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Synchronization of FEL Components with Fiber Laser Techniques

  • Cezary SydloEmail author
  • Jost Müller
  • Holger Schlarb
Living reference work entry

Abstract

Femtosecond X-ray pulses generated by free-electron lasers provide substantial scientific potential for time-resolved experiments. Accurate timing synchronization on the femtosecond scale is an essential installation. To date, the required precision levels can only be achieved by a laser-based synchronization system. A train of sub-picosecond pulses from a mode-locked laser is distributed over actively length-stabilized optical fiber links to an arbitrary number of remote locations which can be kilometers away. These optical fibers have inherently low loss and are immune against any form of electromagnetic interference. The deployed mode-locked laser has to be phase-locked to the master oscillator of the facility, and the distributed optical pulses are used in turn to phase-lock slave laser systems by all-optical schemes. Additionally, distributed low-level RF signals are restabilized at various locations throughout the accelerator. For the phase-locking of RF signals versus optical pulses, a stable and drift-free scheme is established.

Keywords

Amplitude-to-phase conversion Balanced optical cross-correlator Balanced optical-to-microwave phase detector (BOMPD) Dispersion-compensating fiber Erbium-doped fiber amplifier Femtosecond optical synchronization Fiber-loop optical-to-microwave phase (FLOMPD) Mach-Zehnder modulator (MZM) Mode-locked laser Nonlinear crystal Optical fiber links Polarization mode dispersion Polarization maintaining fibers Photodetection Sagnac loop Sum-frequency generation 

Introduction

Several X-ray FELs (XFELs), such as the Linac Coherent Light Source (LCLS) and LCLS II in the USA, SPring-8 Angstrom Compact free-electron LAser (SACLA) in Japan, the European XFEL in Germany, SwissFEL in Switzerland, and Pohang Accelerator Laboratory (PAL)-XFEL in South Korea, have been built within the last decade. All these new facilities, as well as all the already established ones, aim to generate or already achieve femtosecond X-ray pulses with unprecedented quality to observe chemical and physical reactions with subatomic-level spatiotemporal resolution.

The ever shorter X-ray pulses within such facilities require increasingly demanding synchronization systems spanning the entire installation. Generally, a synchronization system is responsible for the distribution of extremely stable timing signals to target systems. The dimensions of such a reference distribution system comprise the whole facility and reach lengths of several kilometers.

While conventional radiofrequency (RF) timing systems have already reached practical limits of a few 10 fs timing precision for such long distances, fiber-optic technologies have evolved and matured to be the next-generation timing systems. Mode-locked laser provides ultralow-noise optical and microwave signals as well as ultrashort optical pulses in the time domain allowing for very high precision in direct usage due to their high pulse peak power. Also, fibers are predestinated for long haul signal transport as they feature very low loss and are immune to electromagnetic disturbances along the path.

Such optical synchronization systems are usually composed of an ultra-stable, low-noise mode-locked laser oscillator, a signal distribution via actively length-stabilized optical fiber links to various locations across the entire facility, and their respective client systems.

These systems are deployed for local re-synchronization of the RF signals, to precisely measure the arrival time of the electron bunch for fast beam-based feedbacks, or to phase-lock optical laser systems for electron bunch generation, beam diagnostics, and user pump-probe experiments with femtosecond temporal resolution.

Laser-to-Laser Synchronization

The breakthrough for all-optical synchronization systems was demonstrated by Thomas R. Schibli in the year 2003. He published the first all-optical laser-lock and also presented first results. Here, a balanced optical cross-correlator (BOXC) has been demonstrated for the first time as an optical equivalent to a balanced microwave phase detector overcoming its typical problems (Schibli et al. 2003).

This development has ever since been an essential feature of every optical synchronization system based on the distribution of pulses from a mode-locked laser oscillator.

In this early work, the output beams of two lasers were combined by a broadband metallic beam splitter. A part of the combined beam has been sent to two nearly identical cross-correlators optimized for sum-frequency generation (SFG). The only difference between the two correlators was the insertion of a 3-mm-thick fused silica window in the optical path of one of them. This glass causes a group delay between both laser beams to shift the pulses of both lasers with respect to each other. For small time differences between the two laser pulses, the difference between the signals of the photodetectors at the ends of the correlators is close to zero and nearly proportional to the time difference between the two pulses. This point of operation makes this scheme insensitive to amplitude noise of each laser.

