Maxwell fields, nonlinear optical properties

The theory of nonlinear optical processes in crystals is based on the phenomenological Maxwell equations, supplemented by nonlinear material equations. The latter connect the electric induction vector D(r,t) with the electric field vector E(r, t). In general, the relations are both nonlocal and nonlinear. The property of nonlocality leads to the so-called spatial dispersion of the dielectric tensor. The presence of nonlinearity leads to the interaction between normal electromagnetic waves in crystals, i.e. makes conditions for the appearance of nonlinear optical effects. 

Maxwell s equations are linear. However, the parameters that describe material properties may become nonlinear in exceptionally strong fields, such as in powerful lasers. In these cases nonlinear terms have to be included. The linear material equations, Eqs. (1.1.6) to (1.1.8), are not applicable to ferroelectric or ferromagnetic substances where the relationship between the electric field strength, E, and the electric displacement, D, or between the magnetic field strength, H, and the magnetic induction, B, are not only nonlinear, but show hysteresis effects as well. In any case. Maxwell s equations are the foundation of electromagnetism, which includes optics and infrared physics. 

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