Beam smoothing characteristics of continuous phase plate with Gaussian distribution

According to the requirement of beam smoothing in laser systems, the continuous phase plate with Gaussian distribution is designed. The far-field distributions of such phase plate with correlation lengths of 39 mm, 30 mm, 10 mm and 3 mm are calculated. The numerical results show that while the correlation length is longer than 10 mm, far-field distribution of the phase plate is inordinate for the ergodic condition is not satisfied. While the correlation length is less than 10 mm, far-field distribution of the phase plate is very close to ideal Gaussian distribution. Using the continuous phase plate with the correlation length of 3 mm, the beam smoothing process is simulated. The results show that after propagating through a phase plate the intensity distribution of the laser beam on the f