The difference signal from cross-correlators is used to lock the repetition rates of the two lasers by controlling the cavity length of the target laser. A timing jitter as low as 300 as rms over the frequency range of 10 mHz to 2.3 MHz has been achieved.

All modern all-optical laser-locking techniques have evolved from this first publication. In the following, the scheme used at the European XFEL (Müller et al. 2015) is described in detail.

Here, the operation of the balanced optical cross-correlator is based on the SFG in a type-I phase-matched nonlinear crystal (NLC). The necessary differential group delay can be realized by a dispersive material – as in the original publication by Thomas R. Schibli – or by a wavelength separator in combination with adjustable mirrors. The latter method allows for an engineered setup adjustable for pulse lengths up to the ps range depending on the target laser, whereas a group delay is only applicable for short pulse lengths in the sub-ps range.

A schematic view of such an optical setup is given in Fig. 1. The pulses from both lasers enter the cross-correlator through a first dichroic mirror employed for collinear combination of both beams. A second dichroic mirror reflects both laser beams toward the type-I phase-matched nonlinear crystal where they are focused at the entrance and collimated at the output. This way, the forward SFG signal is generated in the crystal and separated from both input laser beams at a third dichroic mirror. A fourth dichroic mirror again splits both laser beams for individual reflections back into the very same nonlinear crystal. In this point, this scheme differs from the original demonstration as the nonlinear crystal is used twice. The differential group delay is adjusted by optical delay lines, before both laser beams are reflected back toward the nonlinear crystal. The second pass of both laser beams – having already experienced the differential group delay – generates now the reverse SFG which is separated from both laser beams by the second dichroic mirror. The two SFG signals are individually digitized and subtracted yielding a precise measure for the timing error between the two input laser pulse trains. The actual setup of the described scheme is shown in Fig. 2.
Fig. 1

Timing error detection scheme based on balanced optical cross-correlation used at the European XFEL. The laser input pulses are combined with the optical reference and fed into a nonlinear crystal (NLC) for twofold sum-frequency generation (SFG), whereas a slight temporal shift is applied to the reflected reference signal. The SFG signals are detected, digitized, and subtracted yielding a precise and amplitude-insensitive measure of the timing error between the laser pulses and the optical reference

Fig. 2

Implementation of the balanced optical cross-correlator scheme for precise timing error detection as shown in Fig. 1

A first implementation of a pump-probe laser synchronization system at an FEL using the BOXC technique was demonstrated in Schulz et al. (2015). In this work, a 108.33 MHz Ti:sapphire oscillator with ultrashort (12 fs) pulses was locked to a 216.7 MHz erbium-doped fiber laser with 200 fs pulse width at the telecommunication wavelength of 1550 nm, resulting in 527.7 nm SFG signal wavelength. The synchronization performance was determined using a second cross-correlator in a similar configuration for out-of-loop measurements showing a jitter of 5 fs rms in a bandwidth of 10 Hz to 100 kHz.

In Müller et al. (2018), a similar BOXC-based optical synchronization scheme was implemented within the optical reference distribution system of the European XFEL. The laser oscillator was connected to the optical reference over a length-stabilized optical fiber link of around 3.4 km length. Both oscillators were passively mode-locked systems with a wavelength of 1550 nm and a pulse length of about 200 fs at 216.7 MHz pulse repetition rate. Input power levels at the entrance of the BOXC were 20 and 11.3 mW, respectively. The measured in-loop jitter was less than 1.3 fs rms within a bandwidth of 10 Hz to 10 MHz. This setup demonstrates clearly the implications of an actual installation in a FEL facility designed and built for 24/7 operation in comparison to laboratory experiments.

Besides the synchronization of the laser oscillator as a part of, e.g., a photocathode or pump-probe laser system, it has to be mentioned that such extended systems easily exceed several tens of meters of beamline with hundreds of optic elements installed. Thus, even an oscillator with sub-fs synchronization precision does not prevent from drifts and jitter added on the way to the photocathode or the experimental chamber. For this reason, another BOXC should be placed close to the target to additionally measure and compensate for timing changes with respect to the optical reference.

Optical Reference Distribution via Fiber

Even prior to the employment of balanced cross-correlators for optical reference distribution high-stability and ultralow-jitter signals have been transmitted also through fiber networks due to their low loss and insusceptibility to electromagnetic interference.

