# Poster Session

One key plenary event will be the poster session to be held on **thursday afternoon, from 6PM onwards**. If the weather allows it (and it should), the poster session will take place under the trees below the Grand Château de Valrose. **A standup cocktail buffet will be served as conference dinner, please join!** *(Registration for the dinner is included in the conference registration).*

**Practical information:**

- Poster session takes place thursday 6th of june in the late afternoon
- Location: under the trees in front of Grand Chateau de Valrose
- Format A0 portrait
- Posters will be attached to metal grids, paperclips will be provided
- Poster can be attached starting from 5PM
- Posters will be sorted in alphabetical order of contributor name (a number is attributed to each poster and is apparent in the conference abstract book to be distributed soon)
- The poster session will start at 6:00PM until late in the evening
- Stand-up dinner will be served from 6:30 to 9:00PM back to back with the poster session
- A
**Best Poster Prize will be awarded**during the poster/cocktail evening

**We warmly thank all the contributors to this session:**

## Quantum Fluids of light in atomic vapors

Since its discovery in 1995, Bose-Einstein Condensation (BEC) is a powerful object for quantum experiments. Its coherence offers a lot of possibilities for measuring quantum phenomena. Even though BEC is well studied with ultracold atoms cloud, an analogy for classical waves propagating in a non-linear medium can be established and condensation of classical waves has been predicted. Our experiment is based on the use of an atomic vapor as a non linear medium. By heating a Rubidium cell, we create a nonlinear medium with adjustable non linearity. By modifying the properties of the incident laser beam (shape, size, frequency, etc) we are able to study a wide range of phenomena. After the observation of precondensation of classical waves in this system, we turned to a study of shock wave creation in this system. We will present first results on this investigation, including numerical and experimental comparisons.

## Towards the generation of light-bullets in semiconductor lasers

Localized structures (LS) are nonlinear solutions of dissipative systems characterized by a correlation range much shorter than the size of the system. Since they are individually addressable, LS can be used as fundamental bits for information processing in optical resonators. While spatial LS are confined peaks of light appearing in the transverse section of broad-area resonators, temporal LSs are short pulses travelling back and forth in the longitudinal direction of the cavity. Spatial and temporal LS have been observed independently in semiconductor lasers systems based on a gain medium coupled to a saturable absorber.

In this work we present preliminary results for the generation of spatio-temporal localized structures, also called “Light bullets”, in semiconductor lasers. In this case, light is stored in the three spatial dimensions, leading to information processing with disruptive performances in terms of bit rate, resilience and agility. Despite the effort made in nonlinear optics, only fading LB have been observed so far experimentally. Our approach consists of chasing “dissipative” LB, which will be robust and suitable to applications. Accordingly, once LB will be obtained and characterized, their application to information processing will be addressed by targeting a three-dimensional electro/optical buffer. The results shown were obtained using a vertical external cavity surface emitting laser, composed by a gain mirror and a semiconductor saturable absorber mirror (SESAM). These components have been properly engineered for matching the parameters requirements for implementing light bullets, which require a cavity roundtrip time much larger than the carrier relaxation time, a large Fresnel number and a bistable response of the system. We show that self-imaging condition between the gain section and the SESAM enables the first two conditions, while bistability can be obtained by designing the modulation depth of the SESAM.

## MMS observations of particle velocity distribution functions and field-particle correlator

*Etienne Behar, Fouad Sahraoui*

*Laboratoire de Physique des Plasmas, CNRS - École polytechnique - Sorbonne Université - Observatoire de Paris, Université Paris-Sud, Université Paris-Saclay, F-91128 Palaiseau, France*

We present our current work on the analysis of MMS data carried out in particular with particle velocity distribution functions (VDF). We propose methods that tackle the high time resolution of these four-dimensional data sets, in various reference frames and coordinate systems. In particular, we explore the feasibility of obtaining spatial and time derivatives of the VDF, with the inherent price in terms of time resolution/integration. Together with field measurements, these derivatives enable the quantification of the various terms of the Poisson-Vlasov equations, with the ultimate goal of a direct measurement of the energy exchange taking place between fields and particles, as a function of velocity, following the effort initiated by Howes et al. 2017 and Chen et al. 2019.

