Complex Gaussian functions expansion method applied to truncated Gaussian beams

Abstract

An analytical expression for the beam propagation factor (M 2 factor) of truncated Gaussian beams was derived by using the complex Gaussian functions expansion method. The reasonability of the approximation of complex Gaussian functions expansion method is studied, and a comparison of this method with the generalised truncated second-order moments method and the asymptotic analysis method is also made. In general, an easy analytical expression for the M 2 factor of truncated laser beams can be derived by using the complex Gaussian functions expansion method. The M 2 factor obtained by using the complex Gaussian functions expansion method is more consistent with that in practice than that obtained by using two other methods. The analytical results obtained by using the complex Gaussian functions expansion method can be reduced to that for the non-truncated case when the truncation parameter is sufficiently large. Therefore, the complex Gaussian functions expansion method is a suitable approximation method for studying the M 2 factor of truncated laser beams.