Such a fiber transmission of RF signals is presented, for example, in Holman et al. (2005). Here, a transfer of an RF signal through a 6.9 and a 4.5 km installed fiber resulted in a jitter of 37 and 20 fs rms, respectively, over a bandwidth of 1 Hz to 100 kHz in a laboratory environment. At that time it represented the lowest reported jitter for transfer of a timing signal over kilometer-scale distances using an installed laboratory-based optical fiber network.

The first proposal for an optically stabilized fiber link employing a balanced cross-correlator has been presented by Kim et al. (2004a).

The underlying concept is to couple laser pulses into an optical fiber. At the end of this fiber link, a part of the pulse is back-reflected. The returning pulses are combined with the pulses coming directly out of the laser, and their temporal overlap is measured with a balanced optical cross-correlator (BOXC). Timing changes of the fiber link are corrected using a piezoelectric transducer and a delay stage.

PPKTP Crystal-Based Balanced Cross-Correlator

The first optical fiber link stabilized with a balanced cross-correlator was demonstrated 3 years later (Kim et al. 2007), and at the same time, a self-aligned balanced cross-correlator based on a type-II phase-matched periodically poled KTiOPO4 (periodically poled potassium titanyl phosphate or PPKTP) crystal was introduced.

For a cross-correlator at 1550 nm, the use of a PPKTP crystal is particularly favorable due to the high phase-matching bandwidth of about 100 nm centered near 1550 nm. Using the group delay resulting from the birefringence between the two orthogonal polarizations in the crystal enables the implementation of balanced cross-correlation with optical pulses of the same wavelength. The differential group delay of the orthogonal polarizations and the sum-frequency generation (SFG) function are combined in a single nonlinear crystal. The SFG signal is only generated if both pulses do overlap in time, resulting in a detector signal being free of any background levels.

Figure 3 shows the operation of this single-crystal balanced cross-correlator. Two input pulses with orthogonal polarizations are transmitted through a first dichroic beam splitter DM1. Both input pulses are focused into the type-II phase-matched PPKTP crystal. The generated SFGfor component is transmitted through the second dichroic mirror and detected by a photodiode. The remaining fundamental input pulses are reflected from the second dichroic mirror DM2 and again focused into the PPKTP crystal. The SFG component generated by the back-reflected pulses – SFGrev – is separated by the dichroic beam splitter DM1 and detected by another photodiode. The balanced detection is based on the signal difference of both photodiodes and is proportional to the relative timing between both input pulses.
Fig. 3

PPKTP crystal-based balanced cross-correlator. Two input pulse trains are combined by polarization and cross-correlated by the type-II crystal. The dichroic mirror DM2 reflects both pulses again into the crystal resulting in a balanced operation

The second dichroic mirror is often realized as a coating on the rear side of the crystal to simplify the overall realization. This type of balanced cross-correlator is still used today.

Single-Mode Fiber Link Stabilization

The first link utilizing a balanced optical cross-correlator consisted of 270 m single-mode optical fiber (SMF) and additional 40 m of dispersion-compensating fiber (DCF) resulting in a 310-m-long pulse propagation. The out-of-loop timing jitter integrated between 10 Hz and 100 kHz was 9.2 fs rms, and the total jitter over 100 s was 9.7 fs. This result was the first 10 fs level stabilization of a fiber link with a 300 m length scale in a laboratory environment (Kim et al. 2007).

It should be noted here that only the SMF can be installed on an industrial scale, and hence the length of 310 m of the first fiber stabilization can be misleading.

The European XFEL – for example – has a total length of 3.4 km, but the longest installed fibers have a length of about 3.5 km due to the given fiber installation paths. For these fibers, the total laser pulse propagation distance is about 4.1 km, mainly due to the additional length of required DCF contained in the synchronization room. However, till this day most publications refer to the total fiber length and ignore the limitations of fiber installation.

In Fig. 4 a typical fiber link stabilization scheme is presented. The optical pulse train from the mode-locked laser enters the fiber link stabilization unit via a polarizing beam splitter (PBS). A half-wave plate HW1 before this beam splitter allows to set the split ratio. One part of the beam transmits straight through the beam splitter and is reflected back by a mirror passing twice a quarter-wave plate QW1. This quarter-wave plate is adjusted in such a way that the reflected light from the mirror is rotated perpendicular to the incident polarization. Hence, the reflected light is reflected in PBS toward the balanced cross-correlator.
Fig. 4

Single-mode fiber link stabilization scheme. The input from a mode-locked laser is transported to the balanced optical cross-correlator and the distribution fiber where a Faraday mirror (FRM) reflects a part of the light back to the cross-correlator. To account for losses in the fibers and their interconnections, an erbium-doped fiber amplifier (EDFA) is used

The other part of the incident pulse train from the mode-locked laser is reflected by PBS toward the fiber link. This light needs some preprocessing before it can be sent down the link. In SMFs the polarization of light is nondeterministic. The polarization will tend to drift as the light propagates. However, the client system connected to this fiber link will usually request a defined polarization. This requires polarization stabilization within the fiber link or at the connected client system. In Fig. 4 it is exemplarily shown in the link and consists of a half-wave plate and a quarter-wave plate which needs to be actively controlled.

