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arXiv 2501.09207physics.opticsmath-phmath.MP
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全反射与法布里-珀罗连续谱束缚态的关系

Relationship between total reflection and Fabry-Perot bound states in the continuum

Zitao Mai, Ya Yan Lu

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AI总结：

本研究探究全反射与法布里-珀罗连续谱束缚态（FP-BICs）的关联，发现波数为零或周期层具周期方向反射对称时全反射参数附近存在FP-BICs，非对称且波数非零时无法通过调参找到对应FP-BICs，明确全反射不必然产生FP-BICs。

摘要：

连续谱束缚态（BICs）具有独特的性质，在光子学领域有重要应用。一类特殊的BICs存在于由两片平行周期性介质层、间距为$h$构成的法布里-珀罗（FP，Fabry-Perot）腔中。单个周期性介质层可对特定频率、特定波数的入射平面波产生全反射。已有的FP-BICs均在$h$接近由与反射系数相关的相位匹配条件推导得出的数值时被发现，且这些FP腔中的周期性介质层在周期方向上具有反射对称性。本文进一步阐明了全反射与FP-BICs之间的关联。我们的数值结果表明，当波数为零，或周期性介质层在周期方向上具有反射对称性时，确实可以在全反射对应的参数附近找到FP-BICs。但当波数非零且周期性介质层（在周期方向上）不对称时，我们无法通过调节$h$或其他结构参数找到（频率和波数接近全反射对应参数的）FP-BICs。由此可见，即便调节FP腔的参数，全反射也并不总能产生FP-BIC。

英文摘要：

Bound states in the continuum (BICs) have interesting properties and important applications in photonics. A particular class of BICs are found in Fabry-Perot (FP) cavities formed by two parallel periodic dielectric layers separated by a distance $h$. A periodic dielectric layer can totally reflect a plane incident wave with a particular frequency and a particular wavenumber. Existing FP-BICs are found when $h$ is close to the values deduced from a phase-matching condition related to the reflection coefficient, but they are obtained in FP-cavities where the periodic layers have a reflection symmetry in the periodic direction. In this paper, we further clarify the connection between total reflections and FP-BICs. Our numerical results indicate that if the wavenumber is zero or the periodic layers have a reflection symmetry in the periodic direction, FP-BICs can indeed be found near the parameters of total reflections. However, if the wavenumber is nonzero and the periodic layer is asymmetric (in the periodic direction), we are unable to find a FP-BIC (with a frequency and a wavenumber near those of a total reflection) by tuning $h$ or other structural parameters. Consequently, a total reflection does not always lead to a FP-BIC even when the parameters of the FP-cavity are tuned.

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