Timing Distribution and Synchronization
Timing Distribution and Synchronization for Next Generation Light Sources
Modern large-scale scientific facilities such as X-ray free-electron lasers (FELs) require timing distribution systems with extremely high timing stability to synchronize radio frequency (RF) and optical sources across hundreds of meters to several kilometers (km) (see Fig. 1). Since conventional RF timing systems have already reached a practical limit for timing precision of about 50-100 femtosecond (fs) for such long distances, next-generation timing systems are adopting fiber-optic technology to achieve superior performance with optical signal transport and timing distribution . Current FELs can already produce sub-10-fs X-ray pulses  and concepts for sub-fs X-ray pulse generation are in place which would require sub-fs timing stability.
Our timing system, which is based on the pulsed approach, uses a mode-locked laser as the source of an ultralow-noise optical pulse train which serves as the timing signal . The master laser may be locked to a microwave standard to improve the low-frequency noise of the timing signal. Then, this ultralow-noise signal is transferred through timing stabilized fiber links to the end stations where efficient and robust synchronization of optical and RF subsystems to the pulse train is realized .
Integrated Balanced Optical Cross-Correlators
Balanced optical cross-correlation has been proposed as a sensitive technique for measuring timing jitter of mode locked lasers . In this scheme, two pulses whose relative jitter is to be measured are projected onto orthogonal polarizations, and then launched into a quadratic nonlinear crystal using type-II phase matching. The group velocity mismatch in the crystal causes the two polarizations to walk through each other in time as they propagate through the length of the crystal. This produces a signal at the second harmonic that is dependent on the time separation between the two pulses at the input of the crystal. A dichroic mirror at the output discriminates the fundamental harmonic (FH) from the second harmonic (SH). The forward SH signal is measured by the first detector of a balanced receiver, and the reflected FH fields travel backwards and generate a new SH signal that will be measured by the second detector of the receiver. This process is illustrated in Fig. 2. When the input delay is such that the two pulses are exactly overlapped in time after the forward pass through the crystal, each pass through the crystal will generate the same amplitude of SH signal, which in turn translates to zero voltage at the output of the balanced receiver. In the presence of timing jitter, the varying electrical signal from the receiver provides the jitter statistics at high precision, since the balanced scheme by nature removes effects of amplitude fluctuations from the measured electrical signal.
In previous work, a SH conversion efficiency of 0.4 % was obtained in the telecom band using bulk PPKTP . However, when low pulse energy must be used to avoid fiber nonlinearity, very little power is available for jitter monitoring. In these circumstances a free-space cross-correlator is not a viable option. As a result, we investigated the use of waveguides in KTP instead of bulk crystals to significantly improve the efficiency of the SHG process. The waveguides were fabricated using Rb+ ion exchange, and have a cross-sectional area of approximately 3x3 µm2. A dichroic coating was deposited on the end facet of the waveguide to reflect the forward-propagating FH back in for the reverse pass. For our waveguides, we have measured the normalized conversion efficiency to be 1.76% / (W cm2). In comparison to , assuming identical input pulse parameters as are reported there, this would correspond to a conversion efficiency of 19.5%, an improvement of a factor of 50 over the bulk-optic result. Finally, we mounted the coated waveguides into a fiber-coupled package, pictured in the inset of Fig. 3.
Timing Jitter Characterization of Femtosecond Lasers
Ultrafast optical pulse trains with very low timing jitter have been widely employed in high resolution photonic analog-to-digital conversion, timing distribution systems for next generation X-FELs, and many other fields. However, the conventional jitter measurement method using high speed photo detectors and mixer usually cannot characterize jitter below 1 fs, due to the excess phase noise in the photo detection process and the mixer’s limited timing resolution. Recently, jitter measurements using balanced optical cross-correlators (BOC), which can precisely extract the timing information without introducing intensity conversion noise, have been demonstrated and attosecond (as) jitter resolution has been achieved .
We characterized the jitter performance of two identical commercial lasers mode-locked lasers (170 mW average power, 170 fs pulse width at 1554 nm center wavelength and 216 MHz repetition rate) by using the BOC method as illustrated in Fig. 4. The measurement result which is shown in Fig. 5 indicates an extremely low timing jitter, <100 as, for frequencies greater than 1 kHz. This indicates that this type of lasers is well suited for the development of femtosecond timing distribution systems with sub-fs and eventually even sub-100 as precision over km distances.
