With the gradual exploration and development of ocean resources, human efforts towards dynamic sensing, precise detection, information network construction, and data collection in marine environments will continue to expand, leading to a deeper understanding of the ocean. The marine spatiotemporal benchmark network is a common infrastructure for marine positioning and navigation systems, ocean environmental monitoring networks, and the Internet. Among these, underwater frequency transmission and synchronization constitute a crucial technological foundation for oceanic spatiotemporal benchmarks. With the advancements in science and technology, such as underwater observation networks, there is an increasing demand for higher precision in frequency transmission performance indicators.

This study proposes a high-precision underwater frequency transmission method for the blue-green laser based on digital phase compensation. Referring to the approach used in ground-based fiber optics, a dual-way time-frequency transmission is employed to enhance stability. Compared with the one-way transmission, the dual-way scheme allows for the signal returned from the remote end to be compared against the local reference signal, thereby improving the precision of the noise measurement. Using the blue-green laser as the carrier and digital phase compensation to enhance the frequency transmission noise compensation bandwidth, the method is experimentally verified with a 520 nm green laser diode, achieving bidirectional stable transmission of a 400 MHz frequency signal over an 8 m underwater link. A digital phase compensation system that included error signal acquisition, proportional-integral-derivative (PID) control, and digital phase shifting was established. Digital phase-shifting is applied to pre-compensate for additional phase fluctuations in the process of underwater frequency transmission to maintain the stability of the frequency of the underwater link. The experimental device for the underwater laser frequency transmission based on digital phase compensation is illustrated in Fig. 1, and the experimental setup is depicted in Fig. 2.

According to underwater frequency signal transmission noise performance characterization methods, the transmission performance of the frequency signal is tested in time and frequency domains. The experimental results presented for phase noise (Fig. 3), phase timing delay fluctuation (Fig. 4), and frequency stability (Fig. 5), demonstrate that the digital phase compensation technology can achieve a noise compensation bandwidth of 1 kHz, effectively suppressing noise fluctuations during a free-running operation within an offset frequency range of 1 kHz. The smaller the bias frequency, the more obvious the inhibition effect. Inhibition was 32.0 dB at 0.01 Hz and 15.4 dB at 1 Hz. attaining 2.5 dB at 1 kHz. Following the application of digital phase compensation, the frequency stability reached 7.9×10^-14 at 1 s and improved to 2.1×10^-16 at 1000 s. The frequency stability was improved by two orders of magnitude compared to that before digital phase compensation. The frequency stability attained an order of 10^-14 for the first time. The phase-time delay fluctuation after phase compensation was also effectively suppressed, and the root mean square (RMS) of the phase-time delay fluctuation was 3.2 ps. These experimental results prove the feasibility of laser-based underwater frequency signal transmission using digital compensation technology with significantly improved stability of the frequency signal during underwater transmission. This indicates that digital technology, which facilitates system integration and miniaturization, has important application prospects in underwater navigation, timing synchronization, and construction of underwater spatiotemporal networks.

This study proposes the utilization of blue-green laser technology in conjunction with digital phase compensation techniques to achieve stable underwater transmission of frequency signals. Based on this methodology, a high-precision two-way transmission system was constructed for 400 MHz frequency signals over an 8 m underwater link. Experimental results demonstrate that the proposed digital compensation technology can achieve a compensation bandwidth of 1 kHz. Following compensation, the frequency stability reached 7.9×10^-14 at 1 s, improving to 2.1×10^-16 at 1000 s, significantly enhancing transmission accuracy. Furthermore, the digital phase compensation method exhibited excellent stability, facilitating the implementation in subsequent system engineering projects. This solution offers a new technical approach for underwater transmission and distribution of time-frequency references.