Absorption tensor

Rouse matrix, (7.55) total absorption tensor of a macromolecule, (5.7). 

Unit vector defining the basis set for a polarization state, (1.54), (1.55) segmental absorption tensor, (5.4). 

In the present contribution the discussion of the NLO response is restricted to off-resonant case. The only exception is the purely resonant quantity, namely imaginary part of second-order hyperpolarizability in the resonant regime (Im-y(-tt> tu, —w, w)). This quantity describes the process of simultaneous absorption of two quanta. The two-photon absorption (TPA) process is much better understood than the three-photon absorption. The basic quantity associated with the two-photon absorption process is the two-photon absorption tensor (S ). In the most general case referring to two different photons (different polarizations and different energies is given by [75, 81] ... 

The averaging procedure of die two-photon absorption tensor over all orientations of the absorbing molecule leads to [75, 81] ... 

A sufficient amount of oriented chiral molecules can be obtained in an induced cholesteric liquid crystal phase if the induced helical structure has been untwisted by an electric field. In the following description tensors are needed for the sake of simplicity (At least there are three tensors required the transition moment tensor (absorption tensor ,y), the rotational strength tensor (circular dichroism tensor A ,y), and the order tensor g,y33 (i,j= 1,2,3). If the molecules do not possess any symmetry, the principal axes of all of these tensors are differently oriented with respect to the molecular frame (the coordinate system in which only the three diagonal elements of a tensor are different from zero).) The only tensorial property, needed here explicitly, is the existence of three coordinates (components) of a tensor with respect to three specially chosen mutually perpendicular axes. This means that three information instead of one information about a molecule are needed instead of one CD value, namely Ae, three CD values, namely As, (i=l, 2, 3), have to be introduced. Ac is then one-third of a sum of the three so-called tensor coordinates of the CD tensor ... 

M is the electric dipole transition moment vector T is the two-photon absorption tensor a is the Raman scattering tensor and is a unit vector in the direction of light polarization U. 

Saupe matrix elements T = two-photon absorption tensor U V = photon electric field vector direction (polarization) x, y, = molecular orientation axes x y, z - arbitrary molecular axes X, Y, Z = laboratory axes a, P, / = Euler angles ... 

From the degree of anisotropy R in Figure 14 it follows that the ji and the a transitions are of A A and A B symmetry, respectively, for 9 < From the temperature dependence of the degree of anisotropy (Figure 16) with the help of a computational simulation the tensor coordinates of the absorption tensor and the dipole strength tensor D with respect to the principal axes of the order tensor can be obtained. Furthermore, information about the orientational order of the molecule in the used anisotropic system as stretched polymers or ordered liquid crystal phases can be obtained too. 

The molecular description of the circular dichroism and the absorption tensor... 

Figure 5 Coupling scheme for intensity borrowing of the circular dichroism and absorption tensor coordinates of a forbidden A A...

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