## 2 Fiber-Optic Distribution
### Experimental Setup  
In our experiment, we let a frequency comb propagate through a section of fiber and use a loudspeaker to introduce various types of acoustic perturbations to the fiber. We then compare the output from the fiber with the original comb to find out the amount of excess noise. Figure 1 shows a schematic of the experimental setup. The light source is a commercial femtosecond-laser frequency comb (FC1500, Menlo Systems, Martinsried, Germany) operating at 1.56 \(\upmu\)m, with comb line spacing (_i.e._, pulse repetition rate) of 250 MHz. The optical system is essentially a Mach-Zehnder interferometer sandwiched between two fiber couplers. In the signal arm, an erbium-doped fiber amplifier (EDFA-16-LC, Optilab, Phoenix, AZ, USA; EDFA) and a variable optical attenuator (VOA50, Thorlabs, Newton, NJ, USA; VOA) control the signal power to achieve the optimum signal-to-noise ratio while preventing detector saturation. The fiber link consists of a section of either single-mode fiber (SMF-28; SMF) or polarization maintaining fiber (HB1500T; PMF) wound loosely on a plastic spool. For the SMF, two different fiber lengths, 80 m and 800 m, are tested. A loudspeaker is placed a few centimeters away on the side of the spool and is driven by a signal generator. A polarization controller (PC) is inserted after the fiber link to optimize the output signal. In the reference arm, an acousto-optic frequency shifter (AMM-80, Brimrose, Sparks, MD, USA; AOFS) is used to add an 80 MHz offset to the frequencies of the reference signal. The two arms then combine at a fiber coupler, which directs the interferometer output to a photodetector (DET01 CFC, Thorlabs, Newton, NJ, USA; PD). The reference arm is only several meters long, significantly shorter than the signal arm. Its length is chosen so that pulses from both arms can temporally overlap on the detector. In addition, the pulse repetition rate of the laser is frequently adjusted around its 250 MHz nominal value through a computerized control system to maintain the optimum pulse overlapping condition. This is because a repetition rate change can cause a change of the relative pulse delay in an imbalanced interferometer [22]. The beating between the two overlapped pulses generates an 80 MHz beat note on the photodetector. This heterodyne process, however, is complicated by the fact that a frequency comb is composed of a series of discrete spectral lines and the beat note is hence due to multi-heterodyne. A detailed theoretical analysis of multi-heterodyne phase noise detection has been given elsewhere [19]. Here, we just point out that, in order to minimize the impact of fiber dispersion to the heterodyne signal, a narrow band optical filter centered at 1559.79 nm with a pass band of 0.4 nm (_i.e._, about 100 GHz) is inserted at the output of the laser. The beat note is passed through a bandpass filter and an amplifier before it is mixed in quadrature with the 80 MHz driving signal from the AOFS driver. The resulting dc signal is then frequency analyzed by a fast Fourier transform (FFT) analyzer (SR785, Stanford Research Systems, Sunnyvale, CA, USA) to reveal the noise spectrum. Meanwhile, an oscilloscope (GDS-2204, Instek, Montclair, CA, USA) is used to monitor the 80 MHz beat note in the time domain. It should be noted that the OFC was in free-run (without stabilization of the pulse repetition rate and the carrier-envelope offset frequency) during the measurements. This is valid in our case because, for excess noise measurements, where both the signal and the reference are derived from the same femtosecond laser, the laser phase noise enters the multiheterodyne beat note as a result of arm-length imbalance in the interferometer. In most of our measurements (for both _fiber-optic_ and _free-space_ transfer tests), this imbalance is in the order of 100 m, much less than the coherence length of the OFC (a free-run fiber-based OFC typically has a comb-line linewidth of about 20 kHz near its center wavelength [23]).