Dynamics of chirped finite Olver Gaussian beam propagating paraxial to uniaxial crystal

Paraxial transmission characteristic of a second-order frequency chirped finite Olver Gaussian beam (CFOGB) in the uniaxial crystal orthogonal to the optical axial is investigated based on the generalized Huygens-Fresnel integral equation. The exact expression for the CFOGB passing through the uniaxial crystal is derived. The contour graph of the CFOGB intensity distribution on some transversal cross sections, the side view of this beam propagating in three different kinds of uniaxial crystal models are discussed, the influence of the frequency chirp parameter on the beam evolution properties is explored as well. We make sure that the formulae and the conclusions obtained can provide an effective and quick method to adjust and control this CFOGB evolution path and profile through choosing the proper uniaxial crystal structure and frequency chirp value to meet the practical usage.