## 3 Scheme Using Optical-Electronic Joint Phase Compensation  
From the demonstration of the frequency transfer with the fiber stretcher-based compensation above, we find that it is difficult to achieve a long-term frequency transfer over a long fiber link by using only optical compensation. To increase the range of phase compensation and ensure the resolution, in this paper, we propose a novel technique of frequency transfer over long fiber link with optical-electronic joint compensation. The schematic of the fiber-based frequency transfer using the joint compensation is shown in Figure 3. On the transmitter site, we use a commercial distributed feedback laser (DFB) laser as the light source (COFIBER, NLL-1550). The center wavelength of the light source is 1550 nm and the linewidth is about 100 kHz. With a fiber amplifier (COFIBER, ZG-EDFA), the final output optical power is 60 mW. At the same time, we use a signal generator (RS, SMA100B) as the frequency source to generate a 10 GHz RF signal with the power of 18 mW. In the experimental setup, we first phase-shift the RF signal with a timing delay, and then load the signal onto the optical carrier through an EOM. The modulated light passes through a circulator and a fiber stretcher in sequence, where the stretcher introduces another phase delay to the light. The phase-delayed light is sent into a 50-km fiber-optic link. At the end of the link, on the receiver site, the light is received by another circulator and a 90:10 coupler, and the transmitted light is split into two parts. The high-power part is sent back to the fiber link by the circulator, while the remaining light is converted by a high-speed InGaAs photodiode (PD2) into an RF signal that can be used by the users. The returned light on transmitter site with power of \(\sim\)1 mW passes through the stretcher again, and then is extracted and detected by the circulator and a high-speed photodiode (PD1), respectively. The converted 10 GHz frequency signal with twice phase fluctuations is amplified, phase shifted, and then mixed with the RF reference source signal to generate a phase error signal. The error signal is separated into two parts. One part is fed-back to the fiber stretcher via an analog PI (API) servo controller (AS, NB1005), to compensate the timing fluctuation with a high resolution. The other one is fed-back to the two identical phase shifters via a digital PI (DPI) servo controller, to compensate the phase fluctuations at large range scale. With the two feedback loops, the timing fluctuation introduced in the fiber link can be suppressed at a long-time scale. On the measurement site, the phase fluctuation is obtained by comparing the phase of the frequency signal recovered on the receiver site to the reference signal on the transmitter site. The fluctuation data can be recorded using a digital voltmeter (Keysight, 34461A), which can be further used for stability analysis. Next, the principle of the optical-electronic active phase compensation will be explained in detail. As shown in Figure 3, the initial phase of the RF signal generated by the frequency source is \(\varphi_{0}\). After the frequency signal passes through the electronic phase shifter (PS1), an additional phase delay \(\varphi_{\text{cl}}\) is added. With the EOM, the phase-delayed RF signal is loaded onto the optical carrier, and the phase of the laser amplitude is \(\varphi_{0}+\varphi_{\text{cl}}\). The modulated light passes through a circulator and fiber stretcher, and another phase delay \(\varphi_{\text{cl}2}\) is added. The optical signal is then sent over a 50 km fiber link. During this process, the optical fiber link will bring an extra phase delay to the laser signal due to temperature fluctuations, environmental vibrations, etc. Here, we assume that the phase delay intruded by the fiber link is \(\varphi_{\text{p}}\). The total delay of the forward phase after the light is received on the receiver is \(\varphi_{\text{f}}=\varphi_{0}+\varphi_{\text{cl}}+\varphi_{\text{cl}2}+ \varphi_{\text{p}}\).