Solitary waves have been a fascinating research topic since their first observation in the hydrodynamics context in 1834. The formation of optical solitary waves in a dissipative optical systems is at the center of this project.
Semiconductor light sources are often used in pulsed regimes in which they emit trains of spikes and these regimes are both of technical and fundamental interest. In certain conditions, each of these spikes can be described as a «solitary wave« or «soliton«, a surprising wave packet which does not disperse or change shape or weaken during propagation. The usual approach towards the formation of these wave packets in lasers is to prevent emission of light in a continuous wave by using a component which absorbs light unless light is strong enough to (reversibly) bleach this component. In this way, a strong spike concentrating enough energy can emerge from the laser, while a usual continuous wave in which energy is distributed in the whole space cannot. In this project we set out to explore alternative approaches to the nucleation of solitary optical waves, building on a fundamentally different dynamical phenomenon.
Laser light is characterized by very well defined optical frequency and phase. This phase, randomly «chosen« by the laser system when it is switched on, is ideally constant in the course of time. In reality this phase wanders randomly under the effect of both technical and fundamental noise sources and the «best« lasers are often those whose phase wanders less. In order to circumvent this phase diffusion process, a common approach is that of seeding an imperfect laser with a very pure laser beam coming from another laser of better performance. In practice, this amounts to using an optical metronome to help a poor quality laser keeping the pace. In this project, what we have done is to use an external laser beam to force a laser to emit at a frequency which is very far from the optical frequency it would normally emit. This amounts to constrain laser light via a periodic substrate whose period does not match that of the laser wave. As in solid state physics, the system sooner or later releases this constraint by forming dislocations. Here, the laser phase is uniformly locked to the forcing except where the dislocation is and this dislocation is constituted by a spatially localized relative slip of the laser phase with respect to the forcing phase.
We have prepared a laser whose physical characteristics allow for real time observation of light dynamics and sufficient spatial extension to observe wave localization. We have forced this laser with a coherent beam and studied the instabilities at the edges of the locking region. These measurements resulted in the observation of a wealth of dynamical regimes including plane wave and modulational instabilities, coexistence between locked and chaotic regions, front propagation and localized patterns. Among those observations we have dedicated particular attention to the emergence of highly localized waves packets emerging from chaotic spatial regions and which possess all the features of solitary waves. In this regime we have measured the optical phase of the laser beam with respect to that of the external forcing beam and shown that the solitary waves fundamentally consist in phase rotations and therefore possess a chiral charge.
In principle this chiral charge can be expected to be either positive or negative depending on the direction of the rotation. Here the observation of a unique sign of chiral charge must still be understood. While this stability of only one sign of chiral charge seems to be related to the non-instantaneous medium dynamics, this link is still to be completely elucidated.
On the other hand, the dynamics under study being fundamentally based on the phase of the electric field, these results may open novel perspectives for the processing of coherent optical information.
These results have been reported during several conferences and workshop. The project produced a total of eight articles in peer reviewed international journals, dedicated to the analysis of solitary waves and localized patterns in spatially extended and delayed systems. Three of them are dedicated to these specific solitary waves and future outcome of the project will include later publication of satellite results regarding extreme phenomena statistics and forecasting. On this topic the project has set up a series of workshops on abnormal wave events (http://w-awe.org) dedicated to exploring the interface between optical and hydrodynamical physics in the context of extreme phenomena.
The study of semiconductor lasers operating in the mode-locked regime has undergone considerable developement during the last years, both in extended cavity systems and in monolithic systems. Most of the time these systems (which have phase symmetry) are based on the presence of a saturable absorber and the pulses resulting from mode locking are then described in terms of dissipative solitons.
In parallel, the study of spatial localized structures in optics also called "cavity solitons" has reached some degree of maturity, switching in very few years from model systems (sodium vapor, liquid crystal light valves) to fast and micron-scale systems such as semiconductor microcavities with optical injection.
Thus, it is nowadays possible to nucleate these "dissipative spatial solitons" just as pixels (independent of each other) on a nanosecond time scale or to move them in space at speeds reaching several micrometers per nanosecond. However, in spite of these achievements, these spatial solitons remain confined only in the transverse plane, orthogonal to the light propagation, and are most of the time described in the uniform field limit along the propagation direction. These structures are therefore localized essentially with respect to the diffraction phenomenon.
In a remarkably complementary way, temporal cavity solitons have recently been observed in an optical fiber ring cavity under the application of a coherent beam. Just like in the transverse case, the structures which have been reported are bistable pulses independent of each other, individually controllable. Each pulse propagating inside a ring cavity, it is of course repeated after a period corresponding to the time it needs to travel the whole cavity. The analogy with mode locked lasers is striking, but one has to underline that contrary to passively mode locked laser this system does not have phase symmetry, and incidentally does not have any kind of "laser" gain. These temporal cavity solitons are then detected as trains of pulses all identical to each other and separated by arbitrary time intervals, each train of pulses being repeated at the period given by the optical cavity length. In the temporal case cavity solitons are therefore localized with respect to the dispersion phenomenon.
In this project, we will demonstrate the existence of temporal cavity solitons in a semiconductor ring cavity and relate them to the mode locking phenomenon in lasers. We will make use of the advances realized in fiber systems and we will deploy them in semiconductor systems, which have already shown their potential in the "transverse" domain and whose robustness is an obvious advantage for eventual practical applications. One of the benefits of the system which is envisioned for this project is to use (just as succesfully as it was done for transverse cavity soliton) the capability of semiconductor material to amplify light via stimulated emission of radiation, strongly reducing the optical input power required for nonlinear localization to take place.
The point of view which will be adopted, exploratory and transversal, will enable us to approach the phenomena under study both from a fundamental and applicative point of view. Indeed, we will analyze the formation of temporal cavity solitons (which are optical information units), but we will also dedicate particular attention to statistical aspects of the dynamics, with emphasis on the appearance and control of extreme events.
Monsieur Stéphane Barland (Institut Non Linéaire de Nice Sophia Antipolis) – firstname.lastname@example.org
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
INLN Institut Non Linéaire de Nice Sophia Antipolis
Help of the ANR 250,512 euros
Beginning and duration of the scientific project: September 2012 - 42 Months