Scaling up Frequency-Comb-Based Optical Time Transfer to Long Terrestrial Distances

Frequency-comb-based optical two-way time and frequency transfer (O-TWTFT) can support future ultra-precise clock networks over free-space links. However, demonstrations have thus far only operated at one corner of a complex parameter space, which balances received optical power, timing performance, and update rate. Here, we analyze the performance of O-TWTFT across this parameter space, with a specific focus on extending the link distance at constant launch power and telescope aperture. We perform experiments across a three-node network spanning 28 km of turbulent air, and successfully demonstrate a more than 2000× reduction in the required received optical power corresponding to a potential 45× increase in distance. This distance increase does come with an associated reduction in timing precision, with the uncertainty increasing from 60 as to 20 fs at 10 s averaging times. However, this level of precision is still more than adequate for most applications. In addition, it comes with a reduction in sampling rate, which potentially limits this approach to static links. Interestingly, because this system optimization does not require any hardware modifications, O-TWTFT links could be dynamically tuned to support future long-distance optical clock networks over a range of conditions and applications.

Figure 1

(a) In comb-based O-TWTFT, the two end sites exchange frequency comb pulse trains with their repetition rates, f_r, offset by Δf_r. The comb pulses have femtosecond-level timing jitter and an intensity FWHM, τ_p, of a few hundred femtoseconds. (b) At each site, the heterodyne overlap between the two pulse trains leads to a series of interferograms that reflect the incoming comb pulses but magnified in time by a factor $M=f_r/\mathrm{\Delta }{f}_r$. As indicated in the comparison between the upper and lower panels, a higher M means a greater number of pulses sample the interferogram (circles), yielding a correspondingly higher SNR after a matched filter.

Figure 2

(a) The measured interferogram SNR (circles) and calculated SNR (dashed line) versus magnification factor M (lower axis) or Δf_r (top axis) at a received power of ∼12 nW (460 photons per comb pulse). The right axis gives the projected distance increase, assuming no other system modifications. (b) Measured time deviation at 10-second averaging time vs the magnification factor (lower axis) and Δf_r (upper axis) (filled circles) with the prediction from the residual comb timing noise (red dashed line), Gordon-Haus-like jitter (dashed) and total from Eq (2) (black line).

Figure 3

Modified Allan deviation for M = 200 × 10⁶ (Δf_r = 1 Hz) and M = 10⁵ (Δf_r = 2.2 kHz). To calculate these curves, we apply the corrections to the three-node data for asynchronous sampling at the node X site, as per Ref. [5].

Figure 4

The measured clock offset, $\mathrm{\Delta }{t}_{\mathrm{AB}}$, over the 28-km span of a three-node network at M = 9 × 10⁴ (left column) and M = 200 × 10⁶ (right column) at different median received powers.

Figure 5

Measured timing precision (time deviation), ${\sigma }_t$, vs the median received power at different M values (solid circles) and predicted performance from Eq. (2) (dashed lines). For a given M (Δf_r), the timing precision is roughly constant at high received power as it is dominated by comb timing noise and Gordon-Haus-like jitter. When the median received power drops close to P_min, the timing precision degrades significantly because of a dramatic increase in signal fades $(\alpha \to 0)$ and increased statistical noise.

Figure 6

Example probability distribution function of the received power after 10 dB additional attenuation. Above the minimum received power, P_min [red line, shown for M = 4 × 10⁶ (Δf_r = 50 Hz)], there is sufficient SNR to measure a timestamp, but below P_min the SNR of the interferograms is too low. Inset: Measured interferograms (gray line) and their envelope (black line) at different received powers and SNRs.

Figure 7

PSD of optical frequency noise. There are two sources of optical frequency noise for this the three-node network. First, the residuals of the frequency comb’s optical locks (red). Second, the relative cavity drift between the reference oscillator for sites A and B vs the reference oscillator for site X (light orange). The total frequency noise PSD is the sum of these two PSDs. For the purpose of calculating the total frequency noise variance, this measured PSD is extended to higher Fourier frequency assuming white frequency noise beyond 1 MHz.

Figure 8

Measured PSD for the time-of-flight, S_T, across the 14-km link (blue curve). (This quantity is measured by taking the opposite linear combination of timestamps to that used for the clock comparison). For comparison, we also show the PSD of the relative clock noise (green curve) between the two sites, which is lower in this case.