Time-delayed four-wave mixing using incoherent light has been proposed as a new method to measure the ultrafast population relaxation time T1. Assuming three input beams of incoherent light with much longer duration than T1, the theoretical calculation has shown that the decay curve by T1 appears in the signal profile and that the time resolution is determined by the correlation time of the light. The decay time to be observed is twice that of the transient four-wave mixing with short pulses. We have experimentally confirmed the prediction by observing picosecond population relaxations of organic dye solutions, using nanosecond pulses from a normal broadband dye laser. An advantage of the present method over the pump-probe method using incoherent light is also discussed.
Formation of coherent transients by incoherent light pulses has stimulated renewed interest in time-resolved coherent spectroscopy. Standard theories conveniently account for the weak-field regime experiments, but they fail to interpret the power effects that occur during resonant excitation of a sample by time-delayed, correlated, broadband laser pulses. We report on a new approach to this problem. We have been able to determine the expectation value of the population grating induced by two time-delayed, correlated, broadband light pulses under the limitation that one of the fields is weak. We have developed a diagrammatic technique that seems promising for the calculation of actual coherent-transient signals in the strong-field regime.
We present a simple technique for measuring coherence times for stationary light fields using a single detector with tunable time resolution. By measuring the equal-time second-order correlation function at varying instrument response functions it is possible to determine the coherence time and also the shape of the temporal decay without the need to record time-resolved data. The technique is demonstrated for pseudothermal light. Possible applications for dynamic light scattering and photon statistics measurements are discussed.
Time-resolved three-beam degenerate four-wave mixing with incoherent light for observation of population relaxation, originally proposed by Morita . [ J. Opt. Soc. Am. B4, 1269 ( 1987)] is examined both theoretically and experimentally. Theoretical calculation shows that a large part of the decaying signal in the time-resolved profile originates from the ground-state relaxation if the excited-state relaxation is faster than the ground-state relaxation. It is also shown that the use of a nonzero delay time between the k2 and k1 beams, in addition to that between the k3 and k1 beams (ks = k1 − k2 + k3, where k1–3 and ks are the wave vectors for the incident and the scattered beams, respectively), provides information on population relaxation, especially when the population-relaxation time is far longer than the correlation time of the incoherent light. These theoretical considerations are verified experimentally with the use of a triphenylmethane dye in solution.
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.