Four-wave mixing has been investigated in ${\mathrm{Nd}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{P}}_{5}{\mathrm{O}}_{14}$ crystals as a function of temperature, laser excitation wavelength, and power. The results are interpreted in terms of scattering from a population grating, and the relative intensity of the scattered signal is investigated as well as the grating decay time. The power dependence of the scattered intensity is explained by a model involving interaction with a three-level system, and the properties of the grating decay are associated with the exciton dynamics of the ions in the excited state. Decay patterns characteristic of both incoherent and partially coherent exciton migration can be observed under different experimental conditions. Enhanced migration due to vibronic generation of phonons resonant with the metastable state splitting is also observed. The temperature dependence of the results shows a weak coupling between the excitions and the acoustic phonons of the host. Local heating effects are found to affect the ion-ion and ion-phonon interaction parameters and produce a thermal grating under certain experimental conditions.
Four-wave-mixing techniques were used to establish and probe population gratings of
Cr3+ ions in alexandrite crystals at temperatures between 10 and 300 K. The results were interpreted in terms of the interaction of the laser radiation with a two-level atomic system. They provide information about the characteristics of four-wave-mixing signals for this physical situation as well as being useful in characterizing the properties of energy transfer and dephasing within the ensemble of
Cr3+ ions. The patterns of the transient four-wave-mixing signals are consistent with a model based on the pumping dynamics of ions in the mirror and inversion crystal-field sites. The variation of the signal intensity with laser power is strongly affected by beam depletion. The characteristics of exciton migration among
Cr3+ ions in mirror sites were determined from the results of measuring the variation of the signal decay rate with grating spacing. The temperature dependences of the ion-ion interaction rate, the exciton-phonon scattering rate, and the diffusion coefficient were determined. These are found to be essentially the same for pumping into the
4T2 and
2E levels, but the effects of scattering from a grating of ions in inversion sites is much stronger for
4T2 pumping. The dephasing times for the atomic system were found from analyzing the variation of the signal intensity with grating spacing. For pumping into the
4T2 level the dephasing is dominated by radiationless decay processes. A model is presented for the decay channel that provides a theoretical explanation for the decay process which is consistent with the measured temperature and frequency dependences of the results as well as their variation with crystal-field strength. For pumping into the
2E level the dephasing is dominated by dephasing processes associated with the inhomogeneous linewidth of the transition.
We present a microscopic theory of the nonlinear susceptibility χ(3) of a crystal composed of interacting two-level absorbers. The relationship between the signals in a steady-state four-wave mixing experiment and in a time-resolved transient grating experiment is established. In general, the steady-state signal is not simply the Fourier transform of the time-resolved signal, although such a relationship does hold under certain experimental conditions. We evaluate χ(3) for the Haken–Strobl model. χ(3) displays a dephasing-induced extra resonance, whose intensity and line shape are sensitive to the degree of exciton coherence. We also calculate χ(3) for a crystal of interacting three-level absorbers, under the assumption that population in the higher excited state relaxes rapidly to the lower excited state. We propose steady-state four-wave mixing as an alternative to the transient grating experiment in investigating the nature of exciton motion.
We report degenerate four-wave mixing experiments at room temperature, using a three-beam geometry and sub-picosecond laser to study GaAs/GaAlAs multiple quantum well material. Diffraction efficiencies and grating decay times for two samples of different carrier lifetimes have been measured in the spectral region corresponding to excitonic resonances. The measurements provide values of the nonlinear refractive index per carrier pair (n eh) deriving from the excitonic saturation, and also the recombination times and diffusion coefficients for the samples.