Polarization measurements, nonlinear optics

As discussed in Section X, the most relevant application of this idea is the possibility of measuring nonlinear optical responses (which are properties based, at least in principle, on mechanisms that involve electronic charge polarization), through the measurement of infrared intensities and Raman cross sections. 

S. Mukamel I would like to make a comment regarding interference effects in quantum and classical nonlinear response functions [1, 2]. Nonlinear optical measurements may be interpreted by expanding the polarization P in powers of the incoming electric field E. To nth order we have... 

In this paper it has been attempted to provide an introductory overview of some of the various nonlinear optical characterization techniques that chemists are likely to encounter in studies of bulk materials and molecular structure-property relationships. It has also been attempted to provide a relatively more detailed coverage on one topic to provide some insight into the connection between the macroscopic quantities measured and the nonlinear polarization of molecules. It is hoped that chemists will find this tutorial useful in their efforts to conduct fruitful research on nonlinear optical materials. 

Kaatz, P. and Shelton D.P., Polarized hyper-Rayleigh light scattering measurements of nonlinear optical chromophores. J. Am. Chem.SOc. (1996) 105 3918-3929. 

The potential development of optoelectronic devices based on nonlinear polarization of the MMCT transitions of mixed-valence complexes has been the subject of an investigation 100). The hyperpolarizabilities measured for the complexes [(CN)5Ru(jU.-CN)Ru(NH3)5] and [(T75-C5H5)Ru(PPh3)2( U-CN)Ru(NH3)5]3+ are among the largest known for a solution species. The tunability of MMCT energy is an added advantage for the construction of nonlinear optical devices. 

The derivation of formulae for the frequency-dependent nonlinear susceptibilities of nonlinear optics from the time-dependent response functions can be found in a number of sources, (Bloembergen, Ward and New, Butcher and Cotter, Flytzanis ). Here it is assumed that the susceptibilities can be expressed in terms of frequency-dependent quantities that connect individual (complex) Fourier components of the polarization with simple products of the Fourier components of the field. What then has to be shown is how the quantities measured in various experiments can be reduced to these simpler parameters. 

As already mentioned, the only techniques sensitive to the polar order are even order nonlinear optical techniques such as the already-described second harmonic generation and linear electro-optic effect (cf. Chapter 2). The hrst technique offers a high sensitivity to the fast electronic contributions to susceptibility and is widely used. As already mentioned, it also gives the opportunity to study the kinetics of the poling by in situ measurements [152]. 

The theoretical framework developed above is valid in the electric dipole approximation. In this context, it is assumed that the nonlinear polarization PfL(2 >) is reduced to the electric dipole contribution as given in Eq. (1). This assumption is only valid if the surface susceptibility tensor x (2 > >, a>) is large enough to dwarf the contribution from higher orders of the multipole expansion like the electric quadrupole contribution and is therefore the simplest approximation for the nonlinear polarization. At pure solvent interfaces, this may not be the case, since the nonlinear optical activity of solvent molecules like water, 1,2-dichloroethane (DCE), alcohols, or alkanes is rather low. The magnitude of the molecular hyperpolarizability of water, measured by DC electric field induced second harmonic... 

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