## Study of brownian motion at short time scales

We experimentally study the brownian motion of an optically trapped micrometric particle in liquids at ultrashort timescales in order to reveal the effects of fluid compressibility on its dynamics.

To that purpose, standard trapping and detection schemes are coupled to femtosecond "pump-probe" experiment to take advantage of the high temporal resolution of time resolved ultrafast spectroscopy experiments. The goal is to achieve a proper measurement of the instantaneous velocity of the brownian particle beyond the ballistic regime to probe the influence of compressibility effects on the motion of the trapped sphere, measurement that has never been made and remains elusive. The expected spatial and temporal resolutions ($0.15$ fm at $1$ ps) provided by these techniques will allow us to measure the Velocity Auto Correlation Function to obtain an evidence of compressibility effects on the particle dynamic.

This type of study provides new features into investigations of non equilibrium physics related to brownian motion and optical tweezers.

## Structure and evolution of magnetohydrodynamic solitary waves with Hall and finite Larmor radius effects

Authors: E. Bello-Benítez, G. Sánchez-Arriaga, T. Passot, D. Laveder and E. Siminos. There exist a broad variety of nonlinear-wave phenomena in the solar wind. Different types of stable large-amplitude solitary waves are typically observed in these plasmas. The study of small amplitude waves can be described by well-known equations: Korteweg-de-Vries (KdV), modified KdV, Derivative Nonlinear Schrödinger (DNLS) and triple-degenerate DNLS. However, magnetohydrodynamic (MHD) fluid equations are more suitable for the analysis of large-amplitude structures, which is the approach used in this work [1] —to be precise, MHD equations with Hall effect and Finite Larmor Radius (FLR) corrections to the double adiabatic pressure tensor. Assuming travelling wave solutions, the system of partial differential equations yields a set of 5 ordinary differential equations (ODEs) governing the spatial profile of the velocity and magnetic-field vectors —if double adiabatic equations of state are used for the gyrotropic pressures. The procedure to derive these equations follows Ref. [2], but some discrepancies are shown [1]. The existence of solitary-wave solutions in different parametric regimes is rigorously proved in this system of ODEs using concepts and tools from the theory of dynamical systems. Two key features of the concerning ODEs are: (1) the system is reversible and (2) the existence of an invariant which allows reducing the effective dimension of the system from 5 to 4. These characteristics are guaranteed if equations of state are used for the pressures. Nevertheless, only stable structures have physical interests and are expected to be observed in space. The global stability of the solitary waves is investigated by numerical spectral simulations using two different closures for the pressures: (1) double adiabatic equations and (2) evolution equations including the FLR work terms [3], which guarantee energy conservation and better reproduces the real physics. In case (1), it is found that the solitary waves may have a stable core even if the background is unstable. The background instability seems to disappear when the energy-conserving model (2) is considered. In this case, stable solitary waves are found that survive long time without significant deformation.

References

[1] E. Bello-Benítez, G. Sánchez-Arriaga, T. Passot, D. Laveder and E. Siminos, Phys. Rev. E 99, 023202 (2019).

[2] E. Mjølhus, Nonlin. Proc. Geophys. 16, 251 (2009).

[3] P. L. Sulem and T. Passot, J. Plasma Phys. 81, 325810103 (2015).

