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Nonlinear Guided Wave OpticsA testbed for extreme waves

Nonlinear Guided Wave OpticsA testbed for extreme waves

Stefan Wabnitz, EditorUniversità di Brescia, Dipartimento di Ingegneria dell'Informazione, Brescia, Italy, andIstituto Nazionale di Ottica del CNR, Brescia, Italy, and Novosibirsk State University,

Novosibirsk, Russia

IOP Publishing, Bristol, UK

ª IOP Publishing Ltd 2017

All rights reserved. No part of this publication may be reproduced, stored in a retrieval systemor transmitted in any form or by any means, electronic, mechanical, photocopying, recordingor otherwise, without the prior permission of the publisher, or as expressly permitted by law orunder terms agreed with the appropriate rights organization. Multiple copying is permitted inaccordance with the terms of licences issued by the Copyright Licensing Agency, the CopyrightClearance Centre and other reproduction rights organisations.

Permission to make use of IOP Publishing content other than as set out above may be soughtat [email protected].

Stefan Wabnitz, Editor has asserted his right to be identified as the author of this work inaccordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.

ISBN 978-0-7503-1460-2 (ebook)ISBN 978-0-7503-1458-9 (print)ISBN 978-0-7503-1459-6 (mobi)

DOI 10.1088/978-0-7503-1460-2

Version: 20180101

IOP Expanding PhysicsISSN 2053-2563 (online)ISSN 2054-7315 (print)

British Library Cataloguing-in-Publication Data: A catalogue record for this book is availablefrom the British Library.

Published by IOP Publishing, wholly owned by The Institute of Physics, London

IOP Publishing, Temple Circus, Temple Way, Bristol, BS1 6HG, UK

US Office: IOP Publishing, Inc., 190 North Independence Mall West, Suite 601, Philadelphia,PA 19106, USA

To my wife Olga,and my children Mario and Sasha.

