This is the first of a planned series of three workshops, organized with
support from an International collaborative research grant from the
Swedish Research Council, within the Swedish Research Links programme.
An overall main scientific purpose of the project is to develop and understand
novel ways to use nonlinear effects for controlling light signals in
all-optical devices. We are here particularly focusing on the roles of
nonlinear localization and dynamical instabilities for the possibility to
achieve coherent transport of localized light beams in photonic lattices,
such as arrays of coupled waveguides. However, the topic has a highly
interdisciplinary character, as similar phenomena may arise in widely
different contexts, for example with coupled Bose-Einstein condensates.
The project is a collaboration with scientists from the Vinča Institute
of Nuclear Sciences, Belgrade, and Universidad de Chile, Santiago. The
workshop will bring together scientists from these institutions working
with theoretical, numerical and experimental approaches, as well as few
external speakers. Future workshops are planned to be held in Santiago
Petra Beličev, Belgrade
Simone Borlenghi Garoia, Stockholm/Uppsala
Goran Gligorić, Belgrade
Peter Jason, Linköping
Magnus Johansson, Linköping
Aleksandra Maluckov, Belgrade
Alejandro Martínez, Oxford
Cristian Mejía-Cortés, Santiago
Mario Molina, Santiago
Uta Naether, Zaragoza
Ana Radosavljević, Belgrade
Milutin Stepić, Belgrade
Rodrigo Vicencio, Santiago
Attending the talks is free. However, for logistic reasons, please
email the organiser if you wish
to attend some talk(s) and are not already invited.
(may be subject to changes with short notice) Wednesday 6 August
12.45 Lunch + discussions
15.30 Coffee/tea + discussions
16.50 Radosavljević Thursday 7 August
11.50 Borlenghi Garoia
13.10 Lunch + discussions
15.40 Coffee/tea + discussions
Titles and abstracts
Petra P. Beličev: Modelling and spectral properties of optical fiber long-period grating sensors
Fiber optic long-period gratings (LPGs) are the subject of current research and are of great interest due to their wide application. In general, they consist of small periodic changes in the refractive index or geometry of a fiber which provides the coupling between the fiber modes in the copropagating direction. The period of LPGs is typically in the range 100μm to 1mm. In addition to filters, these devices can be used as sensors for measuring different physical parameters due to the fact that their transmission spectrum depends on the optical properties of the cladding and the surrounding environment in which the fiber and grating are placed. Thus, LPGs have been applied as sensors for detecting bending, stretching, changes in temperature or a change in the refractive index of the surrounding. The sensitivity of the sensor on a particular measurand (temperature, bending, stretching, refractive index of the environment) is different for each resonant line because it depends on the composition of the fiber, as well as on the order of the coupled cladding mode.
Motivated by the use of LPG as a sensor for measuring the curvature caused by physiological pulsations relevant to respiratory and cardiac physical functions, I will present the procedure of modeling LPG inscribed in a single mode fiber. By solving the wave equation for the given system and applying the phase matching condition, as well as the coupled mode theory for guided fiber modes, the transmission spectrum of the lattice will be determined. The impact of changes in the refractive index modulation, length and the period of the grating on the position of resonant wavelengths will be demonstrated, too. In addition, it will be shown how the bending of the grating influences the change in the positions and shape of resonant lines within the spectrum.
Simone Borlenghi Garoia: Spin dynamics far from thermal equilibrium: a new playground for the DNLS
The discovery of the spin-Seebeck effect (SSE) in 2008, according to which a thermal gradient in a magnetic material generates a spin
current, has attracted a lot of attention for its potential application in novel energy-harvesting thermoelectric devices. Despite six years of intense investigation, many aspects of the SSE are not yet understood. In my talk I will describe some recent developments on the theory of the SSE obtained by numerical simulations. In quasi one-dimensional magnetic insulators (spin chains) driven out of equilibrium by a thermal gradient, the propagation of the spin current can be described as the flow of energy and particle current in an off-equilibrium discrete nonlinear Schroedinger equation (DNLS). I will focus on a system where the spins oscillate with different frequencies, which is driven out of equilibrium applying simultaneously a thermal gradient and an external radio frequency (rf) field. Increasing the rf field, the system undergoes a dynamical phase transition from a desynchronised to a synchronised regime. In this transition, the spin current generated by the thermal gradient changes dramatically, while localised energy states appear. Possible mechanisms for the localisation will be discussed.
