Four-wave mixing in alexandrite crystals

Degenerate four-wave mixing was observed in alexandrite crystals (Be${\mathrm{Al}}_2$ ${\mathrm{O}}_4$: ${\mathrm{Cr}}^{3+}$), and the signal beam efficiency and decay rate were measured as functions of pump beam-crossing angle, wavelength, and power. The results are consistent with scattering from excited-state population gratings related to the difference in dispersion of the ${\mathrm{Cr}}^{3+}$ ions in the ground and metastable states. These gratings can be selectively established with ${\mathrm{Cr}}^{3+}$ ions in the inversion or mirror sites depending on the excitation wavelength. Strong scattering occurs only for pump beams polarized parallel to the $b$ direction of the crystal.