Spectral changes of partially coherent flat topped beam in turbulent atmosphere

Spectral characteristics of partially coherent flat-topped (PCFT) beams propagated in a turbulent atmosphere are investigated and an analytical formula for the spectrum S(ω) is derived. It is shown that, if the scaling law is valid, the normalized spectrum S(ω) of PCFT beams propagating through turbulent atmosphere is the same as the normalized source spectrum S⁽⁰⁾(ω), this similarity is valid for any arbitrary order of the circular flat-topped “N”. It is proved that if the scaling law is not valid, S(ω) of PCFT is different from S⁽⁰⁾(ω). Also spectral behavior of PCFT beams in free space and turbulence media is investigated in detail.