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

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

Nonlinear effects in synthetic frequency dimension created by electro-optical modulation of a ring resonator

We numerically investigate the nonlinear dynamics of an optical resonator with electro-optical modulation. In this system we discover chimera states and their transition into new stable states with increasing modulation amplitude. Bifurcation analysis reveals that different parts of the ring might appear at mono- or bi-stable branches, which leads to soliton formation at particular positions inside the cavity, and even to coexistence of chimera states and solitons

Localization in disordered potential in photonic lattice realized in time domain

We describe theoretically and realize experimentally Anderson localization for optical pulses in time domain, using a photonic mesh lattice with random phase modulation implemented with coupled optical fiber loops. We demonstrate that strongest degree of localization is limited and increases in lattices with wider band-gaps.This work is supported by the Russian Science Foundation (16-12-10402). A.A.S. acknowledges support by the Australian Research Council (ARC) (DP160100619

Deriving eigenmode excitation spectrum of synthetic photonic lattices by means of optical heterodyning

A method based on optical heterodyning is proposed for measuring relative optical phases of pulses circulating in synthetic photonic lattices (SPL). The knowledge of the phases can be further used for qualitative reconstruction of an eigenmode excitation spectrum in the SPL.The authors acknowledge the financial support of Russian Science Foundation (grant 16-12-10402)

Universal peregrine soliton structure in optical fibre soliton compression

International audienceSummary form only given. Following its first observation in optics in 2010, the Peregrine soliton (PS) is now recognized as one of the seminal solutions of the nonlinear Schrödinger equation (NLSE) [1]. Although it is widely believed that the PS is uniquely associated with the process of plane wave modulation instability (MI), recent theory has shown that it actually appears more generally as a universal localized structure emerging during high power nonlinear pulse propagation [2]. Some evidence for this has already been seen in partially coherent nonlinear propagation in optical fibers [3], but in this paper, we use frequency-resolved optical gating to fully characterize an evolving high-order optical soliton around the first point of compression, and quantitatively confirm theoretical predictions that the properties of the compressed pulse and pedestal can indeed be interpreted in terms of the PS solution

Dissipative Kerr solitons in a photonic dimer

We study nonlinear dynamics emerging in a photonic microring dimer. It is shown that four wave mixing pathways between the dimer supermodes lead to novel nonlinear phenomena going beyond the single resonator physics. (C) 2020 The Author(s