Contents

Preface xiv

Acknowledgments xix

Editor biography xx

List of contributors xxi

1 Extreme events in forced oscillatory media in zero,one and two dimensions

1-1

1.1 Introduction 1-1

1.2 Zero dimensions 1-2

1.3 One dimension 1-7

1.4 Two dimensions 1-18

1.5 Conclusion 1-25

Acknowledgments 1-26

References 1-26

2 Extreme waves in stimulated backscattering and frequencyconversion processes

2-1


2.2 Fundamental rogue wave solutions 2-2

2.3 Higher-order rogue wave solutions 2-8

2.4 Rogue wave solutions in the degenerate case 2-10

2.5 Rogue wave existence and baseband MI 2-13

2.6 Numerical simulations 2-14

2.7 Conclusions 2-15


References 2-16

3 Irreversibility and squeezing of shock waves 3-1


3.2 Hydrodynamic approximation of dispersive shock waves 3-2

3.3 Highly non-local limit and irreversibility 3-5

3.3.1 Highly nonlocal approximation 3-6

3.3.2 Irreversibility and Gamow vectors 3-7

3.3.3 The reversed harmonic oscillator 3-8

3.3.4 Gamow vector experiments 3-10

vii

3.4 Squeezing 3-13

3.4.1 Mathematical 3-13

3.4.2 Squeezing in nonlinear optics 3-15


References 3-17

4 Observation of the rupture of a photon dam in an optical fiber 4-1


4.2 Theory of classic and dispersive dam breaking 4-2

4.2.1 Hydrostatic dam breaking 4-5

4.2.2 Dispersive dam breaking 4-7

4.2.3 Self-cavitating or vacuum points 4-9

4.2.4 Classical versus dispersive shock waves 4-11

4.3 Experiment 4-12



References 4-17

5 Instabilities and extreme events in all-normal dispersionmode-locked fibre lasers

5-1


5.2 All-normal dispersion mode-locked fibre lasers 5-2

5.2.1 An environmentally stable design 5-4

5.3 Stable mode-locking 5-5

5.4 Noise-like emission 5-7

5.5 Real-time measurements and extreme Raman fluctuations 5-9

5.6 Soliton explosions 5-12

5.6.1 Temporal dynamics 5-15

5.7 Metastable dark solitons in radiation build-up dynamics 5-17


Acknowledgements 5-22

References 5-22

6 Extreme wave dynamics from incoherent dissipative solitonsin fiber laser cavities

6-1

6.1 Introduction: the notion of incoherent dissipative solitons 6-1

6.2 Dissipative rogue waves from chaotic pulse bunching 6-3

Nonlinear Guided Wave Optics

viii

6.2.1 Numerical modeling and investigations 6-4

6.2.2 Fiber laser experiments 6-8

6.2.3 Incoherent solitons around the 2-micron wavelength 6-11

6.3 Extreme vector waves 6-13

6.3.1 Fiber laser setup 6-13

6.3.2 Transient spectro-temporal ordering within incoherentdissipative solitons

6-14

6.3.3 Polarization-switching dynamics 6-15

6.3.4 Explosive dynamics and rogue waves 6-16



References 6-19

7 Ubiquitous nature of modulation instability: from periodic tolocalized perturbations

7-1


7.2 Breather formalism 7-3

7.3 Experimental demonstrations 7-9

7.4 Localized noise-driven modulation instability 7-14



References 7-18

8 Rogue waves in photorefractive media 8-1


8.2 Spatial rogue waves in photorefractive ferroelectrics 8-2

8.2.1 Observing optical extreme waves 8-3

8.2.2 Generalized NLSE framework 8-6

8.3 Optical instabilities and strong wave turbulence 8-7

8.3.1 Evidence of turbulent transitions in beam dynamics 8-8

8.3.2 Spectral and statistical evolution of the wave field 8-9

8.4 Incoherence, saturation, and solitons in extreme waves 8-11

8.4.1 Input wave disorder and extreme event generation 8-11

8.4.2 The characteristic scale of rogue waveforms 8-13

8.4.3 A soliton-based mechanism for the origin of rogue waves 8-15

8.5 Future developments 8-16

References 8-17


ix

9 Vector rogue waves driven by polarisation instabilities 9-1


9.2 Bright and dark rogue waves in mode-locked fibre laser 9-3

9.2.1 Experimental results 9-3

9.2.2 Theoretical results 9-5

9.3 Synchronisation and desynchronisation phenomena in a long cavityEr-doped fibre laser

9-9

9.3.1 Risken–Nummedal–Graham–Haken instability 9-9

9.3.2 Experimental data 9-10

9.3.3 Theoretical results 9-12

9.4 Summary 9-17

Annex I 9-17

Annex II 9-20


References 9-22

10 Fundamental rogue waves and their superpositions innonlinear integrable systems

10-1


10.2 NLSE rogue waves 10-2

10.3 Splitting of higher-order rogue waves 10-6

10.4 Extended equation 10-11

10.5 Integrable extensions 10-12

10.5.1 Rogue waves of the Hirota equation 10-13

10.5.2 Rogue waves of the Sasa–Satsuma equation 10-15

10.6 Infinitely long NLSE extensions 10-18



References 10-23

11 Are rogue waves really rogue? 11-1


11.2 Definition of rogue waves: predictability 11-1

11.3 Rogue waves in the multi-filament scenario 11-3

11.4 Comparison of the three different rogue wave supporting systems 11-6

11.5 Filament rogue waves 11-11

11.6 Predictability of rogue waves 11-12


x

11.7 Conclusion 11-17


References 11-18

12 Rogue waves in integrable turbulence: semi-classicaltheory and fast measurements

12-1


12.1.1 Deviations from Gaussian statistics and the appearanceof heavy tails

12-2

12.1.2 Weakly nonlinear theory 12-3

12.1.3 Integrable turbulence 12-5

12.2 Semi-classical limit of focusing 1D-NLSE and rogue waves 12-8

12.2.1 Focusing dispersive hydrodynamics and the formationof gradient catastrophe

12-8

12.2.2 Regularization of gradient catastrophe and the universalPeregrine soliton dynamics

12-10

12.2.3 Rogue wave formation via the interaction of modulatedwavetrains

12-12

12.3 Integrable turbulence and the inverse scattering transform method 12-13

