Incoherent light photon echoes were observed in organic amorphous systems (cresyl violet in polyvinyl alcohol and 1,4-dihydroxyanthraquinone in polymethacrylic acid) by using temporally-incoherent nanosecond laser pulses. It was found that an echo decay curve of an organic amorphous system is composed of a sharp peak which decays very rapidly and a slowly decaying wing at the tail. We show that the persistent hole burning (PHB) spectra were reproduced by the Fourier-cosine transforms of the echo decay curves. We claim that in general, we must take into account the multi-level feature of the system in order to explain ultrafast dephasing at very low temperatures.
Photon echo and non-photochemical hole burning experiments on cresyl violet in ethanol glass are reported. At 1.5 K the optical dephasing time measured by the picosecond echo is eight times longer than the time measured by hole burning because of the difference in the time scales associated with the measurements. The observed temperature dependence arises from the glass's two-level systems and from a pseudolocal phonon mode at higher temperatures. Comparing the ratios of the echo to hole burning dephasing times for cresyl violet and resornfin, suggests that their dephasing is influenced by the nature of their ethanol solvation shells in addition to the dynamics of the bulk ethanol.
A new method of picosecond and femtosecond transient spectroscopy yielding information about ultrafast relaxation processes without requiring ultrashort light pulses is presented. It is based on the present theoretical analysis of the resonant degenerate four-wave-mixing process excited by two temporally incoherent light beams with wave vectors ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}$ which are originated from a single beam at frequency $\ensuremath{\omega}$ but have mutual time delay $\ensuremath{\tau}$. Under the assumption that the incoherent light field has Gaussian random complex amplitude and that the resonant material consists of the usual two-level atoms, the statistically averaged intensity of the output light field with ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{3}=2{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ at $\ensuremath{\omega}$ is calculated as a function of $\ensuremath{\tau}$. Even with the light having a much longer duration than both
T1 (the longitudinal relaxation time) and
T2 (the transverse relaxation time), the correlation trace, i.e., output intensity versus $\ensuremath{\tau}$, represents a decay profile determined mainly by
T2 for both homogeneously and inhomogeneously broadened transitions, as long as the light correlation time ${\ensuremath{\tau}}_{c}$ is much shorter than the relaxation times. The correlation trace does not always represent a single-exponential decay but is sometimes slightly deformed by the
T1 effect. However, it does not cause a significant error in the determination of
T2. Moreover, as $\frac{{T}_{2}}{{T}_{1}}\ensuremath{\rightarrow}0$, the trace becomes a single-exponential decay curve determined only by
T2. The feature of the results obtained by the present method is similar to that obtained by the conventional coherent transient spectroscopy with short pulses, such as the photon echo. The time resolution in the present method, however, is limited only by ${\ensuremath{\tau}}_{c}$ much shorter than the light duration. By regarding the incoherent light as a series of random ultrashort pulses, the present four-wave-mixing process is also interpreted as the ensemble of numerous transient four-wave-mixing processes caused by various combinations of these pulses.
It has been recently pointed out that incoherent light can be used to generate coherent optical transients and that there are decided advantages in using such broad-band non-laser source to achieve very high time resolution {1,2}. When a light pulse and its time-delayed replica interact with a sample to produce the non-linear optical response, the ultimate time resolution should identify with the correlation time τC of the light field rather than with the pulse duration τL. The situation where τC ≪ τL is easily obtained with broad-band incoherent light sources. Time resolution in the femtosecond range is then attainable using nanosecond light pulses. This has been recently demonstrated through the observation of the relaxation of photon echoes in Nd3+-doped silicate glass {1,2}. In these cases, attention is focused on the measurement of fast homogeneous decay rates and the inhomogeneous broadening ΩD is assumed to be much larger than the spectral width of the excitation light.