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arXiv 1909.05069physics.opticscond-mat.mtrl-sci
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双轴晶体平板中电磁模色散的解析近似

Analytical approximations for the dispersion of electromagnetic modes in slabs of biaxial crystals

Gonzalo Álvarez-Pérez, Kirill V. Voronin, Valentyn S. Volkov, Pablo Alonso-González, Alexey Y. Nikitin

摘要:

各向异性晶体最近吸引了相当大的关注,因为它们能够支持具有各种独特性质的极化激元,如双曲色散,负相速度,或极端限制。特别地,双轴晶体$α$ $_3$已被证明支持声子极化激元,光耦合到晶格振动,具有面内各向异性传播和异常长的寿命。然而,在双轴晶体板电磁模式的理论研究的缺乏阻碍了实验数据的完整解释,以及支持这种高度各向异性极化激元的纳米结构的有效设计。本文推导了由具有任意介电常数的半无限各向同性介质半空间包围的双轴平板中电磁模式的色散关系。除了一般的色散关系,我们在纳米光学的典型实验中提供了非常简单的解析表达式:短极化激元波长和/或非常薄的板的极限。我们的研究结果将允许在新的双轴范德华材料的各向异性极化激元的深入分析。

英文摘要:

Anisotropic crystals have recently attracted considerable attention because of their ability to support polaritons with a variety of unique properties, such as hyperbolic dispersion, negative phase velocity, or extreme confinement. Particularly, the biaxial crystal $α$-MoO$_3$ has been demonstrated to support phonon polaritons, light coupled to lattice vibrations, with in-plane anisotropic propagation and unusually long lifetime. However, the lack of theoretical studies on electromagnetic modes in biaxial crystal slabs impedes a complete interpretation of the experimental data, as well as an efficient design of nanostructures supporting such highly anisotropic polaritons. Here, we derive the dispersion relation of electromagnetic modes in biaxial slabs surrounded by semi-infinite isotropic dielectric half-spaces with arbitrary dielectric permittivities. Apart from a general dispersion relation, we provide very simple analytical expressions in typical experiments in nano-optics: the limits of short polaritonic wavelength and/or very thin slabs. The results of our study will allow for an in-depth analysis of anisotropic polaritons in novel biaxial van der Waals materials.

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