Time-dependent effects in fluorescent line narrowing

Abstract

A study is made of time-dependent effects in fluorescent line narrowing. We analyze the ratio $R\left(t\right)=\frac{I_N\mathrm{}\left(t\right)\mathrm{}}{\left[I_N\mathrm{}\right(t)+I_B\mathrm{}(t\left)\right]}$ where $I_N\mathrm{}\left(t\right)\mathrm{}$ is the intensity of the narrow component and $I_B\mathrm{}\left(t\right)\mathrm{}$ is the intensity of the background. We formulate a theory for $R\left(t\right)\mathrm{}$ based on coupled rate equations, which is applicable when $\mathrm{kT}$ is much greater than the inhomogeneous linewidth. $R\left(t\right)\mathrm{}$ is calculated exactly for an ordered array of optically active ions. In the case of dilute systems the short-time behavior is determined for all values of the concentration. Backtransfer effects are treated in a variety of approximations. Comparison is made with experimental data from ${\mathrm{Pr}}_{0.2}$ ${\mathrm{La}}_{0.8}$ ${\mathrm{F}}_3$, and suggestions are given for further development of the theory.