Timing jitter characterization of mode-locked lasers with <1 zs/√Hz resolution using a simple optical heterodyne technique

Closed-loop polarization mode dispersion mitigation for fiber-optic time and frequency transfer

A polarization-switching pulse interleaver is shown to be effective in reducing timing noise due to polarization mode dispersion in time and frequency transfer based on mode-locked lasers and standard single-mode (SM) fibers. In closed-loop time transfer over a 30-km dispersion-compensated fiber link with 300 fs of differential group delay, polarization interleaving reduced the delay variations to <20 fs. The results indicate that the remaining drift is caused by polarization-dependent loss and by AM-to-PM noise conversion in the photodiodes, suggesting the need for a "double-balanced" phase detector in the receiver, i.e., a phase detector balanced in power and polarization. By mitigating the polarization dependence, this work demonstrates a simple approach that can potentially yield sub-femtosecond-level, long-term time transfer in long-haul fiber links utilizing standard single-mode fibers.

Photonically referenced extremely stable oscillator

Due to their low phase noise at high carrier frequencies, photonic microwave oscillators are continuously expanding their application areas including digital signal processing, telecommunications, radio astronomy, and RADAR and LIDAR systems. Currently, the lowest noise photonic oscillators rely on traditional optical frequency combs with multiple stabilization loops that incorporate large vacuum components and complex optoelectronic configurations. Hence, the resulting systems are not only challenging to operate but also expensive to maintain. Here, we introduce a significantly simpler solution: a Photonically Referenced Extremely STable Oscillator (PRESTO). PRESTO requires only three key components: a femtosecond laser, a fiber delay element, and a pulse timing detector. The generated microwave at 10 GHz has phase noise levels of -125, -145, and <-160 dBc/Hz at 1, 10, and >100 kHz, respectively, with an integrated timing jitter of only 2 fs root mean square (RMS) over [100 Hz-1 MHz]. This approach offers a reliable solution for simplifying and downsizing photonic oscillators while delivering high performance.

Unveiling out-of-loop attosecond timing jitter precision in Ti:sapphire mode-locked lasers with an optical heterodyne technique

The out-of-loop timing jitter exhibited in free-running Ti:sapphire mode-locked lasers with attosecond resolution is demonstrated using an optical heterodyne technique. To assess the feasibility of the experiment and discrimination signal properties, numerical simulations were conducted for Ti:sapphire mode-locked lasers. For accurately characterizing the genuine phase noise exhibited by Ti:sapphire mode-locked lasers, out-of-loop measurements were conducted, and a straightforward yet improved optical heterodyne setup was employed, allowing simultaneous low-bandwidth locking and out-of-loop timing jitter measurements with two Ti:sapphire mode-locked lasers. The out-of-loop phase noise floor for a single mode-locked laser reaches -203.47 d B c/H z, assuming a 10 GHz carrier frequency. Additionally, the out-of-loop integrated timing jitter is 11.9 a s from 10 kHz to the Nyquist frequency (50 M H z).

Spatiotemporal mode-locking and dissipative solitons in multimode fiber lasers

Multimode fiber (MMF) lasers are emerging as a remarkable testbed to study nonlinear spatiotemporal physics with potential applications spanning from high energy pulse generation, precision measurement to nonlinear microscopy. The underlying mechanism for the generation of ultrashort pulses, which can be understood as a spatiotempoal dissipative soliton (STDS), in the nonlinear multimode resonators is the spatiotemporal mode-locking (STML) with simultaneous synchronization of temporal and spatial modes. In this review, we first introduce the general principles of STML, with an emphasize on the STML dynamics with large intermode dispersion. Then, we present the recent progress of STML, including measurement techniques for STML, exotic nonlinear dynamics of STDS, and mode field engineering in MMF lasers. We conclude by outlining some perspectives that may advance STML in the near future.

Attosecond-precision balanced timing detector with a single photodiode

We experimentally demonstrate a novel and practical timing detector based on a double-pass acousto-optic frequency shifter. With time and frequency multiplexing, for the first time to our knowledge, a balanced detection is realized using only a single photodiode, which greatly decreases the excess electronic noise during photodetection. With a total input optical power of 1.4 mW (0.35 mW per pulse train), an almost shot-noise-limited detection floor of 28.3 zs/√Hz is achieved, and the timing jitter integrated from 1 kHz to 1 MHz is reduced from 99.0 as (without eliminating the photodetector electronic noise) to only 30.4 as. Even with an input power of 50 µW per pulse train, 221.4 zs/√Hz detection floor and 268.0 as integrated timing jitter at [1 kHz and 1 MHz] are still maintained. This timing detector provides a powerful tool for high-precision metrology, ultra-long-distance ranging, and large-scale timing synchronization.

