Study on the beam quality factor of sinh-Gaussian(ShG) beams

Based on the angular spectrum representation and the theory of the second intensity moment of non-paraxial scalar beam,the beam waist radius,the far-field divergence angle and the beam quality factor of non-paraxial scalar sinh-Gaussian(ShG) beams were calculated.Compared with the beam quality factor of paraxial scalar sinh-Gaussian (ShG) beams,some new results were obtained.When the beam waist radius is relatively large,the theoretical calculations for the beam quality factor of paraxial and non-paraxial scalar sinh-Gaussian(ShG) beams change in the same way and the theory of the traditional second intensity moment of scalar light field is a valid approximation; when the beam waist radius is very small,they have a great difference and the theory of the second intensity moment of non-paraxial scalar beam must be used.