Transformation regulation of the paraxial finite Airy–Gaussian beam array propagating through uniaxial electro-optic crystals

The transformation regulation of the radial finite Airy–Gaussian beam array (FAiGBA) in uniaxial crystals orthogonal to the optical axis has been explored analytically and numerically under the paraxial approximation. The analytical evolution solution of this beam array in the x- and y-directions has been derived, respectively. The intensity distribution and side view of FAiGBA propagating in three types of uniaxial crystals have been demonstrated in several instances. Furthermore, particular attention has been devoted to the linear effect when this beam array transmits through the electro-optic crystal. The influence of non-paraxial longitudinal component and temperature on FAiGBA evolution characteristics has also been examined to verify the validity of the paraxial mechanism of this beam array propagating in uniaxial crystals. It is anticipated that these research findings will contribute to the advancement of FAiGBA applications in micro- and nano-control, optical fiber communication, optical trapping, and manipulation fields.