High-resolution timing jitter measurement based on the photonics time stretch technique

High-resolution jitter measurement is essential for the next generation of electronic communications and sensor systems. However, most electrical timing jitter measurement equipment has a low resolution because of the limitations of electronic processing accuracy. Meanwhile, photonics-based jitter measurement methods have a higher resolution but cannot measure the widely used electrical signals. This work proposes a potential high-resolution jitter measurement method for electrical signals based on the photonics time stretch technique. The jitter information can be magnified in the optical domain and then measured by electrical equipment. The experimental results demonstrate that the jitter of an electrical pulse is magnified from 59.02 ps to 663.29 ps when the magnification factor is 11.24.

Impact of Laser Intensity Noise on Dual-Comb Absolute Ranging Precision

Noise in mode-locked lasers has been a central issue for dual-comb metrological applications. In this work, we investigate the laser intensity noise on dual-comb absolute ranging precision. Two different dual-comb schemes based on linear optical sampling (LOS) and nonlinear asynchronous optical sampling (ASOPS) have been constructed. In the LOS scheme, the ranging precision deteriorates with the increase in laser relative intensity noise (RIN). This effect can be corrected by implementing a balanced photo-detection (BPD). In the ASOPS scheme, the experiment shows that the conversion from laser RIN to dual-comb ranging precision is negligible, making a balanced detection unnecessary for ranging precision improvement. The different manners of RIN's impact on absolute ranging precision are attributed to the distinct cross-correlation signal patterns and the underlying time-of-flight (TOF) extraction algorithms.

Timing jitter characterization of free-running dual-comb laser with sub-attosecond resolution using optical heterodyne detection

Pulse trains emitted from dual-comb systems are designed to have low relative timing jitter, making them useful for many optical measurement techniques such as optical ranging and spectroscopy. However, the characterization of low-jitter dual-comb systems is challenging because it requires measurement techniques with high sensitivity. Motivated by this challenge, we developed a technique based on an optical heterodyne detection approach for measuring the relative timing jitter of two pulse trains. The method is suitable for dual-comb systems with essentially any repetition rate difference. Furthermore, the proposed approach allows for continuous and precise tracking of the sampling rate. To demonstrate the technique, we perform a detailed characterization of a single-mode-diode pumped Yb:CaF₂ dual-comb laser from a free-running polarization-multiplexed cavity. This new laser produces 115-fs pulses at 160 MHz repetition rate, with 130 mW of average power in each comb. The detection noise floor for the relative timing jitter between the two pulse trains reaches 8.0 × 10^-7 fs²/Hz (∼ 896 zs/Hz), and the relative root mean square (rms) timing jitter is 13 fs when integrating from 100 Hz to 1 MHz. This performance indicates that the demonstrated laser is highly compatible with practical dual-comb spectroscopy, ranging, and sampling applications. Furthermore, our results show that the relative timing noise measurement technique can characterize dual-comb systems operating in free-running mode or with finite repetition rate differences while providing a sub-attosecond resolution, which was not feasible with any other approach before.

Attosecond-precision balanced linear-optics timing detector

A new timing detection method based on acousto-optic modulation is demonstrated. The timing detector is immune to dispersion effects and the environmental and laser amplitude noise can be well suppressed by a balanced configuration. With 1 mW power per pulse train, the measured timing noise floor is about 1×10^-10 fs²/Hz, which is close to the shot noise limit. The integrated timing jitter is 26 as at [1 Hz, 1 MHz]. With 170 fs pulse width and typical detector parameters, the calculated detector's timing noise floor is more than 5 and 12 orders of magnitude lower than that of a BOC, at 1 mW and 1 µW input power, respectively. This timing detector has a variety of potential applications in ultra-long fiber link stabilization, quantum metrology, weak signal timing control, etc.

