Phonon Fluorescence in Superconductors and the Propagation Characteristics of High-Frequency Phonons in Ge: Sb and ${\mathrm{Al}}_2$${\mathrm{O}}_3$: ${\mathrm{V}}^{3+}$

We present a detailed account of phonon generation by superconducting tunnel junctions (Sn-$I$-Sn) and by Sn and ${\mathrm{Pb}}_{0.5}$ ${\mathrm{Tl}}_{0.5}$ films pumped by a heat pulse. The spectrum and propagation characteristics of the generated phonons is studied through the resonance absorption by Sb-donor levels in uniaxially compressed Ge. At all values of generator power (up to a few watts) the emitted phonons show a large density at a value of energy equal to the superconducting energy gap ($2\Delta$). In contrast, the spectrum emitted by a constantan heater is shown to be in quantitative agreement with the blackbody-radiation model. The experiments show that the mean free path of longitudinal and transverse phonons in the superconductor changes discontinuously when $\hslash \omega =2\mathrm{}\Delta$. Theoretical calculations show that significant reabsorption of phonons of energy $2\Delta$ results in a nonlinear buildup of the intensity of the $2\Delta$ phonons. The propagation characteristics of these phonons in Ge: Sb show a frequency and polarization dependence in excellent agreement with the Griffin-Carruthers theory of resonance-fluorescence phonon scattering by donor levels. The magnetic field tunability of the generated $2\Delta$ phonons in Sn is utilized to study the ground state of ${\mathrm{V}}^{3+}$ in ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$. Transverse phonons of energy 1.02 meV propagating along the $c$ axis are resonantly absorbed as expected according to theory.