Goran Gligorić: High- and low-frequency modes in dipolar Bose-Einstein condensates trapped in deep optical lattices
The formation of denisity-wave patterns and the propagation of collective excitation in periodically structured media are fundamental physical effects in condensed-matter physics [1,2]. Many of these condensed media, with very complex intristic dynamics, may be effectely "simulated" by Bose-Einstein condensates (BECs) trapped in optical lattices [3,4].
Here we study normal modes propagating on top of the stable uniform background in arrays of dipolar BEC droplets trapped in a deep optical lattice, taking into account the on-site mean-field dynamics of the droplets and their displacement due to the repulsive nonlocal dipole-dipole interactions . We derive analytically dipersion relations for two modes, high- and low-frequency counterparts of optical and acustic phonon modes in condesed matter, and verify them by direct simulations. We find that the optical-phonon branch exist only in the presence of dipole-dipole interactions.
The obtained results are relevant in the connection to emerging experimenatl techniques enabling real-time imaging of condensate dynamics and direct experimental measurment of phonon dipersion realtions in BECs.
 R. E. Peierls, Quantum Theory of Solids, Oxford University Press, London, 1955.
 P. A. Lee, T. M. Rice, and P. W. Anderson, Solid state Commun. 14, 703 (1974).
 D. Jaksch and P. Zoller, Ann. Phys. 315, 52 (2005).
 A. Maluckov, G. Gligorić, Lj. Hadžievski, B. A. Malomed, and T. Pfau, Phys. Rev. Lett. 108, 140402 (2012).
 A. Maluckov, G. Gligorić, Lj. Hadžievski, B. A. Malomed, and T. Pfau, Phys. Rev. A 87, 023623 (2013).
Peter Jason: Existence, dynamics and mobility of Quantum Compactons in an
extended Bose-Hubbard model
Lattice Compactons, discrete breathers with compact support, were found for a discrete nonlinear Schrödinger (DNLS) equation extended with nearest neighbour intersite nonlinearities , a model originally studied with waveguide arrays in mind. These compactons were shown to exhibit very good mobility if the parameters are tuned close to the compactons stability boundary. The DNLS can also be used to model the behaviour of Bose-Einstein condensates in optical lattices, and the remarkable control over the experiments in this field of research has made it possible to study the quantum mechanics of strongly correlated atoms.
We will define the concept of a Quantum Lattice Compacton  and discuss the existence and dynamics, with special emphasis on mobility , of these in an extended Bose-Hubbard model corresponding to above-mentioned extended DNLS equation in the quantum mechanical limit.
The compactons is given 'a kick' by means of a phase-gradient and it is shown that the size of this phase is crucial for the mobility of the compactons. For small phase-gradients, corresponding to a slow coherent motion in the classical model, the time-scales of the quantum tunnelings become of the same
order as the time-scale of the translational motion and the classical mobility is destroyed by quantum fluctuations. For large phase-gradients, corresponding to rapid classical motion, the classical and quantum time-scales separate so that a mobile, localized coherent quantum state can be translated many sites in the lattice already for small particle numbers of the order of 10 .
Acknowledgements: This project has been financed by the Swedish Research Council.
 M. Öster, M. Johansson, and A. Eriksson 2003 Phys. Rev. E
 P. Jason and M. Johansson 2012 Phys. Rev. A 85 011603(R)
 P. Jason and M. Johansson 2013 Phys. Rev. A 88 033605
Magnus Johansson: Breather mobility and the PN potential -
Brief review and recent progress
The question whether a nonlinear localized mode (discrete soliton/breather)
can be mobile in a lattice has a standard interpretation in terms of the
Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier
for strongly localized solutions becomes large, rendering these essentially immobile.
