Propagation of the finite energy Airy-Hermite-Gaussian beams in uniaxial crystals orthogonal to the optical axis

Abstract

We derive an analytical propagation expression of the finite energy Airy-Hermite-Gaussian beam propagating in a uniaxial crystal orthogonal to the optical axis, and calculate numerical examples to investigate the influences of the propagation distance and the ratio of the extraordinary refractive index to the ordinary refractive index on the beam profile. In addition, we also examine the intensity distribution of the beam propagating in the uniaxial crystals at different observation sections. Our research shows that the initial beam profile of the beam remains nearly invariant for a short propagation distance in the crystal. However, as propagation distance continues to increase, the beam width will gradually enlarge, where the diffusion velocities of the beam in the X and Y directions are different. Moreover, both the ratio of the extraordinary refractive index to the ordinary refractive index and the Hermite order number also strongly affect the beam profile in a uniaxial crystal. Our work may find some potential applications in optical trapping and nonlinear optics involving in the special beam profile.