The pulse train propagating through the fiber is experiencing variations in its propagation time which need to be minimized. For this purpose the fiber link stabilization comprises a method for propagation delay control. Typically, this is a combination of a fast piezoelectric actuator with typically just a few picoseconds of range and a comparably slow motorized optical delay line with a larger range. The most practical realization of a piezoelectric actuator is a piezo-driven fiber stretcher.

Another necessity is the compensation of chromatic dispersion. The light pulses are spread in time as they propagate through a fiber due to the change in refractive index with optical frequency and waveguide dispersion. This is counteracted by the inclusion of dispersion-compensating fiber (DCF). This type of fiber is specially designed to exhibit a strong chromatic dispersion opposite to the behavior of the SMF in the link. During commissioning of a fiber link, the length of the DCF needs to be carefully adjusted to achieve short optical pulses for the client system, for highest peak power in the balanced cross-correlator, and for a wavelength-independent propagation delay.

At the end of a fiber link, the optical pulse train is provided to the attached system. A part of the light has to be sent back the very same fiber path including all additional components to the balanced cross-correlator for timing error detection. In the case of a SMF – where the polarization changes in a nondeterministic way along the propagation path – the reflected pulse train reaches again PBS without a known polarization making this scheme highly unreliable because it is essential to have the correct polarization. This is achieved by deployment of a Faraday mirror (FRM). The state of polarization (SOP) of the reflected light is rotated 90 degrees from that of the input light. A unique property of FRMs is that at any point along the fiber, the SOPs of the forward going and reflected light are always orthogonal to each other, regardless of the birefringence of the fiber. This way a partly reflecting Faraday mirror ensures the correct, orthogonal polarization once returning to PBS.

All the aforementioned components including connections and the fibers itself cause some optical losses. Additionally, most of the light within the pulse train is to be provided to the attached client system. To compensate the optical power losses in the complete fiber link, an optical amplifier is employed. The most practical solution to do this is using an erbium-doped fiber amplifier (EDFA). It can efficiently amplify light in the 1550 nm wavelength region. Its core is the erbium-doped optical fiber, which is typically a single-mode fiber. This active fiber is pumped with light from a laser diode, which most often has a wavelength around 980 nm, where the highest absorption by erbium happens. Amplification is achieved by stimulated emission of photons from the dopant ions in the fiber.

All the components included in a fiber link stabilization and their interdependencies need to interact properly with each other to achieve optimum results.

However, there have been some issues observed with this type of installations. In Schulz et al. (2013), for example, uncompensated drifts of up to 13 fs per hour and 100 fs per 22 h are reported for a 300-m-long fiber installation.

This drift has been attributed to polarization mode dispersion (PMD) in SMF. In SMFs, there is some slight difference in the propagation velocity of light with different polarization states. A differential group delay can occur even for fibers which according to the design should have a perfect rotational symmetry and thus should exhibit no birefringence. This effect results from imperfections or bending of the fibers and is time-dependent. Modern fibers as used in telecommunications have been optimized for low PMD, but the handling and installation of such cables can still have some influence due to mechanical stress.

Therefore, the adoption of SMF in optical reference distribution systems can lead to an asymmetry of forward and reverse propagation of the pulse train. If the forward-traveling pulse train experiences a different propagation time compared to the reverse traveling one, this manifests as a timing error.

This discovery leads to abandoning SMF for accurate optical reference distribution systems where the accumulated drifts over the length of the fiber cause a too large error with respect to the requirements of the system.

This leads to the development of fiber stabilization schemes employing polarization maintaining fibers (PMF). Here, the polarization is always kept identical for forward and reverse traveling pulse trains and is consequently free of the PMD effect.

