Phase-Stabilized Fiber Link

• Phase-stabilized fiber links are optical frequency transfer systems that mitigate environmental phase noise through active feedback and passive error cancellation.
• They enable precise applications such as time/frequency metrology, radio astronomy, quantum networking, and environmental sensing by stabilizing phase and delay fluctuations.
• Key techniques include acousto-optic modulation, bidirectional transmission, and integration with telecom networks to achieve instabilities as low as the 10⁻¹⁸–10⁻²⁰ regime.

A phase-stabilized fiber link is an actively or passively compensated optical or microwave frequency transfer system implemented over standard or dedicated optical fibers, engineered to mitigate environmental phase noise and delay fluctuations accumulated by signals traversing long distances. The core function is to deliver ultrastable frequency references—optical or microwave—with instability and uncertainty in the $10^{-16}$–$10^{-20}$ regime over local, regional, or continental fiber networks, supporting time/frequency metrology, high-precision radio astronomy, quantum networking, synchronized large-scale experiments, and environmental sensing.

1. Principles of Phase-Stabilization

Fiber links are subject to dynamic phase errors from acoustic, thermal, and mechanical fluctuations. Phase-stabilized architectures employ either active feedback (based on round-trip phase detection and actuation) or recent passive and post-processed correction schemes. In the canonical active configuration, a reference optical carrier is launched from the local endpoint, traverses the fiber, and a reflected (or regenerated) return signal is interfered with a local copy. The resultant round-trip phase error is fed to an actuator—typically an acousto-optic modulator (AOM) or fiber stretcher—that pre-compensates the launched phase to cancel the fiber-induced noise in the forward direction (Guéna et al., 2017, Husmann et al., 2021, Droste et al., 2015, 0807.1882).

The open- and closed-loop transfer functions are well-characterized: for round-trip delay $\tau$ and open-loop gain $G(f)$, the closed-loop residual single-pass phase noise is

$$S_{\phi,\rm res}(f) = |1 - H(f)|^2 S_{\phi,\rm in}(f), \quad H(f) = \frac{G(f)}{1 + G(f)}.$$

Residual instability is fundamentally limited by loop delay, yielding an unsuppressed phase-noise floor scaling as $(2\pi f \tau)^2/3$ (0807.1882, Guéna et al., 2017, Husmann et al., 2021).

Passive approaches leverage bidirectional transmission and RF phase mixing without active servo loops at the remote nodes. For ring or branching networks, counter-propagating or branch-dedicated optical carriers are frequency-tagged and mixed to generate error signals for local cancellation, yielding plug-and-play scalability with robust phase error suppression (Hu et al., 2021, Xue et al., 2021).

2. Architectures and Implementations

Long-Distance Point-to-Point

Large-scale links (e.g., Paris–Braunschweig, 1,415 km) employ bi-directional buried telecom fibers, AOMs for phase actuation, and repeater laser stations (RLSs) for signal regeneration without degrading frequency stability (Guéna et al., 2017). The architecture integrates frequency combs for optical-to-microwave synthesis at each endpoint, and networks of bidirectional Erbium-doped or Brillouin amplifiers to overcome fiber losses. Delay-limited phase stabilization is ensured by tuning the controller bandwidth below $1/(2\tau)$.

Metropolitan and Continental Networks

Ring-topology networks (e.g., SWITCH, 456 km) leverage multi-segmented all-fiber Michelson interferometers in each link leg, operating in the C- or L-band to coexist with telecommunication traffic. Commercially available optical add/drop multiplexers (OADMs) confine the metrological signal, and bidirectional EDFAs extend reach while maintaining isolation (Husmann et al., 2021). Regeneration lasers at intermediate points are offset-phase-locked to maintain optical coherence end-to-end.

Passive and Branching Networks

Branching and ring networks adopt passive phase noise cancellation by local error detection and AOM-based actuation, avoiding nested electronic feedback. Branch AOMs act both as frequency distinguisher and optical actuator, supporting arbitrary multi-user scaling. Residual phase noise is dominated by the out-of-loop detection and reaches the $10^{-19}$ regime at $10^4$ s integration (Xue et al., 2021, Hu et al., 2021).

3. Performance Metrics and Experimental Realizations

Allan Deviation and Accuracy

Measured fractional frequency instabilities (overlapping Allan deviation, $\sigma_y(\tau)$) are as low as $1.6\times10^{-15}$ at 1 s and $3.8\times10^{-19}$ at 2,000 s (ring, 456 km) (Husmann et al., 2021), and routinely $10^{-15}$–$10^{-16}$ at 1 s in continental point-to-point links (Guéna et al., 2017, Droste et al., 2015). Ultimate floors are dictated by uncompensated interferometer arms, delay-limited feedback, amplifier and out-of-loop detection noise.

For branching configurations, $\sigma_y(\tau)$ of $3.4\times10^{-15}$ (145 km) to $1.4\times10^{-15}$ (50 km) at 1 s scale to $3.7\times10^{-19}$ and $1.7\times10^{-19}$ at $10^4$ s—approaching back-to-back instrument floors of $2\times10^{-20}$ (Xue et al., 2021). In passively phase-compensated rings, similar performances are realized with phase-jitter suppression factors up to $3\times$ compared to active schemes (Hu et al., 2021).

