Gauge theory of polarized light in nonlinear birefringent media

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A field equation is studied for the light polarization in anistropic media that incorporates the gauge structure. The field of polarization is realized by a spatial distribution of the Stokes vectors which is naturally deduced from the two-component Schroedinger type equation. The field equation can be extended so as to include the coupling with the gauge field. The evolution equation is derived for the Stokes parameter (pseudo-spin) field by constructing the effective Lagrangian, which is similar to the equation of motion of texture in anistropic fluid; superfluid He3 or liquid crystal; the Lagrangian consists of two terms: "bending" and "twisting" in analogy with elastic theory. The resultant Lagrangian is reduced to a form of the nonlinear sigma model, which suggests the topological nature of the light polarization.