Polarization-Maintaining Fiber Link Stabilization

The first report of PMF for optical reference distribution is Cox et al. (2009) albeit with an intermediate scheme. Here, a residual out of loop timing drift of 2.2 fs rms or 11 fs pp has been achieved over 24 h.

In the simplest case, the fiber link stabilization scheme which is used with SMF can be modified to feature PMF. All fibers have to be changed to PMF. This comprises the installed distribution fiber, the dispersion-compensating fiber, the erbium-doped fiber, and the fiber piezo stretcher. Additionally, the FRM at the link end needs to be replaced with a conventional mirror, and the Faraday rotation for discriminating the pulses has to move to the beginning of the fiber part.

This modified scheme is shown in Fig. 5. However, the availability and maturity of polarization-maintaining fibers – especially dispersion-compensating fibers – lag behind the established telecommunication market with its SMF fibers. These deficiencies have led to an investigation of alternative schemes. In Fig. 6, the results of this investigation are shown.
Fig. 5

Polarization-maintaining fiber link stabilization scheme. The principle of operation is nearly identical to the SMF link scheme

Fig. 6

Polarization-maintaining fiber link stabilization scheme used at FLASH and the European XFEL. The SMF scheme – including the FRM – has a defined polarization for the returning pulses. This feature is exploited to realize an efficient and economical PMF link stabilization

As the fiber link stabilization scheme employing SMF already features a defined polarization at its polarization splitting/recombining beam splitter, it is suggesting to make use of this property for PMF stabilization. The complete combination of fibers and the optical delay line can be realized with SMF as it has been described for the single-mode fiber link stabilization. The only difference is that the distributing fiber is omitted. This results in a complete optical preconditioning except for the distributing fiber. The SMF scheme has a defined polarization for the returning pulse train which is taken advantage of to connect PMF as distribution fiber. The PMD remains in the SMF part of the scheme, but the different group velocities for the different polarizations are identical for the forward and reverse propagation now. Therefore, this scheme allows for handling PMF distributions as well as the mature components from the telecommunication market. To the best of the authors’ knowledge, this novel scheme is only used at FLASH and the European XFEL.

In Peng et al. (2013), a 1.2-km-long PMF link (1088 m actual PMF) has been locked for 16 days with an out-of-loop timing variation of 0.6 fs rms in a measurement bandwidth of 0.5 Hz. Here, a total drift of 65 ps was compensated by a motorized optical delay line, while the link output showed a maximum deviation of 2.5 fs. This represents a suppression of timing fluctuations by a factor of more than 20,000 over 16 days, indicating that the PMF was effective in overcoming large 100-fs timing drifts caused by PMD upon significant perturbation to the fiber.

It has been discovered that the less drift the fibers exhibit, the lower the possible residual timing error can be. The same group as before established a 3.5 km PMF link (2946 m actual PMF) in Xin et al. (2014) in combination with a laser lock. Overall, the optical delay line (ODL) corrected only 17 ps of link drift. The remaining timing error at the out-of-loop BOXC showed a maximum deviation of about 10 fs and an rms value of 2.3 fs.

Further stabilization of the link fiber itself makes the overall system more stable as shown in Safak et al. (2014). An active temperature stabilization has been employed for the PMF reducing any drifts. Here, the motorized ODL had to compensate only for 5 ps albeit the PMF link had again a total length of 3.5 km (2946 m actual PMF). This led to only 0.18 fs rms and 1.4 fs pp, which is a record-low value for fiber transmission over such a long distance. However, this type of publications is not helpful for field applications or an actual installation.

The developments for the European XFEL have resulted in a jitter level of about 25 fs pp and 3.3 fs rms over 25 h, while 120 ps of fiber drift have been compensated for an actual PMF length of 3600 m. This would correspond to about 4100 m of the so-called link length. This work reported in Sydlo et al. (2014) concentrated on a realization close to the requirements and boundary conditions of the European XFEL. To this date this is the longest reported link length with the largest compensated fiber drift.

The actual installation at the European XFEL is shown in Fig. 7.
Fig. 7

Optical reference distribution at the European XFEL

Optical-to-Microwave Phase Detectors

The extraction of an RF signal from an optical pulse train emitted by mode-locked lasers using direct photodetection is limited in precision by excess noise. This noise is mainly caused by amplitude-to-phase conversion in the photodetection process, beam-pointing variations, and pulse distortions due to photodetector nonlinearities. Photodiodes – even of the same type – exhibit a unique AM-PM conversion characteristic (Zhang et al. 2012) which needs to be identified individually. While this is possible, it is quite a tedious task and is usually avoided in large-scale installations.

