Studies of the characteristic parameters for a flattened-Gaussian beam through a defocusing lens

By introducing an equivalent focal length, analytical propagation equations of the characteristic parameters for a flattened-Gaussian beam through a defocusing lens in free space are obtained on the basis of Collins diffraction formula and definition of high-order intensity moments. The parametric characteristics of beam width, kurtosis parameter and power in the bucket are analyzed and discussed analytically or numerically. Numerical results show that the effects of different kinds or values of defocusing coefficient of the lens on these parameters are different. It is concluded that the action of the lens with different defocusing coefficient can be compensated by a series of lenses with different focal length in theory.