Stokes rotation matrix

Further, taking into account the expression of the Stokes rotation matrix L (cf. (1.23)) we derive... 

A rotary polarization modulator simply consists of an optical element that rotates uniformly at a frequency Q about the transmission axis of light. In practice, retardation plates and polarizers are used. In either case, the Mueller matrix of such a device is found by simply replacing the angle 6 by Q.t in the equations listed in Appendix I. Typical PSGs based on rotary modulators and the associated Stokes vectors, Sp G, that are produced are listed in table 8.2. 

These two examples give some idea about the use of the Stokes-Mueller method and show its effectiveness. All Mueller matrices for optical polarization components used in the present chapter have been taken at exact positions such as 0°, 90°, 45°, etc. in order to avoid complicated expressions which might obscure the principle of the method. Of course, any arbitrary position of the optical elements could be considered by the Stokes-Mueller method. In such cases the rotated Mueller matrix M 6) is obtained as a result of the transformation. 

If the transmission axes of a polarizer are rotated relative to the laboratory coordinate system (Fig. 11.2) then its Mueller matrix with respect to the laboratory coordinate system also changes. To obtain the resulting Stokes vector with respect to the laboratory coordinate system, we need to... 

Since the expressions (8.5) and (8.15) are identical, they can be combined, by introducing so-called global tensors of friction f and mobility V, including translational and rotational components. In the Stokes flow, these tensors have some universal properties [2], of which the most important are dependence on instant configuration and independence of velocity, as well as symmetry and positive definiteness of matrixes fj and V. ... 

The phase matrix can be related to the scattering matrix by using the rotation transformation rule (1.22), and this procedure involves two rotations as shown in Fig. 1.14. Taking into account that the scattering matrix relates the Stokes vectors of the incident and scattered fields specified relative to the scattering plane, J = and using the transformation rule of the Stokes... 

---