宽带介质镜厚度的下界
Lower bound on the thickness of broadband dielectric mirrors
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中文总结 AI 辅助
该研究推导了宽带无损耗介质镜总厚度的下界，明确了影响下界的因素及材料品质因数，发现可实现厚度约为下界的两倍。
中文摘要 AI 辅助
针对给定波长带内的最小反射率，我们给出了无损耗、无色散介质镜总物理厚度的下界。该下界基于源自声学领域已知结果的因果性求和规则，该规则将任何无损耗一维折射率分布的对数透射率的波长积分表示为构成该分布的各材料总厚度的函数，与层的排列方式无关。计算介质镜的厚度下界时，给定入射介质和基底，仅需薄膜堆中使用的最高和最低折射率，以及给定波长范围内所需的最小反射率。我们发现：（1）该下界由波长范围决定，例如，400-700 nm和800-1100 nm的介质镜具有相同的下界；（2）最小化必要厚度的材料的品质因数为$(n_H-n_L)^2/(n_H+n_L)$，其中$n_H$和$n_L$分别为高折射率和低折射率材料的折射率；（3）反射率每提高一个“9”（例如从99%到99.9%）的要求，会给下界增加固定的额外厚度。非穷尽数值计算表明，可轻松实现的厚度约为我们给出的下界的两倍。
英文摘要
We present a lower bound on the total physical thickness of a lossless, non-dispersive dielectric mirror for a given minimum reflectance across a wavelength band. The bound is based on a causality-based sum rule translated from a known result in acoustics, that expresses the wavelength integral of the logarithmic transmission of any lossless one-dimensional refractive-index profile as a function of the total thickness of each material comprising the profile, independent of how the layers are arranged. Calculating the thickness bound for a dielectric mirror, given some incident medium and substrate, requires only the lowest and highest refractive indices used in the thin-film stack and the minimum desired reflectance for a given wavelength span. We find that (1) the bound is set by the wavelength span so, for example, a 400-700 nm and an 800-1100 nm mirror have the same bound; (2) the figure of merit for materials minimizing the necessary thickness is $(n_H-n_L)^2/(n_H+n_L)$, where $n_H$ and $n_L$ are the indices of the high- and low-index materials; and (3) each additional "nine" of reflectance (e.g., from 99% to 99.9%) requirement adds a fixed amount of additional thickness to the bound. Non-exhaustive numerical calculations show that the readily achievable thickness is about twice our bound.
