Optical Darboux Transformer.

The optical Darboux transformer for solitons is introduced as a photonic device that performs the Darboux transformation directly in the optical domain. This enables two major advances for optical signal processing based on the nonlinear Fourier transform: (i) the multiplexing of solitonic waveforms corresponding to different discrete eigenvalues of the Zakharov-Shabat system, and (ii) the selective filtering of an arbitrary number of individual solitons too. The optical Darboux transformer can be built using existing commercially available photonic technology components and constitutes a universal tool for signal processing, optical communications, optical rogue waves generation, and waveform shaping and control in the nonlinear Fourier domain.

Coexistence of gain-through-filtering and parametric instability in a fiber ring cavity.

We experimentally and numerically investigate the dynamics of a fiber ring cavity in which two different instability can be excited: gain-through-filtering and parametric instability. We demonstrate that they can be triggered individually or collectively depending on the two main control parameters offered by the cavity, namely the pump power and the cavity detuning. The experimental observations are in good agreement with numerical simulations.

Impact of pump pulse duration on modulation instability Kerr frequency combs in fiber Fabry-Pérot resonators.

We report an experimental investigation on the impact of the pump pulse duration on the modulation instability process in fiber Fabry-Pérot resonators. We demonstrate that cross-phase modulation between the forward and the backward waves alters significantly the modulation instability process. By varying the pump pulse duration, we show the modification of the modulation instability threshold and frequency. These experimental observations are in excellent agreement with theoretical predictions.

Parametric amplification based on intermodal four-wave mixing between different supermodes in coupled-core fibers.

Parametric amplifiers relying on the nonlinear four-wave mixing process are known for their signature symmetric gain spectrum, where signal and idler sidebands are generated on both sides of a powerful pump wave frequency. In this article we show analytically and numerically that parametric amplification in two identically coupled nonlinear waveguides can be designed in such a way that signals and idlers are naturally separated into two different supermodes, hence providing idler-free amplification for the supermode carrying signals. This phenomenon is based on the coupled-core fibers analogue of intermodal four wave-mixing occurring in a multimode fiber. The control parameter is the pump power asymmetry between the two waveguides, which leverages the frequency dependency of the coupling strength. Our findings pave the way for a novel class of parametric amplifiers and wavelength converters, based on coupled waveguides and dual-core fibers.

Observation of modulation instability Kerr frequency combs in a fiber Fabry-Pérot resonator.

We report the experimental observation of a modulation instability induced Kerr frequency comb in an all fiber Fabry-Pérot resonator. We fully characterized, in intensity and phase, the frequency comb using a commercial 10 MHz resolution heterodyne detection system to reveal more than 125 comb teeth within each of the modulation instability sidelobes. Moreover, we were able to reveal the fine temporal structure in phase and intensity of the output Turing patterns. The experimental results are generally in good agreement with numerical simulations.

Parametric amplification in lossy nonlinear waveguides with spatially dependent coupling.

We present an analytical and numerical study of optical parametric amplification in coupled waveguides amplifiers accounting for presence of losses and spatially dependent coupling. Spatially dependent coupling enables to compensate for mismatch dynamically arising from pump attenuation and to achieve improved performances in terms of bandwidth and bandwidth-gain product compared to standard single-waveguide solutions. Our results suggest the effective design of a novel class of parametric amplifiers and could be especially relevant for integrated silicon nitride devices.

Discrete light bullets in passively mode-locked semiconductor lasers.

In this paper, we analyze the formation and dynamical properties of discrete light bullets in an array of passively mode-locked lasers coupled via evanescent fields in a ring geometry. Using a generic model based upon a system of nearest-neighbor coupled Haus master equations, we show numerically the existence of discrete light bullets for different coupling strengths. In order to reduce the complexity of the analysis, we approximate the full problem by a reduced set of discrete equations governing the dynamics of the transverse profile of the discrete light bullets. This effective theory allows us to perform a detailed bifurcation analysis via path-continuation methods. In particular, we show the existence of multistable branches of discrete localized states, corresponding to different number of active elements in the array. These branches are either independent of each other or are organized into a snaking bifurcation diagram where the width of the discrete localized states grows via a process of successive increase and decrease of the gain. Mechanisms are revealed by which the snaking branches can be created and destroyed as a second parameter, e.g., the linewidth enhancement factor or the coupling strength is varied. For increasing couplings, the existence of moving bright and dark discrete localized states is also demonstrated.

Exact superregular breather solutions to the generalized nonlinear Schrödinger equation with nonhomogeneous coefficients and dissipative effects.

Superregular breathers are peculiar solutions to the integrable nonlinear Schrödinger equation that constitute the building blocks for analysis of the nonlinear stage of modulation instability developing from a localized perturbation on the nonvanishing condensate background. Here superregular breather solutions are extended to the generalized nonlinear Schrödinger equation with nonhomogeneous coefficients and in the presence of dissipation. Concrete examples are shown that may allow observation of new solutions in fiber optics where dissipation is unavoidable, nonhomogeneous spatial distribution of the amplification profile can be controlled, and current technology allows design of the longitudinal dispersion profile.

