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.

Coherent beam combining of femtosecond third-harmonic generators: towards high-power, high-beam-quality UV light generation.

Coherent beam combining (CBC) of two femtosecond third-harmonic (TH) generators is proposed and demonstrated. By applying phase modulation to one of the fundamental laser pulses, the feedback loop effectively eliminates both phase and pointing errors between the two TH femtosecond laser beams. The system delivers 345-nm femtosecond laser pulses with 22-W average power at 1-MHz repetition rate. The average combining efficiency is 91.5% over approximately 1 h of testing. The beam quality of the combined ultraviolet (UV) laser beam is near-diffraction-limited with M2 factors of M X2=1.36, M Y2=1.24, which are similar to those of the individual channels. This scheme exhibits promising potential for increasing high-beam-quality UV laser power.

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.

5-bit all-optical quantum random number generator based on a time-multiplexed optical parametric oscillator.

Random numbers are of critical importance in many applications, including secure communication, photonics computing and cryptography. Due to the non-deterministic nature of the quantum processes, a degenerate optical parametric oscillator (DOPO) constitutes a solution to produce true randomness. Nevertheless, one of the existing challenges for DOPO in this field is bit sequence scalability. Here, we experimentally report on the generation of 5-bit random number streams in a time-multiplexed femtosecond DOPO system. A multi-pass cell is added to elongate the OPO cavity to scale up the bit sequences. To this end, for a ∼15 m long all free space OPO cavity, resonating 5 signal pulses with a repetition rate of 50 MHz is demonstrated. The above-threshold binary phase nature originates from vacuum fluctuations of a DOPO ensuring the randomness of the system. The phase state of the output is characterized by the interference pattern between the output pulses and the fundamental pump pulses. Different bit sequences are presented here by turning on and off the OPO. Conditional probability is performed to verify the randomness of the output for 1200 bits. Our scheme provides a new direction for an all-optical random number generator.

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.

Caustics of the axially symmetric vortex beams: analysis and engineering.

We demonstrate that our theoretical scheme developed in the previous study on the caustics of the abruptly autofocusing vortex beams [Xiao et al., Opt. Express29, 19975 (2021)10.1364/OE.430497] is universal for all the axially symmetric vortex beams. Further analyses based on this method show the complex compositions of the vortex caustics in real space. Fine features of the global caustics are well reproduced, including their deviations from the trajectories of the host beams. Besides, we also show the possibility of tailoring the vortex caustics in paraxial optics based on our theory. The excellent agreements of our theoretical results with both numerical and experimental results confirm the validity of this scheme.

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.

Caustic Interpretation of the Abruptly Autofocusing Vortex beams.

We propose an effective scheme to interpret the abruptly autofocusing vortex beam. In our scheme, a set of analytical formulae are deduced to well predict not only the global caustic, before and after the focal plane, but also the focusing properties of the abruptly autofocusing vortex beam, including the axial position as well as the diameter of focal ring. Our analytical results are in excellent agreement with both numerical simulation and experimental results. Besides, we apply our analytical technique to the fine manipulation of the focusing properties with a scaling factor. This set of methods would be beneficial to a broad range of applications such as particle trapping and micromachinings.

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.

Dual-mode and two-signal-wavelength femtosecond optical parametric oscillator based on LiB3O5.

We demonstrate a tunable femtosecond dual-beam-mode (cylindrical vector beam [CVB] and Gaussian beam [GB]), dual-signal-wavelength optical parametric oscillator based on a temperature-tuned lithium triborate crystal, synchronously pumped by a frequency-doubled mode-locked Yb-doped fiber laser. When fixing the CVB wavelength at 780 nm, the central wavelength of the GB signal could be continuously tuned from 664 to 722 nm. The maximum total signal output power is 515 mW at a 4 W pump with dual-wavelength operation (664 and 780 nm). All the measured signal pulse durations are around 150 fs. Moreover, sum-frequency-generation with Gaussian mode tuning from 548 to 588 nm is obtained, with the maximum power of 52 mW at 548 nm. Thanks to the dual-channel configuration, the wavelengths of a CVB and GB can be tuned independently. Such a flexible and versatile configuration makes it a practical tool for many applications such as high-resolution microscopy and high-capacity optical communication.

22.7 W mid-infrared supercontinuum generation in fluorotellurite fibers.

In this Letter, we demonstrate 22.7 W mid-infrared (MIR) supercontinuum (SC) generation in all-solid fluorotellurite fibers. All-solid fluorotellurite fibers based on ${{\rm TeO}_2} {\text -} {{\rm BaF}_2}{\text -}{{\rm Y}_2}{{\rm O}_3}$TeO2-BaF2-Y2O3 and ${{\rm TeO}_2}$TeO2 modified fluoroaluminate glasses are fabricated by using a rod-in-tube method. By using a 0.6 m long fluorotellurite fiber with a core diameter of 11 µm as the nonlinear medium and a high-power 1.93-2.5 µm SC fiber laser as the pump source, we obtain 22.7 W SC generation from 0.93 to 3.95 µm in the fiber for a pump power of 39.7 W. The 10 dB bandwidth is about 1633 nm, and the corresponding spectral range is from 1890 to 3523 nm. The optical-to-optical conversion efficiency is about 57.2%. Our results show that all-solid fluorotellurite fibers are promising nonlinear media for constructing high-power MIR SC light sources.

Direct femtosecond laser ablation of large-area TaSe2, SnS2, and TiS2 thick films by a back ablation procedure.

Direct ablation of large-area graphene-like two-dimensional (2D) materials, i.e., tantalum diselenide (TaSe2), stannic disulfide (SnS2), and titanium disulfide (TiS2), by the back ablation method with a femtosecond laser with a repetition rate of 50 MHz and pulse width of 200 fs is studied for the first time to our knowledge. The ablation thresholds of the three kinds of materials are discussed. In addition, the optimization and ablation of narrow grooves on the films are demonstrated. Our work demonstrates the direct femtosecond laser ablation processing of the graphene-like 2D-material films and the potential of 2D-material-film-based devices.

Orthogonally polarized tunable dual-wavelength femtosecond optical parametric oscillator.

We demonstrate a femtosecond optical parametric oscillator that can generate orthogonally polarized dual-wavelength femtosecond pulses. Two periodically poled lithium niobate (PPLN) crystals with mutually orthogonal crystal axes are pumped by a single femtosecond fiber laser. The central wavelength of the two orthogonally polarized signal pulses can be continuously tuned from 1387 to 1588 nm with a maximum frequency separation of 27 THz. Because of the orthogonal dual-crystal scheme, the system is immune to the coherent coupling effect, thus overcoming the limitation of minimum frequency separation.

High-power femtosecond cylindrical vector beam optical parametric oscillator.

We report on high-power femtosecond cylindrical vector beam (CVB) generation from a Gaussian-pumped optical parametric oscillator (OPO). By introducing a half waveplate and a vortex half-wave plate of m = 1 to realize intracavity polarization modulation to the resonant Gaussian signal, the OPO could deliver broadband signal beam in CVB profile, i.e., radially and azimuthally polarized beam profile. The central wavelength of the generated CVB signals can be tuned continuously from 1405 to 1601 nm, while the corresponding pulse durations are all around 150 fs. A maximum average output power of 614 mW at 1505 nm is obtained. Moreover, our OPO cavity design can be extended to generate high order CVB by simply changing the vortex half-wave plate with different orders. Such a high-power CVB OPO configuration has the advantages of flexible control and wide tuning range, making it a practical tool for applications in super-resolution imaging, optical communication and quantum correlations.