Rotation Active Sensors Based on Ultrafast Fibre Lasers

Gyroscopes merit an undeniable role in inertial navigation systems, geodesy and seismology. By employing the optical Sagnac effect, ring laser gyroscopes provide exceptionally accurate measurements of even ultraslow angular velocity with a resolution up to 10-11 rad/s. With the recent advancement of ultrafast fibre lasers and, particularly, enabling effective bidirectional generation, their applications have been expanded to the areas of dual-comb spectroscopy and gyroscopy. Exceptional compactness, maintenance-free operation and rather low cost make ultrafast fibre lasers attractive for sensing applications. Remarkably, laser gyroscope operation in the ultrashort pulse generation regime presents a promising approach for eliminating sensing limitations caused by the synchronisation of counter-propagating channels, the most critical of which is frequency lock-in. In this work, we overview the fundamentals of gyroscopic sensing and ultrafast fibre lasers to bridge the gap between tools development and their real-world applications. This article provides a historical outline, highlights the most recent advancements and discusses perspectives for the expanding field of ultrafast fibre laser gyroscopes. We acknowledge the bottlenecks and deficiencies of the presented ultrafast laser gyroscope concepts due to intrinsic physical effects or currently available measurement methodology. Finally, the current work outlines solutions for further ultrafast laser technology development to translate to future commercial gyroscopes.

Dual trace inter-pulse interferometer for measurement of phase stability of ultra short laser pulse train

A dual trace intra-pulse and inter-pulse spatio-spectral interferometer has been set up to study the temporal stability of a ∼200 fs duration laser pulse train from a cw mode-locked laser oscillator. Simultaneous recording of twin interferograms helps identify the phase error in inter-pulse interferograms due to the diagnostic setup kept in a standard laboratory environment. Applicability of inter-pulse tilted pulse-front interferograms has been demonstrated to constitute an alternative inexpensive method for visual detection and estimation of phase slippage and pulse repetition frequency of an ultra short pulse train. The effect of pump beam intensity on the repetition rate of pulses due to accumulated intra-cavity non-linear phase shifts is also presented.

Real-time jitter correction in a photonic analog-to-digital converter

A real-time jitter meter is used to measure and digitally sample the pulse-to-pulse timing error in a laser pulse train. The jitter meter is self-referenced using a single-pulse delay line interferometer and measures timing jitter using optical heterodyne detection between two frequency channels of the pulse train. Jitter sensitivity down to 3×10^-10fs²/Hz at 500 MHz has been demonstrated with a pulse-to-pulse noise floor of 1.6 fs. As a proof of principle, the digital correction of the output of a high-frequency photonic analog-to-digital converter (PADC) is demonstrated with an emulated jitter signal. Up to 23 dB of jitter correction, down to the noise floor of the PADC, is accomplished with radio-frequency modulation up to 40 GHz.

Femtosecond two-color source synchronized at 100-as-precision based on SPM-enabled spectral selection

We demonstrate both numerically and experimentally that self-phase modulation-enabled spectral selection generates wavelength tunable energetic pulses that are tightly synchronized to the excitation pulses. The synchronization quantified by relative timing jitter is at the 100-as precision level, at least 10 times lower than can be achieved by Raman soliton pulses derived from the same source laser. This ultrafast two-color source is suitable for many important applications that require tight pulse synchronization.

Flexible all-PM NALM Yb:fiber laser design for frequency comb applications: operation regimes and their noise properties

We present a flexible all-polarization-maintaining (PM) mode-locked ytterbium (Yb):fiber laser based on a nonlinear amplifying loop mirror (NALM). In addition to providing detailed design considerations, we discuss the different operation regimes accessible by this versatile laser architecture and experimentally analyze five representative mode-locking states. These five states were obtained in a 78-MHz configuration at different intracavity group delay dispersion (GDD) values ranging from anomalous (-0.035 ps²) to normal (+0.015 ps²). We put a particular focus on the characterization of the intensity noise as well as the free-running linewidth of the carrier-envelope-offset (CEO) frequency as a function of the different operation regimes. We observe that operation points far from the spontaneous emission peak of Yb (∼1030 nm) and close to zero intracavity dispersion can be found, where the influence of pump noise is strongly suppressed. For such an operation point, we show that a CEO linewidth of less than 10-kHz at 1 s integration can be obtained without any active stabilization.

