Beam Propagation Factor of a Cosh-Airy Beam

Based on the second-order moments, the analytical expression of the beam propagation factor of a cosh-Airy beam has been derived. The beam propagation factor was determined by the decay factor and the cosh parameter. Because the beam propagation factors in the x- and y-directions of the cosh-Airy beam have the same form, only the beam propagation factor in the x- direction was selected as the object of numerical calculation and analysis. The effects of the decay factor and the cosh parameter on the beam propagation factor were investigated. When the decay factor was greater than 1, the beam propagation factor first increased and then decreased with the increase of the cosh parameter, and finally, tended to a minimum value. Under the condition that the decay factor was less than 1, the beam propagation factor always increased with the increase of the cosh parameter. As the decay factor increased, the beam propagation factor decreased and tended to a minimum value. Finally, the effects of the decay factor and the cosh parameter on the squares of the beam waist and the divergence were analyzed in more detail.