Subpicosecond Accumulated Photon Echo with Incoherent Light

Abstract

An analytic theory and experimental studies of the accumulated photon echo is presented. We define a temporal correlation function \(\tilde{G}\) of the excitation field E ( t ) as \(\tilde{G}(\tau,t)=(1/T_{1})\int_{0}^{\infty}\mathrm{d}t'E(t-t')E(t-t'-\tau)\cdot\exp(-t'/T_{1})\), where T 1 is the population relaxation time of the sample, and call the width of \(\tilde{G}\) with respect to τ a temporal correlation time \(\tilde{\tau}_{\text{c}}(t)\). It is proved that the echo intensity is written by the temporal correlation functions when (1) T 1 and the duration of the excitation light τ p are much longer than \(\tilde{\tau}_{\text{c}}(t)\) in order to make the function \(\tilde{G}((\tau,t)\) well-defined, (2) T 1 and τ p are much longer than the homogeneous dephasing time T 2 , and (3) one can find a time interval Δ t such that \(\tilde{G}(\tau,t)\) does not change much between t and t + Δ t , where \(\varDelta t{\gg}\tilde{\tau}_{\text{c}}\). Then we can show that the time resolution of the accumulated photon echo is determined by the averaged \(\tilde{\tau}_{\text{c}}(t)\) over an interval of the integration of the echo signal. This discussion is valid for any excitation source if the above conditions are satisfied, and applies to almost all cases of the practical accumulated photon echo experiment. A discussion is also made on the spurious spike on the echo decay curve near zero delay time that appeared in an experiment with a high time resolution in Nd 3+ -doped silicate glass. It is shown that the most probable cause for this spike is uncorrelated inhomogeneous broadenings of the resonant lines of neodymium ions.