Optical frequency comb noise spectra analysis using an asymmetric fiber delay line interferometer

A simple and practical apparatus enabling repetition rate (frep) noise, carrier-envelope frequency (fceo) noise and n^th optical comb mode (νn) noise spectra measurements with high precision is established. The frep and νn noise spectra are measured by a fiber delay line interferometer, while fceo noise spectrum is measured by an f-2f interferometer. We utilize this apparatus to characterize the noise performance of an Er-fiber optical frequency comb (OFC) and analyze the origin of dominant noise sources. Moreover, this apparatus provides a powerful tool for diagnosing noise dynamics intrinsic in mode-locked lasers and OFCs. To this end, we uncover the anti-correlation between frep and fceo noise as well as the impact of servo loops on noise characteristics in the stabilized OFC.

Improvement of bandwidth of phase-locked loop for mode-locked laser with multiple-differentials-based loop filter

A scheme for improving the bandwidth of a phase-locked loop (PLL) for mode-locked laser is proposed. In the proposed scheme, a modified PLL with a multiple-differentials-based loop filter can be used to increases the upper limit bandwidth of the laser-based PLL. The mechanism of the bandwidth improvement is explained in detail, and the experimental results of a laser-based PLL with the proposed scheme show that the upper-limit bandwidth of the PLL has been increased about by one order at offset frequency from 3 kHz to 30 kHz. This scheme with the simple multiple-differential-based loop filter configuration can be easily used in another laser's phase locking system whose bandwidth should be improved.

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

We characterize the timing jitter of the pulse trains from 880 MHz 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 (10 fs rms, integrated from 30 kHz to 5 MHz). 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.

Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement

We present a synthetic-wavelength based heterodyne interferometer of optical frequency combs with wide consecutive measurement range for absolute distance measurement. The synthetic wavelength is derived from two wavelengths obtained by two band-pass filters. The interferometric phase of the synthetic wavelength is used as a marker for the pulse-to-pulse alignment, which greatly improves the accuracy of traditional peak finding method. The consecutive measurement range is enlarged by using long fiber to increase the path length difference of the reference and measurement arms. The length of the long fiber is stabilized according to the interferometric phase of a CW laser. The experimental results show the present system can realize an accuracy of 75 nm in 350 mm consecutive measurement range.

High-sensitivity optical to microwave comparison with dual-output Mach-Zehnder modulators

We demonstrate the use of two dual-output Mach-Zehnder modulators (DO-MZMs) in a direct comparison between a femtosecond (fs) pulse train and a microwave signal. Through balanced detection, the amplitude-to-phase modulation (AM-PM) conversion effect is suppressed by more than 40 dB. A cross-spectrum technique enables us to achieve a high-sensitivity phase noise measurement (−186 dBc/Hz above 10-kHz offset), which corresponds to the thermal noise of a +9 dBm carrier. This method is applied to compare a 1-GHz fs monolithic laser to a 1-GHz microwave signal generated from photodetection of a free-running 500 MHz mode-locked laser. The measured phase noise is −160 dBc/Hz at 4-kHz, −167 dBc/Hz at 10-kHz, and −180 dBc/Hz at offset frequencies above 100-kHz. The measurement is limited by the free-running 500-MHz laser’s noise, the flicker noise of the modified uni-traveling carrier photodiode and the thermal noise floor, not by the method itself. This method also has the potential to achieve a similar noise floor even at higher carrier frequencies.

Efficient laser noise reduction method via actively stabilized optical delay line

We report a fiber laser noise reduction method by locking it to an actively stabilized optical delay line, specifically a fiber-based Mach-Zehnder interferometer with a 10 km optical fiber spool. The fiber spool is used to achieve large arm imbalance. The heterodyne signal of the two arms converts the laser noise from the optical domain to several megahertz, and it is used in laser noise reduction by a phase-locked loop. An additional phase-locked loop is induced in the system to compensate the phase noise due to environmentally induced length fluctuations of the optical fiber spool. A major advantage of this structure is the efficient reduction of out-of-loop frequency noise, particularly at low Fourier frequency. The frequency noise reaches -30 dBc/Hz at 1 Hz, which is reduced by more than 90 dB compared with that of the laser in its free-running state.

