Jones birefringence

Rizzo and Coriani233 have used coupled cluster ab initio methods to calculate the Jones birefringence of He, Ne, Ar and Kr (and also for H2, N2, C2H2 and CO) and compare the values with the birefringence induced by the Cotton-Mouton effect. They find that the latter is between 100 and 3500 times larger than the former. 

In the next section we summarize the theoretical background for coupled cluster response theory and discuss certain issues related to their actual implementation. In Sections 3 and 4 we describe the application of quadratic and cubic response in calculations of first and second hyperpolarizabilities. The use of response theory to calculate magneto-optical properties as e.g. the Faraday effect, magnetic circular dichroism, Buckingham effect, Cotton-Mouton effect or Jones birefringence is discussed in Section 5. Finally we give some conclusions and an outlook in Section 6. 

Jones birefringence (JB) [140-143] this birefringence is observed when linearly polarized light traverses a sample in the presence of both an electric and a magnetic field perpendicular to the direction of propagation but (unlike in the case of MEB) parallel to each other. The theoretical expression for JB is identical to that for MEB, but it should be noted that the two effects correspond to different experiments with the optical axes in the JB directed at 45° with respect to those of the other three birefringences (KE, CME and MEB). 

Roth, T. Experimental verification of the Jones birefringence induced in hquids. Diploma thesis, Darmstadt University of Technology and Grenoble High Magnetic Field Laboratory (2000)... 

If one makes use of the rather limited information available and given above one may infer that a tilt of between 20° and 30° is normal for straight chain azobenzene derivatives when deposited as LB films, even when a homeotropic phase exists. Such a structure can only be produced in a rather loosely packed film. At the moment it is an open question whether monolayers of these materials exist in the hexatic phase as is the case for fatty acids or whether the structure more nearly corresponds to the smectic-A phase. In the case of the birefringent phase described by Jones et al. [151] it was shown that, once this phase was established, further layers deposited by the LB technique go down in an epitaxial manner. 

Many materials are simultaneously birefringent and dichroic. If the tensors n and n" are coaxial, the Jones matrix will be a simple superposition of these two properties ... 

Circular birefringence will induce a differential retardation in the phase of the orthogonal states of circularly polarized light. Circular dichroism, on the other hand, results in anisotropic attenuation of left- and right-circularly polarized light. The Jones matrix of circularly dichroic materials is normally written as ... 

Equation (2.52) satisfies the requirement that the ordering of the lamellae will not affect the final result. Furthermore, the differential propagation Jones matrix for a composite material is simply the sum of the matrices, N., for each of the separate optical effects. The N matrices for different optical properties can be derived using equation (2.44). As an example, consider a birefringent material with retardation S = (InAn z) /X. One form of the Jones matrix for this material is... 

If the birefringence and dichroism are coaxial, (0 = 0"), this material is described by equation (2.25) with the Jones matrix rotated by an angle 0. ... 

In writing this result, it has been assumed that the birefringence is oriented parallel to either the x or y axes. Completing the multiplication in equation (5.47) yields the following Jones matrix elements... 

The present contribution reviews recent advances in the highly accurate calculation of frequency-dependent properties of atoms and small molecules, electronic struc-mre methods, basis set convergence and extrapolation techniques. Reported applications include first and second hyperpolarizabilities, Faraday, Buckingham and Cotton-Mouton effects as well as Jones and magneto-electric birefringence... 

Figure 5. Contributions to the Jones and magneto-electric birefringences of neon. CC3 all-electron response results in atomic units...

For these systems Jones and magneto-electric birefringences yield retardances which are under the usual experimental conditions about two orders of magnitude weaker than those observed for CME. For the rare gases the predicted retardances for the JB and MEB are comparable to those of BE. The current detection limit for retardances of < 2nrad [175] makes their observation in these systems rather challenging, but they should be measurable for Nt, CO and even better for C2H2. 

That response theory encompasses a great number of of properties of various kind, was nicely illustrated in [145] and [146], which presented and analyzed results from the theory of this review applied to five different types of birefringences. These were the Kerr, Cotton-Mouton, Buckingham, Jones and Magneto-electric birefringences... 

Absorbing systems circular dichroism When linearly dichroic dye molecules are dissolved in a cholesteric liquid crystal the medium exhibits circular dichroism because of the helical arrangement of the solute molecules in the structure. The theory developed above can be extended to take into account the effect of absorption by treating the layers as both linearly birefringent and linearly dichroic. Assuming that the principal axes of linear birefringence and linear dichroism are the same, the Jones matrix of any layer with reference to its principal axes is... 

Labarthet, F. L., Buffeteau, T., Sourisseau, C. (1999). Azopolymer holographic diffraction gratings time dependent analyses of the diffraction efficiency, birefringence, and surface modulation induced two linearly polarized interfering beams. /. Phys. Chem. B, Vol. 103, No. 32, (August 1999), pp. 6690-6699, ISSN 1089-5647 Lien, A. (1990). Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence. Appl. Phys. Lett, Vol. 57, No. 26, (December 1990), p>p. 2767-2769, ISSN 0003-6951... 

In the same way that the Jones matrix can be used to numerically calculate the optical properties of non-uniform birefringence film, the MeuUer matrix can be used to numerically calculate the optical properties of a non-uniform birefidngence film. We divide the film into N slabs as shown... 

A macroscopic, quantitative way to analyze birefringence is through Jones (33-40) and Mueller (41) calculus and the Poincare sphere (42). Those tools are widely used in the optical industry and references on them abound. Another active field of birefringence applications is the combination of the technique with polymer rheology, called flow-birefringence (43,44). 

Liquid crystals are birefringent and they therefore influence the state of polarization of light beams. This interaction is described by the Jones calculus [2], which is briefly outlined below, prior to using it to establish basic results in light modulation by ferroelectric liquid crystals. 

The propagation of coherent light through such a birefringent material with this retardation can be expressed as a Jones matrix, assuming that the fast axis is parallel to the y axis... 

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