Energy exchange between the Cartesian components of a paraxial beam in a uniaxial crystal

The evolution of the optical power associated with the Cartesian components of a paraxial beam propagating along the optical axis in a uniaxial crystal is investigated. The energy exchange is found to undergo a saturation that is due to both diffraction and coupling between the chi- and gamma-field components; for linearly polarized circularly symmetric input beams, the asymptotic power exchange always amounts to a quarter of the total power. The general results are applied to the case of astigmatic Gaussian beams, which admits of a fully analytical description. The case of finite length crystals is also considered.