Instabilities, pattern formation, localized solutions, mode-locking and stochastic effects in nonlinear optical systems and beyond

In this thesis the results of scientific research about dierent nonlinear phenomena with particular emphasis to photonic systems are presented. Works about dissipation induced modulation instabilities with applications for signal amplification in nonlinear optics and mode-locking in lasers constitute the main part of the thesis. The dissipa-tive instabilities studied are of two kinds, parametric instabilities induced by a periodic variation of spectral losses and instabilities induced by non varying but spectrally asym-metric losses. Although the main achievements are theoretical successful collaboration with experimentalists are reported too. Other results presented in this thesis concern a new fundamental theory of active mode-locking in lasers having a more general validity than Haus’ one and hence useful for describing mode-locked lasers with a fast gain dynamics such as semiconductor or quantum cascade lasers; the prediction of the novel theoretical model have been successfully compared with experimental findings. Theo-retical studies are also presented about collective phenomena, such as synchronization and localization, in coupled excitable lasers with saturable absorber and localized so-lutions on the non-vanishing background of the two-dimensional nonlinear Schr¨odinger equation with periodic potential: the Bogoliubov-de Gennes bullets

Optical Darboux Transformer

The Optical Darboux Transformer is introduced as a photonic device which performs the Darboux transformation directly in the optical domain. This enables two major advances for signal processing based on the nonlinear Fourier transform: (i) the multiplexing of different solitonic waveforms corresponding to arbitrary number of discrete eigenvalues of the Zakharov-Shabat system in the optical domain, 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

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

Collective dynamics of evanescently coupled excitable lasers with saturable absorber

We present a numerical study of the collective dynamics in a population of coupled excitable lasers with saturable absorber. At variance with previous studies where real-valued (lossy) coupling was considered, we focus here on the purely imaginary coupling (evanescent wave coupling). We show that evanescently coupled excitable lasers exhibit synchronization like the lossy coupled ones. Furthermore, we show that out-of-diagonal disorder-induced localization of excitability takes place for imaginary coupling too, but it can be frustrated by nonvanishing linewidth enhancement factor. Graphical abstract: [Figure not available: see fulltext.]

Array-enhanced synchronization and coherence resonance in coupled excitable semiconductor lasers

Summary form only given. We present a numerical study of the nonlinear dynamics of a population of coupled semiconductor lasers with saturable absorber operating in the excitable regime [1] and described by a set of coupled Yamada models [2]. In particular we have investigated the self-organized synchronization process taking place spontaneously among the lasers, showing significant correlations between the spike-like pulses emitted by different lasers. Our findings demonstrate that synchronization in time and also in intensity occurs in a large region of the parameter space and for different population sizes and furthermore it is robust with respect to random distribution of the lasers' pump parameter which is linked to the excitability threshol

Raman polarizer based on a fiber with a random birefringence

Summary form only given. Raman polarizers are devices able to amplify and simultaneously repolarize optical signals, exploiting the polarization attraction phenomenon induced by the Raman gain anisotropy [1, 2]. To characterize the degree of polarization (DOP) of the signal as a function of the Raman gain (G) in the case of the co-propagating pump and signal pulses, the following formula for ideal Raman polarizer has been recently derived [1]: DOP = 1 - G-1.Detailed experimental study demonstrated the limited validity of this formula in the context of the missed DOP dependence on polarization mode dispersion (PMD) parameter Dp and the random birefringence correlation length Lc [3,4]. Here for the first time we develop a new model of a Raman polarizer that matches the experimental data by accounting for a fiber random birefringence properties in terms of parameters Dp and Lc. Based on our previous model of a fiber Raman amplifier [3,4] utilizing rigorous technique of averaging over the random birefringence of fiber in the case of negligible pump depletion, we derive the following equations for DOP as function of G, Dp and Lc

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

Dissipation Induced Modulation Instability: New Applications for Frequency Combs and Pulses Generation

We present a new technique based on a dissipation induced modulation instability, caused by unbalanced spectral dissipation for signal and idler waves, with applications in amplifiers and parametric oscillators but especially for frequency combs and pulses generation in fiber resonators

Experimental Demonstration of Dual Polarization Nonlinear Frequency Division Multiplexed Optical Transmission System

Multi-eigenvalues transmission with information encoded simultaneously in both orthogonal polarizations is experimentally demonstrated. Performance below the HD-FEC limit is demonstrated for 8-bits/symbol 1-GBd signals after transmission up to 207 km of SSMF

Amplification through losses in nonlinear fiber optics

We present the most recent results about a novel modulation instability of a continuous light wave in a normal dispersion nonlinear optical fiber, induced by spectrally asymmetric losses for signal and idler waves. The presence of such spectrally asymmetric losses profile causes energy transfer from the pump to both signal and idler. A variety of applications concerning both amplification of signals and generation of pulses is discussed