Reference-free, high-resolution measurement method of timing jitter spectra of optical frequency combs

Timing jitter is one of the most important properties of femtosecond mode-locked lasers and optical frequency combs. Accurate measurement of timing jitter power spectral density (PSD) is a critical prerequisite for optimizing overall noise performance and further advancing comb applications both in the time and frequency domains. Commonly used jitter measurement methods require a reference mode-locked laser with timing jitter similar to or lower than that of the laser-under-test, which is a demanding requirement for many laser laboratories, and/or have limited measurement resolution. Here we show a high-resolution and reference-source-free measurement method of timing jitter spectra of optical frequency combs using an optical fibre delay line and optical carrier interference. The demonstrated method works well for both mode-locked oscillators and supercontinua, with 2 × 10-9 fs2/Hz (equivalent to -174 dBc/Hz at 10-GHz carrier frequency) measurement noise floor. The demonstrated method can serve as a simple and powerful characterization tool for timing jitter PSDs of various comb sources including mode-locked oscillators, supercontinua and recently emerging Kerr-frequency combs; the jitter measurement results enabled by our method will provide new insights for understanding and optimizing timing noise in such comb sources.

Quantum-limited timing jitter characterization of mode-locked lasers by asynchronous optical sampling

We demonstrate a novel time domain timing jitter characterization method for ultra-low noise mode-locked lasers. An asynchronous optical sampling (ASOPS) technique is employed, allowing timing jitter statistics on a magnified timescale. As a result, sub femtosecond period jitter of an optical pulse train can be readily accessible to slow detectors and electronics (~100 MHz). The concept is applied to determine the quantum-limited timing jitter for a passively mode-locked Er-fiber laser. Period jitter histogram is acquired following an eye diagram analysis routinely used in electronics. The identified diffusion constant for pulse timing agrees well with analytical solution of perturbed master equation.

Stabilizing carrier-envelope offset frequency of a femtosecond laser using heterodyne interferometry

We propose a time-domain f_ceo stabilization method of a femtosecond laser using heterodyne interferometry. A femtosecond pulse train that is delayed by a spatial delay line interferes with the original pulse train. The phase difference between heterodyne interference signals extracted from different spectral regions is used to stabilize the relative position of the two pulse trains; then the heterodyne interference phase is used to stabilize the carrier-envelope offset frequency f_ceo. The experimental results show that, after being stabilized, the relative Allan deviations of f_ceo are 1.0×10^-9 at 0.5 s and 4.6×10^-10 at 50 s.

Direct measurement of loop gain and bandwidth of phase-locked loop for mode-locked laser

A simple and robust technique for measuring the loop gain and bandwidth of a phase-locking loop (PLL) for mode-locked laser is proposed. This technique can be used for the real-time measurement of the PLL's real loop gain and bandwidth in a closed loop without breaking its locking state. The agreement of the experimental result and theoretical calculation proves the validity of the proposed technique for measuring the loop gain and bandwidth. This technique with a simple configuration can be easily expanded to other laser's locking system whose loop gain and bandwidth should be measured in advance.

Few-femtosecond timing jitter from a picosecond all-polarization-maintaining Yb-fiber laser

We characterize the timing jitter of a picosecond all-polarization-maintaining (all-PM) Yb-fiber laser using the optical cross-correlation method. For the 10 MHz all-normal dispersion mode-locked laser with ~0.5 nm spectral bandwidth, the measured high-frequency jitter is as low as 5.9 fs (RMS) when integrated from 10 kHz to the Nyquist frequency of 5 MHz. A complete numerical model with ASE noise is built to simulate the timing jitter characteristics in consideration of intracavity pulse evolution. The mutual comparison among simulation result, analytical model and experiment data indicate that the few femtosecond timing jitter from the picosecond fiber laser is attributed to the complete elimination of Gordon-Haus jitter by narrow bandpass filtering by a fiber Bragg grating (FBG). The low level of timing jitter from this compact and maintenance-free PM picosecond fiber laser source at a low MHz repetition rate is promising to advance a number of femtosecond-precision timing and synchronization applications.

Efficient carrier-envelope offset frequency stabilization through gain modulation via stimulated emission

A novel scheme for intracavity control of the carrier-envelope offset (CEO) frequency of a 100 MHz mode-locked Er:Yb:glass diode-pumped solid-state laser (DPSSL) based on the modulation of the laser gain via stimulated emission of the excited Er(3+) ions is demonstrated. This method allows us to bypass the ytterbium system few-kHz low-pass filter in the f(CEO) stabilization loop and thus to push the phase lock bandwidth up to a limit close to the relaxation oscillations frequency of the erbium system. A phase lock bandwidth above 70 kHz has been achieved with the fully stabilized laser, leading to an integrated phase noise [1 Hz-1 MHz] of 120 mrad.