Macroscopic nonlinearities

However, its was found possible to infer all four microscopic tensor coefficients from macroscopic crystalline values and this impossibility could be related to the molecular unit anisotropy. It can be shown that the molecular unit anisotropy imposes structural relations between coefficients of macroscopic nonlinearities, in addition to the usual relations resulting from crystal symmetry. Such additional relations appear for crystal point group 2,ra and 3. For the monoclinic point group 2, this relation has been tested in the case of MAP crystals, and excellent agreement has been found, triten taking into account crystal structure data (24), and nonlinear optical measurements on single crystal (19). This approach has been extended to the electrooptic tensor (4) and should lead to similar relations, trtten the electrooptic effect is primarily of electronic origin. 

Certainly for real samples where the distribution function is intermediate between the isotropic and Ising limits the susceptibilities also lie between. Two interesting points can be made. 1) Disregarding variation of F, the macroscopic nonlinearity can be enhanced by up to a factor of five over the maximum achievable in isotropic media by use of liquid crystal host and 2) The nonlinearity which might be used for noncritical phase-matched SHG via the birefringence (which must depend on the magnitude of... 

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. 

Crystals. In the discussion of equation 11, it was pointed out that the macroscopic nonlinear coefficients could be related to the microscopic ones in a relatively straightforward manner. For the hypothetical crystal shown in Figure 5, the relationship is (5)... 

One purpose of this tutorial paper on optical characterization is to provide a brief introduction for chemists to the concepts and methods involved in studies of the nonlinear optical properties of molecules and materials. The intent is to familiarize chemists with the range of commonly used techniques and their physical basis. An attempt is made to provide some background on macroscopic nonlinear optics, relating to what is actually measured, and the connection to molecular nonlinear optical properties. This paper is not intended to be a detailed or comprehensive review. The reader is referred to introductory (1, 2) and advanced (3-6) texts on nonlinear optics for more detailed or complete coverage of the subject. 

In spite of the potential advantages, useful organic NLO materials have not yet been developed because the necessary molecular and macroscopic characteristics have only recently begun to be understood. However, because bulk NLO properties in organic materials arise directly from the constituent molecular nonlinearities, it is possible to decouple molecular and supramolecular contributions to the NLO properties. One can then semiquantitatively predict relative macroscopic nonlinearities based on theoretical analyses of the individual molecules (7). Reliable predictions of this kind are vital for the efficiency of a program aimed towards developing new organic materials with tailored NLO properties. 

Macroscopic Nonlinear Optical Properties from Cavity Models... 

In the study of the KE for a selection of pure liquids [30] the concept of effective polarizabilities was extended to introduce the contribution of the output wave. Radiation at a frequency to induces a macroscopic nonlinear polarization density (pm)NL at the same frequency, the output wave, generating an additional perturbing field. The molecules of the liquid respond with an additional effective polarizability a(—to to), whereby Equation (2.242) becomes... 

Using this formula for Fq and Fi in eqn (7.18) results in the equation employed by Teng and Garito" to convert the macroscopic nonlinearity to a molecular quantity ... 

Whatever the validity of these formulae and the underlying cavity field theories it is very desirable that, before applying them, the definition and consistency of the macroscopic quantities as measured by different groups should be assessed. Much of the discussion in the literature deals directly with the final values of the hyperpolarizability presented in the various experimental papers. In calculating these values different versions of the above procedures may have been employed and, in particular, different values of the molecular dipole moment inserted into y to extract the y value. It is relatively easy to identify how the microscopic parameter has been obtained and which molecular convention is being used provided the identity of the macroscopic quantity is clearly established. The symbol, F), (and its derivative, (9F i/9H )o) is introduced here to denote provisionally a reported macroscopic nonlinearity before assessing its precise definition. The unprimed symbols are defined in accordance with eqn (4.16). The most troublesome ambiguity in the... 

Focussing on the first four lines of the Table 4, all of which are calibrated with the quartz standard, and can be adjusted to the same value for this standard, it is apparent that there is reasonably good agreement between the three determinations of the macroscopic nonlinearity of MNA. This consistency, taken in conjunction with the equations as written in the papers, leads to the conclusion that, with a reasonable degree of certainty, the provisionally defined quantity, F can be identified with the F of eqn (4.16). Having made this assumption, it follows that any differences in reported values that are not proportional to the small percentage differences in the F values must be the result of variations in the method employed to convert macroscopic to molecular parameters. This question is examined in the next section. 

For certain macroscopic nonlinear parameters the tensor notation can be simplified due to the intrinsic symmetry of the experiment, e.g., second-harmonic generation and the linear electro-optic effect. Let us first consider SHG. The second-order contribution to the polarization is given by Eq. (9). 

APPENDIX 8A FROM MOLECULAR TO MACROSCOPIC NONLINEAR OPTICAL PROPERTIES... 

For symmetry reasons, the first macroscopic nonlinear coefficient is zero in unordered polymer materials. On the other hand, azo-dye polymers can exhibit very large values, which is interesting for applications in optical limiting and optical switching devices. We will consider the relationship between microscopic and macroscopic third-order susceptibilities. The most general equation for this relationship can be written as ... 

The only EFISH data for the liquid phase is contained in a paper by Levine and Bethea (1976)63 on associating liquids. In this paper the macroscopic nonlinearity, T, is defined by the equation,... 

To understand and optimize the electro-optic properties of polymers by the use of molecular engineering, it is of primary importance to be able to relate their macroscopic properties to the individual molecular properties. Such a task is the subject of intensive research. However, simple descriptions based on the oriented gas model exist [ 20,21 ] and have proven to be in many cases a good approximation for the description of poled electro-optic polymers [22]. The oriented gas model provides a simple way to relate the macroscopic nonlinear optical properties such as the second-order susceptibility tensor elements expressed in the orthogonal laboratory frame X,Y,Z, and the microscopic hyperpolarizability tensor elements that are given in the orthogonal molecular frame x,y,z (see Fig. 9). 

In tune with the above introductory remarks, we have arranged this review in the following way Section II deals with the oriented gas model that employs simple local field factors to relate the microscopic to the macroscopic nonlinear optical responses. The supermolecule and cluster methods are presented in Section III as a means of incorporating the various types of specific interactions between the entities forming the crystals. The field-induced and permanent mutual (hyper)polarization of the different entities then account for the differences between the macroscopic and local fields as well as for part of the effects of the surroundings. Other methods for their inclusion into the nonlinear susceptibility calculations are reviewed in Section IV. In Section V, the specifics of successive generations of crystal orbital approaches for determining the nonlinear responses of periodic infinite systems are presented. Finally,... 

Selected References Employing the Oriented Gas Approximation to Relate the Microscopic and Macroscopic Nonlinear Optical Responses in Crystals... 

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