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

摘要

The energy level of the exciton around the $\Gamma$ point in CaF$_2$ at about11.1 eV was investigated by reflection measurements on oriented surfaces usingdispersed synchrotron radiation. A small but clear energy shift of the excitonresonance structure was observed which depends on the crystal orientation withrespect to the incoming beam. By interpreting the results in terms of thecomplex dielectric function it becomes possible to determin the respectiveexciton levels and lifetimes. For crystal samples oriented in the (111)direction, the exciton has an excitation energy 0.02 eV above the energy ofsamples oriented in the (100) direction. The results obtained suggest that theexciton-energy shift is related to the spatial anisotropy recently measured inCaF$_2$ at 157 nm.