Jones’ matrices birefringence

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... 

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... 

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... 

If the optical axis of the birefringent film makes an angle (j) with x, we can express the Jones matrix as ... 

We now consider the application of the Jones matrix method to the simple problem of polarized light through a birefringent phase plate or retardation plate... 

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