These observations have led to a couple of developments to overcome the uncertainties in conventional photodiode usage which is described in the following.

Balanced Optical-to-Microwave Phase Detector

The first scheme avoiding these limitations was demonstrated by Jungwon Kim in (2004b). Here, a sub-100 fs timing jitter between the extracted RF signal and the optical pulse train is demonstrated. This scheme is applied to synchronize a mode-locked laser to an RF signal.

The scheme is shown in Fig. 8. The optical pulse train from a mode-locked laser is sent into a Sagnac loop. The input pulse train is split so that counter-propagating pulse trains are formed in the loop. When these pulse trains come together again at the splitter, they interfere with each other. Without any components within this loop, all light would be reflected back to the input as in a loop mirror.
Fig. 8

First balanced optical-to-microwave phase detector (BOMPD) realized with free-space optics. A Sagnac loop is biased unidirectional for balancing by π∕2 element, and a phase shifter is inserted in a way that the optical delay between counter-propagating pulse trains at the phase modulator is set to half of the RF signal period

To balance both outputs of the Sagnac loop, one of the pulse trains does need a phase shift of π∕2. This balancing allows for a stable and drift-free interferometer operation. Here, a quarter-wave plate has been inserted in one of the beams and rotated accordingly.

Additionally, a resonant phase modulator is positioned in the Sagnac loop in such a way that the optical delay between counter-propagating pulse trains at the phase modulator is set to half of the RF signal period. This ensures that the two counter-propagating pulse trains experience opposite phase modulation.

The output beams are detected by a balanced detector that generates a difference signal. In this first scheme, the output signal has been used to lock a 2 GHz voltage-controlled oscillator (VCO) to a 100 MHz optical pulse train from a mode-locked Ti:sapphire laser. The relative timing jitter between the RF signal from the VCO and the optical pulse train integrated from 100 Hz to 10 MHz has resulted in an approximately 60 fs timing jitter. The authors state that the free-space setup causes some issues and can be improved by a fiber implementation of the Sagnac loop for long-term stability.

Only 2 years later, this proposed fiber implementation has been demonstrated (Kim et al. 2006). It was also this publication which introduced the term “balanced optical-microwave phase detector” or BOMPD.

The challenge in the all-fiber implementation was the realization of the unidirectional bias of π∕2 which is essential for the balanced operation. The scheme is shown in Fig. 9. Here, this bias has been realized by an additional modulation of the phase modulator on top of the RF reference signal. For this additional modulation, a part of the input pulse train is tapped off for a photodiode.
Fig. 9

First fiber implementation of a balanced optical-to-microwave phase detector (BOMPD). The unidirectional π∕2 bias is realized by an additional modulation by the phase shifter

This photodiode signal is used to generate a reference signal for a synchronous detection at an odd half of the repetition rate \((n+\frac {1}{2}) \cdot f_{\mathrm {rep}}\) of the optical pulse source. The reference signal is then applied to both, the phase modulator and the downconversion mixer. The rest of the input pulse train is sent to the Sagnac loop with an in-loop phase modulator. The high RF signal frequency (n ⋅ frep) can give an unidirectional phase modulation because of the traveling-wave nature of the phase modulator. The unipolar phase modulation makes the fabrication of the loop easier, as the exact position within the fiber loop is less critical. Consequently, this scheme is best suited for high RF signal frequencies. Most publications use 10 GHz RF signals. For the reference signal, whose frequency does not support the unidirectional modulation, the phase modulator is positioned in such a way that counter-propagating pulses at the phase modulator experience opposite phases due to the reference signal. By this phase modulation, the output pulse train of the Sagnac loop is also amplitude-modulated at the frequency of \((n+\frac {1}{2}) \cdot f_{\mathrm {rep}}\). The pulse train detected at the fiber-loop output is bandpass filtered, mixed in phase with the reference signal and downconverted to the baseband.

This rather complex scheme achieved in its first implementation an in-loop timing jitter of 3 fs integrated from 1 Hz to 10 MHz for a 10.225 GHz VCO locked against a stretched-pulse Er-doped fiber laser with a repetition rate of 44.26 MHz (Kim et al. 2006).

The authors state that the system is limited by the thermal noise of the electronic amplifiers rather than shot noise and assess a limit of about 0.5 fs in this bandwidth.

