Phase transition of cosh-Airy beams in inhomogeneous media

The cosh-Airy beam is a kind of nondiffracting beam that can be considered as a superposition of two Airy beams with different decay factors and the same propagation trajectory. In this study, we investigate the propagation of a cosh-Airy beam in a quadratic-index inhomogeneous medium and show the periodic phase transition of the cosh-Airy beam, which exhibits a beam transition from the Airy profile to a cosine Gaussian profile periodically. After the phase transition, the field distribution of the cosh-Airy beam is inverted, but the self-acceleration direction of the cosh-Airy beam is unchanged. We show that because of the phase difference of two components of the cosh-Airy beam, the interference effect of the two components plays an important role in the phase transition of the cosh-Airy beam in inhomogeneous medium. Our study may lead to some new potential applications in the manipulation of the Airy beam, signal processing, and other fields.