Improving Accuracy of Optical Frequency Transfer Over Non-Modified DWDM Optical Networks

J. Lightwave Technol. 43, 10447-10455 (2025) · DOI: 10.1109/jlt.2025.3617373

License: CC BY 4.0.

Abstract

Dedicated fiber links become the most precise and desirable means of transferring optical frequency at distances up to a few thousand kilometers. However, the need of installing special equipment along the link, and usually renting fibers exclusively for this use, cause that this preferable solution is cumbersome and expensive, and so accessible in severely limited range. In this paper we propose a method which improves the frequency transfer quality when only a standard (i.e., not modified for this purpose) DWDM optical telecommunication network is available. The proposed solution is based on the correlation identified between the residual phase noise present in a DWDM-based optical frequency transfer and the in-loop phase correcting signal, which can be easily registered and used for improving the transfer accuracy by means of data post-processing. As we demonstrated, using the proposed method the frequency comparison uncertainty can be reduced to below 1 × 10−16 for links up to 1500 km long.

Figures

14 panels with data across 8 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

Illustrative figure, no extractable data. Shown in the paper PDF. Page 2 of the PDF.

Fig. 2

• panel (1): Soil temperature (C deg.) 1 m below the surface against time (days) through October 2024, at ten weather stations along the link route. The paper names no station, so the curves are numbered station 1 to 10 in the order they are drawn. The map inset of the printed figure, with the station locations, is not shown. data.csv

Fig. 3

Illustrative figure, no extractable data. Shown in the paper PDF. Page 4 of the PDF.

Fig. 4

• panel (a): Illustration in arbitrary units: the corrected mutual phase $x_{COMP\_COR}$ (a.u.) against time (days) for four trial values of the mismatch parameter, $m_1$, $m_2 = 0$, $\hat{m}$ and $m_3$. data.csv
• panel (b): Illustration in arbitrary units: the daily estimate of the clock frequency difference $y_{AB\_EST}$ (a.u.) against time (days), drawn as day-by-day steps, for the same four trial mismatch values as panel (a), $m_1$, $m_2 = 0$, $\hat{m}$ and $m_3$. data.csv

Fig. 5

Illustrative figure, no extractable data. Shown in the paper PDF. Page 5 of the PDF.

Fig. 6

• panel (1): Long-term round-trip phase fluctuation $x_{NF}+x_{NB}$ (s, left axis) and differential phase fluctuation $x_{NF}-x_{NB}$ (s, right axis) of the DWDM link against time (days), on different vertical scales. The soil-temperature inset of the printed panel is hosted as its own panel. data.csv
• panel (1-inset): Inset of the printed panel: soil temperature (C deg.) against time (days) at five weather stations along the link route. The paper names no station, so the curves are numbered station 1 to 5 in the order they are drawn. data.csv

Fig. 7

• panel (a): Spread $\sigma_{yAB}$ of the daily estimate of the clock frequency difference against the trial mismatch parameter $m$, for the seven-day clock comparison: one curve, $\sigma_{yAB}(m)$. data.csv
• panel (b): Mutual phase $x_{COMP\_COR}$ (s) of the seven-day clock comparison against time (days), from the raw data ($m = 0$) and after the correction ($m = \hat{m}$), at daily points. The dashed line is the mean slope at $\hat{m}$. data.csv

Fig. 8

• panel (1): Excluded data sets as horizontal bars: period length (days) against position along the record, time (days), one bar per window of that length. Orange bars are the windows that violate condition (12), purple bars condition (13). Bars within a row are offset slightly, as printed, so they can be told apart. data.csv

Fig. 9

• panel (a): Clocks comparison error against period length (days), without correction: one open circle per window of each length, with the mean error (green line) and the rms error (red line) at each length. Purple and orange filled circles are the data sets excluded by conditions (13) and (12). The errors are taken relative to the intentionally introduced clock offset. data.csv
• panel (b): Clocks comparison error against period length (days), with the proposed correction: one open circle per window of each length, with the mean error (green line) and the rms error (red line) at each length. The errors are taken relative to the intentionally introduced clock offset. data.csv

Fig. 10

• panel (1): Comparison uncertainty against the clocks' flicker noise, on log-log axes, five points per curve: the total uncertainty with the fibre noise reduced by the proposed method (red) and the impact of the clock noise alone (blue). data.csv

Fig. 11

• panel (a): Phase error (s) against time (days), before and after the correction. The after-correction curve begins after the first week of the record. data.csv
• panel (b): Modified Allan deviation MDEV against averaging time (s), on log-log axes, before and after the correction. The after-correction curve carries its error bars at long averaging times; the error bars the printed panel draws on the before-correction curve are not shown. data.csv
• panel (c): Fractional frequency error calculated day by day against time (days), before correction (crosses) and after correction (open circles). The hosted before-correction series has 51 daily values; the printed panel shows 52 markers. data.csv

Cite

Przemysław Krehlik, Krzysztof Turza, Łukasz Śliwczyński, Kamila Lewandowska. Improving Accuracy of Optical Frequency Transfer Over Non-Modified DWDM Optical Networks. J. Lightwave Technol. 43, 10447-10455 (2025). https://doi.org/10.1109/jlt.2025.3617373

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