Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator

Characterization of sub-20-attosecond timing jitter in erbium-doped fiber laser system

The significance of timing jitter stems from its pivotal role in enhancing the precision of applications like spectroscopy and frequency metrology. In this study, we introduce a comprehensive procedure for achieving low timing jitter values in mode-locked fiber laser systems, highlighting dispersion, intracavity pulse energy, pulse length, and spectral bandwidth as key parameters. Notably, we unveil the influence of fiber amplifier pump power on jitter, a factor neglected in established theories and recent experiments. Applying this procedure to a 200-MHz all-polarization-maintaining (PM) erbium-doped (Er:) nonlinear amplifying loop mirror (NALM) fiber laser system, we demonstrate an exceptionally low timing jitter of 14.25 attoseconds, measured using the balanced optical cross-correlation (BOC) technique and integrated from 10 kHz to 4 MHz. The implementation of our novel method offers the opportunity to improve jitter results in various fiber laser systems and increase the accuracy of fiber laser applications.

Highly stable, flexible delivery of microjoule-level ultrafast pulses in vacuumized anti-resonant hollow-core fibers for active synchronization

We demonstrate the stable and flexible light delivery of multi-microjoule, sub-200-fs pulses over a ∼10-m-long vacuumized anti-resonant hollow-core fiber (AR-HCF), which was successfully used for high-performance pulse synchronization. Compared with the pulse train launched into the AR-HCF, the transmitted pulse train out of the fiber exhibits excellent stabilities in pulse power and spectrum, with pointing stability largely improved. The walk-off between the fiber-delivery and the other free-space-propagation pulse trains, in an open loop, was measured to be <6 fs root mean square (rms) over 90 minutes, corresponding to a relative optical-path variation of <2 × 10^-7. This walk-off can be further suppressed to ∼2 fs rms simply by using an active control loop, highlighting the great application potentials of this AR-HCF setup in large-scale laser and accelerator facilities.

Arrival time fluctuation of the SwissFEL photocathode laser: characterization by a single color balanced cross correlator

The arrival time jitter and drift of the photocathode drive laser has an important impact on the performance of a Free-Electron-Laser (FEL). It adversely affects the beam energy jitter, bunch length jitter and bunch arrival time jitter, which becomes especially important for pump-probe experiments with femtosecond time resolution. To measure both parameters background free and stabilize the drift of the Yb:CaF₂ based laser we use a well designed balanced optical cross correlator. In this paper we present our results using this device and focus particularly on the performance of the amplifier. We achieve a laser drift of less than 200 fs during 60 h, a 4.5 fs rms jitter of the amplifier relative to its seeding oscillator and 11 fs rms for the whole laser relative to a reference clock integrated from 2 mHz to 100 Hz.

Absolute distance measurement to coaxial multi-targets based on optical balanced cross-correlation using a single femtosecond laser

We describe a high-precision ranging method based on an optical balanced cross-correlation system with a scanning repetition rate using a single femtosecond laser. By scanning the repetition rate of a laser, measuring pulses can be overlapped with reference pulses. It is an effective method to make reference pulses overlap with coaxial multiple target pulses without additional mechanical devices. The overlapped pulses are launched to the optical balanced cross-correlation system, which improves the time resolution measurement to the attosecond level. Two nominal distances are measured, and an additional commercial laser interferometer is used as a comparison to evaluate the accuracy of our measurement system. Moreover, the thickness of three stacked glasses is measured by our measurement system to verify that this system can measure coaxial multiple targets more quickly than conventional optical balanced cross-correlation systems using a single optical frequency comb.

High speed time-of-flight displacement measurement based on dual-comb electronically controlled optical sampling

We demonstrate a direct time-of-flight approach that utilizes dual-comb electronically controlled optical sampling (ECOPS) to measure small displacements. ECOPS is enabled by electrically controlling the repetition rate of one laser via an intracavity electric-optical modulator (EOM). The acquisition rate is set by the EOM modulation frequency, which is much higher than commonly used asynchronous optical sampling (ASOPS). In a proof-of-principle experiment, an 80-kHz acquisition rate is obtained with a pair of ∼105 MHz repetition rate Er-fiber lasers. At an average time of 30 ms, a measurement precision evaluated with Allan deviation reaches 26.1 nm for a 40-µm static displacement. In a dynamic measurement, a 500-Hz sinusoidal vibration with 15 µm amplitude has also been identified. The high-precision and high-speed displacement measurement technique can be potentially used in 3D surface profilometry of microelectronic step-structures and real-time monitoring of high frequency mechanical vibrations, etc.