Several ways to improve the mobility by reducing the PN-barrier have been
proposed during the last decade, and the first part gives a brief review of such scenarios
in 1D and 2D. We then proceed to discuss two recently discovered novel
mobility scenarios. The first example is the 2D Kagome lattice, where the existence
of a highly degenerate, flat linear band allows for a very small PN-barrier and mobility
of highly localized modes in a small-power regime. The second example is a 1D
waveguide array in an active medium with intrinsic (saturable) gain and damping,
where exponentially localized, travelling discrete dissipative solitons may exist as
Aleksandra Maluckov: Optical vortices as coherent energy carriers in multicore fibers
Vortex structures are widespread in nature, from macroscopic atmospheric phenomena, such as e.g. tornadoes and the Great Red Spot of Jupiter to microscopic scale objects in quantum physics .
Optical vortices are characterized by the wave field with zero intensity, undefined phase in the vortex center and the presence of a screw dislocation of the wave front . All transmutations of vortices in linear and nonlinear fields obey the conservation of topological charge that is defined as the total change of the phase along a closed curve surrounding the pivotal point of the vortex divided by 2π. Therefore, vortices are able to carry the orbital angular momentum and energy .
Here, we present a new possibility for coherent transfer of high optical power through the nonlinear multicore fibers by discrete optical vortices with certain phase profiles and defined number of peripheral cores . This finding is of particular interest for design the new type of switches, spatial-division-multiplexing fiber structures, sources of high brightness coherent radiation or uniform incoherent sources.
 L. M. Pismen, Vortices in Nonlinear Fields, International Series of Monographs in Physics 100 (Oxford Science Publications, 1999).
 A. Desyatnikov, Yu. Kivshar, and L. Torner, Prog, Opt. 47, 291 (2005).
 Lj. Hadžievski, A. Maluckov, S. Turitsyn, A. M. Rubenchik, submitted to PRA.
Alejandro Martínez: Transport and localization in disordered granular crystals
We study spreading processes of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which is fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated
(Anderson-like) disorder and two types correlated disorders (which are produced by random dimer arrangements). For an Anderson-like uncorrelated disorder, we find a transition from subdiffusive to superdiffusive dynamics that depends on the amount of precompression in the chain. By contrast, for the correlated disorders, we find that the dynamics is superdiffusive for any procompression level. For all three types of disorder, we find for large precompression that the inverse participation ratio saturates even when the second moment grows in time, which is a consequence of a partial localization near the initial wave. This localization phenomenon does not occur in the sonic vacuum regime, which yields the surprising result that spontaneous localization is no longer possible in this regime.
Mobility of solitons in the cubic-quintic DNLSE
We investigate mobility regimes for localized modes in the discrete nonlinear Schrödinger (DNLS) equation with the cubic-quintic onsite terms. Using the variational approximation (VA), the largest soliton's total power admitting progressive motion of kicked discrete solitons is predicted, by comparing the effective kinetic energy with the respective Peierls-Nabarro (PN) potential barrier. The prediction is novel for the DNLS model with the cubic-only nonlinearity too, demonstrating a reasonable agreement with numerical findings. Small self-focusing quintic term quickly suppresses the mobility. In the case of the competition between the cubic self-focusing and quintic self-defocusing terms, we identify parameter regions where odd and even fundamental modes exchange their stability, involving intermediate asymmetric modes. In this case, stable solitons can be set in motion by kicking, so as to let them pass the PN barrier. Unstable solitons spontaneously start oscillatory or progressive motion, if they are located, respectively, below or above a mobility threshold. Collisions between moving discrete solitons, at the competing nonlinearities frame, are studied too
Mario Molina: PT-symmetry and embedded modes in the continuum for magnetic metamaterials
First, we examine the PT-symmetry breaking transition for a magnetic metamaterial of a finite extent, modeled as an array of coupled split-ring resonators in the equivalent circuit model approximation. Small-size arrays are solved completely in closed form, while for arrays larger than N = 5 results were computed numerically for several gain/loss spatial distributions. In all cases, it is found that the parameter stability window decreases rapidly with the size of the array, until at N = 20 approximately, it is not possible to support a stable PT-symmetric phase. A simple explanation of this behavior is given. Next, we consider the problem of building a surface localized mode embedded in the continuous band of a semi-infinite one- dimensional array of split-ring resonators. We suggest an efficient method for creating such surface mode and the local bounded potential necessary to support this mode.
