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arXiv 2103.15697physics.optics
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透明光学材料refractive index的基本限制

Fundamental limits to the refractive index of transparent optical materials

Hyungki Shim, Francesco Monticone, Owen D. Miller

摘要:

增加光学和纳米光子系统的折射率为设计开辟了新的前景:对于从宽带超透镜到半导体光电子器件再到高品质因数谐振器的应用,更高的折射率直接导致具有更大功能的更好的设备。尽管标准透明材料在可见光中的折射率被限制为小于3,但是最近的超材料设计已经实现了高于5的折射率,伴随着高损耗,并且在铁电钙钛矿的相变附近,已经要求高于26的宽带折射率。在这项工作中,我们得到的基本限制的任何材料的折射率,只给出了潜在的电子密度和最大允许色散或最小带宽的利益。Kramers-Kronig关系提供了一个表示任何被动(从而因果)的材料,和一个众所周知的总和规则约束可能的振子强度分布。在小到适度色散的领域,我们的界限非常接近,并且没有被广泛的天然材料超越,这表明自然界已经接近折射率和色散的帕累托边界。令人惊讶的是,我们的边界显示出对电子密度的立方根依赖性,这意味着在所有可见频率上的折射率为26可能是不可能的。相反,对于窄带宽应用,自然界并不提供我们的边界建议应该是可能的高色散,高折射率材料。我们使用复合材料的理论来确定金属基超材料,可以表现出小的损失和相当大的增加折射率超过目前最好的材料。

英文摘要:

Increasing the refractive index available for optical and nanophotonic systems opens new vistas for design: for applications ranging from broadband metalenses to ultrathin photovoltaics to high-quality-factor resonators, higher index directly leads to better devices with greater functionality. Although standard transparent materials have been limited to refractive indices smaller than 3 in the visible, recent metamaterials designs have achieved refractive indices above 5, accompanied by high losses, and near the phase transition of a ferroelectric perovskite a broadband index above 26 has been claimed. In this work, we derive fundamental limits to the refractive index of any material, given only the underlying electron density and either the maximum allowable dispersion or the minimum bandwidth of interest. The Kramers--Kronig relations provide a representation for any passive (and thereby causal) material, and a well-known sum rule constrains the possible distribution of oscillator strengths. In the realm of small to modest dispersion, our bounds are closely approached and not surpassed by a wide range of natural materials, showing that nature has already nearly reached a Pareto frontier for refractive index and dispersion. Surprisingly, our bound shows a cube-root dependence on electron density, meaning that a refractive index of 26 over all visible frequencies is likely impossible. Conversely, for narrow-bandwidth applications, nature does not provide the highly dispersive, high-index materials that our bounds suggest should be possible. We use the theory of composites to identify metal-based metamaterials that can exhibit small losses and sizeable increases in refractive index over the current best materials.

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