Spectral characteristics of chirped pulsed Gaussian beams propagating in turbulent atmosphere

Based on the extended Huygens-Fresnel principle, analytical expressions are derived for the cross-spectral density matrix of chirped pulsed Gaussian beams propagating in turbulent atmosphere, which are then numerically simulated. It is shown that there are blue shifts in the spectra of axis point when the spectral width of chirped pulsed Gaussian beams is more than a certain value of 0.336. The turbulence induces the decrease of relative frequency shift of on-axis spectra; the relative frequency shift of on-axis spectra increases nonlinearly with the increasing light source spectral width. Increasing the beam waist radius can inhibit the relative frequency shift and the beam broadening.