Uta Naether: Localization in Bose Hubbard chains with dissipation and gain
The semi-classical and quantum dynamics of open Bose-Hubbard chains may be treated using approximations based on different orders of correlation functions. If only dissipation is considered, any localized state is predetermined to decay. Including also gain, we are able to recover stationary and dynamically stable localized states as well as a localized oscillating solution type within these approximations. Furthermore, we find a new type of long-range correlated extended nonlinear mode.
Ana Radosavljević: Towards all optical light beam propagation control along one dimensional photonic lattices
Photonic lattices (PLs) represent a special type of optical waveguides in which it is possible to completely optically control the propagation of light by changing the parameters of the system, such as refractive index and grating period of the medium.
Besides unique features of light propagation through periodic linear and nonlinear PLs, the change in the geometry of photonic systems significantly influences the type of localized solutions that may occur in observed PLs. Combing these effects opens a possibility to manipulate light propagation in such system. The idea is tested by performing numerous dynamical numerical simulations, which resulted in structures with fully predictable control of the light propagation proposed in papers JOSA B 30 2340 (2013) and J. Opt. 16 025201 (2014).
In this talk I will give you an overview of already published results, as well as a brief insight into our future work in this area.
Milutin Stepić: Defect driven beam dynamics in linear one-dimensional waveguide arrays
Uniform waveguide arrays, consisting of parallel, weakly coupled channels serve as prime model for both theoretical and experimental investigation of optical beam propagation in periodic media. There are many interesting phenomena, such as diffraction management, discrete Talbot effect, Landau-Zener tunneling, discrete surface states, Fano resonances, Tamm oscillations etc., observed within such system.
However, the emergence of various defects within otherwise perfectly periodic structures is inevitable due to: unpreventable imperfections during sample's fabrication, misusage, accidental damage, etc. Although undesirable in the first place due their unpredictability and decisive role in the breaking of the translational symmetry of the system, these interruptions in waveguide arrays regularity enable the existence of different types of stable, strongly localized defect modes also known as defect solitons. Interestingly, defects may influence motion of light through arrays which, together with available fabrication techniques, open another promising route for realization of all-optical light control.
In this talk, our recent research related to defect induced light propagation in two simple, experimentally achievable setups is presented. The first setup is a linear, one-dimensional waveguide array possessing a single nonlinear defect. The second one is composed from two linear, semi-infinite, dissimilar one-dimensional waveguide arrays with a nonlinear defect inserted in one of sub-lattices nearby the interface of arrays.
Depending on the strength of nonlinear defect, input beam position and phase shift, six different dynamical regimes have been identified in the first setup. We distinguish input parameters set for which a regime of light propagation blockade by the nonlinear defect appears. Obtained results may be useful for all-optical control of transmission of waves in interferometry. On the other hand, various dynamical regimes including simultaneous excitation of different, strongly localized modes are observed inside cavity formed by nonlinear defect and linear, coupling defect located at the interface of two waveguide arrays.
Rodrigo Vicencio: Localization and transport in Discrete Photonic Lattices
In this talk, I will make an overview of the work done for our group during the last year. We will explore a set of different problems in the framework of linear and nonlinear discrete lattices, focused mainly on nonlinear optical waveguide arrays. I will discuss numerical results about diffusion in the presence of disorder and nonlinearity, showing also their experimental realization. We will show results on mobility of nonlinear localized solutions, where the appearance of the so-called intermediate solution is fundamental to observe coherent transport across a given lattice. In this sense, I will show an indirect experimental observation of this kind of solutions in a photovoltaic saturable coupler. We will also discuss the problem of finding the critical nonlinearity to observe localization of energy in different 1D, 2D and 3D lattices, showing that a new quantity can be computed to understand better the transition in terms of the excited frequencies during the dynamics. I will also show very recent results on flat-band systems, including some experiments implemented in Santiago. At the end, I will review the recent progress obtained in our young laboratories.