# Low-temperature infrared dielectric function of hyperbolic $\alpha$-quartz

## TL;DR

This study measures and models the infrared dielectric properties of $ extalpha$-quartz from 1.5 K to 200 K, revealing temperature-dependent phonon behavior and predicting high-quality polaritons in its hyperbolic spectral region.

## Contribution

The paper provides a comprehensive temperature-dependent dielectric function model for $ extalpha$-quartz, extending previous high-temperature data down to 1.5 K and predicting low-temperature polariton quality factors.

## Key findings

- Dielectric function characterized from 1.5 K to 200 K.
- Phonon parameters fitted with a multioscillator model.
- Predicted high-Q polaritons in the hyperbolic spectral region.

## Abstract

We report the infrared dielectric properties of $\alpha$-quartz in the temperature range from $1.5\ \mathrm{K}$ to $200\ \mathrm{K}$. Using an infrared free-electron laser, far-infrared reflectivity spectra of a single crystal $y$-cut were acquired along both principal axes, under two different incidence angles, in S- and P-polarization. These experimental data have been fitted globally for each temperature with a multioscillator model, allowing to extract frequencies and damping rates of the ordinary and extraordinary, transverse and longitudinal optic phonon modes, and hence the temperature-dependent dispersion of the infrared dielectric function. The results are in line with previous high-temperature studies, allowing for a parametrized description of all temperature-dependent phonon parameters and the resulting dielectric function from $1.5\ \mathrm{K}$ up to the $\alpha$-$\beta$-phase transition temperature, $T_C = 846\ \mathrm{K}$. Using these data, we predict remarkably high quality factors for polaritons in $\alpha$-quartz's hyperbolic spectral region at low temperatures.