Paraxial propagation along the optical axis of a uniaxial medium

An approach for describing paraxial propagation of light along the optical axis of a uniaxial medium is introduced. Contrary to previous theoretical schemes, our approach directly deals with the propagation of the whole optical field without resorting to the standard decomposition into ordinary and extraordinary parts, thus avoiding some related mathematical difficulties. A paraxial equation governing the field propagation has been derived, and its formal solution has been deduced. The structure of this solution allows us to think of the optical field in the crystal as the corresponding one propagating in vacuum "dressed" by the effect of anisotropy. This relationship is used to derive two analytical techniques for evaluating the propagated field. Starting from the formal solution, the closed-form expression of the anisotropic propagator is also derived. The proposed approach is used to predict the evolution of an astigmatic Gaussian beam through a calcite crystal, which has been also experimentally investigated. The agreement between theory and experiment is good.