By using far-infrared laser spectroscopy we have studied the temperature dependence of the absorption that is due to transitions between the E ((2)E) and 2A ((2)E) levels of excited Cr(3+) ions in ruby. From the temperature dependence of the linewidth we determined the inhomogeneous and the homogeneous contributions to line broadening. From the homogeneous width the lifetime of the 2A level was obtained. We found that, for emperatures up to 70 K, the lifetime is due mainly to one-phonon relaxation, whereas at higher temperatures another relaxation process, probably a two-phonon Raman process, becomes strong.
A large number of small but sharp changes (increases and decreases) of the R 1 fluorescence in ruby are observed as a function of applied magnetic field between 2 K and 77 K. At liquid helium temperatures, these signals have linewidths much narrower than the inhomogeneous linewidth (∼0.1 cm -1 ) of the R 1 line. All of these signals appear at the fields where the Zeeman splittings in the excited state \bar E ( 2 E ) and the ground state 4 A 2 satisfy an energy-matching condition for simultaneous transitions of two or more ions. Two distinct mechanisms are found to be responsible for the signals: spin-spin cross-relaxation between \bar E ( 2 E ) and 4 A 2 , and resonant self-trapping of the R 1 line. From the temperature dependence of the linewidths of the signals, thermal broadening of \bar E ( 2 E ) is measured below 77 K. Similar signals are observed in the N lines due to energy transfer from isolated ions to pairs.
The time evolution of the non-spin-flip $2\overline{A}\ensuremath{\leftrightarrow}\overline{E}$ spin-lattice relaxation in ruby has been studied with subnanosecond time resolution, following excitation of the broadband
Cr3+ states with a
N2 laser pumped-tunable-dye laser. From the short-time dependence of the
R1 and
R2 emission we directly obtain
T1=1.1 ns for this relaxation. The branching ratio for relaxation from the broadband states to the
E and
2A states, respectively, is found to be 2.6. The significance of these measurements in relation to previous estimates of
T1 and to recent 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonon spectroscopy is discussed.
The fluorescent decay of the 2E level of Cr3+ over the range of 77 to 300 K has been studied in experimental arrangements providing strong trapping of the O-phonon lines. At 300 K, rubies as large as 2.5-cm diameter by 33-cm length were used and were packed in highly reflective BaSO4 powder to provide adequate trapping of the O-phonon fluorescence. The measurements resulted in the determination explicitly of the lifetime vibronic transitions and the O-phonon decay rate. These studies of lifetime enhancement have potential application in the design of efficient solid-state lasers.
We have measured the radiative efficiency (ratio of
R-line photons to the total number of photons emitted) and absorption cross sections for the
R lines of dilute ruby, as a function of polarization and temperature between 20 and 373\ifmmode^\circ\else\textdegree\fi{}K. We have also measured the fluorescent lifetime from 20 to 373\ifmmode^\circ\else\textdegree\fi{}K in optically thin crystals, and from 20 to 273\ifmmode^\circ\else\textdegree\fi{}K in optically thick crystals. The difference between the reciprocal lifetimes in thin and thick crystals is directly comparable (via the Einstein relations) with the integrated absorption in the
R lines. This comparison shows that for the
R lines at 20 and 77\ifmmode^\circ\else\textdegree\fi{}K detailed balance holds to well within the experimental error of 5%, a precision never to our knowledge previously approached in solids. An upper limit of 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ was placed on any Stokes shift of the
R1 line, confirming that it is a no-phonon line. Comparison of $\ensuremath{\sigma}$ and $\ensuremath{\alpha}$ spectra confirms that the
R lines and their vibronic satellites are predominately electric-dipole in character. The radiative efficiency of the
R lines is strongly polarization dependent, a result which differs from that of previous workers. Its temperature dependence agrees well with that calculated from the observed vibronic spectrum at 77\ifmmode^\circ\else\textdegree\fi{}K. The integrated absorption in the
R lines increases by about 20% between 20 and 373\ifmmode^\circ\else\textdegree\fi{}K. The absorption in the vibronic satellites on the high-frequency side of the
R lines appears to be weaker than the corresponding emission on the low-frequency side. The temperature variation of the lifetime agrees well with that calculated from the absorption and radiative efficiency, but about 10% of the decay at 77\ifmmode^\circ\else\textdegree\fi{}K and 30% at 373\ifmmode^\circ\else\textdegree\fi{}K is either nonradiative or by emission at wavelengths outside the range of observation. The implications of our results for laser work are discussed.