Analysis of polarization drift of optical signals over deployed aerial-inground fiber connections

Technical Summary: Analysis of Polarization Drift of Optical Signals over Deployed Aerial-Inground Fiber Connections

Problem Statement
Polarization drift remains a critical challenge for deployed fiber infrastructure used in quantum communications, where precise sub-second polarization stabilization is required to maintain high entanglement throughput and fidelity. Unlike classical multi-terabit systems that utilize polarization-maintaining fibers and digital signal processing to mitigate drift, quantum networks operating on standard deployed infrastructure face highly stochastic and non-stationary polarization variations. These drifts are driven by environmental factors—specifically temperature, humidity, and wind speed—which induce refractive-index modulation and photoelastic effects, leading to spatially uneven birefringence and State of Polarization (SOP) rotations. While previous studies have characterized drift in exclusively aerial or buried fibers, there is a lack of long-term analysis on hybrid aerial-inground connections spanning multiple seasons, particularly regarding the estimation of drift features using environmental measurements rather than just forecasting.

Methodology
The authors conducted an 11-month study (December 2024 to November 2025) on a 15-km hybrid aerial-inground fiber connection at Oak Ridge National Laboratory.

• Data Collection: A continuous-wave 1550-nm polarized signal was transmitted through the fiber. Linear-basis (horizontal-vertical) Stokes measurements were collected continuously. The data was processed using a multi-FFT signal characterization device, generating Fast-Fourier-Transforms (FFTs) every 45 minutes with mHz resolution (0.37-mHz bins).
• Feature Extraction: From the FFTs (specifically the $Y_{Hz}$ dataset spanning 0 to 0.76 Hz), global spectral features were extracted: spectral area ($Y_{Area}$), spectral centroid ($Y_{sp,cen}$), spectral variance ($Y_{sp,var}$), spectral entropy ($Y_{sp,ent}$), and the $\beta$-exponent of the $f^{-\beta}$ trend.
• Environmental Inputs: Meteorological data (temperature, relative humidity, wind speed) were collected at 2-minute intervals from a local station. Input features included current values, changes over 45-minute intervals ($\Delta$), and time of day.
• Theoretical Framework: A theoretical model based on stochastic differential equations and $SO(3)$ rotation operators was developed to describe SOP drift as a product of unitary rotations driven by environmental variables. This model informed the machine learning approach by highlighting the non-linear, multiplicative noise nature of the drift and the delayed thermal response of fiber layers.
• Machine Learning: Random Forest regressors were employed to estimate the spectral features ($Y$) as functions of environmental histories ($X$). The study compared unlagged inputs against lagged inputs (4-hour spaced, 1-day history) to account for the thermal equilibration time of the fiber and external materials (e.g., ice, dirt). Performance was evaluated using Root Mean Square Logarithmic Error (RMSLE) against baseline estimators (time-of-day only and moving average combinations).

Key Contributions and Results

1. Diurnal and Seasonal Characterization: The analysis revealed strong diurnal structures in the spectral area ($Y_{Area}$), with daytime maxima aligning with temperature and wind speed peaks and humidity dips. Nighttime levels were consistently lower. Seasonality was pronounced, with higher mean and variance in summer compared to winter.
2. Spectral Properties: The FFT characteristics indicated strong multiplicative noise, with the signal concentrated within 5.1% of the 0.76 Hz window. The $\beta$-exponent hovered around 1.0 (flicker noise), showing more frequent dips in winter, likely due to wind-induced phenomena like galloping in ice-coated fibers.
3. Environmental Dependencies:
   • Time of Day and Temperature: Showed the strongest dependence on spectral area.
   • Wind Speed: Showed the strongest dependence on spectral centroid and $\beta$-exponent, particularly in winter.
   • Heteroskedasticity: The variance of the spectral area was non-stationary, increasing with seasonal temperature, supporting the theoretical model that higher temperatures make fibers more vulnerable to stress-induced birefringence changes.
4. Machine Learning Performance:
   • Random Forest estimators achieved a small overall gap (<2% relative error) between test and train datasets under RMSLE.
   • Including lagged environmental data (history of 24 hours with 4-hour spacing) improved estimation, particularly for nighttime troughs, by accounting for the delayed thermal response of the fiber.
   • The estimators successfully captured diurnal cycles and seasonal trends but struggled to predict the exact amplitudes of sharp sub-peak features, which are likely driven by intrinsic noise or unmodeled high-frequency environmental dependencies.
   • Baseline models using only time-of-day data performed poorly in winter, confirming that environmental variables are necessary for accurate estimation across seasons.

Significance and Claims
The paper claims to provide a comprehensive characterization of polarization drift over hybrid aerial-inground fibers, bridging the gap between theoretical models and empirical machine learning estimation. The primary significance lies in demonstrating that environmental measurements can be used to estimate the deterministic component of polarization drift features with high reliability (<2% relative error between training and testing), despite the high noise and non-stationarity of the signal.

The authors assert that their framework enables "weather-aware prediction" of SOP-drift features. This capability is presented as a tool for link-state monitoring and control in quantum networks, potentially allowing for proactive scheduling, routing, and the optimization of polarization control parameters (e.g., PID tuning) based on environmental telemetry. The study emphasizes that while absolute prediction of the entire signal is difficult due to noise, estimating the expectation of weather-dependent features is a viable and valuable approach for maintaining network stability. The work does not claim to eliminate the need for active polarization compensation but suggests that environmental estimation can enhance the efficiency and robustness of such systems.