Linear susceptibility components

In an SFG experiment, the frequency of the incoming infrared light is changed. A resonance enhancement occurs if the infrared frequency matches the frequency of the vibrational mode leading to a resonant SFG signal. The frequency dependence of the non-linear susceptibility component can be split into a real and an imaginary part leading to... 

The term xi] is the linear susceptibility we have just discussed in the zincblende structure it was isotropic, Xu = In = X33 = X> other components were... 

Most linear optical phenomena such as refraction, absorption and Rayleigh scattering are described by the first term in Eq. (1) where is the linear susceptibility tensor. The higher order terms and susceptibilities are responsible for nonlinear optical effects. The second-order susceptibility tensor T underlies SFG, whereas and BioCARS arises within As we are concerned with optical effects of randomly oriented molecules in fluids, we need to consider unweighted orientational averages of the susceptibility tensors in Eq. (1). We will show that the symmetries of the corresponding isotropic components and correspond to time-even pseudoscalars the hallmark of chiral observables [2]. 

X = e - 1 is the linear susceptibility and x is the p -ortlcr nonlinear susceptibility which is a tensor of rank p - -1. The actual situation is, in fact, more complicated, as the preceding expression holds for isotropic and homogeneous media with nonlinear susceptibilities being real scalar quantities. In the general case, the susceptibilities are complex tensors, defined through the relationship between the spatiotemporal Fourier components of both the polarization and the electric field [68, 69],... 

The general microscopic expression for the nth-order susceptibility contains n + 1 dipole moment matrix elements, involving n intermediate states. For the linear susceptibility there is only one intermediate state, and if the latter is a hybrid one, the corresponding dipole matrix elements are determined mainly by the Frenkel component of the hybrid state. Thus, the linear susceptibility of the hybrid structure contains the factor (dp/ap)2, as is seen from eqn (13.77). For the second-order nonlinear susceptibility x one must have two intermediate states or three virtual transitions. One of them may be a hybrid one, and as long... 

The broad spectrum of recently developed experimental techniques together with traditional measurements of the surface tension has been applied during the last decade to surface layers of micellar solutions [66-76]. For example, Lehmann et al. studied the correlation between the results of a non-linear optieal technique (second-harmonic generation) and surface tension measurements [66], The concentration dependence of the second-order susceptibility component exhibits a kink point in the vicinity of the CMC with a subsequent levelling off (Fig. 5.5). Such behaviour can be explained by the approximate constancy of the adsorption above the CMC. 

Non-resonant component of the non-linear susceptibility Resonant component of the non-linear susceptibility... 

Here, y, etc. are the six linearly independent components of the susceptibility tensor, their relation to the principal molecular susceptibilities K,. K2, being determined by... 

The zero-field and field-induced optical second harmonic generation (SHG) was investigated for the nematic and smectic A phases of various liquid crystals. The components of the cubic non-linear susceptibility tensor were measured for substances with different molecular structure. The phase-matched SHG was observed for all the compounds investigated. The directions of the phase synchronisms as well as the corresponding non-linear susceptibilities were determined for the ee-o and oe-o interactions. The zero-field phase-matched SHG was observed for the oe-o interaction. It was accounted for by a multipolar mechanism. 

The non-linear susceptibility is a third-rank tensor comprising in total 27 elements each one relates different combinations of the interacting field components to the induced non-linear polarisation. The generated polarisation wave is obtained by the summation of all different combinations and reads in the laboratory frame of reference ... 

The individual tensor components are given by an orientational average of the adsorbed molecules within a volume defined by the coherence length of the incident light. The non-linear susceptibility contains information about the number density N and the orientational average of the molecules. 

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