Pure quadratic or higher-order optical effects in anisotropic crystals induced by external dc fields and probed by a single low-intensity plane electromagnetic wave

The determination of a clear theoretical demarcation between a true or a false quadratic or higher-order low-intensity optical effect induced by an externally applied static or quasistatic (dc) vector field in anisotropic crystals is the scope of the present work. A complete set of necessary and sufficient conditions required for the practical possibility of direct detection, measurement, and tabulation of only those pure optical contributions is finally obtained. The dc electro-optic effect stands out as the most representative of all of these low-power dc optical effects. However, although the dc Kerr effect remains the main topic of application of the analytical treatment developed in this work, the current theoretical formalism is extended to include other dc conventional crystal optics effects, such as electrogyration, electroabsorption, and externally induced ray or energy propagation. Even more, the theoretical conditions are further generalized to apply to any pure higher-order crystal optics effect induced by external dc fields. These can be electric, magnetic, force, and even temperature or concentration gradient fields. The current treatment does not extend to multiple-beam high-intensity nonlinear optics effects induced by optical (ac) fields. Compared to previously published expressions, a more general Fresnel equation is also provided here together with the most general Jones vectors describing the eigenpolarizations of the single probing beam of light. All the generalizations and extensions mentioned in this article are valid as long as the field-dependent coefficients of the particular optical effect under consideration satisfy the equation of a positive-definite complex Hermitian form.