Microscopic properties, nonlinear optics

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... 

Finally, the combination of dendrimers and organometallic entities as fundamental building blocks affords an opportunity to construct an infinite variety of organometallic starburst polymeric superstructures of nanoscopic, microscopic, and even macroscopic dimensions. These may represent a promising class of organometallic materials due to their specific properties, and potential applications as magnetic ceramic precursors, nonlinear optical materials, and liquid crystal devices in nanoscale technology. 

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. 

Of central importance for understanding the fundamental properties of ferroelec-trics is dynamics of the crystal lattice, which is closely related to the phenomenon of ferroelectricity [1]. The soft-mode theory of displacive ferroelectrics [65] has established the relationship between the polar optical vibrational modes and the spontaneous polarization. The lowest-frequency transverse optical phonon, called the soft mode, involves the same atomic displacements as those responsible for the appearance of spontaneous polarization, and the soft mode instability at Curie temperature causes the ferroelectric phase transition. The soft-mode behavior is also related to such properties of ferroelectric materials as high dielectric constant, large piezoelectric coefficients, and dielectric nonlinearity, which are extremely important for technological applications. The Lyddane-Sachs-Teller (LST) relation connects the macroscopic dielectric constants of a material with its microscopic properties - optical phonon frequencies ... 

We Initiate here the microscopic description of PDA within the ir-electron framework of Parlser-Parr-Pople (PPP) theory. Quite aside from the crystallinity and Interesting nonlinear optical properties of PDAs, we are convinced that related it-electron descriptions should apply to PA, PDA, and other conjugated polymers. Furthermore, the nature of the low-lying excited states of polymers Is a prerequisite for understanding their relaxation and dynamics. In sharp contrast to ir-electron models, a more realistic treatment of triple bonds leads to Important and previously overlooked Coulomb correlations. We focus below on the novel aspects of excitations In ene-yne systems. 

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 calculation of the electric properties of individual molecules as found in an infinitely dilute gas has for long been of great interest to quantum chemists. This curiosity has been spurred in recent decades by the increasing importance of the communications industry in the world and the parallel need for materials having specific properties for electronic, optical, and other devices. In particular, the nonlinear-optical quantities, defined at the microscopic level as hyperpolarizabilities and at the macroscopic level as nonlinear susceptibilities, have played a... 

With few exceptions, a useful nonlinear optical material will be in the solid phase for example, a single crystal or a poled polymer embedded in a film. Ironically, the quantum chemical calculations of nonlinear optical properties have for the most part been concerned with a single microscopic species. Much has been learned in this way about appropriate molecular construction, but the ultimate goal must be to investigate the nonlinear optical (NLO) properties in the solid phase. 

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... 

We show how the response of a molecule to an external oscillating electric field can be described in terms of intrinsic properties of the molecules, namely the (hyper)polarizabilities. We outline how these properties are described in the case of exact states by considering the time-development of the exact state in the presence of a time-dependent electric field. Approximations introduced in theoretical studies of nonlinear optical properties are introduced, in particular the separation of electronic and nuclear degrees of freedom which gives rise to the partitioning of the (hyper)polarizabilities into electronic and vibrational contributions. Different approaches for calculating (hyper)polarizabilities are discussed, with a special focus on the electronic contributions in most cases. We end with a brief discussion of the connection between the microscopic responses of an individual molecule to the experimentally observed responses from a molecular ensemble... 

During the last 10-20 years, a large number of efficient theoretical methods for the calculation of linear and nonlinear optical properties have been developed— this development includes semi-empirical, highly correlated ab initio, and density functional theory methods. Many of these approaches will be reviewed in later chapters of this book, and applications will be given that illustrate the merits and limitations of theoretical studies of linear and nonlinear optical processes. It will become clear that theoretical studies today can provide valuable information in Are search for materials with specific nonlinear optical properties. First, there is the possibility to screen classes of materials based on cost and time effective calculations rather then labor intensive synthesis and characterization work. Second, there is Are possibility to obtain a microscopic understanding for the performance of the material—one can investigate the role of individual transition channels, dipole moments, etc., and perform systematic model Improvements by inclusion of the environment, relativistic effects, etc. 

The purpose of this chapter is to introduce the fundamentals of the theory of linear and nonlinear optical processes, and our focus will be on the general features of the theory. We will primarily restrict our discussion to the framework of exact-state Aieories, and focus on the occurrence of linear and nonlinear optical processes from a physical point of view. However, in order to set a frame of reference we provide a brief outline of the most common classes of meAiods in approximate-state theories. We will discuss the partitioning of molecular properties into electronic and vibrational contributions, and close the chapter wlAi a brief discussion of the comparison of Are microscopic properties with those of the bulk. We wish to stress that other chapters of this book will cover these latter aspects in greater detail. 

Our discussion has so far been concerned with the microscopic response of a molecule to an external electric field, and thus with an expansion of the molecular energy in orders of the response with respect to the external field, giving rise to the molecular (hyper)polarizabilities. Although experimental data for nonlinear optical properties of molecules in the gas phase do exist [55], the majority of experimental measurements are done in the liquid or solid states, as these states also are the ones that are of greatest interest with respect to developing materials with specifically tailored (non)linear optical properties. 

In the above discussion, we have only considered the effects due to the CTE-CTE repulsion, which contribute to the resonant nonlinear absorption (as well as to other resonant nonlinearities) by the CTE themselves. Here, however, we want to mention a more general mechanism by which the nonlinear optical properties of media containing CTEs in the excited state can be enhanced. This influence is due to the strong static electric field arising in the vicinity of an excited CTE, If, for example, the CTE (or CT complex) static electric dipole moment is 20 Debye, at a distance of 0.5 nm it creates a field Ecte of order 107 V/cm. Such strong electric fields have to be taken into account in the calculation of the nonlinear susceptibilities, because they change the hyperpolarizabilities a, / , 7, etc. of all molecules close to the CTE. For instance, in the presence of these CTE induced static fields, the microscopic molecular hyperpolarizabilities are modified as follows... 

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). 

Figure 4 shows a scanning electron microscope (SEM) picture of polybenzonitrile film obtained with a glow discharge power of 40 W. It was transparent and homogeneous, fine enough for measurement of nonlinear optical properties. 

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