Spectral properties of chirped Gaussian pulsed beams propagating through the turbulent atmosphere

The spectral properties of chirped Gaussian pulsed beams propagating through the turbulent atmosphere are studied. The analytical expression for the spectrum, algebraic equation governing the position omega(max) of the maximum spectrum and algebraic equation governing the position r(0) without spectral shift are derived. It is shown that the spectrum at the observation point (r, z) depends on the structure constant of the refractive index C-n(2), chirp parameter C and pulse duration T. The normalized on-axis spectrum S(omega) is blue-shifted, and the off-axis spectrum becomes red-shifted with increasing radial coordinate. The effect of turbulence on the spectral shift of chirped Gaussian pulsed beams becomes smaller with decreasing C and increasing T. The position ro without spectral shift is dependent on omega(0), C-n(2), and z, but independent of T and C. In addition, there exists an off-axis spectral transition of a chirped Gaussian pulsed beam in the turbulent atmosphere. The physical explanations of the spectral shift and spectral transition of chirped Gaussian pulsed beams propagating through the turbulent atmosphere are given.