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

Abstract

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 $\alpha$-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.

16 pages, 4 figures

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• Hybridized hyperbolic surface phonon polaritons at α-MoO3 and polar dielectric interfaces
• Nanoscale-confined Terahertz Polaritons in a van der Waals Crystal
• Enabling propagation of anisotropic polaritons along forbidden directions via a topological transition
• Active tuning of highly anisotropic phonon polaritons in van der Waals crystal slabs by gated graphene
• A perspective of twisted photonic structures
• Radiative thermal switch exploiting hyperbolic surface phonon polaritons
• Negative reflection and negative refraction in biaxial van der Waals materials
• Near-field probing of image phonon-polaritons in hexagonal boron nitride on gold crystals
• Radiative heat transfer in low-symmetry Bravais crystal
• Germanium monosulfide as a natural platform for highly anisotropic THz polaritons
• Twisted two-dimensional material stacks for polarization optics
• Spontaneous emission modulation in biaxial hyperbolic van der Waals material
• Probing and steering bulk and surface phonon polaritons in uniaxial materials using fast electrons: hexagonal boron nitride
• Twisted polaritonic crystals in thin van der Waals slabs
• Directional strong coupling at the nanoscale between hyperbolic polaritons and organic molecules
• Unveiling the Mechanism of Phonon-Polariton Damping in α-MoO_3
• Fourier analysis of near-field patterns generated by propagating polaritons
• Low-loss far-infrared surface phonon polaritons in suspended SrTiO3 nanomembranes
• Misalignment between the Directions of Propagation and Decay of Nanoscale-confined Polaritons
• Coupling between hyperbolic phonon polaritons excited in two ultrathin hBN sheets
• Long-range mid-infrared energy transfer mediated by hyperbolic phonon polaritons
• Image polaritons in van der Waals crystals
• Planar nano-optics in anisotropic media: anomalous refraction and diffraction-free lensing of highly confined polaritons
• Bloch phonon-polaritons with anomalous dispersion in polaritonic Fourier crystals
• Polariton Waveguide Modes in Two-Dimensional Van der Waals Crystals: An Analytical Model and Correlative Scanning Near-Field Optical Microscopy Studies