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 \ ildeG of the excitation field E(t) as \ ildeG(τ, t)=(1⁄T₁) ∫₀^∞ dt′E(t−t′)E(t−t′−τ)·exp (−t′⁄T₁), where T₁ is the population relaxation time of the sample, and call the width of \ ildeG with respect to τ a temporal correlation time \ ildeτ_c(t). It is proved that the echo intensity is written by the temporal correlation functions when (1) T₁ and the duration of the excitation light τ_p are much longer than \ ildeτ_c(t) in order to make the function \ ildeG(τ, t) well-defined, (2) T₁ and τ_p are much longer than the homogeneous dephasing time T₂, and (3) one can find a time interval Δt such that \ ildeG(τ, t) does not change much between t and t+Δt, where Δt>>\ ildeτ_c. Then we can show that the time resolution of the accumulated photon echo is determined by the averaged \ ildeτ_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 Nd³⁺-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.