Inverse four-wave mixing and self-parametric amplification in optical fibre

An important group of nonlinear processes in optical fibre involve the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and those arising from self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect—self-parametric amplification—which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. Self-parametric amplification and the observed stable nonlinear spectral propagation with a random temporal waveform can find applications in optical communications and high-power fibre lasers with nonlinear intracavity dynamics.

New nonlinear regimes of pulse generation in mode- locked fiber lasers

Mode-locked fiber lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes. The complex interplay among the effects of gain/loss, dispersion and nonlinearity in a fiber cavity can be used to shape the pulses and manipulate and control the light dynamics and, hence, lead to different mode-locking regimes. Major steps forward in pulse energy and peak power performance of passively mode-locked fiber lasers have been made with the recent discovery of new nonlinear regimes of pulse generation, namely, dissipative solitons in all-normal-dispersion cavities and parabolic self-similar pulses (similaritons) in passive and active fibers. Despite substantial research in this field, qualitatively new phenomena are still being discovered. In this talk, we review recent progress in the research on nonlinear mechanisms of pulse generation in passively mode-locked fiber lasers. These include similariton mode-locking, a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on the possibility of achieving various regimes of advanced temporal waveform generation in a mode-locked fiber laser by inclusion of a spectral filter into the laser cavity.

Design rules for nonlinear spectral compression in optical fibers

We present comprehensive design rules to optimize the process of spectral compression arising from nonlinear pulse propagation in an optical fiber. Extensive numerical simulations are used to predict the performance characteristics of the process as well as to identify the optimal operational conditions within the space of system parameters. It is shown that the group velocity dispersion of the fiber is not detrimental and, in fact, helps achieve optimum compression. We also demonstrate that near-transform-limited rectangular and parabolic pulses can be generated in the region of optimum compression.

Control of the in-cavity dynamics in mode-locked fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral intensity profile, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this talk, we review our recent progress on the realisation of different regimes of pulse generation in passively mode-locked fibre lasers through control of the in-cavity propagation dynamics. We report on the possibility to achieve both parabolic self-similar and triangular pulse shaping in a mode-locked fibre laser via adjustment of the net normal dispersion and integrated gain of the cavity [1]. We also show that careful control of the gain/loss parameters of a net-normal dispersion laser cavity provides the means of achieving switching among Gaussian pulse, dissipative soliton and similariton pulse solutions in the cavity [2,3]. Furthermore, we report on our recent theoretical and experimental studies of pulse shaping by inclusion of an amplitude and phase spectral filter into the cavity of a laser. We numerically demonstrate that a mode-locked fibre laser can operate in dif- ferent pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [4]. An application of technique using a flat-top spectral filter is demonstrated to achieve the direct generation of sinc-shaped optical Nyquist pulses of high quality and of a widely tuneable bandwidth from the laser [5]. We also report on a recently-developed versa- tile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soli- ton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [6]. References: 1. S. Boscolo and S. K. Turitsyn, Phys. Rev. A 85, 043811 (2012). 2. J. Peng et al., Phys. Rev. A 86, 033808 (2012). 3. J. Peng, Opt. Express 24, 3046-3054 (2016). 4. S. Boscolo, C. Finot, H. Karakuzu, and P. Petropoulos, Opt. Lett. 39, 438-441 (2014). 5. S. Boscolo, C. Finot, and S. K. Turitsyn, IEEE Photon. J. 7, 7802008 (2015). 6. J. Peng and S. Boscolo, Sci. Rep. 6, 25995 (2016).

Enhanced spectral compression in nonlinear optical fibres

We propose two new approaches to enhance the spectral compression process arising from nonlinear pulse propagation in an optical fibre. We numerically show that an additional sinusoidal temporal phase modulation of the pulse enables efficient reduction of the intensity level of side lobes in the spectrum. Another strategy is to select a regime of propagation in which normal group-velocity dispersion reshapes the initial stretched pulse to a near-Fourier-transform-limited rectangular waveform.

Enhanced nonlinear spectral compression in fiber by external sinusoidal phase modulation

We propose a new, simple approach to enhance the spectral compression process arising from nonlinear pulse propagation in an optical fiber. We numerically show that an additional sinusoidal temporal phase modulation of the pulse enables efficient reduction of the intensity level of the side lobes in the spectrum that are produced by the mismatch between the initial linear negative chirp of the pulse and the self-phase modulation-induced nonlinear positive chirp. Remarkable increase of both the extent of spectrum narrowing and the quality of the compressed spectrum is afforded by the proposed approach across a wide range of experimentally accessible parameters.

Enhanced nonlinear spectral compression in fibre by sinusoidal phase modulation

We propose a simple approach to enhance the spectral compression arising from nonlinear pulse propagation in a Kerr medium. We numerically show that an additional sinusoidal temporal phase modulation enables efficient reduction of the intensity level of spectral side lobes.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

Statistics of three interacting optical solitons

We examine the statistics of three interacting optical solitons under the effects of amplifier noise and filtering. We derive rigorously the Fokker-Planck equation that governs the probability distribution of soliton parameters.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

Statistics of three interacting optical solitons

We examine the statistics of three interacting optical solitons under the effects of amplifier noise and filtering. We derive rigorously the Fokker-Planck equation that governs the probability distribution of soliton parameters.

Stochasticity and coherent structures in ultra-long mode-locked lasers

Ultra-long mode-locked lasers are known to be strongly influenced by nonlinear interactions in long cavities that results in noise-like stochastic pulses. Here, by using an advanced technique of real-time measurements of both temporal and spatial (over round-trips) intensity evolution, we reveal an existence of wide range of generation regimes. Different kinds of coherent structures including dark and grey solitons and rogue-like bright coherent structures are observed as well as interaction between them are revealed.

Coherent propagation and energy transfer in low-dimension nonlinear arrays

We present a theory of coherent propagation and energy or power transfer in a low-dimension array of coupled nonlinear waveguides. It is demonstrated that in the array with nonequal cores (e.g., with the central core) stable steady-state coherent multicore propagation is possible only in the nonlinear regime, with a power-controlled phase matching. The developed theory of energy or power transfer in nonlinear discrete systems is rather generic and has a range of potential applications including both high-power fiber lasers and ultrahigh-capacity optical communication systems. © 2012 American Physical Society.

Experimental observation of autosoliton propagation in a dispersion-managed system guided by nonlinear optical loop mirrors

Observation of autosoliton propagation in a dispersion-managed optical transmission system controlled by in-line nonlinear fiber loop switches is reported for what is believed to be the first time. The system is based on a strong dispersion map with large amplifier spacing. Operation at transmission rates of 10 and 40 Gbits/s is demonstrated. ©2004 Optical Society of America.

Picosecond soliton propagation using nonlinear optical loop mirrors as intensity filters

The authors show that by inserting nonlinear optical loop mirrors into an optical fibre transmission line, 1.5 ps solitons may be transmitted over at least 750 km, with amplifiers spaced at 15 km intervals.