Polarization properties nonlinear quantum optics

In this paper, an overview of the origin of second-order nonlinear optical processes in molecular and thin film materials is presented. The tutorial begins with a discussion of the basic physical description of second-order nonlinear optical processes. Simple models are used to describe molecular responses and propagation characteristics of polarization and field components. A brief discussion of quantum mechanical approaches is followed by a discussion of the 2-level model and some structure property relationships are illustrated. The relationships between microscopic and macroscopic nonlinearities in crystals, polymers, and molecular assemblies are discussed. Finally, several of the more common experimental methods for determining nonlinear optical coefficients are reviewed. 

We have seen how the molecular properties in nonlinear optics are defined by the expansion of the molecular polarization in orders of the external electric field, see Eq. (5) beyond the linear polarization this definition introduces the so-called nonlinear hyperpolarizabilities as coupling coefficients between the two quantities. The same equation also expresses an expansion in terms of the number of photons involved in simultaneous quantum-mechanical processes a, j3, y, and so on involve emission or absorption of two, three, four, etc. photons. The cross section for multiphoton absorption or emission, which takes place in nonlinear optical processes, is in typical cases relatively small and a high density of photons is required for these to occur. 

The understanding and reliable prediction of the influence of the solute-solvent interactions on the nonlinear optical properties of molecular systems is a significant issue for a width range of theoretical and experimental areas of studies. In this review, it was shown that the simple two-state approximations combined with tlie solvatochromic methods are an effective tools in prediction tlie direction of tlie changes of molecular nonlinear responses as a function of solvent polarity. This methodology based on the description of the solvent effects at the molecular level should be treated as a supporting for the most sophisticated quantum chemical approaches. 

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