Electromagnetic Gyration: -- Hamiltonian Dynamics of the Stokes Parameters --

Starting with a Schrödinger-type equation derived from the Maxwell theory of electromagnetism, a general formalism is presented for the change of light polarization in nonlinear birefringent media, which we call “optical gyration” or more generally, “electromagnetic gyration” and applications are considered. The theory is formulated in terms of the Hamiltonian dynamics of the Stokes parameters which turns out to be the equation for a classical spin. As applications, we consider two models: (a) As the first application, we analyze solvable models admitting analytic solutions, which exhibit the structure change in the behavior of the Stokes parameter caused by the mutual interplay between linear and nonlinear birefringence. (b) The second application is the optical analogue of the so-called nuclear magnetic resonance (NMR) or Rabi resonance. This is investigated in the case of purely linear birefringence and coexisting of linear and nonlinear birefringence.