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Propagation of a Pearcey beam in uniaxial crystals

An analytical propagation expression of a Pearcey beam in uniaxial crystals orthogonal to the optical axis is derived. The propagations of the Pearcey beam in the tourmaline and the quartz are investigated. The phase distribution and the angular momentum of the Pearcey beam in the tourmaline are also performed. The result shows that the positions of the auto-focusing and the inversion simply relate to the extraordinary refractive index of the crystals. In other words, we can choose the suitable crystals to adjust the positions of auto-focusing and inversion of the Pearcey beam to meet the actual needs.