illustrates that the BIC is converted into quasi-BIC from another aspect. Where the larger the Q value is, the greater the sensing sensitivity is, and the better the sensing characteristics. The larger the Q value, the stronger the sensing sensitivity and the better the sensing characteristics. The quality factor (Q-factor) is calculated using the expression Q = f₀/Δf, where f₀ is the resonance frequency, and Δf is the full width at half maximum (FWHM) of the resonance peak.

EIT is a technique to achieve optical transparency effects by modulating the physical properties of materials. In the EIT effect, atoms or molecules in a material are excited to a specific energy state, under certain conditions, and the absorption and scattering of light are suppressed, allowing light waves to pass through the medium nearly losslessly. The modulation of the EIT effect can be realized by adjusting the external electric field or changing the structure of the material, which in turn changes the distribution of the electric field in the material. This kind of modulation has a wide range of applications in optical sensors, filters, and other fields.

Figure 4 reflects that when the angle of incidence gradually increases, the field potential will show a significant increase, for example, in Figure 4c, where the angle of incidence of 4.2° of the electric field strength is significantly greater than the angle of incidence of 0° of the electric field strength. However, this enhancement is not infinite, as can be seen in Figure 5; the electric field strength at an incident angle of 3.15° is more than twenty times that at an incident angle of 0°, but the field strength does not change significantly as the incident angle continues to increase to 6.3°. This is because the quasi-BIC will appear to have weak radiation leakage; due to this phenomenon, the general engineering applications of BICs will allow multiple leakage film interference and formation, so that a great deal of the mode radiation is lost, retaining most of the energy of the mode in the structure inside. The electric field distributions are shown in arbitrary units.

To further investigate the modulation of EIT-BIC and its sensing characteristics, we introduced an additional square ring resonator with identical dimensions to the original structure, as illustrated in Figure 6a. For the EIT window centered at the dipole resonance, the geometric parameters were optimized as follows: the bar resonator was designed with a length L₃ of 210 μm and width W₃ of 37.695 μm, while the square ring resonators were configured with dimensions of L₁ = 115.5 μm, W₁ = 68.25 μm, L₂ = 102.375 μm, and W₂ = 55.125 μm. The silicon dioxide substrate thickness was maintained at 25.41 μm. To ensure optimal coupling strength, the periodic parameters P_x and P_y were both set to 210 μm, resulting in an inter-resonator spacing (D) of 17.9025 μm. A schematic of a cycle consisting of three coupled resonators and the main view of the metasurface structure are illustrated in Figure 6b,c.

Under optical illumination, the bilayer symmetric structure exhibits two bound states in the continuum (BICs) at lower frequency ranges. As the incident angle increases, these BICs transform into quasi-BICs with progressively broadening linewidths. Within this spectral region, the two quasi-BICs form high-quality-factor transparency windows, effectively creating two electromagnetically induced transparency (EIT) phenomena. Compared to the transmission spectrum of a monolayer structure, the bilayer configuration maintains the presence of BICs in this frequency range, with quasi-BICs similarly generating EIT windows. However, the distinctive feature of the bilayer structure is the formation of dual BICs and dual EIT effects in this spectral region. Furthermore, at higher frequency ranges, the bilayer metasurface also demonstrates a BIC, whose linewidth gradually increases with the incident angle. Notably, the number of BICs at this higher frequency remains constant regardless of the increase in structural layers. This phenomenon is schematically illustrated in Figure 7a. Figure 7b illustrates the evolution of the transmission spectra as a function of the interlayer spacing, which corresponds to the thickness variation of the silicon dioxide substrate. A distinct blue shift of the bound state in the continuum (BIC) is clearly observed in the spectral response.

3. Conclusions

Transmission spectra of a metasurface composed of strip and square ring were investigated, and we analyzed the effect of a single component and the whole structure on BIC characteristics. Specifically, the individual component did not exhibit EIT-BIC in the appropriate frequency range, but EIT-BICs appear when the resonators couple to each other. However, it appears when the symmetry of the system is broken. The Q-factor of the quansi-BICs can exceed 10⁴. In contrast, the bilayer structure exhibits dual BICs and dual EIT phenomena in the same spectral range, demonstrating enhanced spectral modulation capabilities. Notably, in the high-frequency region, both configurations maintain a single BIC, with the number remaining independent of structural layer count. The number and spectral positions of BICs can be effectively modulated through variations in incident angle and structural symmetry. Particularly, the bilayer configuration demonstrates superior modulation characteristics under oblique incidence conditions, where the quasi-BIC linewidth broadens with increasing incident angle, forming a broader high-Q transparency window. This comparative study between monolayer and bilayer systems not only elucidates the influence of structural layers on BIC characteristics but also provides new insights for flexible spectral control. These findings hold significant implications for artificial linear modulation and play a crucial role in the design of future ultra-high-sensitivity sensors, particularly in optimizing performance through structural layer engineering. The results of this study have important guiding significance for the design of ultra-high-sensitivity sensors based on terahertz metasurfaces.