Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond

TLDR

The paper aims to describe monochromatic light propagation in uniaxial crystals and to develop a paraxial scheme for beams traveling orthogonal to the optical axis. The authors achieve this by solving Maxwell’s equations exactly and then formulating a paraxial approximation for the orthogonal beam. They find that the Cartesian field components are uncoupled, with the ordinary component following standard Fresnel diffraction while the extraordinary component exhibits anisotropic diffraction that can be decomposed into two spatial geometrical affinities and a Fresnel step, and that nonparaxial corrections couple the components, producing a larger longitudinal field and analytic expressions for both the extraordinary Gaussian beam and its nonparaxial correction.

Abstract

We describe monochromatic light propagation in uniaxial crystals by means of an exact solution of Maxwell's equations. We subsequently develop a paraxial scheme for describing a beam traveling orthogonal to the optical axis. We show that the Cartesian field components parallel and orthogonal to the optical axis are extraordinary and ordinary, respectively, and hence uncoupled. The ordinary component exhibits a standard Fresnel behavior, whereas the extraordinary one exhibits interesting anisotropic diffraction dynamics. We interpret the anisotropic diffraction as a composition of two spatial geometrical affinities and a single Fresnel propagation step. As an application, we obtain the analytical expression of the extraordinary Gaussian beam. We then derive the first nonparaxial correction to the paraxial beam, thus giving a scheme for describing slightly nonparaxial fields. We find that nonparaxiality couples the Cartesian components of the field and that the resultant longitudinal component is greater than the correction to the transverse component orthogonal to the optical axis. Finally, we derive the analytical expression for the nonparaxial correction to the paraxial Gaussian beam.