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.
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 ${\mathrm{cm}}^{\ensuremath{-}1}$.
The relaxation of resonant 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons trapped in a laser-excited cylinder of submillimeter diameter is investigated under the conditions of modulated pumping in ruby of 130, 700, and 2500 at. ppm
Cr3+ at 1.5 K. The decay time
Teff of the 2\ifmmode \bar{A}\else \={A}\fi{}
(2E) population, which is a measure of the phonon relaxation time, appears to depend on the metastable population
N∗ and the cylinder diameter L as the product
N∗L only, establishing boundary-limited phonon decay. At
N∗L below 5\ifmmode\times\else\texttimes\fi{}
1015 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, pure spatial diffusion prevails.At higher
N∗L, where the measured
Teff levels off at about 1 \ensuremath{\mu}s, dependent on the ground-state concentration, the phonon relaxation is adequately accounted for by the assumption of enhancement by mediation of frequency-shifting Orbach processes at metastable
Cr3+ subject to diagonal exchange with ground-state
Cr3+. Shifts away from resonance to the extent that the phonons escape the zone by ballistic flight are considered active, which predominantly involve distant
Cr3+ neighbors.Furthermore, a random distribution of
Cr3+ is assumed, while the exchange is calibrated with reference to pair spectra. The spin-nonflip transitions of metastable
Cr3+ that are part of the pairs remain at resonance with the phonons because the exchange splittings of \ifmmode \bar{E}\else \={E}\fi{}
(2E) and 2\ifmmode \bar{A}\else \={A}\fi{}
(2E) are comparable. This is borne out by a separate calculation based on a perturbative molecular field. In addition, experiments have been performed as a function of an external magnetic field up to 4 T parallel to the c axis to disclose the effects of successive separation of the spin-flip and spin-nonflip transitions. The resultant complex development of
Teff with field as well as similar data on the
R2 luminescent intensity taken with continuous optical pumping are consistent with exchange-invoked relaxation and, further, yield effective spectral widths of the 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ transitions of the weakly coupled metastable
Cr3+ of order 1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.
According to several recent studies, the width of the sharp zero-phonon lines in the electronic spectra of impurities in solids, such as the
R lines of ruby, is due to Raman scattering of phonons by the impurity ions. The question whether such zero-phonon lines are homogeneously broadened is an important one, both for its own interest and for optical-maser applications. From a detailed study of the stimulated-emission spectra of a ruby laser operating in the traveling-wave modes, we obtain conclusive evidence that such zero-phonon lines are homogeneously broadened. Because the
R1 line of ruby is essentially homogeneously broadened at room temperature, the traveling-wave laser oscillates for all practical purposes only in a single mode. The spectral width of the laser emission is extremely sharp. It is less than 0.005 ${\mathrm{cm}}^{\ensuremath{-}1}$ at room temperature as compared to a width of the order of 1 ${\mathrm{cm}}^{\ensuremath{-}1}$ for conventional ruby lasers of comparable intensity. In addition, the output intensity no longer shows random spikes but shows a predictable train of regularly spaced spikes which agree well with theory.