Open-loop polarization mode dispersion mitigation for fibre-optic time and frequency transfer

The non-reciprocal and dynamic nature of polarization mode dispersion (PMD) in optical fibers can be a problem for accurate time and frequency transfer. Here, a simple, passive solution is put forward that is based on transmitting optical pulses with alternating orthogonal polarization. The fast and deterministic polarization modulation means that the PMD noise is pushed far away from the frequencies of interest. Furthermore, upon reflection from a Faraday mirror at the receiver, the pulses have a well-defined polarization when they return to the transmitter, which facilitates stable optical phase detection and fibre phase compensation. In an open-loop test setup that uses a mode-locked laser and a simple pulse interleaver, the polarization mode dispersion is shown to be reduced by more than two orders of magnitude.

Time-of-flight detection of femtosecond laser pulses for precise measurement of large microelectronic step height

We propose and demonstrate a new method which employs time-of-flight detection of femtosecond laser pulses for precise height measurement of large steps. By using time-of-flight detection with fiber-loop optical-microwave phase detectors, precise measurement of large step height is realized. The proposed method shows uncertainties of 15 nm and 6.5 nm at sampling periods of 40 ms and 800 ms, respectively. This method employs only one free-running femtosecond mode-locked laser and requires no scanning of laser repetition rate, making it easier to operate. Precise measurements of 6 μm and 0.5 mm step heights have been demonstrated, which show good functionality of this method for measurement of step heights.

High-dynamic-range arrival time control for flexible, accurate and precise parametric sub-cycle waveform synthesis

We introduce a simple all-inline variation of a balanced optical cross-correlator (BOC) that allows to measure the arrival time difference (ATD), over the full Nyquist bandwidth, with increased common-mode rejection and long-term stability. An FPGA-based signal processing unit allows for real-time signal normalization and enables locking to any setpoint with an unprecedented accuracy of 0.07 % within an increased ATD range of more than 400 fs, resulting in attosecond resolution locking. The setup precision is verified with an out-of-loop measurement to be less than 80 as residual jitter paving the way for highly demanding applications such as parametric waveform synthesizers.

The SwissFEL Experimental Laser facility

The hard X-ray laser SwissFEL at the Paul Scherrer Institute is currently being commissioned and will soon become available for users. In the current article the laser facility is presented, an integral part of the user facility, as most time-resolved experiments will require a versatile optical laser infrastructure and precise information about the relative delay between the X-ray and optical pulse. The important key parameters are a high availability and long-term stability while providing advanced laser performance in the wavelength range from ultraviolet to terahertz. The concept of integrating a Ti:sapphire laser amplifier system with subsequent frequency conversion stages and drift compensation into the SwissFEL facility environment for successful 24 h/7 d user operation is described.

All polarization-maintaining Er fiber-based optical frequency combs with nonlinear amplifying loop mirror

A fully stabilized all polarization-maintaining Er frequency comb with a nonlinear amplifying loop mirror with below 0.2 rad carrier-envelope-offset frequency phase noise is demonstrated. The integrated timing jitter is measured as 40 attosecond from 10 kHz to 10 MHz, which is the lowest value of any Er fiber frequency comb to date.

All fiber-coupled, long-term stable timing distribution for free-electron lasers with few-femtosecond jitter

We report recent progress made in a complete fiber-optic, high-precision, long-term stable timing distribution system for synchronization of next generation X-ray free-electron lasers. Timing jitter characterization of the master laser shows less than 170-as RMS integrated jitter for frequencies above 10 kHz, limited by the detection noise floor. Timing stabilization of a 3.5-km polarization-maintaining fiber link is successfully achieved with an RMS drift of 3.3 fs over 200 h of operation using all fiber-coupled elements. This all fiber-optic implementation will greatly reduce the complexity of optical alignment in timing distribution systems and improve the overall mechanical and timing stability of the system.

