Long-distance and high-precision ranging with dual-comb nonlinear asynchronous optical sampling.

Precise distance metrology and measurements play an important role in many fields of scientific research and industrial manufacture. Dual-comb laser ranging combines sub-wavelength ranging precision, large non-ambiguity range, and high update rate, making it the most promising candidate in precise distance metrology and measurements. However, previous demonstrations of dual-comb ranging suffer from short working distances, limited by the decoherence of lasers in interferometric schemes or by the low sensitivity of the photodetectors in response to the sparse echo photons. Here, we propose and demonstrate time-of-flight laser ranging with dual-comb nonlinear asynchronous optical sampling and photon counting by a fractal superconducting nanowire single-photon detector, achieving ranging precision of 6.2 micrometers with an acquisition time of 100 ms and 0.9 micrometers with an acquisition time of 1 s in measuring the distance of an outdoor target approximately 298 m away.

Collision dynamics between soliton molecules and a single soliton: exploding soliton pair and periodic soliton explosions.

Inherent periodic collisions in dual-wavelength mode-locked fiber lasers (MLFLs) stimulate various intra-cavity collision dynamic phenomena. Analogous to the collision of matter particles, collisions between optical soliton molecules (SMs) and single solitons (SSs) have been observed by the real-time spectral measurements. It is demonstrated that the energy accumulation after the collision caused by internal motion within bound pulses leads to soliton pair (SP) explosions, while the periodic soliton explosions with another cavity parameter setting are almost unaffected by the collision. Additionally, the collision between a SP and a SS is reproduced through numerical simulations, and the collision-induced double Hopf-type bifurcation of SP is predicted. These findings provide novel insights, to the best of our knowledge, for further understanding the complex collision dynamics in dual-wavelength MLFLs and will help in the design of high-performance dual-comb sources.

Bistable response and quasi-periodicity excitation of the internal dynamics of soliton molecules.

Soliton molecules, a frequently observed phenomenon in most mode-locked lasers, have intriguing characteristics comparable to their matter molecule counterparts. However, there are rare explorations of the deterministic control of the underlying physics within soliton molecules. Here, we demonstrate the bistable response of intramolecular motion to external stimuli and identify a general approach to excite their quasi-periodic oscillations. By introducing frequency-swept gain modulation, the intrinsic resonance frequency of the soliton molecule is observed in the simulation model. Applying stronger modulation, the soliton molecule exhibits divergent response susceptibility to up- and down-sweeping, accompanied by a jump phenomenon. Quasi-periodic intramolecular oscillations appear at the redshifted resonance frequency. Given the leading role of bistability and quasi-periodic dynamics in nonlinear physics, our research provides insights into the complex nonlinear dynamics within dissipative soliton molecules. It may pave the way to related experimental studies on synchronization and chaos at an ultrafast time scale.

Collision-induced Hopf-type bifurcation reversible transitions in a dual-wavelength femtosecond fiber laser.

Collisions refer to a striking nonlinear interaction process in dissipative systems, revealing the particle-like properties of solitons. In dual-wavelength mode-locked fiber lasers, collisions are inherent and periodic. However, how collisions influence the dynamical transitions in the dual-wavelength mode-locked state has not yet been explored. In our work, dispersion management triggers the complex interactions between solitons in the cavity. We reveal the smooth or Hopf-type bifurcation reversible transitions of dual-color soliton molecules (SMs) during the collision by the real-time spectral measurement technique of time-stretch Fourier transform. The reversible transitions between stationary SMs and vibrating SMs, reveal that the cavity parameters pass through a bifurcation point in the collision process without active external intervention. The numerical results confirm the universality of collision-induced bifurcation behavior. These findings provide new insights into collision dynamics in dual-wavelength ultrafast fiber lasers. Furthermore, the study of inter-molecular collisions is of great significance for other branches of nonlinear science.

Observation of RIN reduction via spectral broadening in an NPR-based stretched pulse fiber laser.

We show that an optimum mode-locking state with low relative intensity noise (RIN) can be identified by continuous broadening of an optical spectrum in a stretched-pulse fiber laser based on nonlinear polarization rotation (NPR). Under the premise of keeping the overall spectral shape unchanged, either gradually increasing the pump power or unidirectionally adjusting the polarization controller (PC) can effectively reduce RIN as the optical spectral bandwidth broadens. The optimized intensity noise performance of the laser can be attributed to the increased pulse energy and reduced intra-cavity net dispersion. Moreover, the integrated RIN will further decrease as the maximum 3-dB bandwidth extends. In our experiment, the detected minimum integrated rms RIN is below 0.003% (from 100 Hz to 100 kHz). Our experimental results find that the absolute spectral width is not a necessary key condition for obtaining low RIN mode-locked laser, whereas it may help understand and design versatile low-noise ultrafast laser sources.