## Deformation of an elastic material paired with a tree structure

## Plasma acceleration by the non-linear interaction of three crossed parallel Alfvén wave packets

## Competition between Kelvin-Helmholtz and nonlinear Lower Hybrid drift instabilities along Mercury-like magnetopause

## Optimal Analog Data Compression with Reconfigurable Wave-Chaotic Systems

## Smooth branch of travelling waves for the Gross-Pitaevskii equation in dimension 2 for small speed

We construct a smooth branch of travelling wave solutions for the 2 dimensional Gross-Pitaevskii equations for small speed. These travelling waves exhibit two vortices far away from each other. We also compute the leading order term of the derivatives with respect to the speed. We construct these solutions by an implicit function type argument. In collaboration with David Chiron

## Fluids of light in nonlinear crystals

Quantum fluids of light merge many-body physics and nonlinear optics, revealing quantum hydrodynamic features of light when it propagates in nonlinear media. One of the most outstanding evidence of light behaving as an interacting fluid is its ability to carry itself as a superfluid. Here, we report a direct experimental detection of the transition to superfluidity in the flow of a fluid of light past an obstacle in a bulk nonlinear crystal. In this cavityless all-optical system, we extract a direct optical analog of the drag force exerted by the fluid of light and measure the associated displacement of the obstacle. Both quantities drop to zero in the superfluid regime characterized by a suppression of long-range radiation from the obstacle. The experimental capability to shape both the flow and the potential landscape paves the way for simulation of quantum transport in complex systems.

## Alternative exact law for homogeneous compressible turbulent flows: from Hall-MHD to hydrodynamics

Fluid and plasma turbulence is a longstanding problem in physics. Studying its dynamics can help understanding various processes such as mass transport and energy dissipation, in particular in collisionless systems like most of the astrophysical plasmas. The solar wind heating problem, which is manifested by a slower decrease of the ion temperature as function of the heliocentric distance than the prediction from the adiabatic expansion model of the wind, is one example of such problems where turbulence can help give an explanation.

A way to study fluid or plasma turbulence is to estimate the total energy cascade rate, which is the energy transferred from the largest scales into the dissipative scales of the system. This is made possible by the use of exact laws, which link the energy cascade rate to the physical variables of the flow. Significant progress has been made in recent years on deriving various forms of exact laws for different compressible flows: HydroDynamics (HD), MagnetoHydroDynamics (MHD) and Hall-MagnetoHydroDynamics (HMHD). Some of them were used successfully to estimate the energy cascade rate in the solar wind and the magnetosheath, but at the expense of making additional assumptions that made different mathematical terms involved in the laws accessible to in-situ measurements.

Here we present an alternative exact law for compressible Hall-MHD turbulence. This law is more compact and easier to compute in numerical simulations and spacecraft data, thus reducing the memory load and time required to compute the energy cascade rate. We also show the validity of this new law in the limit of compressible HD using high-resolution simulation data of HD turbulence spanning the subsonic and supersonic regimes.

## Light scattering by arrays of ultracold atoms with sub-walength spacing

Ultracold atoms offer a unique platform to study the interaction of near-resonant light with an ensemble of resonant emitters. Our experiments probe an ensemble of alkali atoms cooled to a temperature where the inhomogeneous Doppler broadening is negligible and a two-level system can be isolated, so that cooperative scattering effects take place. We study in particular the dense regime where the interatomic distance is shorter than the wavelength of the light. In this regime the atoms interact strongly via the resonant dipole-dipole interactions, and their collective response is significantly modified with respect to the individual one. The geometrical arrangement plays in addition a crucial role in the enhancement of cooperative effects. We will present our recent experimental progress towards tailoring atomic ensembles with sub-wavelength interatomic distance, as well as perspectives in the short term for light-matter interaction experiments in such ensembles.

