Time-dependent effects in fluorescent line narrowing

A study is made of time-dependent effects in fluorescent line narrowing. We analyze the ratio R(t)=IN(t)[IN(t)+IB(t)] where IN(t) is the intensity of the narrow component and IB(t) is the intensity of the background. We formulate a theory for $R(t)$ based on coupled rate equations, which is applicable when kT is much greater than the inhomogeneous linewidth. $R(t)$ 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 Pr0.2{La}0.8F₃, and suggestions are given for further development of the theory.