High-precision surface profilometry on a micron-groove based on dual-comb electronically controlled optical sampling.

We demonstrate an optical method for 3D profilometry of micro-nano devices with large step structures. The measurement principle is based on a dual-comb direct time-of-flight detection. An electronically controlled optical sampling (ECOPS) approach is used to improve the acquisition rate. In a proof-of-principle distance measurement experiment, the measurement precision reaches 15 nm at 4000-times averages. The method has been used to characterize the profile of a large aspect-ratio rectangular micron-groove with 10 µm width and 62.3 µm depth. By point-by-point scanning, a 3D point cloud image is obtained, and the 3D profile of the micro-structure is quantitatively reconstructed with sub-micrometer precision. The proposed high-precision, high-speed surface 3D profile measurement technology could be applied to profilometry and inspection of complex microelectronics devices in the future.

Controllable high-speed rotated femtosecond cylindrical vector beam based on optical heterodyne interference.

Structured light beams that possess unique polarization distribution could offer a new degree of freedom for a variety of applications, and hence its flexible polarization manipulation is necessary. Here we experimentally report a heterodyne interference-based method for generating femtosecond cylindrical vector beam (CVB) with high-speed controllable rotated polarization states. The femtosecond CVBs are created through the superposition of two optical vortices with opposite handedness. The use of two acoustic-optical modulators (AOMs) with frequency differences allows to achieve polarization rotation in a hopping-free scheme at on demand speed. Up to 1 MHz of the rotation frequency is demonstrated by visualizing the fast rotation events through a fast-frame-rate CCD camera. Moreover, we show our method can be readily extended to produce higher order CVBs with more complex rotated polarization distributions. Such a simple yet versatile femtosecond polarization-controlled laser system has the capability to act as a nonlinear trapping platform, thus opening tremendous potential opportunities in the fields of micromachining, nanofabrication, and so force.

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.

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.

Orbital-angular-momentum-resolved diagnostics for tracking internal phase evolution in multi-bound solitons.

The generation of multi-bound solitons is a fascinating subject of investigation in many conservative and dissipative systems, such as photonics, fluid mechanics, Bose-Einstein condensates, and so on. In this study, we demonstrate the successful extraction of phase dynamics between solitons in bound multiple solitons with up to seven constituents in a mode-locked Er laser system. By mapping the internal phase motions of multi-bound solitons to the spatial phase movement of cylindrical vector beams using orbital angular momentum (OAM)-based diagnostics, different categories of internal pulsations are revealed. We show that bound state of four solitons exhibits linear drifting relative phase evolution dynamics; while for bound multiple solitons with constituents from five to seven pulses, stationary relative phase dynamics are observed. These findings highlight the possibility of the OAM-based method access to the internal motion of multi-soliton molecules with more freedom of degrees and fuel the analogy with research on chemistry molecule complex.

Quantum limited timing jitter of soliton molecules in a mode-locked fiber laser.

Soliton molecules in mode-locked lasers are expected to be ideal self-organization patterns, which warrant stability and robustness against perturbations. However, recent ultra-high resolution optical cross-correlation measurements uncover an intra-molecular timing jitter, even in stationary soliton molecules. In this work, we found that the intra-molecular timing jitter has a quantum origin. Numerical simulation indicates that amplified spontaneous emission (ASE) noise induces a random quantum diffusion for soliton pulse timing, which cannot be compensated by soliton binding mechanism. By suppressing indirectly coupled timing jitter at close-to-zero cavity dispersion, a record-low 350 as rms intra-soliton-molecular jittering is obtained from an Er-fiber laser in experiment. This work provides insight into the fundamental limits for the instability of multi-soliton patterns.

Route to stable dispersion-managed mode-locked Yb-doped fiber lasers with near-zero net cavity dispersion.

We numerically investigate the stability of a dispersion-managed mode-locked Yb-doped fiber laser of near-zero net cavity dispersion. The instability is primarily due to the filtering effect of the chirped fiber Bragg grating. The size of the unstable region is dependent on the modulation depth of the saturable absorbers. At modulation depth higher than 30%, stable mode-locking can operate throughout the dispersion region. Based on the simulation results, stable mode-locking around zero cavity dispersion is experimentally viable by a SESAM with a 34% modulation depth. The fiber laser can generate laser pulses with a 17-nm spectral bandwidth and a 139-fs dechirped pulse duration.

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 nth 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.

Intracavity cylindrical vector beam generation from all-PM Er-doped mode-locked fiber laser.

