Dynamics and Topology of Polarization Texture

We present an introductory account of the dynamical and topological aspect for a polarization texture from several aspects. (i) We first give an elementary explanation for a description of polarization in terms of an evolutional equation of the Stokes parameters. This is carried out on the basis of para-axial approximation. (ii) We next consider a field dynamics of the Stokes vectors by using the Lagrangian for the two-component non-linear Schrödinger equation. This results in a form of hydro-dynamical theory of anisotropic fluid. This formulation is also based on the para-axial approximation. (iii) Finally we give a brief sketch for a trial to extend theory to the non-para-axial scheme.