Infrared permittivity of the biaxial van der Waals semiconductor $\alpha$-MoO$_3$ from near- and far-field correlative studies

TL;DR

This study accurately characterizes the infrared dielectric function of biaxial $ ext{MoO}_3$ using combined far-field and near-field optical methods, validated by simulations and DFT insights, advancing nanomaterial optical modeling.

Contribution

It introduces a correlative approach combining far- and near-field studies to precisely determine the dielectric function of $ ext{MoO}_3$, surpassing traditional methods.

Findings

Achieved quantitative agreement between far- and near-field optical properties.

Validated the dielectric model with simulations and DFT calculations.

Provided new insights into vibrational states affecting optical properties.

Abstract

The biaxial van der Waals semiconductor $\alpha$-phase molybdenum trioxide ($\alpha$-MoO$_3$) has recently received significant attention due to its ability to support highly anisotropic phonon polaritons (PhPs) -infrared (IR) light coupled to lattice vibrations in polar materials-, offering an unprecedented platform for controlling the flow of energy at the nanoscale. However, to fully exploit the extraordinary IR response of this material, an accurate dielectric function is required. Here, we report the accurate IR dielectric function of $\alpha$-MoO$_3$ by modelling far-field, polarized IR reflectance spectra acquired on a single thick flake of this material. Unique to our work, the far-field model is refined by contrasting the experimental dispersion and damping of PhPs, revealed by polariton interferometry using scattering-type scanning near-field optical microscopy (s-SNOM) on thin flakes of $\alpha$-MoO$_3$, with analytical and transfer-matrix calculations, as well as full-wave simulations. Through these correlative efforts, exceptional quantitative agreement is attained to both far- and near-field properties for multiple flakes, thus providing strong verification of the accuracy of our model, while offering a novel approach to extracting dielectric functions of nanomaterials, usually too small or inhomogeneous for establishing accurate models only from standard far-field methods. In addition, by employing density functional theory (DFT), we provide insights into the various vibrational states dictating our dielectric function model and the intriguing optical properties of $\alpha$-MoO$_3$.