## 2 Methods  
### Basic Principle of Safety Optical Fiber Time Transfer Equipment  
The optical fiber time transfer equipment developed in this paper is based on the two-way time transfer method [22] using optical fiber. This method can overcome the asymmetry of the transmission link. The basic principle is that the pulse signal, frequency signal, and time information of a clock source from a local site are sent to a remote site. The remote site also needs to send pulse signal, frequency signal, and time information to the local site while receiving the time-frequency signal sent by the opposite site. By measuring the time difference between the pulse signals sent by the local and remote sites, the clock difference between the two sites is calculated. The clock difference is used to adjust the phase of the remote site equipment based on the local site equipment, which can realize the time synchronization of the two sites. Before the time information is transmitted from the local to the remote site, the time difference information measured by the time interval counter (TIC) of the local site is encrypted, while the decryption comparison is completed at the remote site. This can realize a secure optical fiber time transmission scheme, as shown in Figure 1. Tx stands for the laser transmitter, and Rx stands for the optical receiver of small form-factor pluggable (SFP). TIC stands for measuring the signals at both sides of the link using time interval counters. \(\lambda_{1}\) is the wavelength of the fiber forward propagation. Additionally, \(\lambda_{2}\) is the wavelength of the fiber backward propagation. The time difference information \(T_{LR}\) measured by the TIC of the local site is encrypted. One way the encrypted information is sent to the remote site is via the external sending unit. Additionally, the other way is modulated to Tx of the SFP laser at the local site through intensity modulation, which is connected to the optical fiber through the circulator. The encrypted information transmits to the remote site equipment via the optical fiber. The encrypted information is received using Rx of SFP and decoded through a decoder at the remote site. Then, the data of the optical fiber link are decrypted and compared with the data received by the external unit with a decryption unit and the main control unit. If the data are the same, the clock difference is calculated and synchronized by using Formula (3). The remote site equipment transfers 1 PPS and 10 MHz signals, along with \(T_{RL}\), to the local site equipment using the same optical fiber through the circulator. The local site equipment uses an ultra-high precision TIC to measure the 1 PPS signal from the remote site and the local reference 1 PPS signal to obtain the result \(T_{LR}\), as shown in Formula (1). The remote site compares the 1 PPS signal from the local site with the 1 PPS signal held by the remote site to obtain data \(T_{RL}\), as shown in Formula (2). \[T_{LR}=\Delta T+\tau_{R}^{T}+\tau_{RL}^{F}+\tau_{R}^{R} \tag{1}\]  
\[T_{RL}=-\Delta T+\tau_{L}^{T}+\tau_{LR}^{F}+\tau_{R}^{R} \tag{2}\]  
\[\Delta T=\frac{1}{2}\Big{[}(T_{LR}-T_{RL})+\left(\tau_{LR}^{F}-\tau_{RL}^{F} \right)+\left(\tau_{L}^{T}-\tau_{R}^{T}\right)+\left(\tau_{R}^{R}-\tau_{L}^{R }\right)\Big{]} \tag{3}\]  
where \(T_{LR}\) and \(T_{RL}\) are, respectively, two-way time comparison results measured by the local site and the remote site equipment. \(\tau_{L}^{T}\) and \(\tau_{R}^{T}\) are time-delay values at the local- and remote-site-sending units of the equipment. \(\tau_{L}^{R}\)and \(\tau_{R}^{R}\) are time-delay values of the receiving unit at the local and remote sites, respectively. \(\tau_{LR}^{F}\) and \(\tau_{RL}^{F}\) are, respectively, the time transfer delay of the signal from the local to the remote site and from the remote to the local site in the optical fiber link. \(\tau_{L}^{T},\tau_{R}^{T},\tau_{L}^{R}\), and \(\tau_{R}^{R}\) are calibration in advance. \(\Delta T\) is the time difference value between the local and remote sites by the system.