Propagation of sinh-Gaussian beams in gradient-index medium

In order to study the propagation characteristics of sinh-Gaussian beams in gradient-index medium,the analytical expression of the intensity was derived based on the general Huygens-Fresnel diffraction integral.Based on the second-order moment definition,the analytical expression for the beam width and the waist location were deduced.The intensity,facular size,beam waist and its position were calculated.The results show that the axial intensity changes periodically and the transverse intensity distribution are largely affected by the nonlinearity of the medium and the modulation parameter of the beams.The spot site and waist location can be changed by adjusting the parameter appropriately.