Non-paraxial transformation of finite Airy Gaussian beam array in isotropic space

Based on vector Rayleigh-Sommerfeld diffraction integration, we investigate the non-paraxial transmission behavior of the finite Airy Gaussian beam array (FAGBA) in isotropic space. The intensity distribution of the x- component and longitudinal component of the FAGBA at different cross section of the free space are described numerically, respectively. The influences of truncation factor, distribution parameter, wavelength, beam waist radius and refractive index on the FAGBA evolution at several observation planes as well as its side transmission view in isotropic space are also discussed. Through the obtained analytical formulae and conclusions, the beam array transmission locus can be controlled more precisely in non-paraxial situation by altering these parameters to meet the practical usage, especially in area of optical trapping and optical tweezers.