Repetition rate multiplication of femtosecond light pulses using a phase-locked all-pass fiber resonator

We describe an all-pass fiber resonator with active phase-locking capability for accurate multiplication of the repetition rate of femtosecond light pulses. The cavity length of the resonator is precisely controlled using the Pounder-Drever-Hall phase-locking technique so that the repetition rate is multiplied in stabilization to the Rb atomic clock. Our test result proves the proposed phase-locking scheme is an effective means of generating higher repetition rate pulses with no significant power loss while providing a high degree of long-term stability.

Femtosecond all-optical synchronization of an X-ray free-electron laser

Many advanced applications of X-ray free-electron lasers require pulse durations and time resolutions of only a few femtoseconds. To generate these pulses and to apply them in time-resolved experiments, synchronization techniques that can simultaneously lock all independent components, including all accelerator modules and all external optical lasers, to better than the delivered free-electron laser pulse duration, are needed. Here we achieve all-optical synchronization at the soft X-ray free-electron laser FLASH and demonstrate facility-wide timing to better than 30 fs r.m.s. for 90 fs X-ray photon pulses. Crucially, our analysis indicates that the performance of this optical synchronization is limited primarily by the free-electron laser pulse duration, and should naturally scale to the sub-10 femtosecond level with shorter X-ray pulses.

Few-femtosecond synchronization at free-electron lasers is key for nearly all experimental applications, stable operation and future light source development. Here, Schulz et al. demonstrate all-optical synchronization of the soft X-ray FEL FLASH to better than 30 fs and illustrate a pathway to sub-10 fs.

Remote two-color optical-to-optical synchronization between two passively mode-locked lasers

Using balanced detection in both the radio frequency (RF) and the optical domain, we remotely synchronize the repetition rate of a Ti:sapphire oscillator to an Er-doped fiber oscillator through a 360 m length-stabilized dispersion compensated fiber link. The drift between these two optical oscillators is 3.3 fs root mean square (rms) over 24 hours. The 68 MHz Er-doped fiber oscillator is locked to a 476 MHz local RF reference clock, and serves as a master clock to distribute 10 fs-level timing signals through stabilized fiber links. This steady remote two-color optical-to-optical synchronization is an important step toward an integrated femtosecond fiber timing distribution system for free-electron lasers (FELs); it does not require x-ray pulses, and it makes sub-10-fs optical/x-ray pump-probe experiments feasible.

Stable radio-frequency phase distribution over optical fiber by phase-drift auto-cancellation

We report a new radio-frequency (RF) phase stabilization approach for long-haul optical fiber distribution. The phase drift of an RF signal induced by fiber-length variations can be canceled out automatically via RF mixing without using active phase discrimination and dynamic phase tracking. A key significance of our approach is that no assistant local oscillator (LO) signal is needed. Consequently, frequency estimation of the received RF signal, as well as frequency locking between the LO and the received RF signal, is no longer required, which simplifies the system. A proof-of-concept experiment shows that the phase drift of the received RF signal at 9.6 GHz is significantly reduced using the proposed method. The root mean square (RMS) timing jitter is 0.76 ps when a tunable optical delay line (TODL) inserted between the remote antenna unit (RAU) and local station is changed from 0 to 300 ps.

One-femtosecond, long-term stable remote laser synchronization over a 3.5-km fiber link

Long-term stable timing distribution over a 3.5-km polarization maintaining (PM) fiber link using balanced optical cross-correlators (BOC) for optical-to-optical synchronization is demonstrated. Remote laser synchronization over 40 hours showed a residual timing jitter and drift of 2.5 fs for the whole locking period and only 1.1 fs integrated from 100 μHz to 1 MHz. This result corresponds to the lowest jitter and drift achieved to date for a multi-km fiber link and remote timing synchronization operating continuously over multiple days.

