By starting with the Maxwell theory of electromagnetism, we study the change of polarization state of light transmitting through optically anisotropic media. The basic idea is to reduce the Maxwell equation to the Schroedinger like equation for two levels (or states) representing polarization. By using the quantum mechanical technique, the density matrix, and path integral, the evolution of the Stokes parameters results in the equation of motion for a pseudospin representing a point on the Poincare sphere. Two typical examples relevant to actual experiments are considered; the one gives the generalized Faraday effect, and the other realizes an optical analog of magnetic resonance.

The Maxwell-Schrödinger equation can be reduced to the Schroedinger equation for two levels of polarization, revealing the equation of motion for a pseudospin on the Poincare sphere.

Maxwell-Schrödinger Equation for Polarized Light and Evolution of the Stokes Parameters

Key Takeaway: The Maxwell-Schrödinger equation can be reduced to the Schroedinger equation for two levels of polarization, revealing the equation of motion for a pseudospin on the Poincare sphere.