Optical and RF Transfer

Hybrid fiber links simultaneously transfer Hz-level optical carriers, SI-traceable RF standards, and UTC time-tags with independent phase/delay stabilization. Reported optical stability is below $5\times10^{-18}$ at 100 s, RF stability $2\times10^{-15}$ at 100 s, and time deviation (TDEV) under 1 ps for 1 s–10,000 s (Krehlik et al., 2017).

For stabilized RF transfer, e.g., 160 MHz over 166 km, Allan deviations of $9.7\times10^{-12}$ at 1 s and $3.9\times10^{-14}$ at 1,000 s have been achieved, surpassing previous RF-over-fiber systems in stability and footprint (Gozzard et al., 2017). Frequency comb-assisted microwave transfer with fiber-loop optical-microwave phase detectors yields instability of $7.6\times10^{-18}$ at 1,000 s and $6.5\times10^{-19}$ at 82,500 s (2.3 km) (Jung et al., 2013).

Quantum Networking and Applications

For quantum protocols, phase-stabilized links enable sub-attosecond timing jitter ($<100$ as, 2.1 km link), supporting path-entanglement with fidelity $>0.998$ and isolation $\gtrsim10^{10}$ between classical and quantum channels via advanced time/frequency multiplexing (Nardelli et al., 17 Oct 2025, Johnson et al., 10 Sep 2025). Correction of source-laser drift to as low as $0.05$ mHz/s enables relaxed frequency requirements for twin-field QKD systems, reducing QBER by a factor $\sim73$ compared to unstabilized links (Johnson et al., 10 Sep 2025).

Environmental Sensing

Active phase noise cancellation links can be repurposed as distributed environmental sensors, with the correction frequency $\Delta\nu(t)$ providing a direct, quantitative measure of integrated strain from seismic events over lengths exceeding 1,000 km, delivered transparently without instrumentation changes or metrological performance loss (Noe et al., 2023).

4. Architectural and Theoretical Innovations

Delay- and Dispersion-Limited Performance

The feedback bandwidth across all active schemes is fundamentally limited by fiber round-trip delay ($f_c \lesssim 1/(4\tau)$), dictating the correction speed for phase excursions and the residual delay-limited noise floor $$S_{\phi,\rm res}(f) \propto (2\pi f \tau)^2 S_{\phi,{\rm free}}(f)$$ (Guéna et al., 2017, Husmann et al., 2021, 0807.1882). For broad-band signals (e.g., incoherent light in 170 km optical interferometry), residual chromatic dispersion imposes a hard limit on phase coherence, mitigated by dispersion-compensating modules or fiber Bragg gratings (Collier et al., 15 Oct 2025).

Multi-User, Scalable, and Redundant Networks

The scalability of passive branching architectures and ring topologies naturally supports many-user distribution, rapid phase recovery, and plug-in expansion, opening new network models for metrology and time/frequency-sensitive science (Xue et al., 2021, Hu et al., 2021). L-band operation and DWDM compatibility allow overlay of metrology channels on existing telecom infrastructure without interfering with C-band data traffic (Husmann et al., 2021).

5. Limitations and Prospective Developments

Performance bottlenecks arise from delay-limited servo bandwidth, amplifier-induced noise (amplified spontaneous emission, non-reciprocity), polarization-mode dispersion, and out-of-loop uncompensated interferometric drifts. Repeater laser stations add electronic and optical complexity but are indispensable for continental reach. Future improvements include higher bandwidth fiber actuators, feed-forward compensation, integration of data traffic and metrology, and deployment of hollow-core fibers or advanced photonic repeaters (Guéna et al., 2017, Husmann et al., 2021).

Laser source drift remains a critical parameter for quantum applications; integrated drift compensation to sub-millihertz per second is now feasible (Johnson et al., 10 Sep 2025). For Earth observation and environmental sensing, precise calibration of fiber-to-ground coupling and geometry is essential for robust geophysical interpretation (Noe et al., 2023).

6. Applications and Impact on Fundamental and Applied Sciences

Phase-stabilized fiber links are the backbone of present and emergent networks for optical clock comparisons, SI-traceable frequency and time dissemination, long-baseline interferometry in astronomy (SKA, VLBI, optical/quantum astronomy), quantum networking (QKD, entanglement swapping), and precision synchronization in geodetic and inertial sensor arrays.

Demonstrated implementations confirm consistent performance at, or below, the $10^{-18}$–$10^{-20}$ regime for frequency transfer and environmental sensing, with bit-error-free coexistence with high-capacity data traffic and robust operation across thousands of kilometers. These techniques render satellite-based transfer unnecessary for high-resolution comparisons, enable new metrological capabilities, and extend the scientific reach of frequency-and phase-sensitive experiments across the full spectrum of fundamental and applied physics (Guéna et al., 2017, Husmann et al., 2021, Collier et al., 15 Oct 2025, Xue et al., 2021, Noe et al., 2023).