Coherent master equation for laser modelocking.

Modelocked lasers constitute the fundamental source of optically-coherent ultrashort-pulsed radiation, with huge impact in science and technology. Their modeling largely rests on the master equation (ME) approach introduced in 1975 by Hermann A. Haus. However, that description fails when the medium dynamics is fast and, ultimately, when light-matter quantum coherence is relevant. Here we set a rigorous and general ME framework, the coherent ME (CME), that overcomes both limitations. The CME predicts strong deviations from Haus ME, which we substantiate through an amplitude-modulated semiconductor laser experiment. Accounting for coherent effects, like the Risken-Nummedal-Graham-Haken multimode instability, we envisage the usefulness of the CME for describing self-modelocking and spontaneous frequency comb formation in quantum-cascade and quantum-dot lasers. Furthermore, the CME paves the way for exploiting the rich phenomenology of coherent effects in laser design, which has been hampered so far by the lack of a coherent ME formalism.

Gain-through-filtering enables tuneable frequency comb generation in passive optical resonators.

Optical frequency combs (OFCs), consisting of a set of phase-locked, equally spaced laser frequency lines, have enabled a great leap in precision spectroscopy and metrology since seminal works of Hänsch et al. Nowadays, OFCs are cornerstones of a wealth of further applications ranging from chemistry and biology to astrophysics and including molecular fingerprinting and light detection and ranging (LIDAR) systems, among others. Driven passive optical resonators constitute the ideal platform for OFC generation in terms of compactness and low energy footprint. We propose here a technique for the generation of OFCs with a tuneable repetition rate in externally driven optical resonators based on the gain-through-filtering process, a simple and elegant method, due to asymmetric spectral filtering on one side of the pump wave. We demonstrate a proof-of-concept experimental result in a fibre resonator, pioneering a new technique that does not require specific engineering of the resonator dispersion to generate frequency-agile OFCs.

All-optical pulse bursts generation from a nonlinear amplifying loop mirror.

A novel method for the generation of bursts of optical pulses is proposed. It is shown analytically that a nonlinear amplifying loop mirror in single pass configuration can transform a low power input pulse into a burst consisting of pulses with individual energy up to tens of nJ. The burst features; number of pulses; and their peak power, energy, and duration can be tuned and controlled. Numerical simulations show robustness of the technique to presence of Raman scattering and that sub-picosecond pulse duration can be achieved. The latter highlights the relevance of the proposed pulse bursts generator for material processing and in medical applications involving optical ablation.

Gain through losses in nonlinear optics.

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. These instabilities are at the heart of symmetry breaking, condensate dynamics, self-organisation, pattern formation, and noise amplification across diverse disciplines, including physics, chemistry, engineering, and biology. In nonlinear optics, modulation instabilities are generally linked to the so-called parametric amplification process, which occurs when certain phase-matching or quasi-phase-matching conditions are satisfied. In the present review article, we summarise the principle results on modulation instabilities and parametric amplification in nonlinear optics, with special emphasis on optical fibres. We then review state-of-the-art research about a peculiar class of modulation instabilities (MIs) and signal amplification processes induced by dissipation in nonlinear optical systems. Losses applied to certain parts of the spectrum counterintuitively lead to the exponential growth of the damped mode themselves, causing gain through losses. We discuss the concept of imaging of losses into gain, showing how to map a given spectral loss profile into a gain spectrum. We demonstrate with concrete examples that dissipation-induced MI, apart from being of fundamental theoretical interest, may pave the way towards the design of a new class of tuneable fibre-based optical amplifiers, optical parametric oscillators, frequency comb sources, and pulsed lasers.

High-repetition-rate, multi-pulse all-normal-dispersion fiber laser.

In this Letter, a fiber laser that exploits the dissipative Faraday instability as a pulse-generating mechanism is presented, and its dynamics are studied numerically. The proposed laser operates in the all-normal-dispersion regime and produces a train of quasi-parabolic pulses, with a repetition rate that can be controlled depending on the cavity dispersion and nonlinearity, ranging from 10 to 50 GHz. It exploits a lumped amplification scheme, which can be potentially realized with rare-earth gain media. The issues concerning the stability of the pulses are discussed, and the differences with similar pulsed lasers are highlighted. In particular, the transition from the ordered multi-pulse regime proposed here to the random pulse operation mode already studied in the literature is discussed.

Mode-locking via dissipative Faraday instability.

Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. There are several well-studied classical modulation instabilities, such as Benjamin-Feir, Turing and Faraday instability, which play a critical role in the self-organization of energy and matter in non-equilibrium physical, chemical and biological systems. Here we experimentally demonstrate the dissipative Faraday instability induced by spatially periodic zig-zag modulation of a dissipative parameter of the system-spectrally dependent losses-achieving generation of temporal patterns and high-harmonic mode-locking in a fibre laser. We demonstrate features of this instability that distinguish it from both the Benjamin-Feir and the purely dispersive Faraday instability. Our results open the possibilities for new designs of mode-locked lasers and can be extended to other fields of physics and engineering.