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.
In recent years, a series of nonlinear optical processes with incoherent light, such as time-delay four-wave mixing, optical Kerr effect and coherent Stokes Raman scattering, were developed and attracted much attention. It has been demonstrated that these processes can be used to measure the ultrafast dephasing times of excitations (shorter than 1 psec.) with nanosecond pulse lasers or even CW lasers. In this talk, after a short review of the works done by others previously theoretical and experimental investigations in this field in my laboratory are presented.
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.
Until now all reported studies of transient spectroscopy with incoherent light, including photon echo and pump-probe spectroscopy, were concerned with two-level systems where quasi-monochromatic light of only one frequency couples the two levels.[1-4] However, there exist various coherent transient phenomena where light of two or more frequencies are concerned, and time resolution of the transient spectroscopies using these phenomena are also expected to be limited not by the duration of used light pulses but by the correlation time of the radiation fields.[5]
Forced light scattering using broad-bandwidth incoherent pump light (${\ensuremath{\lambda}}_{\mathit{B}}$=508 nm, full width at half maximum \ensuremath{\Delta}${\ensuremath{\lambda}}_{\mathit{B}}$=13.8 nm), and narrow-bandwidth probe light is investigated experimentally and compared with self-diffraction. Forced light scattering improves the dynamic range of measurement by an order of magnitude compared to self-diffraction. A theoretical analysis of this scheme is presented. The technique is used to measure the dephasing kinetics of solutions of crystal violet and bis-(dimethylamino)heptamethine. Resulting from the relatively large autocorrelation time of 40 fs, the experimental signals show no influence from inhomogeneous broadening of the absorption bands; the dephasing kinetics can be characterized by a dephasing time
T2\ensuremath{\approxeq}10 fs and an intrinsic correlation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{C}}$\ensuremath{\approxeq}30 fs with a weak modulation (center frequencies ranging from 800 to 1200 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$), which is attributed to a coherent motion of the molecule (vibration). The dephasing kinetics of crystal violet shows a close agreement with the dephasing kinetics of malachite green previously reported for two-pulse photon echoes with ultrashort pulses [P. C. Becker et al., Phys. Rev. Lett. 63, 505 (1989)].