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Lecture

Solving the NLSE: Split-Step Fourier Method

In course

PHYS-607: Nonlinear fibre optics

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

Description

This lecture covers the split-step Fourier method to solve the Nonlinear Schrödinger Equation (NLSE) in the context of nonlinear fiber optics. It discusses the generalized NLSE valid for few optical cycles, including terms like loss, dispersion, self-steepening, and phenomena like SPM, FWM, and Raman scattering. The lecture also explains the numerical method of split-step Fourier, which approximates the combined effects of dispersion and nonlinearity during pulse propagation. It details the improved accuracy of the method by including nonlinearity in the middle of the segment, known as symmetrised SSFM.

Instructors (2)

Camille Sophie Brès

Prof. Camille-Sophie Brès is an Associate Professor in the Institute of Electrical Engineering within the School of Engineering of EPFL. Her primary research interests are centered optical communications and on parametric and nonlinear processes in optical fiber and non-silica platforms for ultrafast signal processing, all optical networks, sensing and light sources. She has authored over thirty peer-reviewed journal articles and has presented more than 15 papers at international conferences. She received the Gordon Wu Fellowship for her graduate studies, the NSF CIANs Diversity Postdoctoral Fellowship in 2009, the Early Career Woman in Engineering Award in 2016. She is a senior member of the IEEE and OSA. 2019 - present: Associate Professor in the Institute of Electrical Engineering, EPFL 2011 - 2018: Assistant Professor in the Institute of Electrical Engineering, EPFL 2010 - 2011: Assistant Project Scientist, University of California San Diego (UCSD) 2007 - 2010: Postdoc in ECE, University of California San Diego (UCSD) 2002 - 2007: Ph.D in Electrical Engineering, Princeton University 1998 - 2002: B.Eng with Honours in Electrical Engineering, McGill University

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 (23)

Dispersion (optics)

In optics and in wave propagation in general, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for specificity to optics in particular. A medium having this common property may be termed a dispersive medium (plural dispersive media). Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, and in gravity waves (ocean waves).

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Numerical methods for partial differential equations

Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.

Numerical methods for linear least squares

Numerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).

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