Fig. 1. (a) Basic concept of the LOTD. FC, fiber collimator. (b) Simulated timing characterization curve, α = 1, τ = 170 fs. (c) Normalized timing sensitivity with different timing errors.

Fig. 2. (a) Basic concept of the LOTD using balanced structure. (b) Balanced timing characterization curve with different delay T_D. (c) Balanced normalized timing sensitivity with different delay T_D.

Fig. 3. (a) The experimental setup for the BLOTD. λ/2, half-wave plate; λ/4, quarter-wave plate; PBS, polarization beam splitter; RFL, retroreflector; 50:50, 3 dB coupler; PC, personal computer; DA, differential amplifier. (b) Measured balanced timing characterization curve. (c) Measured results: TJSD and corresponding IDTJ.

Fig. 4. Experimental setup for residual dispersion compensation and results. (a) Experimental setups. (b) Timing curve with different fiber patch cord lengths. (c) Measured timing curves with and without the timing link. (d) Timing curve measured with MDL movements in the forward and backward directions. (e) Normalized timing sensitivity with different fiber patch cord lengths.

Fig. 5. Detailed scheme of the link network stabilization. HVA, high-voltage amplifier; T40/R60, transmission 40%/reflection 60% fiber mirror; FR, Faraday rotator.

Fig. 6. Feedback flow diagrams of (a) in-loop timing link stabilization and (b) out-of-loop jitter measurement. Here, ω is the complex frequency and s = jω; J_I, inherent jitter of the mode-locked laser; J_E, environmental jitter imposed on the link for single-trip link transmission; J_IL, detected timing jitter by the in-loop BLOTD; H_BLD, transfer function of the in-loop BLOTD; E_N, electronic noise in the in-loop BLOTD electronics; H_DA, transfer function of the differential amplifier in the BLOTD; H_PI, transfer function of the PI controller; E_PI, electronic noise of the PI controller; H_FS, transfer function of the fiber stretcher; J_C, equivalent timing delay generated by the control loop for compensation; J_S, shot-noise-equivalent timing jitter; T_L, single-trip link transmission time; J_O, relative timing jitter between the link output pulses and the original pulses from the mode-locked laser.

Fig. 7. Simulation results for a 10.4 km timing link stabilization system. (a) The coefficient for the environmental noise imposed on the link. (b) The coefficient for the electronic noise. (c) The coefficient for the noise from the PI controller. (d) The coefficient for the shot noise. (e) The coefficient for the laser’s inherent jitter. (f) Out-of-loop integrated timing jitter with different PI gains and corner frequencies (1 mW optical power at each PD of the in-loop BLOTD).

Fig. 8. Out-of-loop jitter simulation results of individual jitter contributions with the optical power of (a) 1 mW and (b) 1 μW at each PD of the in-loop BLOTD. The timing link length is 10.4 km. The legend on the right shows the color code of the jitter spectral densities. Integrated jitter in this graph is shown on a logarithmic scale.

Fig. 9. Out-of-loop jitter simulation results of individual jitter contributions at the in-loop PD power of (a) 1 μW with transmission length of 20 km and (b) 240 nW with transmission length of 5.2 km.

Fig. 10. (a) Noise model of the PI controller. V_in and V_out, input and output voltage; V_n, input voltage noise of the PI controller; R_in and i_th,in, input impedance and its thermal noise current; R_f and i_th,f, feedback gain resistance and its thermal noise current; C, integrating capacitance. (b) Equivalent circuit of the fiber stretcher.