We develop a path integral approach for analyzing the stationary light propagation in general dielectric media. The Hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle with spin-orbit coupling and position dependent mass. After appropriate ordering several path integral representations of a solution are constructed. First we keep the propagation of the polarization degrees of freedom in an operator form integrated over paths in a coordinate space. The use of spin 1 coherent states allows representing this part as a path integral over such states. Finally a path integral in a transversal momentum space with explicit transversality enforced at every time slice is also given. As an example the geometrical optics limit is discussed and the ray equation is recovered together with the Rytov rotation of the polarization vector.
© 2010 Optical Society of America
Diffraction and Gratings
Original Manuscript: October 21, 2009
Revised Manuscript: February 3, 2010
Manuscript Accepted: February 8, 2010
Published: April 12, 2010
Yair Dimant and Shimon Levit, "Path integrals for light propagation in dielectric media," J. Opt. Soc. Am. B 27, 899-903 (2010)