Analysis of spectral propagating properties of Gaussian beam

In order to analyze the spectral propagating properties of laser beam,spectral propagation equations of Gaussian beam propagating through free space and turbulent atmosphere were derived according to the extended Huygens-Fresnel formula,and then numerical simulation was carried out for the beam with center frequency 1.78×1015rad/s and bandwidth 8.39×1013rad/s.Results indicate that when Gaussian beam propagating through free space and turbulent atmosphere,spectrum blue-shifted exists at the scopes of near-axis and red-shifted happens if the distance from z-axis increases to a critical value.Turbulent atmosphere has the ability to reduce spectrum shift for off-axis scope,and increase of spectrum bandwidth in source can make spectrum shift phenomena more obvious.Intensity distribution vertical to z-axis at 5000m for Gaussian beams with frequency 1.78×1015rad/s and 1.75×1015rad/s shows that,for a fixed position light intensity of center frequency becomes weaker than intensity of some other frequency,and this can leads to spectral shift,besides,the phenomena of spectral changing with some parameters can be explained with the theories of Gaussian beam propagation and turbulent atmosphere beam width-spreading effect.