## Propagation of waves along superfluid vortices trapping particles

Superfluids like liquid helium or ultracold atomic Bose-Einstein condensates are an exotic state of matter in which quantum effects appear on a macroscopic scale. One of the main features of superfluids is the presence of topological defects with quantised circulation, known as quantum vortices. These vorticity filaments can reconnect dissipating energy through sound emission and thus they play a central role in superfluid turbulence. At the same time, helicoidal waves (called Kelvin waves) can propagate along the vortex filaments and interact nonlinearly among themselves, contributing to the energy transfer towards small scales. An important experimental breakthrough occurred in 2006, when quantum vortices were directly visualised by using micrometer-sized hydrogen particles. Since these particles are trapped inside the vortex core they can be used to track the motion of vortices themselves. Thanks to this method, quantum vortex reconnections and Kelvin wave propagation have been observed. Nowadays, particles are still the main experimental tool used to visualise quantum vortices and to study their dynamics. Our aim is to study the propagation of waves along a superfluid vortex filament, when active particles are trapped inside its core. We perform numerical simulations of a self-consistent model based on the Gross-Pitaevskii (GP) equation, in which particles are described as localised potentials depleting the superfluid and following a Newtonian dynamics. In a former work we have shown that this model is able to reproduce the capture of a particle by a quantum vortex line. Now we study how the dynamics of a collection of particles (impurities) already set inside the vortex reflects the motion of the vortex itself. We measure the spatiotemporal spectra of the system, showing how the presence of particles induces a nontrivial modification of the vortex wave dispersion relation. In order to explain the numerical results, we develop a theory that mixes hydrodynamic equations and basic solid-state concepts. In particular, we point out a remarkable analogy with the propagation of electrons in a crystal lattice.

## Magnetic coherent structures in the presence of equilibrium temperature anisotropy

Coherent magnetic structures such as magnetic vortex chains have been observed in the solar wind close to the Earth by the Cluster space mission (Perrone et al. (2016, 2017)). Making use of a gyrofluid model, we investigate the existence of analytical solutions of magnetic vortex type and study their stability. The adopted model can provide a nonlinear description of turbulent collisionless magnetized plasmas accounting for ion finite Larmor radius, equilibrium temperature anisotropy and fluctuations of the component of the magnetic field parallel to the direction of a strong and uniform guide field. The model possesses a noncanonical Hamiltonian structure which provides a convenient framework for the use of analytical tools, such as the Energy-Casimir method for determining stability conditions. We carry out investigations for some asymptotic regimes of the model, such as for instance in the limit of a large ion-to-electron perpendicular equilibrium temperature ratio, with negligible electron inertia effects, and compare our results with those found recently in the framework of a reduced magnetohydrodynamics model (Jovanovic et al. 2018).

D. Perrone, O. Alexandrova, O. W. Roberts, S. Lion, C. Lacombe, A. Walsh, M. Maksimovic and I. Zouganelis. The Astrophysical Journal, 849:49, 2017

D. Perrone, O. Alexandrova, A. Mangeney, M. Maksimovic, C. Lacombe, V. Rakoto, J. C. Kasper, and D. Jovanović. The Astrophysical Journal, 826:196, 2016

D. Jovanović, O. Alexandrova, M. Maksimović, M. Belić. J. Plasma Phys., vol. 84, 2018

## Kinetic Turbulence in Astrophysical Plasmas: Waves and/or Structures?

## A Hamiltonian regularisations of barotropic Euler equations

The inviscid Burgers, Euler and Saint-Venant equations are nonlinear hyperbolic PDEs modeling fluid flows and surface water waves propagating in shallow water. These equations, prominent in physics, are the subject of numerous mathematical and numerical investigations. It is well-known that these equations develop shocks in finite time, even for regular initial conditions. These shocks are problematic, in particular, for numerical simulations. Therefore, several techniques have been proposed to regularized these equations. Adding viscosity or/and dispersion into the equations can avoid the formation of shocks. Here, we study a regularization of barotropic Euler equations, which conserves the energy, and generalize the conservative regularization of the Saint-Venant equations proposed by Clamond and Dutykh in 2017.

## Short-distance propagation of nonlinear optical pulses

## 2D spatiotemporal extreme event in quadratic nonlinear crystal

Solitonic waves are nonlinear self-sustained waves observable in a large number of conditions and various fields of physics, from electronics to optics via fluidics. Quadratic quasi-solitons have been early predicted by Karamzin et al. [1] and later observed by Torruellas et al. [2]. These types of self-guided beams have been seen, after modulation instability, in 2D spatial structures [3]. More recently, it has been shown that Peregrine solitons, and Akhmediev Breathers, could be obtained in quadratic materials [4].

