Single-shot interferometric measurement of pulse-to-pulse stability of absolute phase using a time-stretch technique.

Measurement of the absolute phase of ultrashort optical pulses in real-time is crucial for various applications, including frequency comb and high-field physics. Modern single-shot techniques, such as dispersive Fourier transform and time-lens, make it possible to investigate non-repetitive spectral dynamics of ultrashort pulses yet do not provide the information on absolute phase. In this work, we demonstrate a novel approach to characterise single-shot pulse-to-pulse stability of the absolute phase with the acquisition rate of 15 MHz. The acquisition rate, limited by the repetition rate of the used free-running mode-locked Erbium-doped fibre laser, substantially exceeds one of the traditional techniques. The method is based on the time-stretch technique. It exploits a simple all-fibre Mach-Zehnder interferometric setup with a remarkable resolution of ∼7.3 mrad. Using the proposed method, we observed phase oscillations in the output pulses governed by fluctuations in the pulse intensity due to Kerr-induced self-phase modulation at frequencies peaked at 4.6 kHz. As a proof-of-concept application of the demonstrated interferometric methodology, we evaluated phase behaviour during vibration exposure on the laser platform. The results propose a new view on the phase measurements that provide a novel avenue for numerous sensing applications with MHz data frequencies.

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.

Tailoring of spatial coherence in a multimode fiber by selectively exciting groups of eigenmodes.

Control of the properties of speckle patterns produced by mutual interference of light waves is important for various applications of multimode optical fibers. It has been shown previously that a high signal-to-noise ratio in a multimode fiber can be achieved by preferential excitation of lower order spatial eigenmodes in optical fiber communication. Here we demonstrate that signal spatial coherence can be tailored by changing relative contributions of the lower and higher order multimode fiber eigenmodes for the research of speckle formation and spatial coherence. It is found that higher order spatial eigenmodes are more conducive to the final speckle formation. The minimum speckle contrast occurs in the lower order spatial eigenmodes dominated regime. This work paves the way for control and manipulation of the spatial coherence of light in a multimode fiber varying from partially coherent or totally incoherent light.

Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser.

We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.

Spatio-temporal generation regimes in quasi-CW Raman fiber lasers.

We present experimental measurements of intensity spatio-temporal dynamics in quasi-CW Raman fiber laser. Depending on the power, the laser operates in different spatio-temporal regimes varying from partial mode-locking near the generation threshold to almost stochastic radiation and a generation of short-lived pulses at high power. The transitions between the generation regimes are evident in intensity spatio-temporal dynamics. Two-dimensional auto-correlation functions provide an additional insight into temporal and spatial properties of the observed regimes.

Intensity dynamics and statistical properties of random distributed feedback fiber laser.

We present first experimental investigation of fast-intensity dynamics of random distributed feedback (DFB) fiber lasers. We found that the laser dynamics are stochastic on a short time scale and exhibit pronounced fluctuations including generation of extreme events. We also experimentally characterize statistical properties of radiation of random DFB fiber lasers. We found that statistical properties deviate from Gaussian and depend on the pump power.

Narrow-band generation in random distributed feedback fiber laser.

Narrow-band emission of spectral width down to ~0.05 nm line-width is achieved in the random distributed feedback fiber laser employing narrow-band fiber Bragg grating or fiber Fabry-Perot interferometer filters. The observed line-width is ~10 times less than line-width of other demonstrated up to date random distributed feedback fiber lasers. The random DFB laser with Fabry-Perot interferometer filter provides simultaneously multi-wavelength and narrow-band (within each line) generation with possibility of further wavelength tuning.

Author Correction: Analysis of laser radiation using the Nonlinear Fourier transform.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Analysis of laser radiation using the Nonlinear Fourier transform.

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions.

Spectral correlations in a random distributed feedback fibre laser.

Random distributed feedback fibre lasers belong to the class of random lasers, where the feedback is provided by amplified Rayleigh scattering on sub-micron refractive index inhomogenities randomly distributed over the fibre length. Despite the elastic nature of Rayleigh scattering, the feedback mechanism has been insofar deemed incoherent, which corresponds to the commonly observed smooth generation spectra. Here, using a real-time spectral measurement technique based on a scanning Fabry-Pérot interferometer, we observe long-living narrowband components in the random fibre laser's spectrum. Statistical analysis of the ∼104 single-scan spectra reveals a preferential interspacing for the components and their anticorrelation in intensities. Furthermore, using mutual information analysis, we confirm the existence of nonlinear correlations between different parts of the random fibre laser spectra. The existence of such narrowband spectral components, together with their observed correlations, establishes a long-missing parallel between the fields of random fibre lasers and conventional random lasers.

Laminar-Turbulent Transition in Raman Fiber Lasers: A First Passage Statistics Based Analysis.

Loss of coherence with increasing excitation amplitudes and spatial size modulation is a fundamental problem in designing Raman fiber lasers. While it is known that ramping up laser pump power increases the amplitude of stochastic excitations, such higher energy inputs can also lead to a transition from a linearly stable coherent laminar regime to a non-desirable disordered turbulent state. This report presents a new statistical methodology, based on first passage statistics, that classifies lasing regimes in Raman fiber lasers, thereby leading to a fast and highly accurate identification of a strong instability leading to a laminar-turbulent phase transition through a self-consistently defined order parameter. The results have been consistent across a wide range of pump power values, heralding a breakthrough in the non-invasive analysis of fiber laser dynamics.

Real-time high-resolution heterodyne-based measurements of spectral dynamics in fibre lasers.

Conventional tools for measurement of laser spectra (e.g. optical spectrum analysers) capture data averaged over a considerable time period. However, the generation spectrum of many laser types may involve spectral dynamics whose relatively fast time scale is determined by their cavity round trip period, calling for instrumentation featuring both high temporal and spectral resolution. Such real-time spectral characterisation becomes particularly challenging if the laser pulses are long, or they have continuous or quasi-continuous wave radiation components. Here we combine optical heterodyning with a technique of spatio-temporal intensity measurements that allows the characterisation of such complex sources. Fast, round-trip-resolved spectral dynamics of cavity-based systems in real-time are obtained, with temporal resolution of one cavity round trip and frequency resolution defined by its inverse (85 ns and 24 MHz respectively are demonstrated). We also show how under certain conditions for quasi-continuous wave sources, the spectral resolution could be further increased by a factor of 100 by direct extraction of phase information from the heterodyned dynamics or by using double time scales within the spectrogram approach.