Paraxial ray theory for Maxwell's equations

Paraxial ray theory for Maxwell's equations in the case of an inhomogeneous isotropic medium with finite conductivity and smooth interfaces is developed. We show that the ray centered coordinates are suitable for describing amplitudes and polarization of waves in their propagation and reflection/refraction on a smooth interface. Expressions for the geometrical spreading and second order derivatives of the eikonal are obtained in terms of certain solutions of the equations in variations, i.e., equations which describe rays close to the central ray in linear approximation.