12.3.1 A brief review of the application of the IST method to theanalysis of random wave fields

12-13

12.3.2 Regularization of gradient catastrophes in the focusingregime: local IST analysis

12-15

12.4 Experiments in optical fibers 12-17

12.4.1 Formulation of the problem 12-18

12.4.2 Observation of ultrafast random dynamics: time lensand time microscope

12-19

12.4.3 Universal regularization of gradient catastrophe: thegeneration of Peregrine solitons

12-25



References 12-27

13 Rogue wave formation in highly birefringent fiber 13-1


13.2 Model and linear stability analysis 13-3

13.3 Statistical analysis of the RW in the highly birefringent fiber 13-4

13.4 Results in the normal dispersion regime 13-5

13.4.1 Impact of the walk-off parameter 13-5


xi

13.4.2 Impact of the third-order dispersion 13-6

13.4.3 Interplay between the walk-off parameter and thethird-order dispersion

13-7

13.5 Results in a normal dispersion 13-9

13.5.1 Impact of the walk-off parameter 13-9

13.5.2 Impact of the third-order dispersion 13-9

13.5.3 Interplay between the walk-off and the third-order dispersion 13-11


References 13-12

14 Spatiotemporal nonlinear dynamics in multimode fibers 14-1


14.2 Spatial beam self-cleaning 14-2

14.2.1 Experiments in lossless fiber systems 14-3

14.2.2 Experiments in dissipative fiber systems 14-6

14.3 Theoretical models of spatiotemporal dynamics 14-9

14.3.1 Wave condensation and turbulence in a multimode fiber 14-9

14.4 Spatiotemporal instabilities 14-15

14.5 Supercontinuum generation 14-17

14.5.1 Second-harmonic generation in multimode fibers 14-20

14.5.2 Conclusions 14-21


References 14-21

15 Noise-initiated dynamics in nonlinear fiber optics 15-1


15.2 Modulation instability and breather solutions 15-1

15.3 Noise-driven modulation instability 15-7

15.4 Measuring chaotic dynamics in real time 15-9


References 15-18

16 Cavity soliton dynamics and rogue waves in drivenKerr cavities

16-1


16.2 Spatiotemporal chaos in Lugiato–Lefever model 16-2

16.3 Cavity soliton dynamics and rogue waves in the delayed LLE 16-7


xii

16.3.1 Impact of time-delayed feedback: a linear stabilty analysis 16-7

16.3.2 Drift of cavity solitons induced by delayed feedback 16-11

16.3.3 Two-dimensional dissipative rogue waves inLugiato–Lefever model

16-15



References 16-20


xiii

Preface

In spite of their presumed rarity, the occurrence of extreme events is today perceivedas an overhang that may suddenly affect each and every human life. Among extremeevents, we may classify wars, revolutions, epidemics, stock market crashes, tsuna-mis, earthquakes, hurricanes, giant rogue ocean waves, and even fatal events such asthe heart attack. Despite their disparate origins, perhaps all extreme events share onecommon feature: nobody could ever forecast them in advance. In hindsight, peoplequickly adjust to the occurrence of an extreme event, to the point of considering itinescapable. Another common characteristic of extreme events, is that their suddenand brief occurrence may lead to long term consequences, and often to paradigmshifts in human society.

If we want to develop any capability to forecast extreme events, it is necessary tobuild a theory that can be confronted with past observations. To this end, it would bevery interesting if one could exploit analogue physical systems where the fastacquisition of large amounts of data under well controlled conditions can be carriedout. The development of such a testbed can be based on the observation that manydifferent phenomena in physical and social sciences can be described in terms of thesame universal statistical distributions. These statistics are characterized by thepresence of extreme events, which are associated with the properties of the tail endsof the corresponding distributions. Consider for example hydrodynamics (turbulence,hurricanes, tsunamis), geosciences (earthquakes, floods, landslides), economics (finan-cial markets), social sciences (distributions of populations), medical sciences (neuronalavalanches, epileptic seizure), material failures, power grid and computer networks(black-outs) environment and climate sciences (forest fires, evolution and competitionof animal and plant species). There is an ongoing philosophical debate: should weconsider extreme events as essentially unpredictable, as out springs of the popularblack swan theory, a manifestation of self-organized criticality?

Such a viewpoint is inherently pessimistic: the lack of predictability ultimatelyentails a lack of accountability for scientists, who were unable to make any priorwarning about the occurrence of the extreme event. Fortunately, a new theory ofextreme events has been emerging over the past few years, that associates theirpresence with the generation of coherent wave structures, such as for examplenonlinear waves or solitons, which do not belong to the same population of randomlinear waves. The appearance of extreme events in the form of solitons is thensubject to their own ‘dragon-king’ kind of statistical distribution. The importantconsequence of this new point of view is that predictability of the occurrence of theextreme event, based on the observation of a suitable precursor, should indeed bepossible. This may entail the possibility of controlling, or even suppressing, theemergence of the extreme event, if the observation of precursors was able to triggera proper feedback signal.

