## 2 Fiber-Optic Distribution
### Experimental Results  
In the experiment, we first verify that our detection system can allow us to see the excess phase noise due to pulse propagation in the fiber. This is done by measuring the phase noise at the output of the interferometer with the speaker turned off and with different lengths of SMF inserted in the signal arm. The phase noise is found to be proportional to the fiber length, indicating a direct correlation between the excess phase noise and the fiber. We then focus our attention on the noise behavior under external perturbations. The simplest way of acoustic perturbation is harmonic perturbation (single-tone). In principle, a more realistic broadband perturbation can be treated as the superposition of many single-tone perturbations. Thus, we focus only on single-tone perturbations in the current study. We have tested two different speaker locations, including putting the speaker on the side of the fiber spool without physical contact and putting it directly on the fiber spool with physical contact. Other than some minor differences in the amplitude, the overall noise spectra follow a similar trend in both cases. Therefore, we only present here the results obtained with the speaker sitting on the side of the fiber spool. Figure 2 shows the excess phase noise spectra with eight different perturbation frequencies. All the data are obtained with an 80 m transmission distance in SMF, and are measured within the span of about 1 hour in normal lab conditions. The driving power to the speaker remains the same for all eight figures. The acoustic power is estimated to be about 80 dB in decibel scale. It is evident from Figure 2 that the single-tone perturbations cause an increase of phase noise power density within the spectral range of the perturbation frequency and its first few harmonics. Such a behavior agrees with the commonly accepted notion that external acoustic perturbations to optical fibers induce phase fluctuations in the light propagating through the fiber. What is interesting, according to our measured data, is the simultaneous reduction of the noise spectral density at frequencies below the  
Figure 2: Excess phase noise spectra with (solid) and without (dashed) external acoustic perturbations. Measurement is done with 80 m single-mode fiber (SMF) at eight single-tone perturbation frequencies: **(a)** 50 Hz; **(b)** 100 Hz; **(c)** 200 Hz; **(d)** 500 Hz; **(e)** 1 kHz; **(f)** 2 kHz; **(g)** 5 kHz; and **(h)** 10 kHz. The driving power is the same for all the frequencies. perturbation frequency. Such an effect exists within the entire tested frequency span, but is especially pronounced between 100 Hz and 1 kHz. The same test is also done with an 800 m transmission distance, and a similar change of the phase noise spectral shape is observed. The decrease of phase noise at frequencies below the excitation frequency indicates that single-tone acoustic perturbation can effectively suppress low-frequency phase noise. The stronger effect within 100-1000 Hz is likely due to the greater acoustic efficiency of the speaker in this frequency range. One possible mechanism that can lead to the coupling between acoustic excitation and excess transmission phase noise is polarization fluctuation. Physical vibration of the fiber in an external acoustic field can alter the polarization state of the laser beam, resulting in phase fluctuations due to the fiber birefringence. To find out if the noise suppression is related to polarization, we change the 80 m SMF to 80 m PMF in the signal arm and perform the same test at the same perturbation frequencies. Figure 3 shows the excess phase noise spectra under perturbation frequencies of 100 Hz, 200 Hz, 500 Hz and 1 kHz, respectively, along with the spectrum without the perturbation. Compared to the SMF results at the same frequencies, similar noise suppression is observed at low frequencies even with the PMF. This indicates that it is unlikely the noise suppression effect is due to acoustically excited polarization fluctuation.