Two-photon excitation of the anti-Stokes photoluminescence of Ca$_{1-x}$Er$_{x}$F$_{2+x}$ crystals

Crystals of the composition Ca$_{1-x}$Er$_{x}$F$_{2+x}$ (0 $<x\le$ 0.02) have been grown from the melt by the Bridgman method. The absorption, luminescence excitation, and photoluminescence spectra of this material in the case of the Stokes and anti-Stokes mechanisms of the optical excitation from two radiation sources simultaneously have been analyzed. It has been found that the visible luminescence manifests itself upon sequential absorption of two resonance infrared photons with different energies. This effect is associated with the fact that, in this material, there are metastable states of the excited levels $^{4}I_{11/2}$ of the Er$^{3+}$ ions, from which transitions to higher energy levels occur due to the absorption of infrared photons.