Calculations of the ${\mathit{A}}_1$ Phonon Frequency in Photoexcited Tellurium

Calculations of the $A_1$ phonon frequency in photoexcited tellurium are presented. The phonon frequency as a function of photoexcited carrier density and phonon amplitude is determined. Recent pump-probe experiments are interpreted in light of these calculations. It is proposed that, in conjunction with measurements of the phonon period in ultrafast pump-probe reflectivity experiments, the calculated frequency shifts can be used to infer the evolution of the density of photoexcited carriers on a subpicosecond time scale.