Balanced Optical Cross-correlation Research Articles

From breather soliton molecules to chaos in a laser cavity: the scenario of intermittent transitions

Intermittency is widely observed in various nonlinear dynamical systems as an intriguing transient dynamic far from equilibrium. The internal dynamics formed by a pair of interacting optical solitons are often analogized to typical nonlinear systems. However, whether intermittency exists within the intramolecular motion remains to be investigated. Here, we study the intermittent dynamics of soliton molecules in ultrafast lasers, employing balanced optical cross-correlation techniques with sub-femtosecond temporal resolution. We demonstrate the occurrence of the bursting phase of intense variations of pulse separation within regular breather rhythms. In addition, we discover the intermittent transitions route to chaotic soliton molecules, facilitated by gain control. A series of analysis methods are used to assess the chaotic signals, providing compelling experimental evidence that soliton molecules can be analogized to their matter molecule counterparts. Our experimental findings shed light on the non-equilibrium intramolecular dynamics, providing insight into the transition of the attractors within interacting dissipative solitons in laser and fiber resonators.

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.

Quasi-Period Dynamics of Soliton Molecules: Route to Chaos and Intrinsic Frequency Entrainment

Soliton molecules in optical resonators have attracted remarkable attention in nonlinear dynamics, driven by their compelling analogies with matter molecules. So far, while extensive research has been conducted on their generation, pulsations, and dissociation behaviors, the investigation of their quasi-periodic dynamics has been relatively limited. Here, we present a systematic exploration of the quasi-periodic dynamics of soliton molecules using advanced balanced optical cross-correlation techniques. The incommensurable quasi-period bifurcations constituted of cascaded Hopf bifurcations are found, providing an unambiguous pathway toward chaotic soliton molecules. The chaotic intramolecular dynamics are analyzed by time series, radio frequency spectra, phase portraits, and Lyapunov exponent analysis. In addition, we reveal an intrinsic frequency entrainment phenomenon experimentally. Such frequency entrainment provides a novel perspective on synchronization in optical resonators, encompassing the competition and interaction of oscillations across multiple temporal scales. Our experimental findings offer clear proof that the gain dynamics serve as the origin of the binding forces between solitons within the molecule, which are well supported by the numerical simulations. By advancing the understanding of sub-femtosecond resolved quasi-period dynamics of optical soliton molecules, this study contributes to the broader field of complex nonlinear dynamics, paving the way for future explorations into the intricate behaviors of solitons within optical resonators and relevant fields.

Synchronization of the internal dynamics of optical soliton molecules

Compact bound states of light pulses in ultrafast lasers are known as optical soliton molecules. They constitute nonlinear superstructures of choice to investigate complex dynamical phenomena that manifest similarly in a wide range of nonlinear systems. Akin to matter molecules, optical soliton molecules can feature vibrational motions between their internal constituents. However, these vibrations are intrinsically nonlinear, with oscillation frequencies sensitive to system parameters. Therefore, vibrating soliton molecules present an opportunity for control. We here investigate the precise control of their oscillation frequencies through the universal mechanism of synchronization between master and slave oscillators. Self-oscillating soliton molecules are prepared within a passively mode-locked fiber laser. We experimentally demonstrate the synchronization of the internal vibrations of soliton molecules through the optical injection of a master oscillator signal. Direct observation of the synchronization process is enabled by balanced optical cross-correlation detection, a technique allowing real-time detection of intramolecular separation with femtosecond temporal resolution. We show efficient sub-harmonic, fundamental, and super-harmonic synchronization, forming a pattern of Arnold tongues with respect to the injection strength. Numerical simulations support experimental observations. By retrieving these universal synchronization features, the role of the soliton molecule as a nonlinear dynamical system of chief importance is further highlighted.

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.

Sub-Femtosecond Timing Jitter From a SESAM Mode-Locked Yb-Fiber Laser

We demonstrate sub-femtosecond timing jitter of ultrashort pulses from a dispersion managed Yb-fiber laser mode-locked by a SESAM. Timing jitters of the mode-locked Yb-laser under different dispersion conditions (when the intra-cavity dispersions are −0.005 ps2, +0.001 ps2, +0.006 ps2) are characterized by the single-crystal balanced optical cross-correlator. In our experiment, an ultra-low timing jitter of 48 attoseconds is achieved when the jitter spectral density is integrated from 3 kHz to 1 MHz offset frequency. We think that the obtained timing jitter level is the lowest for fiber lasers mode-locked by real saturable absorbers. This ultra-low timing-jitter, stably mode-locked fiber laser source is expected to be used for high precision applications outside of the laboratory.

Timing Fluctuation Correction of A Femtosecond Regenerative Amplifier

We report on the long-term correction of a timing fluctuation between the femtosecond regenerative amplifier and the reference oscillator for the seed 100 PW laser system in the Station of Extreme Light (SEL). The timing fluctuation was characterized by a noncollinear balanced optical cross-correlator that maps the time difference to the sum frequency intensity of the amplifier and oscillator laser pulses. A feedback loop was employed to correct the timing jitter by adjusting the time delay line in the amplifier beam path. The timing fluctuation was reduced to 1.26 fs root-mean-square from hundreds of fs over 10 hours. Benefitting from excellent performance and long-term stability, this timing jitter correction scheme, as a component of optical synchronization in the 100 PW laser facility, will be integrated into SEL.

