Lecture

Modulation Instability in Optical Waveguide

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In course

PHYS-607: Nonlinear fibre optics

Presentation of the different sources of optical nonlinearities in an optical fibre ...

Description

This lecture explores modulation instability in optical waveguides, a phenomenon where continuous wave light can break up into ultrashort pulses due to the interplay between nonlinearity and dispersion. The instructor discusses the definition, diverse fields where modulation instability is studied, and its observation in various physics domains. Linear stability analysis inside a waveguide is presented, focusing on the dispersion relation and stability conditions against perturbations. Gain in power for small perturbations and the impact of dispersion values on instability gain are also covered, with suggestions for simulation experiments.

Instructors (2)

Luc Thévenaz

Luc Thévenaz received in 1982 the M.Sc. degree in astrophysics from the Observatory of Geneva, Switzerland, and in 1988 the Ph.D. degree in physics from the University of Geneva, Switzerland. He developed at this moment his field of expertise, i.e. fibre optics. In 1988 he joined the Swiss Federal Institute of Technology of Lausanne (EPFL) where he currently leads a research group involved in photonics, namely fibre optics and optical sensing. Research topics include Brillouin-scattering fibre sensors, nonlinear fibre optics, slow & fast light and laser spectroscopy in gases. His main achievements are: - the invention of a novel configuration for distributed Brillouin fibre sensing based on a single laser source, resulting in a high intrinsic stability making for the first time field measurements possible, - the development of a photoacoustic gas trace sensor using a near infra-red semiconductor laser, detecting a gas concentration at the ppb level, - the first experimental demonstration of optically-controlled slow & fast light in optical fibres, realized at ambient temperature and operating at any wavelength since based on stimulated Brillouin scattering. The first negative group velocity of light was also realized in optical fibres using this approach. In 1991, he visited the PUC University in Rio de Janeiro, Brazil where he worked on the generation of picosecond pulses in semiconductor lasers. In 1991-1992 he stayed at Stanford University, USA, where he participated in the development of a Brillouin laser gyroscope. He joined in 1998 the company Orbisphere Laboratories SA in Neuchâtel, Switzerland, as Expert Scientist to develop gas trace sensors based on photoacoustic laser spectroscopy. In 1998 and 1999 he visited the Korea Advanced Institute of Science and Technology (KAIST) in Daejon, South Korea, where he worked on fibre laser current sensors. In 2000 he co-founded the spin-off company Omnisens that is developing and commercializing advanced photonic instrumentation. In 2007 he visited Tel Aviv University where he studied the all-optical control of polarization in optical fibres. During winter 2010 he stayed at the University of Sydney where he studied applications of stimulated Brillouin scattering in chalcogenide waveguides. In 2014 he stayed at the Polytechnic University of Valencia where he worked on microwave applications of stimulated Brillouin scattering. He was member of the Consortium in the FP7 European Project GOSPEL "Governing the speed of light", was Chairman of the European COST Action 299 "FIDES: Optical Fibres for New Challenges Facing the Information Society" and is author or co-author of some 480 publications and 12 patents. He is now Coordinator of the H2020 Marie Skłodowska-Curie Innovative Training Networks FINESSE (FIbre NErve Systems for Sensing). He is co-Executive Editor-in-Chief of the journal "Nature Light: Science & Applications" and is Member of the Editorial Board (Associate Editor) for the journal "APL Photonics" & "Laser & Photonics Reviews". He is also Fellow of both the IEEE and the Optical Society (OSA).

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Related concepts (24)

Stability theory

In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.

Lyapunov stability

Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).

Computer experiment

A computer experiment or simulation experiment is an experiment used to study a computer simulation, also referred to as an in silico system. This area includes computational physics, computational chemistry, computational biology and other similar disciplines. Computer simulations are constructed to emulate a physical system. Because these are meant to replicate some aspect of a system in detail, they often do not yield an analytic solution. Therefore, methods such as discrete event simulation or finite element solvers are used.

Ultrashort pulse

In optics, an ultrashort pulse, also known as an ultrafast event, is an electromagnetic pulse whose time duration is of the order of a picosecond (10−12 second) or less. Such pulses have a broadband optical spectrum, and can be created by mode-locked oscillators. Amplification of ultrashort pulses almost always requires the technique of chirped pulse amplification, in order to avoid damage to the gain medium of the amplifier. They are characterized by a high peak intensity (or more correctly, irradiance) that usually leads to nonlinear interactions in various materials, including air.

Simulation

A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.

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