In this paper we show spontaneous 2D quadratic extreme events, generated and controlled with non-collinear beams. We launched a large collimated beam (R = 200 µm, 30 ps) in a 8X8X30 mm KTP crystal cut for type II second harmonic generation. Beams first experienced a strong self-focusing leading to a stable 2D confined propagation. Because of the spatial walk-off due to the nonlinear crystal anisotropy, the trapped beams come with spatial reorientation, controlable by the initial polarization state. Additional self-confined events can appear in the transverse output pattern by increasing the input peak power. Such nonlinear spatial reshaping of the initial beam can also provide a way to control the apparition of 2D nonlinear periodic structures, a situation that reminds the Akhmediev Breathers solution, only valid in 1D.

These effects could be used to implement all-optical logic functions with ultrafast switching, but also to mimic the effect of a nonlinear saturable absorber able to realize ultrafast temporal pulse reshaping. The self-trapping process acts like a spatial self-cleaning process, which changes a set of initial non-collinear beams into a single one.

[1] Yu. N. Karamzin et al., Sov. Phys. JETP 41,414 (1976).

[2] W. E. Torruellas et al., Phys. Rev. Lett. 74, 5036 (1995).

[3] M. Delqué, et al., Optics Comm. 284, 1401–1404 (2011).

[4] F. Baronio et al., Opt. Lett., 42, 1756-1759 (2017).

## A microwave realization of the chiral GOE

The universal features of the spectra of chaotic systems are well reproduced by the corresponding quantities of the random matrix ensembles [1]. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles: the Gaussian orthogonal (GOE), the Gaussian unitary (GUE), and the Gaussian symplectic ensemble (GSE). With a further particle-antiparticle symmetry there are in addition the chiral variants of these ensembles [2]. Relativistic quantum mechanics is not needed to realize the latter symmetry. A tight-binding system made up of two subsystems with only interactions between the subsystems but no internal interactions, such as a graphene lattice with only nearest neighbor interactions, will do it as well. First results of a microwave realization of the chiral GOE (the BDI in Cartan's notation) will be presented, where the tight-binding system has been constructed by a lattice made up of dielectric cylinders [3].

[1] O. Bohigas, M. J. Giannoni, and C. Schmit. Characterization of chaotic spectra and universality of level fluctuation laws. PRL 52, 1 (1984).

[2] C. W. J. Beenakker. Random-matrix theory of Majorana fermions and topological superconductors. Rev. Mod. Phys. 87, 1037 (2015).

[3] S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne. Disordered graphene and boron nitride in a microwave tight-binding analog. PRB 87, 035101 (2013).

## Local energy transfers in incompressible MHD turbulence

We present a local (in space and time) approach to the study of scale-to-scale energy transfers in magnetohydrodynamic (MHD) turbulence. This approach is based on performing local averages of the physical fields, which amounts to filtering scales smaller than some parameter $\ell$. A key step in this work is the derivation of a local Kármán-Howarth-Monin relation which can be interpreted as a coarse-grained energy balance. This provides a local form of Politano and Pouquet’s 4/3-law without any assumption of homogeneity or isotropy, which is exact, non-random, and connects well to the usual statistical notions of turbulence. After a brief presentation of this approach, we first apply it to turbulent data obtained via a three dimensional direct numerical simulation of the forced, incompressible MHD equations from the John Hopkins turbulent database. The local Kármán-Howarth-Monin relation holds well. The space statistics of local cross-scale transfers is studied, their means and standard deviations being maximum at inertial scales, and their probability density functions (PDFs) displaying very wide tails. Events constituting the tails of the PDFs are shown to form structures of strong transfers, either positive or negative, which can be observed over the whole available range of scales. As $\ell$ is decreased, these structures become more and more localized in space while contributing to an increasing fraction of the mean energy cascade rate. Second, we show how the same approach can be applied to spacecraft data where the main difficulty lies in the fact that measurements are restricted to few points, in one small region of space at a time, and a single scale. We compare our approach to results obtained from Cluster and MMS data using the LET proxy, and highlight its importance to the understanding of solar wind turbulence and solar wind heating.

