Recent Progress in Four-Wave Mixing Spectroscopy in Crystals

Abstract

The general framework for describing the large variety of nonlinear optical phenomena caused by an electric polarization cubic in the electric field amplitudes

$${{P}_{i}}\left( {{\omega }_{4}},\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{r}\right)=\frac{1}{2}X_{ijk\ell}^{\left(3\right)}\left(-{{\omega}_{4}},{{\omega}_{1}},-{{\omega}_{2}},{{\omega}_{3}}\right){{E}_{j}}\left({{\omega}_{1}}\right)E_{k}^{*}\left({{\omega}_{2}}\right){{E}_{\ell}}\left({{\omega}_{3}}\right)\exp\left[i\left({{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k}}}_{1}}-{{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k}}}_{2}}+{{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k}}}_{3}}\right)\centerdot\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{r}-i{{\omega}_{4}}t\right]+c.c.$$

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