Two Color Balanced Optical Cross Correlator to Synchronize Distributed Lasers for SHINE Project

Two Color Balanced Optical Cross Correlator to Synchronize Distributed Lasers for SHINE Project

Attosecond timing jitter within a temporal soliton molecule

The interactions of optical solitons in passively mode-locked lasers result in abundant bound states that reflect intriguing nonlinear attractor behaviors in complex dissipative systems. In this study, we tested the strength limits of the fixed-point attractors that govern bound soliton molecule formation in passively mode-locked lasers. To this end, we probed the relative timing jitter in a closely separated stationary doublet soliton molecule produced by a Kerr-lens mode-locked Ti:sapphire laser. By adopting a balanced optical cross-correlation method with a 5 z s / 0 H z temporal resolution, we derive an upper estimate of 60 as intramolecular timing jitter, which is integrated from 100 Hz to the Nyquist frequency (60 MHz). To the best of our knowledge, this is the first evidence for attosecond timing jitter within robust bound solitons in dissipative systems.

Measurement of absolute timing jitter of SESAM mode-locked lasers with yoctosecond sensitivity

Absolute timing jitter from a mode-locked laser is characterized with a record low noise floor of 122ys/Hz (1.5×10-14s2/Hz). We develop a novel measurement technique using cross-spectrum methods in combination with a dual balanced optical cross-correlator system, with three independent low-noise mode-locked lasers.

Timing jitter reduction through relative intensity noise suppression in high-repetition-rate mode-locked fiber lasers.

We reported the timing jitter reduction of an 882 MHz mode-locked NPE Yb:fiber lasers through active relative intensity noise suppression. The timing jitter spectra measurements based on balanced optical cross-correlation (BOC) technique show a reduction of ~10 dB in the Fourier frequency range from ~3 kHz to ~30 kHz with a unity-gain crossing point of 80 kHz. The results verify the theoretical prediction that the relative intensity noise (RIN) induced timing jitter by self-steepening effect dominates the jitter performance below ~100 kHz. Further comparison with the analytic model shows that the effect of RIN decays below ~3 kHz. Thus, the timing jitter reduction is not obvious at low frequency. To the best of our knowledge, this is the first experimental report on the timing jitter reduction through active RIN suppression in high-repetition-rate mode-locked fiber lasers.

Timing jitter of high-repetition-rate mode-locked fiber lasers.

We characterize the timing jitter of the pulse trains from 880MHz Yb-doped nonlinear polarization rotation mode-locked fiber lasers based on a balanced optical cross-correlation method. Jitter spectral density at different net-cavity dispersions has been characterized, and the near-zero dispersion shows the lowest rms timing jitter (10fs rms, integrated from 30kHz to 5MHz). The measurements have been compared with analytical models. The comparison shows that the RIN-coupled timing jitter by nonlinearity is the dominated origin of the measured timing jitter below ∼100 kHz, while amplified spontaneous emission noise makes a major contribution in the high frequency range above hundreds of kilohertz. To the best of our knowledge, this is the first high-precision timing jitter characterization for the ∼gigahertz level repetition rate mode-locked fiber lasers. The results will be of great importance for further improving the laser performance for many applications.

Femtosecond single-shot timing and direct observation of subpulse formation in an infrared free-electron laser

We experimentally demonstrate a single-shot arrival time monitor for short picosecond infrared free-electron laser (IR FEL) pulses based on balanced optical cross-correlation with a synchronized fs table-top laser. Employing this timing tool at the Fritz Haber Institute IR FEL, we observe a shot-to-shot timing jitter of only 100 fs and minute-scale timing drifts of a few picoseconds, the latter being strictly correlated with the electron beam energy of the accelerator. We acquire sum-frequency cross-correlation data with micropulse resolution, providing full access to the IR FEL pulse shape evolution within the macropulse. These measurements provide unprecedented insights into the occurrence of limit-cycle oscillations of the FEL intensity as a consequence of subpulse formation. Our experimental results are complemented by four-dimensional simulations of the nonlinear pulse dynamics in a low-gain FEL oscillator based on Maxwell-Lorentz theory.

Observation of subfemtosecond fluctuations of the pulse separation in a soliton molecule.

In this work, we study the timing instability of a scalar twin-pulse soliton molecule generated by a passively mode-locked Er-fiber laser. Subfemtosecond precision relative timing jitter characterization between the two solitons composing the molecule is enabled by the balanced optical cross-correlation (BOC) method. Jitter spectral density reveals a short-term (on the microsecond to millisecond timescale) random fluctuation of the pulse separation even in the robust stationary soliton molecules. The root-mean-square (rms) timing jitter is on the order of femtoseconds depending on the pulse separation and the mode-locking regime. The lowest rms timing jitter is 0.83fs, which is observed in the dispersion managed mode-locking regime. Moreover, the BOC method has proved to be capable of resolving the soliton interaction dynamics in various vibrating soliton molecules.

