Macroscopic, second-order optical nonlinearities

Nonintuitive Light Propagation Effects In Third-Order Experiments. One of the first tasks for a chemist desiring to quantify second- and third-order optical nonlinear polarizability is to gain an appreciation of the quantitative manifestations of macroscopic optical nonlinearity. As will be shown this has been a problem as well for established workers in the field. We will present pictures which hopefully will make these situations more physically obvious. 

For dipolar chromophores that are the subject of this chapter, only one component of the molecular hyperpolarizability tensor, Pzzz, is important. Thus, the summation in Eq. (8) disappears. Electric field poling induces Cv cylindrical polar symmetry. Assuming Kleinman [12] symmetry, only two independent components of the macroscopic second-order nonlinear optical susceptibility tensor... 

In the literature however, other related parameters, besides x are often used to describe the macroscopic second-order NLO properties of materials. The SHG nonlinear coefficient d and the linear electro-optic coefficient r are the parameters commonly used for second-harmonic generation and the Pockels effect respectively [3, 5]. They are related to x according to Eqs. (4) and (5). 

The macroscopic second-order nonlinearity x is zero if the molecules are randomly oriented within the polymer. From the preceding relationships, it follows that during photoisomerization changes occur in the nonlinear optical properties and as well as the linear terra... 

Churikov, V. M., Hung, M. F., Hsu, C. C., Shiau, C. W, and Luh, T. Y. (2000). Encoding of macroscopic second order nonlinearity via all-optical polar alignment in substituted nor-bornene polymer thin films. Chem. Phys. Lett. 3 2, 19-25. 

For these classes of conjugated molecular and polymer structures, the principal property is that their nonreson-ant, nonlinear optical responses are dominated by ultrafast, virtual excitations of the ir-electron states. This was directly demonstrated by MNA (2-methyl-4-nitroaniline) single crystal measurements of macroscopic second order susceptibilities at do (j 3) and optical frequencies (13-1 ) and combined second harmonic measurements and theo-... 

In recent years there has been a growing interest in the search for materials with large macroscopic second-order nonlinearities [20-22] because of their practical utility as frequency doublers, frequency converters and electro-optic modulators [23] by means of second-harmonic generation, parametric frequency conversion (or mixing) and the electro-optic (EO) effect. They are described by X (2w w, u)), 0, w), respectively. In order to optimize... 

In the early days, optical nonlinearity of organic materials was measured usually with powder samples, mainly because it is very difficult to isolate organic compounds in the form of molecular crystals. In the case of centrosymmetric crystal lattices, macroscopic second-order nonlinear optical characteristics are not detected. Molecular crystals are organized assemblies of individual molecules held together by intermolecular forces. Their macroscopic nonlinear optical constants are estimated as the sum of the molecular polarizability of individual molecules. Thus, neglecting intermolecular interactions in the crystal, the nonlinear optical constant, dtlK, is expressed by... 

Macroscopic second-order nonlinear optical susceptibility, can be expressed as... 

The intramolecular charge transfer through zr-electron conjugation gives large optical nonlinearities in the molecular level, whereas the centro-symmetry of the crystal structure determines the macroscopic second order nonlinearity... 

The macroscopic second-order NLO effects are not only dependent on the value of molecular hyperpolarizability, but are also dependent on the orientations of the molecules in the unit cells. The relation between microscopic and macroscopic second-order NLO effects have been studied by Zyss et al. [37]. When there are no significant intermolecular effects, the lowest-order macroscopic optical nonlinearity can be expressed as the ten-... 

The focus of the present chapter is the application of second-order nonlinear optics to probe surfaces and interfaces. In this section, we outline the phenomenological or macroscopic theory of SHG and SFG at the interface of centrosymmetric media. This situation corresponds, as discussed previously, to one in which the relevant nonlinear response is forbidden in the bulk media, but allowed at the interface. 

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. 

Second-Order Molecular and Macroscopic Optical Nonlinearities... 

The EO effect is a second-order nonlinear optical (NLO) effect. Only non-centrosymmetrical materials exhibit second-order NLO effects. This non-centrosymmetry is a condition, both at the macroscopic level of the bulk arrangement of the material and at the microscopic level of the individual molecule. All electro-optic modulators that are presently used by telecom operators are ferro-electric inorganic crystals. The optical nonlinearity in these materials is to a large fraction caused by the nuclear displacement in the applied electric field, and to a smaller fraction by the movement of the electrons. This limits the bandwidth of the modulator. The nonlinear response of organic materials is purely electronic and, therefore, inherently faster. 

In this review, the focus is on electro-optic materials. Such materials are members of the more general class of second-order nonlinear optical materials, which also includes materials used for second harmonic generation (frequency doubling). The term second-order derives from the fact that the magnitude of these effects is defined by the second term of the power series expansion of optical polarization as a function of applied electric fields. The power series expansion of polarization with electric field can be expressed either in terms of molecular polarization (p Eq. 1) or macroscopic polarization (P Eq. 2)... 

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