## Investigating properties of solar wind turbulence at sub-ion scales with in situ data and numerical simulations

We investigate the transition of the solar wind turbulent cascade from MHD to sub-ion range by means of in situ observations and hybrid numerical simulations. First, we focus on the angular distribution of wave-vectors in the kinetic range, between ion and electron scales, using Cluster magnetic field measurements. Observations suggest the presence of a quasi-2D gyrotropic distribution around the mean field, confirming that turbulence is characterised by fluctuations with $k_\perp>>k_|$ in this range; this is consistent with what is usually found at larger MHD scales, and in good agreement with our hybrid simulations.

We then consider the magnetic compressibility associated with the turbulent cascade and its evolution from large-MHD to sub-ion scales. The ratio of field-aligned to perpendicular fluctuations, typically low in the MHD inertial range, increases significantly when crossing ion scales and its value in the sub-ion range is a function of the total plasma beta, with higher magnetic compressibility for higher beta. Moreover, we observe that this increase has a gradual trend from low to high beta in the data; this behaviour is well captured by the numerical simulations. The level of magnetic field compressibility that is observed in situ and in the simulations is in fairly good agreement with the prediction based on kinetic Alfvén waves (KAW), especially at high beta, suggesting that in the kinetic range explored the turbulence is supported by KAW-like fluctuations.

## Imbalanced kinetic Alfvén wave turbulence

## Combination of Kerr Beam Self-Cleaning and Supercontinuum Generation in Tapered Ytterbium-doped Multimode Fiber with Parabolic Core Refractive Index and Doping Profile

## Multidimentional Iterative Filtering: a new approach for investigating plasma turbulence in numerical simulations.

## Dissipation induced modulation instabilities: gain-through-losses in nonlinear optics

## Temporal solitons in a delayed model of a semiconductor laser

## ELECTRON PHYSICS IN KELVIN-HELMHOLTZ INSTABILITY IN MAGNETIZED PLASMAS

Rolled-up vortices associated to the Kelvin-Helmholtz instability (KHI) have been detected by in-situ observations around the Earth, Saturn and Mercury magnetospheres due to the interaction with the solar wind. KHI in magnetized plasmas have been widely studied numerically in the framework of a fluid, hybrid, and full kinetic approach, while only very few studies have focused on the physics of electrons because of computational constraints. In this work we present a full kinetic particle in cell study of the KHI spanning a range of scales going from fluid to electron scales. The simulation is initialized with an extended fluid equilibrium including finite ion Larmor radius effects. Our large-scale configuration includes two-possible alignment of the vorticity with the background magnetic field each one corresponding to the interaction of the solar wind with the dawn and dusk side of a planet. We discuss electron heating and acceleration by analyzing temperature anisotropy and particle distribution functions. Two fluid simulations have suggested that KHI instability can lead to the onset of the mirror instability. Our full kinetic approach confirms such hypothesis. We discuss the formation of mirror modes in our simulations.

## Can the state space of spatially extended systems and of time delayed systems be reconstructed from the time series of a scalar variable?

## Olfactory navigation by hunting octopuses: how to take decisions using a broken signal.

## Nozaki-Bekki Holes in a Long Laser

## A simplified model of aquatic locomotion

We have developed a simple model of aquatic locomotion. Using the theory of complex variables, we have estimated the hydrodynamic forces acting on an infinite thin rigid plate of length L, following the seminal Work of Theordorsen [1].

By considering the different possible motions of the swimmer, we calculate the velocity potential to derive the pressure by means of the generalised Bernoulli relation. We show that the effect of flow unsteadiness is the principal mechanism for locomotion [2].

