Propagation of Lorentz-Gaussian beam in gradient-index medium

The optical field of a Lorentz-Gaussian beam propagating in a gradient-index medium is derived. Based on the second-order moment of the intensity distribution, the analytical expressions of the half beam width and its changing rate are also presented. The influence of the gradient-index coefficient on the propagation properties of the Lorentz-Gaussian beam is mainly analyzed. The numerical results show that the variation of the normalized intensity distribution, the half beam width and its changing rate are periodic, and the period is times the gradient-index coefficient. The maximum on-axis intensity appears at the half period. The gradient-index coefficient nearly doesnt affect the normalized intensity distribution and the half beam width, but it influences the changing rate of the half beam width.