Modeling and Optimization of Bidirectional Fiber-Optic Links for Time and Frequency Transfer

In this paper, a bidirectional fiber-optic link is considered, composed of two end terminals, connected by a number of fiber spans and bidirectional optical amplifiers. The end terminals exchange time and frequency information by sending and receiving intensity modulated optical signals in both directions, which is required to compensate the fluctuation of the propagation delay of the transmission medium. In such a link for its optimal performance, the gains of the bidirectional optical amplifiers need to be adjusted to minimize the noise resulting from Rayleigh backscattering and amplified spontaneous emission. A model of the link is proposed using a transmission matrixes approach, which allows estimating the signal-to-noise ratio (SNR) at the ends of the main link (i.e., connecting the end terminals) and at the extraction (tapping) nodes located along the main link. The transmission matrixes of a fiber span and Er-doped fiber amplifier are presented and required formulas are derived. In addition, wavelength selective isolators are considered, which allow intentional breaking of the propagation of backscattered signals and are effective in improving the SNR when long fiber spans are involved. The model is experimentally verified in a laboratory link composed of four bidirectional amplifiers and five fiber spans of total length up to 420 km, showing the agreement between the measured and calculated SNRs not worse than 2 dB.