Abstract
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.
Highlights
The Airy wave packet was first proposed in 1979 [1]
The purpose of this paper is to further reveal the propagation properties of a cosh-Airy beam from the second-order moments
The beam propagation factor was determined by the decay factor a and the cosh parameter γ
Summary
The Airy wave packet was first proposed in 1979 [1]. An Airy beam has the ability to resist diffraction over long distances and can freely accelerate during beam propagation [2,3]. The analytical expression of the beam propagation factor of an Airy beam has been derived on the basis of the Ermakov–Pinney equation [19]. Airy beams have been studied more in the optics domain, they have been investigated in the millimeter wave and radio frequency domains [23,24]. Cosh-Airy beams have similar propagation properties to Airy beams, and they possess more. The propagation properties of cosh-Airy beams have been investigated in free space [25] and uniaxial crystals orthogonal to the optical axis [26], respectively. The above studies on cosh-Airy beams reveal certain characteristics of the beams, but they are not thorough. In the rest of this article, the beam propagation factor of a cosh-Airy beam is investigated. The purpose of this paper is to further reveal the propagation properties of a cosh-Airy beam from the second-order moments
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