The nonlinear signal in a degenerate four-wave mixing experiment as a result of diffraction of a spatially distributed third-order nonlinearity is studied theoretically. The approach has been applied for the case of monochromatic and ultrashort pulses. As a consequence, the degenerate four-wave mixing signal is found to be independent of light-coherence parameters and cannot be explained as a product of diffraction on a dynamic grating. In this model only the fast component of the signal (the coherent artifact) is related directly to third-order nonlinear processes. The main features (the origins, temporal shapes, dependencies of pump intensity, and modulation effects) of the coherent artifact and a slow-decay component are discussed theoretically and experimentally.
Microscopic dynamics. of materials can be studied by time delayed four-wave mixing spectroscopy. Dephasing constants can be measured by such experiments. Experimental results are easily analysed when the correlation time r of the exciting electric field is much shorter than the dephasing time ''2 However when these quantities are on the same time scale numerical fits are necessary. In the present work we analysed theoretically a time delayed four-wave mixing experiment. The material is described by an ensemble of two-level systems and a large inhomogeneous broadening is assumed. Using the third order term of the density matrix we establish a relation between 1''2 -r and ''Tm the time delay for which the maximum of the diffracted light intensity is observed. The conditions to obtain an estimate of T2 from the measurement of Tm are discussed.
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.
The theory of phase conjugation in laser amplifiers by saturable-gain degenerate four-wave mixing with copolarized beams is developed for pulses of arbitrary temporal shape and duration in the limit of a weak signal beam. The influence of the input pulse’s characteristics (energy, temporal pulse shape, duration) on the phase-conjugate reflectivity and on the conjugate pulse shape is analyzed. A sharp instantaneous peak of phase-conjugate reflectivity is predicted at high intensities of the four-wave mixing beams. This effect is experimentally demonstrated at λ0 = 1064 nm in a Nd:YVO4 amplifier pumped by a cw Ti:sapphire laser. A transient peak reflectivity of R ∼ 50% is thus obtained, corresponding to an enhancement of 1.6× compared with the maximum steady-state reflectivity. The experimental results and the theoretical predictions are in good agreement.
Phase relaxation of optical excitations in condensed matter can be studied by coherent four—wave—mixing experiments in the time domain without requiring assumptions on the spectral properties of the material. For inhomogeneously broadened transitions, three laser pulses at times t = 0, t = t21 and t = T with wave vectors k1, k2 and k3, respectively, generate a stimulated photon echo pulse, emitted time—delayed at t = T+t21 in the momentum—matching direction according to k3+k2−k1. As a function of t21 the echo amplitude decays due to scattering events, described by the dephasing time constant T2 [1].