The disadvantage for lower frequencies has been addressed in Felber et al. (2010) where at an RF frequency of 1.3 GHz about 10.7 fs rms, over more than 15 h have been achieved.

Fiber-Loop Optical-Microwave Phase Detector

The original concept of the balanced optical-microwave phase detector has two challenges. One is the required directional phase modulation in the counter-propagating pulse trains within the Sagnac loop. This is notedly simplified by the traveling-wave nature of optical phase modulators which results in unidirectional phase shifts for high RF signal frequencies. The second challenge is the necessity of a nonreciprocal π∕2 or quarter-wave bias for the optimum operation point. While one possibility is the employment of a complex electronic scheme as described before, a substantially more elegant solution was first described in Jung and Kim (2012).

In this work a true intensity imbalance between both outputs of a Sagnac loop interferometer has been used. A circulator is inserted into the feeding fiber to complete the balancing. This scheme is used to address an ultralow residual short-term phase noise and long-term phase drifts and is shown in Fig. 10. The necessity for the π∕2 bias has been solved by employing a scheme published in Dennis et al. (1996). Here, the electrooptic bias is replaced with an intrinsically passive nonreciprocal bias mechanism which eliminates the need for extensive RF electronics. The bias mechanism consists of a quarter-wave plate encased between two oppositely oriented 45 Faraday rotators. A pulse train propagating through the quarter-wave plate in one direction is orthogonally polarized to the oppositely propagating light. The optimum operation point is obtained by orienting the birefringence according to both axis generated by both Faraday rotators.
Fig. 10

The first fiber-loop optical-to-microwave phase (FLOMPD). The unidirectional π∕2 bias consists of a quarter-wave plate encased between two oppositely oriented 45 Faraday rotators

By employing a unidirectional phase modulator, the power difference between the two Sagnac loop outputs is proportional to the phase error between the optical pulse train and the RF signal and is optimized for a balanced photodetector.

The advantage of this scheme is its simplicity and the absence of any restriction on the usable repetition rate of the deployed mode-locked laser.

In this pioneering work, an 8.06 GHz RF signal from a VCO is synchronized with a 77.5 MHz mode-locked Er-fiber laser. The out-of-loop jitter has been measured to be 0.84 fs in the bandwidth of 1 Hz up to 1 MHz. The long-term out-of-loop drift has been measured to be 0.85 fs rms over 2 h. The authors report a slow phase drift which is caused by a phase drift of the π∕2 bias unit due to the temperature-dependent birefringence in the quarter-wave plate.

This scheme has been further optimized, and the passive nonreciprocal π∕2 bias mechanism – which necessitates free-space components – has been further simplified in Jeon et al. (2018). In this work, a sub-femtosecond-resolution phase detector has been realized by using a 3 × 3 optical coupler as a means for biasing the Sagnac loop in a simple and long-term stable way. The concept is adopted from the work on low-cost fiber-optic gyroscopes in Poisel et al. (1990) eliminating the necessity of magneto-optic components or complex RF electronics for biasing the Sagnac loop. The relative phase shift characteristic of single-mode multiport fiber couplers is exploited.

The polarization-maintaining fiber Sagnac loop interferometer is built with a 3x3 coupler and an unidirectional phase modulator as shown in Fig. 11.
Fig. 11

Simplified fiber-loop optical-to-microwave phase detector (FLOMPD). The pulse trains experience different phase shift as a function of phase modulation and the intrinsic phase shift of used coupler. The resulting interfered signals are emitted to the output ports and have a phase relation of 2π∕3 with respect to each other

When the optical pulse train is applied to the input, two counter-propagating pulse trains circulate in the Sagnac loop. They experience different phase shift as a function of phase modulation and the intrinsic phase shift of the used coupler. The resulting interfered signals are emitted to the output ports and have a phase relation of 2π∕3 with respect to each other. The output power difference between two of the three output fibers creates a quasi-linear error signal via balanced photodetection.

With a 250 MHz mode-locked Er-fiber laser and an 8 GHz microwave oscillator, the minimum timing jitter of 0.97 fs rms was achieved in the bandwidth of 1 Hz up to 1 MHz. The long-term rms timing drift and frequency instability was 0.92 fs within 5000 s with a sampling rate of 0.2 Hz.

Mach-Zehnder Modulator Phase Detector

Another phase detector technique has been invented and first reported in Lamb et al. (2011). This phase detector – based on a Mach-Zehnder modulator (MZM) – is also well suited for lower frequencies, e.g., 1.3 GHz at FLASH and the European XFEL. Femtosecond accuracy at this lower RF signal frequency requires a substantially improved phase detector sensitivity and careful engineering.

