Microscopic, second-order optical nonlinearities

Through cascade second-order effects, the second-order optical nonlinearities result on a third-order optical effect in a multistep or cascade process. This process is a due to the existence of microscopic electric fields that are generated by second-order nonlinear aligning of molecular dipoles. 

The n-electron excitations are viewed as occuring on molecular sites weakly coupled to their neigbors and providing sources of nonlinear optical response through the on-site microscopic second order nonlinear electronic susceptibility... 

Over the past decade it has been learned that organic materials containing appropriately constituted or substituted conjugation systems may exhibit highly enhanced electronic nonlinear optical polarization responses Since the microscopic second-order... 

In Equation 6, n (a>.) is the intensity independent refractive index at frequency u).,.0 Tlie sum in Equation 5 is over all the sites (n) the bracket, < >, represents an orientational averaging over angles 0 and . Unlike for the second-order effect, this orientational average for the third-order coefficient is nonzero even for an isotropic medium because it is a fourth rank tensor. Therefore, the first step to enhance third order optical nonlinearities in organic bulk systems is to use molecular structures with large Y. For this reason, a sound theoretical understanding of microscopic nonlinearities is of paramount importance. 

In order to obtain a useful material possessing a large second order nonlinear susceptibility tensor % 2) one needs to use molecules with a large microscopic second order nonlinear hyperpolarizability tensor B organised in such a way that the resulting system has no centre of symmetry and an optimized constructive additivity of the molecular hyperpolarizabilities. In addition, the ordered structure thus obtained must not loose its nonlinear optical properties with time. The nonlinear optical (NLO) active moieties which have been synthesized so far are derived from the donor-rc system-acceptor molecular concept (Figure 1). 

In summary, we have briefly reviewed current research highlights from studies of second order nonlinear optical responses in organic and polymeric media. We have stressed how fundamental studies have led to microscopic understanding of important electronic states that comprise the origin of the large second order nonlinear responses in these... 

A specific set of experiments which must be mentioned, being directly associated with the main topic of this paper, is the work of Bergman, et. al. (22) dealing with the second-order nonlinear optical properties of polyvinylidene fluoride (PVF2). Nonvanishing the second-order nonlinear electric dipole susceptibility, is expected in PVF2 since it exhibits other properties requiring noncentrosymmetric microscopic structure. These properties appear... 

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. 

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. 

Density matrices of the state functions provide a compact graphical representation of important microscopic features for second order nonlinear optical processes. The transition moment y is expressed in terms of the transition density matrix p jji(r,r ) by nn " /j, ptr Pjj t(r,r )dr and the dipole moment difference Ay by the difference density function p - p between the excited and ground state functions = -e / r( p -p )dr where p is the first order reduced density matrix. 

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). 

The oriented gas model was first employed by Chemla et al. [4] to extract molecular second-order nonlinear optical (NLO) properties from crystal data and was based on earlier work by Bloembergen [5]. In this model, molecular hyperpolarizabilities are assumed to be additive and the macroscopic crystal susceptibilities are obtained by performing a tensor sum of the microscopic hyperpolarizabilities of the molecules that constitute the unit cell. The effects of the surroundings are approximated by using simple local field factors. The second-order nonlinear response, for example, is given by... 

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-... 

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