## 3 Free-Space Distribution
### Experimental Setup  
Figure 4 shows the schematic of the experimental system. The entire setup is located on the rooftop of our laboratory building on the campus of the University of Alabama in Huntsville. A commercial fiber laser (FFL-1560, Precision Photonics, Boulder, CO, USA) acts as the laser source generating a near-infrared (center wavelength 1560 nm) femtosecond pulse train with a 4 mW average power, a 90 MHz pulse repetition rate, and a pulse width of about 150 fs. A highly-doped erbium-doped fiber amplifier developed in house is used to amplify the pulse train to 100 mW average power with the pulsewidth shortened to less than 100 fs. A fiber coupler (AC Photonics, Santa Clara, CA, USA) splits 30% of the power to the reference arm and the remaining power is used for the transmission. For the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Acoustic Noise** \\ **Frequency** \\ \end{tabular} } & \multicolumn{2}{c}{**SMF**} & \multicolumn{2}{c}{**PMF**} \\ \cline{2-7}  & **Total Noise** & **Absolute** & **Percentage** & **Total Noise** & **Absolute** & **Percentage** \\  & **Power** & **Power Change** & **Power Change** & **Power Change** & **Power Change** & **Power Change** \\ \hline
**No Perturbation** & \(3.89\times 10^{-2}\) & - & - & \(3.63\times 10^{-2}\) & - & - \\
**100 Hz** & \(4.33\times 10^{-2}\) & \(4.37\times 10^{-3}\) & \(11.21\%\) & \(4.00\times 10^{-2}\) & \(3.76\times 10^{-3}\) & 10.38\% \\
**200 Hz** & \(4.28\times 10^{-2}\) & \(3.84\times 10^{-3}\) & \(9.87\%\) & \(3.83\times 10^{-2}\) & \(2.06\times 10^{-3}\) & 5.69\% \\
**500 Hz** & \(3.92\times 10^{-2}\) & \(2.07\times 10^{-4}\) & \(0.53\%\) & \(3.93\times 10^{-2}\) & \(3.02\times 10^{-3}\) & 8.34\% \\
**1 kHz** & \(4.38\times 10^{-2}\) & \(4.84\times 10^{-3}\) & \(12.42\%\) & \(3.84\times 10^{-2}\) & \(2.11\times 10^{-3}\) & 5.80\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Total excess phase noise powers at different perturbation frequencies.  
purpose of optical heterodyning detection, the reference beam is frequency-shifted by passing it through an acousto-optic modulator (AMM-80, Brimrose, Sparks, MD, USA; AOM) driven at 80 MHz and selecting the first order deflection. It then goes through a tunable delay line, which ensures temporal overlapping of the femtosecond pulses from the reference and the transmission paths. The transmission pulse train is collimated into a 7 mm diameter beam at a fiber collimator and launched into the atmospheric transmission link. The beam is reflected back to the experimental setup by a 2-inch gold mirror housed in a sturdy fixture mounted on the rooftop platform at a distance of 30 m (_i.e._, 60 m round-trip distance). The collected transmitted beam is resized through a telescope before being collinearly combined with the reference beam at a beam-splitter. When optical pulses in both beams temporally overlap, an 80 MHz beat signal is generated. The beat signal is picked up by a photodiode and then sent to a double-balanced mixer, where it is compared to a local oscillator drawn from the original 80 MHz signal driving the AOM. The local signal acquires a slight frequency offset (500 kHz) from 80 MHz at a single-sideband modulator (SSBM). As a result, a 500-kHz beat note is generated by the mixer. It is then sent to a fast Fourier transform (FFT) analyzer (SR785, Stanford Research Systems, Sunnyvale, CA, USA) for a direct measurement of the noise spectrum and a frequency counter for the measurement of the Allan deviation.