Optical phase noise from atmospheric fluctuations and its impact on optical time-frequency transfer

The time of flight for a laser beam through the atmosphere will fluctuate as the path-averaged index of refraction varies with atmospheric turbulence, air temperature, and pressure. We measure these fluctuations by transmitting optical pulses from a frequency comb across a 2-km horizontal path and detecting variations in their time of flight through linear optical sampling. This technique is capable of continuous measurements, with femtosecond resolution, over time scales of many hours despite turbulence-induced signal fading. The power spectral density for the time of flight, or equivalently for the optical phase, follows a simple power-law response of $\ensuremath{\propto}$${f}^{\ensuremath{-}2.3}$ measured down to Fourier frequencies, $f$, of 100 \ensuremath{\mu}Hz. There is no evidence of a roll-off at low frequencies associated with an outer scale for turbulence. Both of these results depart from the predictions of turbulence theory, but are consistent with some other results in the literature. We discuss the implications for the stability and accuracy of one-way optical time-frequency transfer.