Polariton Waveguide Modes in Two-Dimensional Van der Waals Crystals: An Analytical Model and Correlative Scanning Near-Field Optical Microscopy Studies

Two-dimensional van der Waals (vdW) crystals can sustain various types of polaritons with strong electromagnetic confinements, making them highly attractive for the nanoscale photonic and optoelectronic applications. While extensive experimental and numerical studies are devoted to the polaritons of the vdW crystals, analytical models are sparse. Particularly, applying such a model to describe the polariton behaviors visualized by state-of-art near-field optical microscopy requires further investigation. Herein, we develop an analytical waveguide model to describe the polariton propagations in vdW crystals. The dispersion contours, dispersion relations, and electromagnetic field distributions of different polariton waveguide modes are derived. The model is verified by near-field optical imaging and numerical simulation of phonon polaritons in the {\alpha}-MoO3, a typical vdW biaxial crystals. The model can be extended to other types of polaritons in vdW crystals, thus allowing for describing and understanding their localized electromagnetic behaviors analytically.