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

Abstract

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 ∝f −2.3 measured down to Fourier frequencies, f , of 100 μHz. 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.

Broadband Phase Spectroscopy over Turbulent Air Paths

“…(The parabolic phase profile originates from dispersion of the additional 3.2 m of fiber to the reference channel and the 2-km air path.) Figure 2b shows the PSD of the C t extracted over a ~ 11 hour time period, from which we estimate C n 2~3 ×10 −14 m −2/3 [22]; note the overall shape follows a power law of f − and does not exhibit the expected low frequency cutoff at ~U t /L 0 , in agreement with previous turbulence phase measurements [22]. Turbulence will also cause signal intensity variations mainly on timescales longer than 1 r f − Δ (see Fig.…”

“…where U t = 1 m/s is the transverse wind speed [17,[20][21][22], The dominant problem is not this carrier phase noise but rather the remaining differential phase noise across the several THz-wide comb that will mask the phase spectrum. In turbulence theory, this differential phase noise is captured by the (spatially averaged) two-frequency mutual coherence function, ( ) 0 m ν ν ν Γ Δ = − , whose width is the coherence bandwidth and whose Fourier transform is the pulse broadening due to turbulence [15,[23][24][25][26][27][28].…”

Measurement of the impact of turbulence anisoplanatism on precision free-space optical time transfer

“…Ref. [26] also reports an absence of an outer scale roll-off potentially due to temporal variations not captured by the frozen turbulence model, such a temporal effect would be common to the separated paths. Similar agreement between the model and measurements are seen for the other separations.…”

Robustness of quantum-enhanced adaptive phase estimation

“…Here both methods are applied to adaptive phase estimation including phase noise, which could arise from pathlength fluctuation in the interferometer [27,28].…”