DIFFUSION OF BOTTLENECKED 29-CM-1 PHONONS IN OPTICALLY-EXCITED RUBY

Spatial and, additionally, spectral diffusion of 29-cm-1 phonons trapped in an excited cylindrical region with diameter ∼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 σ on the excited-state concentration N* up to N*∼3×1017/cm3. At higher N*, attainable in 700- and 2500-ppm ruby, the observed reduction of σ relative to the second-power dependence, as well as the increased width of the dependence of σ 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 σ. At full separation of the Zeeman transitions 2Ā(E2)Ē(E2), σ 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 (2Ā,Ē) 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∼4×1013/cm2 up to at least N*R2∼1014/cm, with R the characteristic dimension of the excited region. Spectral diffusion, treated as a perturbation, satisfactorily fits the data at higher σ, yielding a diffusive step of ∼2% of the linewidth. At low bottlenecking, the functional form of the magnetic field dependence of σ, 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. © 1979 The American Physical Society.