Spatial laser beam shaping using aspheric Galilean beam expansion system

It's desirable to design a set of aspheric Galilean laser beam expansion system which can reshape high power TEA CO2 laser beam with waist of 8mm to a diameter of 25mm.Based on the mathematical model and the Romberg numerical integrating algorithm,an array with 40 sets of data was obtained to describe the aspheric surfaces.By fitting the data with the method of the nonlinear least square,the sag's analytical equations of aspheric surfaces were obtained.Using the optical design software package,ZEMAX,the Gaussian beam with beam waist 8mm was emulated passing through the designed beam reshaping system.The results show that the designed system can reshape the entrance Gaussian beam,the peak-valley wavefront error of the flat-top output with a diameter of 25mm is about 25 waves,which proves it being collimated.It makes necessary preparation for further applications.