Linear optical processes

The present study demonstrates that the analytic calculation of hyperpolarizability dispersion coefficients provides an efficient alternative to the pointwise calculation of dispersion curves. The dispersion coefficients provide additional insight into non-linear optical properties and are transferable between the various optical processes, also to processes not investigated here as for example the ac-Kerr effect or coherent anti-Stokes Raman scattering (CARS), which depend on two independent laser frequencies and would be expensive to study with calculations ex-plictly frequency-dependent calculations. 

Liquid interfaces are widely found in nature as a substrate for chemical reactions. This is rather obvious in biology, but even in the diluted stratospheric conditions, many reactions occur at interfaces like the surface of ice crystallites. The number of techniques available to carry out these studies is, however, limited and this is particularly true in optics, since linear optical methods do not possess the ultimate molecular resolution. This resolution is inherent to nonlinear optical processes of even order. For liquid-liquid systems, optics turns out to be rather powerful owing to the possibility of nondestructive y investigating buried interfaces. Furthermore, it appears that planar interfaces are not the only config-... 

We consider a model for the pump-probe stimulated emission measurement in which a pumping laser pulse excites molecules in a ground vibronic manifold g to an excited vibronic manifold 11 and a probing pulse applied to the system after the excitation. The probing laser induces stimulated emission in which transitions from the manifold 11 to the ground-state manifold m take place. We assume that there is no overlap between the two optical processes and that they are separated by a time interval x. On the basis of the perturbative density operator method, we can derive an expression for the time-resolved profiles, which are associated with the imaginary part of the transient linear susceptibility, that is,... 

There is great interest in preparing materials which could facilitate the development of electrooptic devices. Such devices could permit broad band optical signal encoding so that telephone, data, television, and even higher frequency transmissions could simultaneously be sent down a single optical fiber. The nonlinear optical process which makes this possible is the linear electrooptic effect (EO). It is based on the first field nonlinearities (Z ) of the molecular dipole moment, / ,... 

Spectroscopic methods are very useful for determining molecular properties. Time-resolved spectroscopic methods are useful for monitoring the evolution of the molecular properties in real time. Moreover, time-resolved spectroscopic techniques have the best time resolution available among all kinds of time-resolved experimental techniques. Thus, very often time-resolved spectroscopic methods reveal the dynamics of a molecular system in the non-equilibrium regime. In this section, the density matrix method is applied to calculate the spectroscopic properties of molecular systems. These include the linear and non-linear optical processes, in equilibrium or non-equilibrium cases. The approach is based on the susceptibility theory. 

A more general framework to treat local field effects in linear and nonlinear optical processes in solution has been pioneered, among others [45], by Wortmann and Bishop [46] using a classical Onsager reaction field model (see the contribution by the Cammi and Mennucci for more details). Such a model has not been extended to treat vibrational spectra. 

A surface is illuminated with a high-intensity laser, and photons are generated at the second-harmonic frequency through non-linear optical process. For many materials only the surface region has the appropriate symmetry to produce a SHG signal. The non-linear polarizability tensor depends on the nature and geometry of adsorbed atoms and molecules. 

Nonlinear Raman scattering spectroscopy is a multiphoton spectroscopy that enables access to vibrationally excited molecular levels. Through nonlinear optical processes, this technique allows us to study rich molecular information which cannot be reached by linear optical method. 

Linear and nonlinear optical processes are described as follows [16]. The dipole moment fA, induced in a molecule placed in an electromagnetic held with frequency of oj is given by... 

An axially symmetric molecule is characterized by its linear polarizability in the principal axes a x and a y = a" and a" = af/. It is a good approximation to assume that its second- and third-order polarizability tensors each have only one component and respectively, which is parallel to the z principal axis of the molecule. For linear and nonlinear optical processes, the macroscopic polarization is defined as the dipole moment per unit volume, and it is obtained by the linear sum of the molecular poiarizabilities averaged over the statistical orientational distribution function G(Q). This is done by projecting the optical fields on the molecular axis the obtained dipole is projected on the laboratory axes and orientational averaging is performed. The components of the linear and nonlinear macroscopic polarizabilies are then given by ... 

Sekkat, Z., Pretre, P., Knoesen, A., Volksen, W., Lee, Y. Y., Miller, R. D., Wotxl, J., and Knoll, W. Correlation between polymer architecture and sub-glass-transiiion-temperature light-induced molecular movement in azo-polyimide polymers influence on linear and second- and third-order nonlinear optical processes. Journal of the Optical Society of America B (Optical Physics), vol. I S, (no. 1), Opt. Soc. America, m. 1998, p. 401-41.1. 

For a centrosymmetric medium incoming fields E (o) and -E[(o) must Induce polarizations P (2 ) and-P (2o)). respectively. This, however, is not consistent with equation (3.7.16) unless is zero, indicating that SHG is forbidden. At an interface the inversion symmetry is broken and SHG is no longer forbidden. Interfacial non-linear radiation is emitted by a sheet of coherently driven dipoles oscillating at the same frequency. Therefore, non-linear emission is coherent and has a well-defined direction, in contrast to linear optical processes like Raleigh and Raman scattering (see 1.7.3 and 1.7.8). 

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. 

We have seen how the molecular properties in nonlinear optics are defined by the expansion of the molecular polarization in orders of the external electric field, see Eq. (5) beyond the linear polarization this definition introduces the so-called nonlinear hyperpolarizabilities as coupling coefficients between the two quantities. The same equation also expresses an expansion in terms of the number of photons involved in simultaneous quantum-mechanical processes a, j3, y, and so on involve emission or absorption of two, three, four, etc. photons. The cross section for multiphoton absorption or emission, which takes place in nonlinear optical processes, is in typical cases relatively small and a high density of photons is required for these to occur. 

Abstract We give an overview of linear and nonlinear optical processes that can be specific... 

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