Nonlinear optical response

So far we have considered the optical properties of surfaces and interfaces under the assumption that the amplitude of the incident light wave, E,-, is negligible in comparison with the intra-atomic field strengths and hence the electric displacement vector is a linear function of E, (see Eq. (3.63)). For larger amplitudes the polarization which is induced by the light wave can be quite generally written in the form of a power series 

1) The typical intra-atomic field strengths are of the order 10 -10 V/cm. 

Optics and Spectroscopy at Surfaces and Interfaces. Vladimir G. Bordo and Horst-Giinter Rubahn Copyright 2005 WILEY-VCH Verlag GmbH Co. KGaA. Weinheim ISBN 3-527-40560-7 

If a group of monochromatic plane waves strikes the interface, the electric field E, must be replaced by the sum  

introducing the Fourier-transformed quantities by means of the equation 

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Kobayashi T 1994 Measurement of femtosecond dynamics of nonlinear optical responses Modern Noniinear Optics part 3, ed M Evans and S Kielich Adv. Chem. Rhys. 85 55-104... 

In order to illustrate some of the basic aspects of the nonlinear optical response of materials, we first discuss the anliannonic oscillator model. This treatment may be viewed as the extension of the classical Lorentz model of the response of an atom or molecule to include nonlinear effects. In such models, the medium is treated as a collection of electrons bound about ion cores. Under the influence of the electric field associated with an optical wave, the ion cores move in the direction of the applied field, while the electrons are displaced in the opposite direction. These motions induce an oscillating dipole moment, which then couples back to the radiation fields. Since the ions are significantly more massive than the electrons, their motion is of secondary importance for optical frequencies and is neglected. 

The linear and nonlinear optical responses for this problem are defined by e, 2, e and respectively, as indicated in figure Bl.5.5. In order to detemiine the nonlinear radiation, we need to introduce appropriate pump radiation fields E(m ) and (co2)- If these pump beams are well-collimated, they will give rise to well-collimated radiation emitted tlirough the surface nonlmear response. Because the nonlinear response is present only in a thin layer, phase matching [37] considerations are unimportant and nonlinear emission will be present in both transmitted and reflected directions. 

Luce T A and Bennemann K H 1998 Nonlinear optical response of noble metals determined from first-principles electronic structures and wave functions calculation of transition matrix elements P/rys. Rev. B 58 15 821-6... 

Tamarat P, Lounis B, Bernard J, Orrit M, Kummer S, Kettner R, Mais S and Basche T 1995 Pump-probe experiments with a single molecule ac-Stark effect and nonlinear optical response Phys. Rev. Lett. 75 1514-17... 

Tad)eddine, M. and Flament, J.P. (1999) Analysis of a nonlinear optical response of CN- ions adsorbed on metal electrode tentative interpretation by means of ab initio molecular calculations. Chemical Physics, 240, 39-50. 

Figure 6.1 Nonlinear optical responses, (a) Second-order SF generation, the transition probability is enhanced when the IR light is resonant to the transition from the ground state g to a vibrational excited state V. CO is the angular frequency of the vibration, (b) Third-order coherent Raman scheme, the vibrational coherence is generated via impulsive stimulated...

In order to describe the problems of the nonlinear optical response from biological systems, the question of chirality must be addressed. Linear circular dichroism (CD) has been investigated extensively for biological compounds and a wealth of data are available on... 

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... 

In addition to studies of diacetylene single crystals, current research, activities are focused on studies of the second X and third x order nonlinear optical responses of disubstituted diacetylene polymer films as active optical guided wave structures. Diacetylene polymers possess X values comparable to germanium(j 7). In the first stage, three major questions are being addressed ... 

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... 

In this section, the experimental techniques described in the previous section are applied to the study of thin Langmuir-Blodgett films of chiral molecules and polymers. We will show in detail how the second-order susceptibility of chiral thin films can be analyzed and discuss the influence of chirality on the nonlinear optical response of these films. 

The systems discussed up to now all showed chiral susceptibilities that were of the same order of magnitude or smaller than the achiral susceptibility components. The system that we discuss in this section has chiral susceptibilities that dominate the nonlinear optical response.53 The material is a chiral helicenebisquinone derivative shown in Figure 9.22. In bulk samples, the nonracemic, but not the racemic, form of the material spontaneously organizes into long fibers clearly visible under an optical microscope. These fibers comprise columnar stacks of helicene molecules.54,55 Similar columnar stacks self-assemble in appropriate solvents, such as n-dodecane, when the concentration exceeds 1 mM. This association can be observed by a large increase in the circular dichroism (CD) of the solutions. 

The study of chiral materials with nonlinear optical properties might lead to new insights to design completely new materials for applications in the field of nonlinear optics and photonics. For example, we showed that chiral supramolecular organization can significantly enhance the second-order nonlinear optical response of materials and that magnetic contributions to the nonlinearity can further optimize the second-order nonlinearity. Again, a clear relationship between molecular structure, chirality, and nonlinearity is needed to fully exploit the properties of chiral materials in nonlinear optics. 

For the practical application to nonlinear optics, further, noncentrosymmetric LB films are required to possess not only large nonlinear optical response but excellent optical quality and thickness appropriate to optical devices. In this study, a family of pyrazine derivatives was found to be an LB film-forming material applicable to waveguide devices. The optical nonlinearity in the pyrazine LB films and the application of the pyrazine LB films to a frequency-doubling waveguide device is demonstrated in the latter part. 

Design of amphiphiles for noncentrosymmetric LB films with large nonlinear optical response... 

Up to now, many conjugated polymers have been found to possess large and very rapid third-order nonlinear optical response, which originates from the one-dimensionally delocalized ji-conjugation system along the polymer chain. Their application to the all optical signal processing devices has been expected. 

Assuming the tensor component of xf x parallel to the polymer chain direction is dominant for the nonlinear optical response, one can use the following equation ... 

These studies demonstrate how the nonlinear optical response from the surface can provide both a qualitative and quantitative probe of chemisorption. 

A. Suryanto, E. van Groesen, M. Hammer, and H. J. W. M. Hoekstra, "A finite element scheme to study the nonlinear optical response of a finite grating without and with... 

Shuai, Z., Bredas, J.L., Saxena, A., Bishop, A.R. Linear and nonlinear optical response of polyenes a density matrix renormalization group study. J. Chem. Phys. 1998, 109(6), 2549. 

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. 

D. A. Micha, A. Santana, and A. Salam. Nonlinear optical response and yield in the femtosecond photodesorption of CO from the Cu(001) surface a density matrix treatment. J. Chem. Phys., vvv ppp, 2002. to appear. 

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