Scaling effects in time-delayed nonlinear optics – TINO

The scientific work plan will be organized in five main tasks, each of them being devoted to a progressive development of the above exposed scientific objectives. Here is a summary. TASK 1 is devoted to the project supervision. TASK 2 is devoted to fundamental aspects of time-delayed systems and to the set up of numerical tools for the simulation of appropriate dynamical models. TASK 3 is related to the experimental analysis of the time-dependent dynamics of time-delayed systems, and to the investigation of the corresponding scaling effects when varying the time-delay with respect to system internal time-scales. The work will include the set up of the experimental platform where a laser diode will be subject to phase conjugate feedback using a large variety of photorefractive crystals with different dimensions and crystallographic properties and also different nonlinear optics time-scales. TASK 4 is related to the experimental analysis of the spatial-dependent dynamics of time- delayed systems, and to the investigation of the corresponding scaling effects when varying the external cavity length with respect to system characteristic dimensions. The work will include the set up of an experimental platform for a photorefractive nonlinear cavity. Time-delay will induce a large variety of patterns and self-organization phenomena, which will be analysed as a function of the time- delay parameter. Time-delayed inducing rogue waves or rare events, drifting patterns, and moving dissipative structures, will be among the targets of the research work, and will be characterized in their spatio-temporal dynamics by high- resolution camera and arrays of fast photodiodes. TASK 5 is devoted to the dissemination of the research work and is under the main responsability of the project coordinator, although contributions are expected from all project contributors.

This projet makes an original combination of two issues that are of great interest on both societal and technological aspects: (1) nonlinear dynamics of complex systems in time and space, (2) advanced experiments on optical systems and applications (optical signal processing, optical storage). How complex systems behave in space and time is certainly one of the most and still fascinating questions of today modern physics. Inspired by the discovery of chaos in 1963 and the works on the physics of non-equilibrium systems and spatial pattern formation in 1950s, there is today a very active community working on the understanding of emergence of order in time and space in a large variety of systems: social networks and collective behaviors, economy, chemical reactions, neuronal networks, gene expression, lasers and optical nonlinear cavities. A common feature but often neglected aspect of all these complex systems is the presence of a time- delay, which emerges e.g. from the feedback of an output signal back to the system input. When accounted for, time-delay is responsible for the emergence of disorder such as spatio-temporal chaos in otherwise steady dynamical systems, or by contrast may lead to extremely regular system outputs and spatio-temporal self-organization. Although they appear so crucial, studies remain scarce because first the modelling and numerical treatment of time-delayed system needs the most sophisticated techniques to deal, but also because experimentally time-delay is not easily scalable and accessible in e.g. biological, chemical or physical systems. We address here the question of time-delayed system dynamics by making use of advanced photonic systems where the time-delay is easily scalable and its impact can be analyzed with high-resolution measurements. On the other hand, understanding and controlling light dynamics and spatial properties enables new applications and improved performances in photonic devices.

In a communication from 30/09/2009 the European Commission has listed 'Photonics' as one of the five Key Enabling Technologies (KET) whose development will allow for the creation of new goods and services hence will help for the creation of sustained employment opportunities and high quality jobs. According to the 'Photonics21' Technological Platform the current global photonics market is estimated to be €300 billion, and photonics companies currently employ about 290,000 people in Europe. In a document called 'Photonics: our vision for a key enabling technology in Europe' (May 2011), it is explicitly mentioned that effort must be made on the development of «novel optical techniques for signal processing«. Our project by combining the most advanced photonic systems and new paradigms coming from nonlinear science (in time-delayed systems), targets these economic goals and contributes to new ideas for optical signal processing.

(1) first demonstration of deterministic coherence resonance induced by time-delay in a physical system. The inclusion of an optimal amount of time-delayed signal in an optical system induces an optimal regularity of the pulsating laser output. This situation called coherence resonance (1997), is here obtained without the addition of noise and is due to the addition of time-delay.

(2) first demonstration of optical rogue waves in a time-delayed optical system. We show that the addition of time-delayed signal in the dynamics of a laser system yields high intensity pulses, whose height is by far exceeding the average of the system output. These high-intensity pulses show statistical properties similar to those of so-called rogue or freak waves in hydrodynamics.

(3) first demonstration of interaction of nonlocality and vorticity in an optical pattern forming system. The addition of nonlocal feedback dues to feedback mirror misalignement suppresses the rotating pattern dynamics due to the input vortex light beam.

A common ingredient of many dynamical systems is the presence of time-delay when e.g. feedback couples the output signal back to the input. Examples are found e.g. in biology (neurons, gene regulatory networks) and in social networks (car traffic jams, internet). Time-delayed coupling or feedback impacts the system dynamics dramatically and can be responsible for chaos or spatial self-organisation in patterns. The emerging dynamics depends on the ratio between the feedback/coupling strength and the signal strength, but also and in a more complex way on the ratio between the time-delay or coupling/feedback length and other internal system time constants and characteristic size. This project will take advantage of the engineering of advanced optical systems to provide a first in-depth understanding of these scaling effects in time-delayed systems and to turn them into innovative applications. Phase conjugation in semiconductor photorefractive crystal will be used to feedback light from a laser diode, with a time-delay being controllable by the nonlinear optics time-scale (nanoseconds up to seconds). All-optical self-pulsations at below nanosecond time-scale and chaos control will be obtained depending on the scaling of the time-delay versus the system time constants, with applications to optical signal processing and chaos communications. Optical pumping of photorefractive extended optical cavities and semiconductor vertical cavities will be used to generate feedback-induced dissipative solitons or patterns. Scalable material dimensions and external cavity length will help to control the propagation characteristics of these light structures, leading to alternative solutions for optical storage. Through this original combination of laser physics, nonlinear science and nonlinear optics, the project addresses the generic question of how a complex system behaves in space and time, that is, one of the most fundamental question of today modern physics.