Sub-femtosecond precision timing synchronization systems

We present a timing synchronization system that can synchronize optical and microwave signals with attosecond-level precision across kilometer distances. With this technique, the next-generation photon science facilities like X-ray free-electron lasers and intense laser beamlines can be enabled to observe ultra-fast dynamics in atoms, molecules and condensed matter taking place on an attosecond time scale. We discuss some key technologies including master-laser jitter characterization, local one-color laser synchronization, remote two-color laser synchronization, and analyze technical noise contributions in the system. A 4.7-km laser–microwave network with 950-attosecond timing jitter is realized over tens of hours of continuous operation. Finally, an integrated balanced optical cross correlator is introduced. With the same input power level, the required operational power for each timing link is significantly reduced.

Coherent synthesis of ultrashort pulses based on balanced optical cross-correlator

Coherent synthesis of laser pulses is a major trend in the generation of ultrafast pulse field. There is no good way to compensate for the whole spectrum when the spectrum of ultrashort pulses is wide enough to reach an octave, so it is difficult to realize a sub-cycle pulse in a single-path laser system even if the spectrum range is wide enough. In this paper, 0.8 mJ, 30 fs laser pulses at 1 kHz repetition rate with 790 nm center wavelength from a Ti:sapphire chirped pulse amplifier (CPA) system are focused into hollow fiber with an inner diameter of 250 μm and a length of 1 m to produce an octave-spanning white-light supercontinuum (450-950 nm). Using this supercontinuum, we conduct two sets of comparative experiments. 1) We split the supercontinuum into two pulses with different spectrum ranges (450-750 nm and 650-1000 nm) by a dichroic mirror (HR, 500-700 nm; HT, 700-1000 nm), and we compress the two pulses by the double-chirped mirrors and wedge pairs to generate two few-cycle pulses:the long and short wavelength yielding pulses are 7.9 fs and 6.1 fs, respectively. Then we coherently synthesize two pulses by using another dichroic mirror, and controlling the relative time delay between the two pulses, and thus we synthesize a pulse of 4.1 fs. 2) We directly compress the supercontinuum by the double-chirped mirrors and wedge pairs, and obtain an optimization result of 5.3 fs, of which the pulse duration is wider than that in experiment 1. In these comparative experiments, the advantage of coherent synthesis for shorter pulse duration is preliminarily verified. Besides, the balanced optical cross-correlator technique is used to lock the relative time delay between two pulses. The root-mean-square value of relative time delay drift is less than 80 as in the case with feedback control loop, which ensures the stability of coherent synthesis system. This scheme can be adopted to accurately compensate for the dispersion and obtain the sub-cycle synthesized pulse, which is useful for generating the high harmonic and atto-second pulse.

Noise characteristics of high power fiber-laser pumped femtosecond optical parametric generation.

We study, both numerically and experimentally, the relative intensity noise (RIN) and timing jitter characteristics of optical parametric generation (OPG) process in MgO-doped periodically poled LiNbO3 (MgO:PPLN) pumped by fiber femtosecond laser. We directly characterize the RIN, and measure timing jitter spectral density of the OPG process based on the balanced optical cross-correlator (BOC) technique for the first time as well, which are both in a fairly good agreement with numerical simulation. Both the numerical and experimental study reveals that OPG can suffer from a smaller intensity fluctuation but a lager temporal jitter when it is driven into saturation. Furthermore, we demonstrate that with a 30 mW CW diode laser injection seeding the OPG output results in superior noise performance compared to the vacuum fluctuations seeded OPG.

High-precision active synchronization control of high-power, tiled-aperture coherent beam combining.

We propose and demonstrate a high-precision active control technique for tiled-aperture coherent beam combining suitable for high-power laser pulses. The method is a hybrid structure based on the near-field interference fringe technique and single-crystal balanced optical cross-correlation, which enables the active loop to exhibit high accuracy, wide dynamic range, and good capacity for resisting energy disturbance. In the proof-of-principle experiment, we realized an adjustable beam combining bandwidth of approximately 100Hz (limited by the speed of the piezoelectric transducer) and root-mean-square deviation of approximately λ/51 for two beam channels with a combining efficiency of 93%.

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.

Long-term stable coherent beam combination of independent femtosecond Yb-fiber lasers.

We demonstrate coherent beam combination between independent femtosecond Yb-fiber lasers by using the active phase locking of relative pulse timing and the carrier envelope phase based on a balanced optical cross-correlator and extracavity acoustic optical frequency shifter, respectively. The broadband quantum noise of femtosecond fiber lasers is suppressed via precise cavity dispersion control, instead of complicated high-bandwidth phase-locked loop design. Because of reduced quantum noise and a simplified phase-locked loop, stable phase locking that lasts for 1 hour has been obtained, as verified via both spectral interferometry and far-field beam interferometry. The approach can be applied to coherent pulse synthesis, as well as to remote frequency comb connection, allowing a practical all-fiber configuration.