Propagation properties of elliptical Gaussian beam in uniaxial crystals along the optical axis

• The equations of elliptical Gaussian beam in uniaxial crystals along optical axis are derived.
• The components AoxAox and AexAex of the elliptical Gaussian beam are obtained by numerical examples.
• The propagation properties of elliptical Gaussian beam in uniaxial crystals are analyzed.

Based on the paraxial vectorial theory of beams propagating in uniaxial anisotropic crystal, we have derived the analytical propagation equations of elliptical Gaussian beam in uniaxial crystal along the optical axis, and given the typical numerical example to illustrate our analytical results. It is found that the x-polarized Gaussian beams split into an ordinary beam and an extraordinary beam, which independently propagate along the optical axis, and the elliptical Gaussian beam loses its initial profile with the propagation distance increasing.