## 3 Synchronization of Laser  
Precise synchronization to XFEL pulses is realized by controlling the cavity length of the mode-locked oscillator using the 5.7-GHz RF signal for the accelerator operation. The schematic diagram of the control system is shown in the oscillator part of Figure 1. The timing between the pulse train from the oscillator and the RF signal is detected by a BOMPD, which is based on a detecting technique of a phase-error dependent intensity imbalance between two outputs from a \"Sagnac-loop\" interferometer [31; 32; 33]. The repetition rate of the oscillator is locked by applying the phase error signal from 'in-loop' BOMPD (BOMPD-8-SD, Cycle GmbH, Hamburg, Germany) to the linear actuator of the cavity mirror in the mode-locked oscillator. In general, a control system in a feedback loop keeps all the noise sources at the frequencies lower than the locking bandwidth at zero, including the detector's and feedback system's noises and environmental sensitivity. Therefore, an 'out-of-loop' BOMPD (BOMPD-8-MD, Cycle GmbH, Hamburg, Germany) is necessary to characterize the long-term relative phase error between the mode-locked oscillator and the RF signal. The 5.7-GHz RF signal is split and connected with the 'in-loop' and the 'out-of-loop' BOMPDs. About 10% of the oscillator output, which is split by a polarization beam splitter (PBS) and a half waveplate at the oscillator exit, is required as the 'in-loop' BOMPD input for a stable feedback loop. The remaining beam split by the PBS has the almost minimum pulse energy required as a seeder of the regenerative amplifier. Therefore, the zero-order beam of the AOPDF output is used for the 'out-of-loop' BOMPD. The first-order beam diffracted at 960 Hz by the AOPDF is injected into the regenerative amplifier, while the zero-order beam with enough power is delivered to the BOMPD through an optical fiber. We analyzed the phase error, i.e., jitter, from a phase noise spectral density of the 'out-of-loop' BOMPD output measured by a phase noise analyzer (FSWP8, Rohde & Schwarz GmbH & Co. KG, Munich, Germany) with a  
Figure 11: (**a**) Focusing spot profile; (**b**) variety of centroid positions normalized by the beam size (FWHM) in 24 h at EH2. calibrated sensitivity of 0.22 mV/fs, as shown in Figure 12. A jitter of 47 fs was achieved by integrating the spectral density from 10\({}^{0}\) to 10\({}^{6}\) Hz. Precisely synchronized RF and timing signals of 5712 MHz, 238 MHz, and 60 Hz are provided from the SACLA accelerator to LH1 over several hundred meters through multiple optical fiber delivery systems. The fiber length of this system is feedback-controlled by an interferometer between the going and returning signals. The required signals of 960 Hz and 60 Hz for the laser operation are produced by counting 238-MHz RF and re-clocking with 5712-MHz RF in a timing delay unit (TDU: 86 DgR238B01, CANDOX Systems, Cyoda, Japan) [34]. Because the accelerator operation is synchronized to the AC power line for the stabilization of the electron beam, the timing of the electron bunch has a shot-to-shot fluctuation of about 50 \(\upmu\)s. The synchronization to the electron bunch is realized by resetting the count of RF with the 60-Hz timing signal reflecting the timing of the electron bunch. The TDU, including counters and in-phase and quadrature (IQ) phase shifters, can delay the 5.7 GHz, 960 Hz, and 60 Hz timing signals for the synchronized laser system simultaneously. The block diagram of the TDU is drawn in Figure 13. Users can change a time interval between the optical laser and the XFEL pulses using the TDU from \(-2\) to +990 microsecond (positive: the XFEL pulses arrives after the optical laser pulses, negative: opposite) with sub-picosecond accuracy. We have developed a relative arrival timing monitor between the XFEL and the optical laser pulses.