Stable fiber delivery of radio-frequency signal based on passive phase correction

A novel passive phase correction method for stable fiber transfer of radio-frequency (RF) signal is proposed and demonstrated. By employing only one local oscillator and two frequency mixers in the local station, an RF signal received by an optical remote antenna unit is transmitted to the local station with very small phase jitter. An experiment is performed. When a 6 GHz RF signal is delivered through a 20 km single-mode fiber, effective cancellation of the RF signal's phase jitter induced by environmental perturbations is achieved. The residual jitter is less than 1.33 ps (about 0.05 rad). The proposed scheme requires no active mechanism to compensate the fiber-length fluctuations, and is thus compact, cost-effective, and easy to implement.

Fiber-coupled balanced optical cross-correlator using PPKTP waveguides

We present a fiber-coupled balanced optical cross-correlator using waveguides in periodically-poled KTiOPO(4) (PPKTP). The normalized conversion efficiency of the waveguide device is measured to be η(0) = 1.02% / [W · cm(2)], which agrees well with theory and simulation. This result represents an expected improvement of a factor of 20 over previous bulk-optic devices. The sensitivity of the cross-correlator is characterized and shown to be comparable to the free-space bulk-optic version, with the potential for significant performance enhancements in the future.

Long-term stable, sub-femtosecond timing distribution via a 1.2-km polarization-maintaining fiber link: approaching 10(-21) link stability

Long-term stable, sub-femtosecond timing distribution over a 1.2-km polarization-maintaining (PM) fiber-optic link using balanced optical cross-correlators for link stabilization is demonstrated. Novel dispersion-compensating PM fiber was developed to construct a dispersion-slope-compensated PM link, which eliminated slow timing drifts and jumps previously induced by polarization mode dispersion in standard single-mode fiber. Numerical simulations of nonlinear pulse propagation in the fiber link confirmed potential sub-100-as timing stability for pulse energies below 70 pJ. Link operation for 16 days showed ~0.6 fs RMS timing drift and during a 3-day interval only ~0.13 fs drift, which corresponds to a stability level of 10(-21).

Phase fluctuation compensation for long-term transfer of stable radio frequency over fiber link

We developed a new radio frequency dissemination system based on an optical fiber link. A 1.55 μm mode-locked fiber laser was used as optical transmitter in the system. To actively reduce the phase fluctuation induced by the fiber length variations with high resolution, we proposed a novel compensation technique. In our technique, we directly control the phase of optical pulses generated by the laser to compensate the fluctuation. The phase-controlling method is based on both pump power modulation and cavity length adjusting. We performed the transfer in a 22-km outdoor fiber link, with a transfer stability of 3.7 × 10(-14) at 1 s and 6.6 × 10(-18) at 16000 s. The integrated timing jitter in 24 hours was reduced from 14 ps to 35 fs.

Pulse synthesis in the single-cycle regime from independent mode-locked lasers using attosecond-precision feedback

We report the synthesis of a nearly single-cycle (3.7 fs), ultrafast optical pulse train at 78 MHz from the coherent combination of a passively mode-locked Ti:sapphire laser (6 fs pulses) and a fiber supercontinuum (1-1.4 μm, with 8 fs pulses). The coherent combination is achieved via orthogonal, attosecond-precision synchronization of both pulse envelope timing and carrier envelope phase using balanced optical cross-correlation and balanced homodyne detection, respectively. The resulting pulse envelope, which is only 1.1 optical cycles in duration, is retrieved with two-dimensional spectral shearing interferometry (2DSI). To our knowledge, this work represents the first stable synthesis of few-cycle pulses from independent laser sources.

Long-term stable frequency transfer over an urban fiber link using microwave phase stabilization

We report a novel technique for highly stable transfer of a frequency comb over long optical fiber link. The technique implements an electronic compensation loop to cancel out the phase fluctuations that is introduced by the fiber. We utilized this technique to transfer a stable microwave frequency through a 20 km urban fiber link and an 80 km open air fiber link respectively. For the 20 km urban fiber link, the active compensation system reduced the phase fluctuation from 75 mrad (118 ps) to 4 mrad (6.3 ps) in 48 hours, and the frequency stability was improved by three orders of magnitude. For the 80 km open air fiber link, the active compensation system reduced the rms phase fluctuation from 580 mrad (914 ps) to 10 mrad (16 ps) in 24 hours, and the frequency stability was improved by two orders of magnitude.

