A nonlinear crystal is one which has a nonlinear susceptibility of the type:
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In practice, most materials have a nonlinear component which, however, is either negligible or nil for certain orders (glass has a null component of order two and a weak order three component). The most widely studied case (thanks to the invention of the laser) is the component of order two. In practice, it is in the form of a spatial dissymmetry of charges within a non-centrosymmetric crystal (crystals such as lithium niobate or BBO (beta barium borate), and is used for the parametric generation of pairs of photons.