Timing Stabilized Fiber Links
The working principle of our timing stabilized fiber links is demonstrated in Fig. 6. In an unstabilized link, environmental noise will induce errors in the output pulse arrival times. In order to stabilize the link, first the round-trip timing error must be detected. An output coupler reflects part of the pulse back to the input, where it gets recombined with a new laser pulse. There, a BOC measures the relative timing error between these pulses and generates an error voltage . A feedback loop is then engaged to adjust a variable delay such that the change in link propagation time compensates for the detected timing error.
Fig. 7 shows the long-term drift results of the link stabilization experiment. The timing link was 1.2 km long polarization maintaining (PM) fiber and the laser was an Er-doped fiber laser which outputs 170 fs pulses centered at 1558 nm with 100 mW average power and a 200 MHz repetition rate. The fiber link was stabilized for 16 days straight and the remaining drift was only 0.6 fs RMS and 2.5 fs peak-to-peak.
After arriving to the end stations through the timing stabilized fiber link, the optical pulse can be used to synchronize other optical and microwave devices.
The method developed by our group for optical-to-optical synchronization relies on balanced optical cross-correlation in a similar manner like for the link-stabilization . As described in Fig. 8, two pulses from the link output and the mode-locked laser which we want to synchronize are combined at the beam splitter and the timing mismatch between the two pulses, Δt is detected by the BOC. Finally, the repetition rate error of the remote laser is compensated with a feedback signal applied to a PZT.
For the case of optical-to-microwave synchronization, we employ an optoelectronic phase-locked loop (see Fig. 9) which locks the zero-crossings of a microwave signal to the optical pulse train. Here, the optical pulse train from the link output and the microwave signal from the VCO are applied to a balanced optical-microwave phase detector (BOM-PD). The phase error between the two signals is extracted via electro-optic sampling in the optical domain, thus circumventing excess phase noise issues at detection. Two variations of the BOM-PD have so far been developed; Fig. 9a is based on a differentially-biased Sagnac loop interferometer  and Fig. 9b is based on a complementary output Mach-Zehnder interferometer modulator . The error signal from BOM-PD is fed back to the VCO to complete the optoelectronic phase-locked loop.
Fig. 10 is the measurement result of the relative timing jitter between an optical pulse train with 200.5 MHz repetition rate and the regenerated 10.225 GHz (the 52st harmonic) microwave signal for 10 h of operation time. The measurement shows that the timing jitter in a 1 MHz bandwidth integrated over 10 h is 6.8 fs RMS which results in an unprecedented 1.9x10-19 relative timing stability of the microwave signal .
1. M. Y. Peng, P. T. Callahan, A. H. Nejadmalayeri, S. Valente, M. Xin, L. Grüner-Nielsen, E. M. Monberg, M. Yan, J.M. Fini, and F. X. Kärtner, “Long-term stable, sub-femtosecond timing distribution via a 1.2-km polarization-maintaining fiber link: approaching 10−21 link stability,” Opt. Express 21, 19982 (2013).
2. Y. Ding, F. J. Decker, P. Emma, C. Feng, C. Field, J. Frisch, Z. Huang, J. Krzywinski, H. Loos, J. Welch, J. Wu, and F. Zhou, “Femtosecond x-ray pulse characterization in free-electron lasers using a cross-correlation technique,” Phys. Rev. Lett. 109, 254802 (2012).
3. H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers”, IEEE J. Quantum. Electron. 29, 983 (1993).
4. J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2, 733 (2008).
5. T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kärtner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28, 947 (2003).
6. J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32, 1044 (2007).
7. J. A. Cox, A. H. Nejadmalayeri, J. Kim, and F. X. Kärtner, “Complete characterization of quantum-limited timing jitter in passively mode-locked fiber lasers,” Opt. Lett. 35, 3522 (2010).
8. J. Kim, F. X. Kärtner, and F. Ludwig, “Balanced optical-microwave phase detectors for optoelectronic phase-locked loops”, Opt. Lett. 31, 3659 (2006).
9. A. H. Nejadmalayeri and F. X. Kärtner, “Mach-Zehnder based balanced optical microwave phase detector,” CLEO 2012, paper CTu2A (2012).
10. M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W.-T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Science & Applications 6, e16187; DOI: 10.1038/lsa.2016.187 (2017).
11. K. Şafak, M. Xin, Q. Zhang, S.-H. Chia, O. D. Mücke, and F. X. Kärtner, “Jitter analysis of timing-distribution and remote-laser synchronization systems,” Opt. Express 24, 21752 (2016).
12. M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, P. T. Callahan, W. Wang, O. D. Mücke, and F. X. Kärtner, “Breaking the Femtosecond Barrier in Multi-Kilometer Timing Synchronization Systems,” IEEE J. Sel. Top. Quantum Electron. 23, 8800212 (2017).