Theory of amplified dispersive Fourier transformation

Amplified dispersive Fourier transformation (ADFT) is a powerful technique that maps the spectrum of an optical pulse into a time-domain waveform using group-velocity dispersion (GVD) and simultaneously amplifies it in the optical domain. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector, greatly simplifying the system and, more importantly, enabling ultrafast real-time spectroscopic measurements. Here we present a theory of ADFT by deriving the general equation and spectral resolution for ADFT and studying the evolution of the pulse spectrum into time, the effect of GVD coefficients on ADFT, and the requirement for dispersion. This theory is expected to lend valuable insights into the process and implementation of ADFT. © 2009 The American Physical Society.published_or_final_versio

Theory of amplified dispersive Fourier transformation

Amplified dispersive Fourier transformation (ADFT) is a powerful technique that maps the spectrum of an optical pulse into a time-domain waveform using group-velocity dispersion (GVD) and simultaneously amplifies it in the optical domain. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector, greatly simplifying the system and, more importantly, enabling ultrafast real-time spectroscopic measurements. Here we present a theory of ADFT by deriving the general equation and spectral resolution for ADFT and studying the evolution of the pulse spectrum into time, the effect of GVD coefficients on ADFT, and the requirement for dispersion. This theory is expected to lend valuable insights into the process and implementation of ADFT. © 2009 The American Physical Society.published_or_final_versio

Observation of Kuznetsov-Ma soliton dynamics in optical fibre

The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation

The laminar-turbulent transition in a fibre laser

Studying the transition from a linearly stable coherent laminar state to a highly disordered state of turbulence is conceptually and technically challenging, and of great interest because all pipe and channel flows are of that type. In optics, understanding how a system loses coherence, as spatial size or the strength of excitation increases, is a fundamental problem of practical importance. Here, we report our studies of a fibre laser that operates in both laminar and turbulent regimes. We show that the laminar phase is analogous to a one-dimensional coherent condensate and the onset of turbulence is due to the loss of spatial coherence. Our investigations suggest that the laminar-turbulent transition in the laser is due to condensate destruction by clustering dark and grey solitons. This finding could prove valuable for the design of coherent optical devices as well as systems operating far from thermodynamic equilibrium

Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers

Formation of coherent structures and patterns from unstable uniform state or noise is a fundamental physical phenomenon that occurs in various areas of science ranging from biology to astrophysics. Understanding of the underlying mechanisms of such processes can both improve our general interdisciplinary knowledge about complex nonlinear systems and lead to new practical engineering techniques. Modern optics with its high precision measurements offers excellent test-beds for studying complex nonlinear dynamics, though capturing transient rapid formation of optical solitons is technically challenging. Here we unveil the build-up of dissipative soliton in mode-locked fibre lasers using dispersive Fourier transform to measure spectral dynamics and employing autocorrelation analysis to investigate temporal evolution. Numerical simulations corroborate experimental observations, and indicate an underlying universality in the pulse formation. Statistical analysis identifies correlations and dependencies during the build-up phase. Our study may open up possibilities for real-time observation of various nonlinear structures in photonic systems

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565

Single-shot compressed ultrafast photography at one hundred billion frames per second

The capture of transient scenes at high imaging speed has been long sought by photographers, with early examples being the well known recording in 1878 of a horse in motion and the 1887 photograph of a supersonic bullet. However, not until the late twentieth century were breakthroughs achieved in demonstrating ultrahigh-speed imaging (more than 10^5 frames per second). In particular, the introduction of electronic imaging sensors based on the charge-coupled device (CCD) or complementary metal–oxide–semiconductor (CMOS) technology revolutionized high-speed photography, enabling acquisition rates of up to 10^7 frames per second. Despite these sensors’ widespread impact, further increasing frame rates using CCD or CMOS technology is fundamentally limited by their on-chip storage and electronic readout speed. Here we demonstrate a two-dimensional dynamic imaging technique, compressed ultrafast photography (CUP), which can capture non-repetitive time-evolving events at up to 10^(11) frames per second. Compared with existing ultrafast imaging techniques, CUP has the prominent advantage of measuring an x–y–t (x, y, spatial coordinates; t, time) scene with a single camera snapshot, thereby allowing observation of transient events with temporal resolution as tens of picoseconds. Furthermore, akin to traditional photography, CUP is receive-only, and so does not need the specialized active illumination required by other single-shot ultrafast imagers. As a result, CUP can image a variety of luminescent—such as fluorescent or bioluminescent—objects. Using CUP, we visualize four fundamental physical phenomena with single laser shots only: laser pulse reflection and refraction, photon racing in two media, and faster-than-light propagation of non-information (that is, motion that appears faster than the speed of light but cannot convey information). Given CUP’s capability, we expect it to find widespread applications in both fundamental and applied sciences, including biomedical research

Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers

Physical systems with co-existence and interplay of processes featuring distinct spatio-temporal scales are found in various research areas ranging from studies of brain activity to astrophysics. The complexity of such systems makes their theoretical and experimental analysis technically and conceptually challenging. Here, we discovered that while radiation of partially mode-locked fibre lasers is stochastic and intermittent on a short time scale, it exhibits non-trivial periodicity and long-scale correlations over slow evolution from one round-trip to another. A new technique for evolution mapping of intensity autocorrelation function has enabled us to reveal a variety of localized spatio-temporal structures and to experimentally study their symbiotic co-existence with stochastic radiation. Real-time characterization of dynamical spatio-temporal regimes of laser operation is set to bring new insights into rich underlying nonlinear physics of practical active- and passive-cavity photonic systems

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