Nonlinear field effects

Here the ijk coordinate system represents the laboratory reference frame the primed coordinate system i j k corresponds to coordinates in the molecular system. The quantities Tj, are the matrices describing the coordinate transfomiation between the molecular and laboratory systems. In this relationship, we have neglected local-field effects and expressed the in a fomi equivalent to simnning the molecular response over all the molecules in a unit surface area (with surface density N. (For simplicity, we have omitted any contribution to not attributable to the dipolar response of the molecules. In many cases, however, it is important to measure and account for the background nonlinear response not arising from the dipolar contributions from the molecules of interest.) In equation B 1.5.44, we allow for a distribution of molecular orientations and have denoted by () the corresponding ensemble average ... 

Liquid crystal polymers are also used in electrooptic displays. Side-chain polymers are quite suitable for this purpose, but usually involve much larger elastic and viscous constants, which slow the response of the device (33). The chiral smectic C phase is perhaps best suited for a polymer field effect device. The abiHty to attach dichroic or fluorescent dyes as a proportion of the side groups opens the door to appHcations not easily achieved with low molecular weight Hquid crystals. Polymers with smectic phases have also been used to create laser writable devices (30). The laser can address areas a few micrometers wide, changing a clear state to a strong scattering state or vice versa. Future uses of Hquid crystal polymers may include data storage devices. Polymers with nonlinear optical properties may also become important for device appHcations. 

When a strong static electric field is applied across a medium, its dielectric and optical properties become anisotropic. When a low frequency analyzing electric field is used to probe the anisotropy, it is called the nonlinear dielectric effect (NLDE) or dielectric saturation (17). It is the low frequency analogue of the Kerr effect. The interactions which cause the NLDE are similar to those of EFLS. For a single flexible polar molecule, the external field will influence the molecule in two ways firstly, it will interact with the total dipole moment and orient it, secondly, it will perturb the equilibrium conformation of the molecule to favor the conformations with the larger dipole moment. Thus, the orientation by the field will cause a decrease while the polarization of the molecule will cause an... 

In the following sections we will first in Section 2 briefly discuss the necessary background to understand optical activity effects in linear and nonlinear optics and to illustrate the similarities and differences between both types. In Section 3 we present a more thorough analysis of nonlinear optical effects in second-harmonic generation, both from a theoretical and an experimental point of view. Section 4 deals with experimental examples that illustrate the usefulness of nonlinear optical activity in the study of chiral thin films and surfaces. Finally, in Section 5 we give an overview of the role of chirality in the field of second-order nonlinear optics and show that chiral molecules can be useful for applications in this field. 

Figure 9.3 Schematic illustration of second-order nonlinear optical effects, (a) Second-harmonic generation. Two light fields at frequency go are incident on medium with nonvanishing / 2. Nonlinear interaction with medium creates new field at frequency 2 go. (b) Frequency mixing. One light field at frequency GO and one at frequency go2 is incident on nonlinear medium. Nonlinear interaction with medium creates new field at frequency goi + go2. (c) electro-optic effect. Static electric field E (0) applied over nonlinear medium changes phase of an incoming light field.

In order to describe second-order nonlinear optical effects, it is not sufficient to treat (> and x<2) as a scalar quantity. Instead the second-order polarizability and susceptibility must be treated as a third-rank tensors 3p and Xp with 27 components and the dipole moment, polarization, and electric field as vectors. As such, the relations between the dipole moment (polarization) vector and the electric field vector can be defined as ... 

The second-order character of the electron hopping process is responsible for the nonlinear expression of the term that depicts the field effect. 

P. Ye and Y. R. Shen, Local field effect on linear and nonlinear optical properties of... 

Williams, J.D. Cox, K.A. Cooks, R.G. McLuckey, S.A. Hart, K.J. Goeringer, D.E. Resonance Ejection Ion Trap Mass Spectrometry and Nonlinear Field Contributions The Effect of Scan Direction... 

Such a behavior of the total field is observed provided that the beam power is smaller than a definite value P which depends on the waveguide width (for a = 1.8pm, P 8). The spatial dynamics of a light beam with P > Pi is more complicated because nonlinear self-effects in radiation field increase so that the formation of soliton-like light beams propagating in the waveguide cladding is observed. 

Note 3 A polymer that exhibits a nonlinear optical effect due to anisotropic electric susceptibilities when subjected to electric field together with light irradiation is called an electro-optical polymer. A polymer that exhibits electro-optical behavior combined with photoconductivity is called a photorefractive polymer. 

Abstract Optical techniques for three-dimensional micro- and nanostructuring of transparent and photo-sensitive materials are reviewed with emphasis on methods of manipulation of the optical field, such as beam focusing, the use of ultrashort pulses, and plasmonic and near-field effects. The linear and nonlinear optical response of materials to classical optical fields as well as exploitation of the advantages of quantum lithography are discussed. 

From the foregoing discussion of electric field effects In Ionic equlibria It Is clear that a solution of a weak electrolyte shows a non-linear behavior In conductance (or resistance) at high field strengths. With an Interdisciplinary look at the field of electronics we note that such nonlinearities are at the heart of all modern electronic circuits and devices. We therefore can use a solution of a weak electrolyte subjects to high electric fields as an electronic device, which Is the basic Idea of the Field Modulation Tecnnlque, the general principles we will discuss now. 

Hyperpolarizabilities of molecules are an active field of study, because they determine a variety of important nonlinear optical effects. However, the deduction of hyperpolarizabilities from these nonlinear optical experiments is a very complicated business. The experiments are carried out at finite frequencies, so some extrapolation is required to obtain an estimate of the static (zero frequency) value. Also, there is a contribution to the hyperpolarizability from molecular vibrations, so even after extrapolation to zero frequency the experimental result may not correspond to what is desired. It is therefore very useful to study atoms, both theoretically and experimentally, since this vibrational contribution is necessarily absent. Calculations... 

The analytical solutions to Fick s continuity equation represent special cases for which the diflusion coefficient, D, is constant. In practice, this condition is met only when the concentration of diffusing dopants is below a certain level ( 1 x 1019 atoms/cm3). Above this doping density, D may depend on local dopant concentration levels through electric field effects, Fermi-level effects, strain, or the presence of other dopants. For these cases, equation 1 must be integrated with a computer. The form of equation 1 is essentially the same for a wide range of nonlinear diffusion effects. Thus, the research emphasis has been on understanding the complex behavior of the diffusion coefficient, D, which can be accomplished by studying diffusion at the atomic level. 

The terms beyond odE are not linear in E they are referred to as the nonlinear polarization and give rise to nonlinear optical effects. Also note that at small fields the polarization will more nearly approximate a linear response however, with increasing field strength, nonlinear effects become more important. Since a p, y, there were few observations of NLO effects before the invention of the laser with its associated large electric fields. 

Interest in the field of nonlinear optics has grown tremendously in recent years. This is due, at least partially, to the technological potential of certain nonlinear optical effects for photonic based technologies. In addition, the responses generated through nonlinear optical interactions in molecules and materials are intimately related to molecular electronic structure as well as atomic and molecular arrangement in condensed states of matter. 

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