To give an example, of great interest today is the study of the mechanism ofextreme or rogue waves in oceanography. In the regime of deep waters, theencounter with a rogue wave may destroy a ship. Whereas in the regime of shallow

xiv

waters, catastrophic damage may be produced by the on-shore arrival of a tsunami.The advance forecast of such an extreme wave could save many human lives, andhave great impact on our economies.

The scope of this book is to highlight the use of optical fiber and waveguideexperiments, where optical pulse propagation can be modelled by simple, and yetuniversal nonlinear evolution equations (e.g., the nonlinear Schrödinger equation(NLSE), the nonlinear shallow water equation (NLSWE), the Ginzburg–Landauequation (GLE), etc), as a simply accessible test bed for exploring, in a well-controlled manner, the dynamics of complex systems phenomena that exhibitextreme events. As we shall see throughout the sixteen chapters of this book,nonlinear guided wave optics provides a practical testbed for the accessible statisticalstudy of extreme event generation in the many diverse domains of science andtechnology.

A key advantage of the guided wave optics platform is the possibility ofcontrolling not only the boundary conditions for the excitation of extreme waves,but also the number of spatial dimensions involved in the temporal evolution of thewaves. Chapter 1 analyses precisely the role of spatial dimensions in the emergence,and statistics, of rogue wave phenomena in semiconductor lasers or optical para-metric oscillators in the presence of an external forcing. Some extreme wavephenomena, such as turbulent vortices, may only occur in the presence of twotransverse spatial dimensions.

The number of spatial dimensions is not the only means to control the degrees offreedom for extreme waves in nonlinear guided waves optics. Another importantpossibility is provided by the number of waves, or components of a vector wavesystem. Chapter 2 discusses the explicit analytic rogue wave solutions, and theirstability in the presence of noise, for the system of three coupled resonant waves,which describes stimulated Brillouin or transient Raman scattering in optical fibers,or parametric mixing in quadratic nonlinear waveguides.

Besides rogue waves, another important category of extreme waves where guidedwave optics has the capability of providing a controllable testbed are shock waves.Since their discovery by Ernst Mach 230 years ago, who observed a shock frontgenerated by the motion of a body traveling at supersonic speed, shock waves havebeen observed in many physical systems ranging from hydrodynamics to astrophy-sics, dispersive gas dynamics, plasma physics, granular systems, and Bose–Einsteincondensates. Chapter 3 introduces a new formalism, based on the so-called Gamowvectors, to describe shock wave dynamics in optical nonlocal nonlinear defocusingmedia. This approach permits establishing that optical shock waves are an intrinsi-cally time-irreversible phenomenon. Moreover, when considering the quantumnature of light, the new formalism is used to describe the spontaneous squeezingof a photon fluid in a nonlocal nonlinear medium, which may have importantapplications to optical metrology, and lead to analogies with quantum gravity.

In the limiting case where the highly nonlinear and instantaneous response of themedium dominates over the dispersive behavior, the hydrodynamic approximationcan be made, which reduces the description of shock wave generation in opticalfibers to the nonlinear shallow water regime of oceanography. Chapter 4 illustrates


xv

experiments where the water dynamics of dam-breaking are emulated by studyingthe temporal dynamics of an equivalent photon fluid, represented by a suitablyprepared optical waveform propagating in the normal dispersion regime of a shortpiece of optical fiber.

A particularly useful testbed for exploring complex rogue wave and extreme eventdynamics and their statistics is provided by fiber lasers. In these devices, dissipativetemporal light structures are spontaneously formed from quantum noise, and theircontinuous recirculation through the cavity permits the rapid collection of statisticaldata. Chapters 5 and 6 present an overview of the complex dynamics of extreme eventsand roguewaves occurring inmode-lockedfiber lasers. Forfiber lasers operating in thenormal dispersion regime, chapter 5 shows that stimulated Raman scattering maydisrupt stable laser emission, and lead to noise-like pulses with long-tailed statistics. Inthese lasers, transient ‘soliton explosions’ and rogue dark solitons may appear in thecavity field build-up phase. Moreover, chapter 6 reveals the emergence, in theanomalous dispersion regime of the cavity, of incoherent dissipative solitons. Theseconsist of chaotic soliton bunches mixed with noise-like pulses.