The principle of operation relies on the sampling of the RF signal with the laser pulse train as shown in Fig. 12. At the operating point, all laser pulses pass the MZM at different zero crossings of the applied RF signal. At the output of the setup, two control signals are obtained. One signal is used to lock the RF signal to the laser pulse train. The second signal is used to lock the bias voltage of the MZM, which is necessary to compensate drift effects.
Fig. 12

Mach-Zehnder-based phase detector. The principle of operation relies on the sampling of the RF signal with the laser pulse train. At the operating point all laser pulses pass the MZM at different zero crossings of the applied RF signal

The underlying principle is based on four optical pulses generated by the two delays. These are detected in amplitude and phase. This scheme is shown in Fig. 13.
Fig. 13

Modulated pulse trains before detection. The four red arrows represent the generated pulse train. The modulation frequency is depicted as the sinusoidal signal and is split in two parts, representing both arms within the Mach-Zehnder modulator. While the first two pulses are generated from one output, the last two pulses result from the second output and are consequently modulated oppositely indicated by the dashed curve. The resulting envelope signal is extracted at the fundamental frequency is show in blue. The three subfigures represent different cases: (a) Bias and phase error minimized. No error signal generated. (b) Signals with a bias error. The error signal has 0 phase shift. (c) Signals with a phase error. The error signal has 90 phase shift

The reference pulse train of the mode-locked laser is split into two paths of which one is delayed by ΔT1. Then it is recombined with the original one and fed into the MZM. This time delay is chosen in such a way that both pulses sample opposite slopes of the RF signal. The MZM itself has two outputs, compared to only one output at a traditional modulator. Those two output signals have an inverted modulation. If the optical power at one output rises, the power at the other output decreases and vice versa. Both outputs of the MZM have now the two pulses from the first delay ΔT1 with additional modulation of the RF signal.

Now, both signals are recombined with a second time delay ΔT2. The second time delay is chosen in a way that the inverted modulation of the MZM outputs is again inverted in phase. Hence, the modulation of the combined outputs has twice the slope. The repetition rate has increased fourfold compared to the original repetition rate. If the phase detector is in its operating point, all four laser pulses have the same power.

While this type of phase detector is better suited for the comparably low frequency of 1.3 GHz as used at FLASH and the European XFEL, the complete scheme is more complicated. Two delays and power splitting ratios need to be set up accurately. It requires also a closed-loop regulation of the DC bias voltage for the MZM to counterbalance its DC drift.

In the first implementation, this scheme demonstrated a high sensitivity despite the comparably low frequency. The drift within 40 h of measurement was 14.9 fs pp and 3.8 fs rms (Lamb et al. 2011). This was the best performance measured for a 1.3 GHz optical-to-microwave phase detector at that time.

This scheme was also used at a frequency of 2.998 GHz in Titberidze et al. (2017). Here, a Ti:sapphire photoinjector laser at the Relativistic Electron Gun for Atomic Exploration (REGAE) with a repetition rate of 83.275 MHz was synchronized to this RF frequency. An out-of-loop jitter of 7 fs rms and 31 fs pp has been measured over 43 h in the bandwidth of 20 Hz.

Conclusion

In conclusion, the all-optical methods described here are comparably established and demonstrate a very high level of precision. However, when leaving the all-optical domain, the implementations are getting quite diverse.

The laser-to-laser synchronization is historically the most established scheme and – at least from a scientific point of view – the least complicated. This is also recognizable by the achieved accuracies.

While the optical reference distribution via fibers is also a pure optical scheme, the amount of additional components and subsystems adds a substantial level of complexity. Also, the ambient conditions of the installed fibers do have an effect on the performance. All this is complicating developments and the overall optimization of such systems.

The transition from the optical domain into the microwave regime is experiencing the highest amount of scientific novelties. Here, the highest amount of diversity is found. Different schemes and approaches are still developing and have not converged to a widely established method yet. Also, a wide range of complexity levels is found among all the schemes.

While all the described methods are demonstrating already quite high levels of precision, the research continues to push forward and improve the precision for the increasing demands of free-electron laser facilities.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Timing and SynchronizationPaul Scherrer InstitutVilligenSwitzerland
  2. 2.Accelerator Division (MSK)Deutsches Elektronen SynchrotronHamburgGermany

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