We demonstrate a practical method that is used to generate on-demand first- and higher-order cylindrical vector beams, in the 1550 nm band, directly from an all polarization maintaining mode-locked Er-fiber laser. On demand typical 1st order CVBs, including the radially and azimuthally polarized beams, can be easily achieved by properly adjusting the angle of a half-wave plate with respect to the fast axis of the vortex wave plate. The spatial beam mode can be flexibly switched with no disturbance on the time domain mode-locking output. The laser outputs the desired vector beams at 1571 nm with a spectral bandwidth at full-width at half-maximum of 32 nm. The mode-locked laser pulses have a repetition rate of 74.9 MHz. Moreover, the proposed method can be easily extended to create higher-order CVBs. Our research provides a convenient way to generate ultrafast pulses in highly flexible-controlled structured modes, which is essential for optical fabrication and light trapping applications.

Pulse dynamics manipulation by the phase bias in a nonlinear fiber amplifying loop mirror.

Pulse dynamics controlling is of great importance for high quality pulse generation in ultra-short pulse fiber lasers. The pulse quality characteristics in terms of pulse duration, energy, chirp profile, tunability, as well as noise feature substantially depend on intracavity pulse propagation dynamics. Here we found that a nonlinear amplifying loop mirror mode-locked thulium-doped fiber laser can switch among enabling operation conventional soliton, stretched-pulse soliton and dissipative soliton regimes only by manipulating an intracavity phase bias device. This provides a simple approach to tailoring ultra-short laser characteristics to different applications.

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.

Active f-to-2f interferometer for record-low jitter carrier-envelope phase locking.

The f-to-2f interferometer plays a key role for carrier-envelope phase (CEP) measurement and subsequent stabilization. The CEP measurement typically relies on the application of two optical nonlinearities, namely supercontinuum generation and second-harmonic generation. Then the cascadation of these nonlinearities often leads to signal levels on the order of a few photons per pulse. We experimentally demonstrate that the introduction of optical gain into the infrared arm of an f-to-2f interferometer can mitigate this detection bottleneck and improve signal-to-noise ratios by 20 dB compared to purely passive schemes. We further show that this measure allows for residual phase jitters between the carrier and envelope of about 10 mrad, corresponding to record-breaking timing jitters in the single attosecond regime. Moreover, the method appears generally applicable to a wide range of oscillators in the near-infrared and may enable stable CEP locking of mode-locked oscillators that so far have resisted stabilization. Finally, we propose a parametric variant of the active f-to-2f interferometer that can be used for laser amplifiers with kilohertz repetition rates and below.

All-polarization-maintaining dual-wavelength mode-locked fiber laser based on Sagnac loop filter.

We demonstrate an all polarization-maintaining (PM) fiber based dual-wavelength mode-locked Er-fiber laser. A nonlinear amplifying loop mirror (NALM) with an intracavity nonreciprocal phase shifter is used for self-started mode-locking. A short segment of PM fiber is angle-spliced to the NALM, functioning as a PM Sagnac loop filter, thus enabling dual-wavelength mode-locking. The wavelength separation is solely determined by the angle-spliced PM fiber length. Stable dual-wavelength mode-locking operation is switchable between 1570/1581 nm and 1581/1594 nm. The two-color pulse trains oscillating in the same cavity have an inherent offset repetition rate of ~1 kHz owing to cavity dispersion, allowing future high precision dual-comb applications with a simple and robust configuration.

Dual-comb spectroscopy with a single free-running thulium-doped fiber laser.

We demonstrate dual-comb spectroscopy in the vicinity of 2 µm wavelength based on a single dual-wavelength dual-comb Thulium-doped fiber laser. The shared laser cavity ensures passively maintained mutual coherence between the two combs due to common mode environmental noise rejection. In a proof-of-principle experiment, the absorption characteristics caused by the water in the optical path that composes the dual-comb spectrometer are measured. The retrieved spectral positions of the water absorption dips match with the HITRAN database.

Femtosecond laser pulse generation with self-similar amplification of picosecond laser pulses.

Compressing picosecond laser pulses to the femtosecond level is an attractive shortcut for obtaining femtosecond laser pulses. However, dechirped pulses generated by nonlinear compression with self-phase modulation (SPM) show obvious pedestals, which are induced by nonlinear chirp accumulation in spectral broadening process and cannot be easily suppressed. Here, we report systematic numerical simulations and experimental studies on self-similar amplification of picosecond pulses in a short gain fiber for obtaining ~100-fs laser pulses with nearly transform-limited (TL) temporal quality. It is demonstrated that self-similar amplification with picosecond seed pulses is only sensitive to pulse duration and pulse energy. Based on this optimization guideline, we built a compact self-similar amplification fiber system with a picosecond fiber laser as the seed source. This system outputs 66-fs pulses with 6.1-W average power at a repetition rate of 30 MHz. Due to the linear chirp produced in self-similar evolution process, compressed pulses show nearly TL temporal quality. It promises an efficient way of obtaining high-quality femtosecond laser pulses from a picosecond laser source.