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.
The ruby
R2-line intensity at 2.1 K is observed to be nearly quadratically depedent on the
R1 intensity, indicative of strongly bottlenecked 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons generated by the $2\overline{A}(^{2}E)\ensuremath{\rightarrow}\overline{E}(^{2}E)$ decay in the optical pumping cycle. The spectral width of the phonon excitation is probed by separating the degenerate phonon packets in a magnetic field and monitoring the decrease of the bottlenecking.
Direct relaxation within the optically excited
E(2E) level of 700-ppm ruby is investigated in magnetic fields up to 65 kG making an angle to the
c axis. At low pump intensities, the experimental relaxation rates are found to be in excellent agreement with the theory by Blume et al., predicting a fifth-power dependence on field and a ${cos}^{3}\ensuremath{\theta}{sin}^{2}\ensuremath{\theta}$ dependence on orientation. The observed proportionality constant of 4.7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}19}$ ${\mathrm{G}}^{\ensuremath{-}5}$${\mathrm{s}}^{\ensuremath{-}1}$ is close to the theoretical estimate based on static experiments in ruby. When increasing optical pumping, the phonon-bath conduction is demonstrated to become the limiting process due to resonant trapping of the phonons. Following pulsed excitation, a prolonging of the decay time by a factor up to 13 is attained at excited-state concentrations ${N}^{*}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. In stationary experiments, a nonlinear increase with
N∗ is observed of the equilibrium population of the upper Zeeman level of
E to over a decade above the nonbottlenecked value, corresponding to bottlenecking factors of over \ensuremath{\sim}200. Under the assumption of a constant phonon lifetime of the order of the flight time through the illuminated region, rate equations appear to consistently account for the experiments. A Gaussian-type resonance line, fully homogenized supposedly by magnetic interactions with the surrounding Al nuclei and
Cr3+ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the
E direct transition in ruby as a tunable phonon generator and detector with bandwidth 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ in the practical frequency range of 2-15 ${\mathrm{cm}}^{\ensuremath{-}1}$.
Spatial and, additionally, spectral diffusion of 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons trapped in an excited cylindrical region with diameter \ensuremath{\sim}0.1 mm has been investigated under continuous optical pumping of ruby. For 130- and 700-ppm ruby, phonon decay strictly limited by spatial diffusion is reflected in a quadratic dependence of the bottlenecking factor $\ensuremath{\sigma}$ on the excited-state concentration
N∗ up to ${N}^{*}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. At higher
N∗, attainable in 700- and 2500-ppm ruby, the observed reduction of $\ensuremath{\sigma}$ relative to the second-power dependence, as well as the increased width of the dependence of $\ensuremath{\sigma}$ on magnetic field, reveal that spectral diffusion from inhomogeneous packet to packet is operative. In the spatially diffusive regime, evidence for Zeeman-induced spectral diffusion is found in a characteristic narrowing of the magnetic-field dependence of the
R2 fluorescence upon raising $\ensuremath{\sigma}$. At full separation of the Zeeman transitions $2\overline{A}(^{2}E)\ensuremath{\leftrightarrow}\overline{E}(^{2}E)$, $\ensuremath{\sigma}$ is reduced to 15-40% relative to zero field, depending on
N∗ and ground-state concentration. Rate equations governing the
Cr3+ populations in the two-level scheme (
2A,
E) with inclusion of spatial diffusion and anharmonic decay of the phonons account for the second-power dependence. Diffusive phonon decay turns out to dominate from ${N}^{*}R\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}{10}^{13}/{\mathrm{cm}}^{2}$ up to at least ${N}^{*}{R}^{2}\ensuremath{\sim}{10}^{14}/\mathrm{cm}$, with
R the characteristic dimension of the excited region. Spectral diffusion, treated as a perturbation, satisfactorily fits the data at higher $\ensuremath{\sigma}$, yielding a diffusive step of \ensuremath{\sim}2% of the linewidth. At low bottlenecking, the functional form of the magnetic field dependence of $\ensuremath{\sigma}$, including its width and level at full separation, is closely described by use of rate equations, taking the line shape to be Gaussian-type, and assuming the phonons associated with spin flip and those with non spin flip to belong to distinct classes.
Trapping of 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons by optically excited
Cr3+ ions in ruby is studied at phonon occupations of up to order unity. The 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons are supplied by transient excitation of a metallic point contact and subsequent conversion of the injected phonons to resonance. The growth and the decay of the trapped phonon population are markedly non-single-exponential quantities, particularly at higher phonon populations. A quantitative analysis of these effects is made on the basis of phenomenological rate equations of the ion and phonon populations. These equations make explicit allowance for the line shape of the E\ifmmode\bar\else\textasciimacron\fi{}
(2E)-2A\ifmmode\bar\else\textasciimacron\fi{}
(2E) phonon transition as well as for feeding and loss of resonant phonons by mediation of weakly exchange-coupled
Cr3+ pairs. At the higher phonon occupations, the transition appears to be dynamically broadened by stimulated phonon emission, which reduces the trapping efficiency.