Hollow-Core Fiber for Long-Span Optical Frequency Transfer: Improved Instability and Extended Single-Span Reach

Phase-coherent optical frequency transfer is essential for optical clock networking, relativistic geodesy, and distributed precision metrology. However, realizing coherent optical networks spanning thousands of kilometers in standard single-mode fiber (SMF) generally requires densely distributed amplifiers or repeater stations together with complex operational control, while long-term instability remains limited by thermally driven residual phase fluctuations. Here we show that hollow-core fiber (HCF) can simultaneously improve transfer instability and relax the reach limitation of long-span optical frequency transfer. Compared with SMF, HCF exhibits lower fiber-induced phase noise and shorter propagation delay, supporting improved short-term instability, while its much lower thermal sensitivity supports nearly one-order-of-magnitude better long-term instability. In addition, for long-haul HCF links, no observable stimulated Brillouin scattering induced saturation is found up to the maximum available injected power of 34 dBm, whereas the threshold of an equal-length SMF link remains only a few dBm. Together with the lower attenuation achievable in modern HCF, this enables ultra-long single-span optical frequency transfer. Using a 152 km HCF link with an average attenuation of 0.18 dB/km, we demonstrate single-span optical frequency transfer, achieving a fractional frequency instability of 7.3 x 10^-21 at 10,000 s and a fractional uncertainty of 1.8 x 10^-20. These results establish HCF as a transmission medium that simultaneously improves instability and extends single-span reach, opening a practical route toward future intercontinental optical frequency networks with ultrahigh precision.