Four-wave mixing theory

Dugan M A and Albrecht A C 1991 Radiation-matter oscillations and spectral line narrowing in field-correlated four-wave mixing I theory Rhys. Rev. A 43 3877-921... 

The three-pulse experiments contain more information than two-pulse methods when the direction and timing of all three pulses is controlled. We have seen that this additional information cannot be interpreted within a Bloch picture. We will therefore outline in the following a more detailed theory, which includes spectral diffusion and which simultaneously explains the linear response (absorption spectrum) and the nonlinear response (four wave mixing, photon echo, transient grating, pump-probe) of vibrational transitions. 

Banerjee and Harbola [69] have worked out a variation perturbation method within the hydrodynamic approach to the time-dependent density functional theory (TDDFT) in order to evaluate the linear and nonlinear responses of alkali metal clusters. They employed the spherical jellium background model to determine the static and degenerate four-wave mixing (DFWM) y and showed that y evolves almost linearly with the number of atoms in the cluster. 

The nonlinear susceptibility is evaluated using third-order perturbation theory, and resonant enhancement is readily demonstrated to occur. Four-wave mixing is a useful experimental technique to extend the energy range available to tunable dye lasers [468]. It is also of interest that processes involving excitation by three photons allow transitions between even and odd parity states to be excited, as do single-photon transitions. 

Dynamic four wave mixing experiments in the nematic phase were performed by Eichler and Macdonald [150] and Khoo et al. [151, 152] using picosecond lasers. They have observed that the short excitation pulse is followed by a delayed reorientation process, indicating a large inertial moment. The observed dynamics were explained by flow-alignment theory, taking into account translational motion of the molecules under the action of the optical field. Build-up and decay times of the diffraction grating were... 

Steffen T and Duppen K 1996 Time resolved four- and six-wave mixing in liquids I. Theory J. Chem. Phys. 105 7364-82... 

Steffen T, Fourkas JT, Duppen K. Time resolved four and six-wave mixing in liquids. I. Theory. J Chem Phys 1997 105 7364-7382. 

Several different laser techniques for generating VUV and XUV radiation are now available, and these have been discussed briefly, along with the relevant theory. Of these, harmonic generation and four-wave frequency mixing have been shown to provide coherent and monochromatic radiation which is tunable over broad regions of the spectrum, from 200 nm to 70 nm, and with limited tunability to 50 nm. While these laser-driven sources are not presently available commercially, they have been developed in several laboratories around the world, and have been used in various fields of research. 

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