Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals

Abstract

Spectroscopic studies and the efficiency of optical coherent transient devices can be adversely affected by interference arising from several distinct Rabi frequencies associated with crystallographically equivalent but orientationally inequivalent crystal sites. General symmetry principles have been used to find light field directions that guarantee both optimum single-Rabi-frequency interaction and the most efficient coherent transient generation in arbitrary crystals. This theoretical analysis has been applied experimentally to a wide range of rare earth crystals, many of which are important for technological applications. Site interference in optical nutation provides a simple illustration of this effect. Optimum single-Rabi-frequency nutation signal was obtained for the ${}^{3}{H}_{6}(1)$ to ${}^{3}{H}_{4}(1)$ transition of 0.1% ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ when the light $\stackrel{\ensuremath{\rightarrow}}{E}$ vector is along special crystal directions $〈111〉$ or $〈001〉.$ Quantitative comparison of nutation frequencies for light polarized along different directions allowed the determination of the optical transition dipole moment to be along $〈110〉$ for this transition. The transition dipole moment derived from the nutation signal agrees within 15% with that obtained from absorption experiments. Other applications of nutation measurements are discussed, including a procedure for determining site occupancy in crystals with crystallographically inequivalent sites.