A crucial question arises: can rogue waves and extreme events be predicted beforetheir occurrence, and if yes, to what degree? Although such a formidable challengeremains to date largely unsolved, it is fundamental to unveil the conditions that maylead to rogue and extreme waves formation. The necessary, but not sufficient,condition for rogue wave formation is the instability, with respect to spatiotemporalmodulations, of the steady state wave pattern (e.g., a flat sea). Chapter 7 analyzesand compares the emergence of modulation instabilities in hydrodynamics and infiber optics, where the instabilities may be initiated by noise or by small coherentperturbations, and connects the presence of these instabilities with the formation ofgiant, isolated rogue waves.

Extreme events are often the result of wave dynamics in physical systemscharacterized by the simultaneous presence of disorder and nonlinearity. As anexample of such a testbed in the context of well controllable optical experiments,chapter 8 presents a statistical study of the extreme waves arising in a stronglyturbulent scenario of waves propagating in photorefractive ferroelectric crystals. Inthis context, experiments permit one to analyze the role of system dimensionalityand incoherence of the optical field in the appearance of extreme waves.

An important degree of freedom of light waves in optical fibers is provided bytheir state of polarization. Chapter 9 shows that the coherent coupling betweenpolarization components of a light pulse within a fiber laser may result in complexpolarization instabilities, which originate the formation of both bright and darkrogue pulses with the characteristic statistical properties of extreme waves.

Pulse propagation in the optical fiber testbed may be described with very goodaccuracy by means of a completely integrable (or exactly solvable) nonlinear waveevolution equation, the nonlinear Schrödinger equation. Chapter 10 takes advant-age of the integrability of the underlying wave propagation model, and presents awhole hierarchy of analytical solutions that can be associated with the emergence ofhigh intensity extreme peaks of light, which correspond to the class of rogue wavesolutions.


xvi

Coming back to the main question, concerning the predictability of rogue orextreme waves, it is very difficult to answer this question in many scenarios thatexhibit rogue waves, for example in oceanography, due to the scarcity of availabledata and measurements. But our fast data collection capabilities are stronglyenhanced when using the testbed of nonlinear and fiber optics. Chapter 11 addressesthe connection between rogue wave predictability and the presence of heavy tailstatistical distributions, in the frame of both unidimensional propagation in singlemode fibers, and multidimensional beam filamentation in water and gas cells. Acareful statistical analysis of these experiments permits one to conclude thatpredictability and the presence of heavy tails statistics are largely unrelated. Infact, predictability is associated with some degree of deterministic, althoughcomplex, behavior in the wave evolution. A small-scale degree of predictabilitycan be observed for ocean waves and for multiple filamentation events, whereas it islargely absent for fiber optics rogue pulses emerging in supercontinuum generationas a result of quantum noise fluctuations that initiate the nonlinear pulse dynamics.

The evolution of noisy waves in a physical system described by an integrablenonlinear wave equation leads to a phenomenology known as ‘integrable turbu-lence’. Chapter 12 presents theory and experiments that characterize the emergenceof rogue wave events in the evolution of light pulses propagating in optical fibers in aregime which is analogous to the shallow water regime of waves near a beach. In thiscontext, different fast measurement techniques have been used to resolve thetemporal dynamics of these waves.

The polarization degree of freedom can be exploited in the optical fiber testbedfor the generation of rogue waves also in the absence of an optical cavity. Chapter 13presents a numerical study of rogue wave events generated from initially noisy pulsesthat propagate in birefringent optical fibers either in the normal or the anomalousdispersion regime, and discusses the influence of the various fiber parameters tocontrol the properties of the statistical distribution of extreme events.

An emerging platform for the controlled study of complex spatiotemporalnonlinear wave dynamics is that of multimode optical fibers. By varying the numberof modes, which can be achieved simply by tuning the wavelength of the laser, onemay explore the whole range of dynamical behaviors ranging from the one-dimensional case of a single mode fiber, up to the limit case of nearly free spacepropagation with two transverse dimensions leading to filamentation phenomena.Chapter 14 describes recent experimental studies of the nonlinear wave dynamics inhighly multimode, passive and active optical fibers. This platform permits the studyof the emergence of extreme waves, in the form of stable nonlinear coherentattractors characterized by low-order transverse mode patterns.

