标题： 高介电超表面中高-$Q$共振的时域耦合模理论 显示英文标题

标题： Temporal coupled mode theory for high-$Q$ resonances in dielectric metasurfaces

摘要： 在本工作中，我们提出了一种耦合模理论，用于周期性介质超表面中准导模的共振响应。 首先，我们通过能量守恒和时间反演对称性推导出时间耦合模理论参数的一般约束条件，以不变形式表示，允许耦合和解耦系数之间的不对称性。 所提出的的方法应用于由孤立准导模在镜面反射区域引起的Fano共振问题。 我们的核心结果是在二维电磁动力学框架下，无损耗超表面透射率中Fano共振的通用线形公式。 我们考虑了超表面基本单元的所有可能对称性，并揭示了对称性对由孤立高-$Q$模引起的Fano共振轮廓的影响。 结果显示，所提出的方法正确描述了光谱中鲁棒反射和透射零点的存在以及连续体中束缚态的光谱特征。 该方法应用于具有非对称基本单元的超表面上的单向导引共振模。 发现此类模的存在及其光谱邻域的透射率与理论预测一致。 此外，该理论预测单向导引共振模与一种特殊类型的反向传播模相对应，该模在超表面两侧都与向外传播的波耦合，但仍然仅与入射波单侧耦合。 显示英文摘要

摘要： In this work, we propose a coupled mode theory for resonant response from quasi-guided modes in periodic dielectric metasurfaces. First, we derived a generic set of constraints imposed onto the parameters of the temporal coupled mode theory by energy conservation and time-reversal symmetry in an invariant form that allows for asymmetry between the coupling and decoupling coefficients. The proposed approach is applied to the problem of Fano resonances induced by isolated quasi-guided modes in the regime of specular reflection. Our central result is a generic formula for the line-shape of the Fano resonance in transmittance for the lossless metasurfaces in the framework of 2D electrodynamics. We consider all possible symmetries of the metasurface elementary cell and uncover the effects that the symmetry incurs on the profile of the Fano resonance induced by an isolated high-$Q$ mode. It is shown that the proposed approach correctly describes the presence of robust reflection and transmission zeros in the spectra as well as the spectral signatures of bound states in the continuum. The approach is applied to uniderictionally guided resonant modes in metasurfaces with an asymmetric elementary cell. It is found that the existence of such modes and the transmittance in their spectral vicinity are consistent with the theoretical predictions. Furthermore, the theory predicts that a uniderictionally guided resonant mode is dual to a counter-propagating mode of a peculiar type which is coupled with the outgoing wave on both sides of the metasurface but, nonetheless, exhibits only a single-sided coupling with incident waves.