Complete characterization of quantum-limited timing jitter in passively mode-locked fiber lasers

We characterize the timing jitter of passively mode-locked, femtosecond, erbium fiber lasers with unprecedented resolution, enabling the observation of quantum-origin timing jitter up to the Nyquist frequency. For a pair of nearly identical 79.4MHz dispersion-managed lasers with an output pulse energy of 450pJ, the high-frequency jitter was found to be 2.6fs [10kHz, 39.7MHz]. The results agree well with theoretical noise models over more than three decades, extending to the Nyquist frequency. It is also found that unexpected noise may occur if care is not taken in optimizing the mode-locked state.

Electron bunch timing with femtosecond precision in a superconducting free-electron laser

High-gain free-electron lasers (FELs) are capable of generating femtosecond x-ray pulses with peak brilliances many orders of magnitude higher than at other existing x-ray sources. In order to fully exploit the opportunities offered by these femtosecond light pulses in time-resolved experiments, an unprecedented synchronization accuracy is required. In this Letter, we distributed the pulse train of a mode-locked fiber laser with femtosecond stability to different locations in the linear accelerator of the soft x-ray FEL FLASH. A novel electro-optic detection scheme was applied to measure the electron bunch arrival time with an as yet unrivaled precision of 6 fs (rms). With two beam-based feedback systems we succeeded in stabilizing both the arrival time and the electron bunch compression process within two magnetic chicanes, yielding a significant reduction of the FEL pulse energy jitter.

Timing jitter measurement of transmitted laser pulse relative to the reference using type II second harmonic generation in two nonlinear crystals

A new method is proposed and analyzed for measuring the timing jitter of the transmitted pulse relative to the reference pulse using two type II phase-matched nonlinear crystals for second harmonic generation (SHG). The polarizations of the two pulses are exchanged in two crystals and the difference between two detected second harmonic signals can reflect the transmitted jitter. This new method provides a high sensitivity and timing resolution compared with the conventional RF (radio frequency) method. Since the overlapping levels in the two crystals are the same, the final output is zero when there is no time delay between the two pulses. Thus no offset is necessary to be subtracted from the final output and no time delay adjustment is required between the two pulses, compared with the previous optical method using one crystal and two dichroic beamsplitters. The jitter measuring performance is studied theoretically using non-stationary nonlinear wave-coupled equations for type II SHG of two pulses. The theoretical computation and analysis show that the sensitivity and the dynamic range of this new method depend on pulse width, crystal pulses and group velocity difference between two fundamental pulses.

Guided wave optics in periodically poled KTP: quadratic nonlinearity and prospects for attosecond jitter characterization

For the first time to our knowledge, continuous nonsegmented channel waveguides in periodically poled KTiOPO(4) with guided orthogonal polarizations are used to demonstrate type II background-free second harmonic generation in the telecom band with 1.6%/(W cm(2)) normalized conversion efficiency. This constitutes a 90-fold improvement in aggregate conversion efficiency over its free space counterpart. Simulations show that the guided wave device should enable the measurement of timing fluctuations of optical pulse trains at the attosecond level in an optical cross correlation scheme.

Attosecond-resolution timing jitter characterization of free-running mode-locked lasers

Timing jitter characterization of optical pulse trains from free-running mode-locked lasers with attosecond resolution is demonstrated using balanced optical cross correlation in the timing detector and the timing delay configurations. In the timing detector configuration, the balanced cross correlation between two mode-locked lasers synchronized by a low-bandwidth phase-locked loop is used to measure the timing jitter spectral density outside the locking bandwidth. In addition, the timing delay configuration using a 325 m long timing-stabilized fiber link enables the characterization of timing jitter faster than the delay time. The limitation set by shot noise in this configuration is 2.2 x 10(-8) fs(2)/Hz corresponding to 470 as in 10 MHz bandwidth.