Quantum Methodologies in Maxwell Optics

A unified formalism of light beam optics and light polarization is presented. The starting point of our formalism is an exact matrix-representation of Maxwell's equations in an inhomogeneous medium, which is presented in detail. The beam-optical Hamiltonians are derived without any specifications on the form of the varying refractive index. The new formalism generalizes the traditional and non-traditional prescriptions of Helmholtz optics. As for the light polarization, the elegant Mukunda–Simon–Sudarshan rule for transition from scalar to vector wave optics is obtained as the paraxial limit of the general formalism presented here. The new formalism is a suitable candidate to extend traditional theory of polarization beyond the paraxial approximation. The unified formalism of light beam-optics and light polarization further strengthens the Hamilton's optical-mechanical analogy, particularly in the wavelength-dependent regime.