The effect of initial random noise in driving the dynamics of rogue and extremewave processes is extensively investigated in chapter 15. Here, the quantum noiseseeding of modulation instability in optical fibers is shown to lead to a variety ofrogue waveforms, which can be very well approximated in terms of the analyticalrogue wave solutions that have been presented in chapter 10. Various ultrafastmeasurement techniques, similar to those employed in the studies of chapter 12,


xvii

have permitted capture in real-time of the dynamics of rogue waves emerging fromnoise-seeded modulation instability.

Another guided wave platform that has emerged over the past few years for thestudy of complex spatiotemporal optical wave dynamics is that of externally drivencavities and microcavities. The nonlinear response of such driven resonators leads tothe generation of optical frequency combs and cavity solitons, which may havewidespread use in the near future for optical communications and metrologyapplications. Chapter 16, the final chapter, analyzes dissipative rogue waveformation phenomena of different dimensionalities in both passive Kerr and active(semiconductor laser) cavities. The computation of the probability distribution ofpulse height shows that a rogue wave can be generated for moderate injected fieldintensities, which facilitates their experimental observation.

In summary, the content of this book provides an up-to-date overview of thecapabilities of the nonlinear guided optical wave platform for the study of extremewave phenomena and their statistics. The strength of this testbed mainly rests on thepossibility of precisely controlling the input conditions and the parameters of thephysical system, and on the availability of advanced data acquisition techniques thatpermit extensive and fast characterization of the statistical properties of the extremeevents distribution. It is our hope that these advances will foster progress in otherfields of science, technology and human activities at large, where the analysis andforecast of extreme events could have a tremendous role for the progress of thewealth and health of mankind.

The value of this book is testified by its impressive team of contributors,renowned scientists in the field of rogue and extreme nonlinear optical waves.Therefore, I would like to conclude by thanking all members of this team for sharingtheir time and effort in producing such a comprehensive manuscript in a timelymanner.

Stefan WabnitzNovosibirsk, Russian Federation, November 15, 2017


xviii

Acknowledgments

The Editor acknowledges support from the Ministry of Education and Science of theRussian Federation (Grant No. 14.Y26.31.0017).

xix

Editor biography

Stefan Wabnitz

Stefan Wabnitz obtained the Laurea Degree in ElectronicsEngineering from the University of Rome ‘La Sapienza’ in 1982,the MS in Electrical Engineering from Caltech in 1983, and thePhD in Applied Electromagnetism from the Italian Ministry ofEducation in 1988. He was with the Ugo Bordoni Foundationbetween 1985 and 1996. In 1996 he became full professor in Physicsat the University of Burgundy in Dijon, France. Between 1999 and

2003 he was with Alcatel Research and Innovation Labs in France and with XteraCommunications in Texas. Since 2007 he is full professor the Department ofInformation Engineering of the University of Brescia, Italy. His research activitiesinvolve nonlinear propagation effects in optical communications and informationprocessing devices. He is the author and co-author of over 700 international refereedpapers, conference presentations, and book chapters. He is the Deputy Editor ofElsevier Optical Fiber Technology, a Fellow member of the Optical Society ofAmerica, and senior member of IEEE-Photonics Society.

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List of contributors

N Akhmediev The Australian National University, Canberra, Australia

Adrian Ankiewicz The Australian National University, Canberra, Australia

Stéphane Barland Université de Nice, Sophia Antipolis, France

Fabio Baronio Istituto Nazionale di Ottica del CNR and Università di Brescia,Brescia, Italy

Alain Barthélemy Université de Limoges, Limoges, France

Maria Chiara Braidotti University of L’Aquila, L’Aquila, Italy

Massimo Brambilla CNR-IFN and Dipartimento di Fisica Interateneo Politecnicoe Università di Bari, Bari, Italy

Neil G R Broderick The University of Auckland, Auckland, New Zealand

A Chabchoub The University of Sydney, Sydney, Australia

Shihua Chen Southeast University, Nanjing, China

Marcel G Clerc Universidad de Chile, Santiago, Chile

Aurélien Coillet Université Bourgogne Franche-Comté, Dijon, France

Lorenzo Columbo CNR-IFN and Dipartimento di Fisica Interateneo Politecnicoe Università di Bari, Bari, Italy