We impose a periodic rotation of the tail in order to approximate the undulatory motion of the swimmer. We show the linear dependence of longitudinal velocity on the angular frequency predicted by Gazzola et al [3] . We also predict that the transverse motion presents the same frequency as the forcing whereas the longitudinal motion is a linear function of time plus a periodic term with double frequency.

Finally, by taking the angle of the tail as a small parameter we perform a perturbative expansion to obtain an equation linking swimming velocity to the different parameters involved in swimming. The results arised from this perturbative method are in high accordance with the numerical results.

[1] Theodorsen, T., General theory of aerodynamic instability and the mechanism of flutter, NACA TR No. 496, 1934

[2] Garrick, I. E., Propulsion of a flapping and oscillating airfoil, NACA TR No. 567, 1936

[3] Gazzola, M., Argentina, M., & Mahadevan, L , Scaling macroscopic aquatic locomotion, Nature Physics 10 (10), 758-761, 2014

## Neuron-like dynamics of semiconductor lasers with optical feedback

## Multisection semiconductor laser for optical coherence tomography

Optical coherence tomography (OCT) is a non-invasive three-dimensional imaging technique of scattering media used in applications such as medical diagnostics and industrial testing in manufacturing lines. Swept Source-OCT (SS-OCT) requires a laser whose wavelength can be rapidly and continuously swept over a broad spectral range. Nowadays, most swept source lasers (SSL) technologies rely on mechanical filters whose sweeping speed is limited to 100 kHz. Multisection semiconductor lasers are electrically tunable lasers that offer the possibility to reach sweeping speeds up to the MHz regime. The technology is based on semiconductor slot mirrors having comb reflectivity spectra. The spacing of the comb spectral lines is imposed by the periodicity of the slots. The electrical injection of these mirror sections allows to shift the reflectivity spectra by the variation of the refractive index of the medium. By ensuring that the period of the slots are different between the front and back mirrors, two incommensurate comb reflection spectra can be formed. The Vernier effect occurs due to the interference of the two offset combs when independent electrical tuning of the two mirror sections is realised. This Vernier effect is responsible for wide and fast frequency sweeps. However such SS lasers based on the Vernier effect display mode hops during the laser operation that induce a loss of coherence.

In this work, we analyse the spectral features of semiconductor multisection slot lasers when the mirror sections are electrically tuned. Based on our cartographies of the laser emission wavelength as a function of the mirrors currents, we intend to provide an electrical path for a rapid and quasi-continuous wavelength sweep over a broad bandwidth. This work paves the way for further explorations of the opto-electronic control of the multisection lasers coherence during a full wavelength sweep.

## Spontaneous Symmetry Breaking, Instability, and Chaos in Ring Resonators

When a ring resonator is pumped with laser light of sufficient intensity, then the refractive index -- and so the resonant frequency -- of the resonator can be modulated by the intensity of the light within it -- a phenomenon known as the Kerr nonlinearity. If the resonator is pumped with two laser beams, then this effect can give rise to spontaneous symmetry breaking in the two optical modes within the resonator. We present analytical, numerical, and experimental evidence for a rich range of exotic behaviours exhibited by this symmetry-broken light, including oscillations (implying periodic energy exchange between the modes), period-doubling, and chaos. These optical modes are described by the following coupled system of ordinary differential equations:

$$\dot{e}_{1,2}=\tilde{e}_{1,2} -[1+i(A|e_{1,2}|^{2}+B|e_{2,1}|^{2}-\Delta_{1,2})]e_{1,2},$$

where $\tilde{e}_{1,2}$ and $e_{1,2}$ are the input and coupled electric field amplitudes for each beam, respectively, and $\Delta_{1,2}$ are the frequency detunings of the laser beams, with respect to the non-Kerr-shifted cavity resonance frequency. The coefficients $A$ and $B$ denote the strengths of self- and cross-phase modulation, respectively -- i.e., the extent to which the modes interact with themselves and with each other. The physics of this dynamical system is not only of fundamental interest, but is also important for the construction of integrated all-optical circuitry and devices, such as isolators, circulators, logic gates, advanced sensors, oscillators, and scramblers.