Spatial anisotropy of the exciton level in CaF$_2$ at 11.1 eV and its relation to the weak optical anisotropy at 157 nm

TL;DR

This study investigates the spatial anisotropy of the exciton level in CaF$_2$ at 11.1 eV through reflection measurements, revealing orientation-dependent energy shifts that relate to weak optical anisotropy at 157 nm.

Contribution

It provides the first detailed measurement of exciton energy anisotropy in CaF$_2$ and links it to optical anisotropy at 157 nm.

Findings

Exciton energy varies with crystal orientation by 0.02 eV.

Reflection measurements reveal anisotropic exciton properties.

The exciton energy shift correlates with optical anisotropy at 157 nm.

Abstract

The energy level of the exciton around the $\Gamma$ point in CaF$_2$ at about 11.1 eV was investigated by reflection measurements on oriented surfaces using dispersed synchrotron radiation. A small but clear energy shift of the exciton resonance structure was observed which depends on the crystal orientation with respect to the incoming beam. By interpreting the results in terms of the complex dielectric function it becomes possible to determin the respective exciton levels and lifetimes. For crystal samples oriented in the (111) direction, the exciton has an excitation energy 0.02 eV above the energy of samples oriented in the (100) direction. The results obtained suggest that the exciton-energy shift is related to the spatial anisotropy recently measured in CaF$_2$ at 157 nm.