Matteo Conforti Université de Lille, Lille, France

Claudio Conti University Sapienza, Rome, Italy

Vincent Couderc Université de Limoges, Limoges, France

S Coulibaly Université de Lille, Lille, France

Eugenio DelRe Università di Roma ‘La Sapienza’, Rome, Italy

Ayhan Demircan Leibniz Universität, Hannover Germany

L Drouzi Université de Lille, Lille, France

John M. Dudley Université Bourgogne Franche-Comté, Dijon, France

Pierre Ealczak Université de Nice, Sophia Antipolis, France

Gennady El Loughborough University, Loughborough, UK

Miro Erkintalo The University of Auckland, Auckland, New Zealand

Bruno Garbin Université de Nice, Sophia Antipolis, France

A Gelash Novosibirsk State University, Novosibirsk, Russia

Silvia Gentilini University Sapienza, Rome, Italy

xxi

Goëry Genty Tampere University of Technology, Tampere, Finland

Christopher J Gibson University of Strathclyde, Glasgow, UK

Massimo Giudici Université de Nice, Sophia Antipolis, France

Philippe Grelu Université Bourgogne Franche-Comté, Dijon, France

François Gustave Université de Nice, Sophia Antipolis, France

Saïd Hamdi Université Bourgogne Franche-Comté, Dijon, France

V Kalashnikov Vienna University of Technology, Vienna, Austria

H Kbashi Aston University, Birmingham, UK

Edmund J R Kelleher University of British Columbia, Vancouver, Canada, andDepartment of Physics, Imperial College London, London, UK

B Kibler Université Bourgogne Franche-Comté, Dijon, France

SV Kolpakov Aston University, Birmingham, UK

Katarzyna Krupa Università di Brescia, Brescia, Italy

Alexandre Kudlinski Université de Lille, Lille, France

K Laabidi Université Mohamed Premier, Oujda, Morocco

Giulia Marcucci University Sapienza, Rome, Italy

A Martinez Aston University, Birmingham, UK

Cristina Masoller Universitat Politècnica de Catalunya, Terrassa, Spain

Guy Millot Université Bourgogne Franche-Comté, Dijon, France

C Mou Aston University, Birmingham, UK

Arnaud Mussot Université de Lille, Lille, France

Mikko Närhi Tampere University of Technology, Tampere, Finland

K Nithyanandan Université Bourgogne Franche-Comte, Dijon, France

Miguel Onorato Università degli Studi di Torino, Torino, Italy

Gian-Luca Opo University of Strathclyde, Glasgow, UK

Krassimir Panajotov Vrije Universiteit Brussel, Brussels, Belgium and Institute ofSolid State Physics, Sofia, Bulgaria

Antonio Picozzi Université Bourgogne Franche-Comté, Dijon, France

Davide Pierangeli Università di Roma ‘La Sapienza’, Rome, Italy

Franco Prati Unversità dell’Insubria, Como, Italy

Stéphane Randoux Université de Lille, Villeneuve d’Ascq, France


xxii

Cristina Rimoldi Université de Nice, Sophia Antipolis, France

Roberto José Rios-Leite Universidade Federal de Pernambuco, Recife, Brazil

Antoine F J Runge University of Southampton, Southampton, UK

SV Sergeyev Aston University, Birmingham, UK

José Maria Soto-Crespo Consejo Superior de Investigaciones Cientcas (CSIC),Madrid, Spain

Günter Steinmeyer Max-Born-Institut, Berlin, Germany

Pierre Suret Université de Lille, Villeneuve d’Ascq, France

C G L Tiofack Université de Lille, Lille, France

Giovanna Tissoni Université de Nice, Sophia Antipolis, France

Mustapha Tlidi Université libre de Bruxelles, Brussels, Belgium

Shanti Toenger Tampere University of Technology, Tampere, Finland

Alessandro Tonello Université de Limoges, Limoges, France

Jorge R Tredicce Université de la Nouvelle Calédonie, Nouvelle Calédonie,France

Stefan Wabnitz Università di Brescia, Brescia, Italy and IstitutoNazionale di Ottica del CNR, Italy and Novosibirsk State University, Novosibirsk,Russia

Robert I Woodward Macquarie University, New South Wales, Australia

Gang Xu Université de Lille, Lille, France

Allison Yao University of Strathclyde, Glasgow, UK

VE Zakharov Novosibirsk State University, Novosibirsk, Russia and LebedevPhysical Institute, Russian Academy of Sciences, Moscow, Russia, and Universityof Arizona, Tucson, Arizona, USA

Jordi Zamora-Munt Universitat Politècnica de Catalunya, Terrassa, Spain


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