Nonlinear field-dependent propertie

For strong external fields, the dependence of the response on the strength of the forces can be expressed by a power expansion in the forces, which then - in addition to the linear parameters x - defines nonlinear field-dependent materials properties x " (F), where... 

The importance of the hyperpolarizability and susceptibility values relates to the fact that, provided these values are sufficiently large, a material exposed to a high-intensity laser beam exhibits nonlinear optical (NLO) properties. Remarkably, the optical properties of the material are altered by the light itself, although neither physical nor chemical alterations remain after the light is switched off. The quahty of nonlinear optical effects is cmciaUy determined by symmetry parameters. With respect to the electric field dependence of the vector P given by Eq. (3-4), second- and third-order NLO processes may be discriminated, depending on whether or determines the process. The discrimination between second- and third-order effects stems from the fact that second-order NLO processes are forbidden in centrosymmetric materials, a restriction that does not hold for third-order NLO processes. In the case of centrosymmetric materials, x is equal to zero, and the nonhnear dependence of the vector P is solely determined by Consequently, third-order NLO processes can occur with all materials, whereas second-order optical nonlinearity requires non-centrosymmetric materials. 

Thus, in general, the electric and viscoelastic properties of liquid crystal polymers are field dependent and the response of the materials to an external field is essentially nonlinear. Unfortunately, in the major part of the electrooptical experiments this nonlinearity is not taken into account, and the results are interpreted in terms of the conventional nematodynamics with constant material parameters. 

Polarization which can be induced in nonconducting materials by means of an externally appHed electric field is one of the most important parameters in the theory of insulators, which are called dielectrics when their polarizabiUty is under consideration (1). Experimental investigations have shown that these materials can be divided into linear and nonlinear dielectrics in accordance with their behavior in a realizable range of the electric field. The electric polarization PI of linear dielectrics depends linearly on the electric field E, whereas that of nonlinear dielectrics is a nonlinear function of the electric field (2). The polarization values which can be measured in linear (normal) dielectrics upon appHcation of experimentally attainable electric fields are usually small. However, a certain group of nonlinear dielectrics exhibit polarization values which are several orders of magnitude larger than those observed in normal dielectrics (3). Consequentiy, a number of useful physical properties related to the polarization of the materials, such as elastic, thermal, optical, electromechanical, etc, are observed in these groups of nonlinear dielectrics (4). 

Bishop s attention turned to accurate calculations of electrical and magnetic properties, especially those of importance in nonlinear optics. Since most experiments in this field measure ratios, not absolute values, it is necessary to have a calculated value. Universally, Bishop s helium nonlinear optical properties are used. In the same field, he was the first to seriously investigate the effects of electric fields on vibrational motions, with a much-quoted paper.65 His theory and formulation has now been added to two widely used computational packages HONDO and SPECTROS. He has also derived a rigorous formula to account for the frequency dependence (dispersion) in nonlinear optical properties.66 He used this theory to demonstrate that the anomalous dispersion in neon, found experimentally, is an artifact of the measurements. 

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