The possibility of using incoherent photon echo in spectroscopy of optically dense impurity media is considered. A theoretical approach to description of this phenomenon is presented. The experimental data on incoherent photon echo in ruby at liquid-helium temperature, with transport of an excitation pulse through a fiber, are reported. The spectral dependence of the echo intensity is studied. The decay curve for an incoherent echo signal is investigated, and the phase relaxation time is found to be 98 ns.
One of the long-standing difficulties in working with intense incoherent light has been the lack of a theory for predicting and explaining experimental results. The diagrammatic theory of Friedberg and Hartmann provides a solution to this problem by allowing one to study the interaction of intense incoherent light and matter with no restrictions on the intensity of the pulses. In the present investigation, two-pulse photon-echo experiments were performed with intense incoherent light in atomic sodium vapor and the results were compared with predictions calculated from the Friedberg-Hartmann diagrammatic theory. The dependence of the echo signal on the intensity of the constituent excitation pulses was studied. The results of this investigation indicate that the two-pulse incoherent photon-echo experimental data are consistent with the calculations obtained from the theory presented in the diagrammatic paper of Friedberg and Hartmann when the atomic relaxation times are included. The two-pulse-echo data show good agreement with the theoretical predictions for the case in which 4T2 = T1 (the atomic and transverse lifetimes, respectively), which represents more of a decay than has been theoretically predicted for the experimental parameters used.
Experiments are described in which a dilute ruby crystal is found to emit spontaneously a short pulse of light, the photon echo, at a time $\ensuremath{\approx}{\ensuremath{\tau}}_{s}$ after irradiation by two successive ruby-laser pulses separated by ${\ensuremath{\tau}}_{s}$. The phenomenon is explained in terms of a macroscopic oscillating electric dipole moment, which is momentarily reformed at the time the photon echo is observed. The analysis predicts the echo polarization as well as the propagation direction relative to the input pulses. A necessary condition for obtaining echoes in ruby is the application of a moderate magnetic field close to the optic axis of the crystal, and a simple model based on
Cr3+-Al interactions is offered to account for this magnetic-field behavior. The relaxation time of the echo is found to exceed 250 nsec at 4.2\ifmmode^\circ\else\textdegree\fi{}K but to be less than 70 nsec at 14\ifmmode^\circ\else\textdegree\fi{}K, and is thought to be due to phonon-induced transitions in the excited
2E(E) level. Multiple echo formation is also described.
An analytic theory and experimental studies of the accumulated photon echo is presented. We define a temporal correlation function
G~ of the excitation field E ( t ) as
G~(τ,t)=(1/T1)∫0∞dt′E(t−t′)E(t−t′−τ)⋅exp(−t′/T1), where T 1 is the population relaxation time of the sample, and call the width of
G~ with respect to τ a temporal correlation time
τ~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
τ~c(t) in order to make the function
G~((τ,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
G~(τ,t) does not change much between t and t + Δ t , where
Δt≫τ~c. Then we can show that the time resolution of the accumulated photon echo is determined by the averaged
τ~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.