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All-dielectric terahertz metasurface based on bound states in the continuum and the research of its equivalent parameter
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摘要
本研究提出了一种基于连续域束缚态(bound states in the continuum, BIC)的全介质太赫兹超表面。超表面的每个结构单元由两个横截面为正方形的矩形块和衬底组成。衬底材料为石英，表面矩形块材料为无折射率损耗的硅。矩形块横截面面积的改变破坏了超表面的对称性，激发了准BIC，得到了具有极窄线宽的谐振。采用有限元方法(finite element method, FEM)和控制变量法研究了不同非对称参数、结构参数和材料参数下的透射光谱。同时，对所提出的超表面的
Q 值进行了计算，其Q 值可达1.1006×104，高于列出的相关文献中的Q 值。此外，该研究针对目前对全介质超表面等效参数的研究相对较少的局限性，利用S 参数提取法计算并分析了所提出的超表面的等效参数，并从该角度初步研究了超表面的物理性质。Abstract
In this research, an all-dielectric terahertz metasurface based on bound states in the continuum (BIC) is proposed. Each structural unit of the metasurface consists of two rectangle blocks with square cross-sections and a substrate. The substrate material is quartz, and the rectangle block material of the surface is lossless silicon. The symmetry of the metasurface is broken by tchanging the cross-section area of the rectangle block, and the quasi-BIC is excited. The resonance with extremely narrow linewidth is obtained. The transmission spectra with different asymmetric, structural and material parameters are studied using finite element method (FEM) and control variable method. Meanwhile, the
Q factor of the proposed metasurface is calculated, which can reach 1.1006×104 and is higher than theQ factors from related listed references. In addition, this study is aimed at the limitations of the relatively limited research on the equivalent parameters of all-dielectric metasurfaces, theS -parameter extraction method is utilized to calculate and analyze the equivalent parameters of the proposed metasurface and the physical properties of the metasurface is studied from this perspective preliminarily. -
Overview
Overview: In this research, an all-dielectric terahertz metasurface based on bound states in the continuum (BIC) is proposed. Each structural unit of the metasurface consists of two rectangle blocks with square cross-sections and a substrate. The asymmetric parameter Δw is defined as the reduction in edge length. The substrate material is quartz with a refractive index of 1.48, and the rectangular block material is silicon with a refractive index of 3.48 and no loss. The symmetry of the metasurface is broken by changing the cross-section area of the rectangle block, and the quasi-BIC is excited. The resonance with extremely narrow linewidth is obtained. The transmission spectra obtained from incident waves with different polarizations indicate that the resonance characteristics of the metasurface are significantly different under the two polarization modes, demonstrating its polarization dependence.
To study the resonance mechanism at the resonance frequency and gain a deeper understanding of the characteristics and behavior of the electric and magnetic fields, multipole decomposition is performed in Cartesian coordinates. At 1.6922 THz, the toroidal dipole (TD) dominates and the electric quadrupole (Qe) is suppressed, therefore the resonance type here is TD resonance. At 1.7611 THz, Qe dominates and TD is suppressed, therefore the resonance type here belongs to Qe resonance. The transmission spectra with different asymmetric , structural and material parameters are studied by using finite element method (FEM) and control variable method. Meanwhile, the Q factor of the proposed metasurface is calculated, which can reach 1.1006×104. From the table, compared to the metasurfaces listed in other literature, the proposed metasurface achieves a higher Q value. In addition, under the selected conditions, as the absolute value of Δw increases, the Q value decreases significantly. That is, under certain conditions, the Q value has an inverse quadratic relationship with the asymmetric parameter Δw, satisfying the equation Q ∝ Δw−2. At the same time, it can be seen that the closer the absolute value of Δw is to zero, the more the obtained Q value tends to infinity, which is in line with QBIC characteristics. In addition, this study is aimed at the limitations of the relatively limited research on the equivalent parameters of all-dielectric metasurfaces, the S-parameter extraction method is utilized to calculate and analyze the equivalent parameters of the proposed metasurface and the physical properties of the metasurface is studied from this perspective preliminarily.
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图 1 提出的全介质超表面结构与端口设置。(a)正视图；(b)俯视图；(c)端口设置
Figure 1. The structure of the proposed all-dielectric metasurface. (a) Front view; (b) Top view; (c) Port setting
图 2 不同偏振入射下的透射谱图。(a) x偏振；(b) y偏振
Figure 2. Transmission spectra under different polarization incidence. (a) x-polarization; (b) y-polarization
图 3 不同$ \Delta w $下的透射谱图
Figure 3. The transmission spectra under different $ \Delta w $
图 4 Δw = 1 μm时的多极子分解结果
Figure 4. The result of multipole decomposition under Δw = 1 μm
图 5 1.6922 THz与1.7611 THz处的位移电流密度、磁场分布与电场分布。(a) 1.6922 THz处位移电流密度；(b) 1.6922 THz处的电场；(c) 1.6922 THz处的磁场；(d) 1.7611 THz处移位电流密度；(e) 1.7611 THz处的电场；(f) 1.7611 THz处的磁场
Figure 5. Displacement current density, magnetic field distribution and electric field distribution at 1.6922 THz and 1.7611 THz. (a) The displacement current density at 1.6922 THz; (b) The electric field distribution at 1.6922 THz; (c) The magnetic field distribution at 1.6922 THz; (d) The displacement current density at 1.7611 THz; (e) The electric field distribution at 1.7611 THz; (f) The magnetic field distribution at 1.7611 THz
图 6 不同结构参数下的透射谱图。(a)衬底边长Px；(b)矩形块高度H；(c)矩形块间距g；(d)矩形块横截面边长w
Figure 6. Transmission spectra under different structural parameters. (a) Substrate size Px; (b) Rectangular block height H; (c) Rectangular block spacing g; (d) Rectangular block side length w
图 7 不同折射率损耗下得到的透射光谱
Figure 7. Transmission spectra obtained under different refractive index losses
图 8 Q值与$ \Delta w $的关系
Figure 8. The relationship between the Q value and the $ \Delta w $
图 9 提出的超表面的等效参数。(a)相对折射率；(b)等效阻抗；(c)相对磁导率；(d)相对介电常数
Figure 9. The equivalent parameters of the proposed metasurface. (a) Refractive index; (b) Equivalent impedance; (c) Relative permeability; (d) Relative dielectric constant
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