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Lecture

Fourier Transform and Propagation Constants

In course

EE-440: Photonic systems and technology

The physics of optical communication components and their applications to communication systems will be covered. The course is intended to present the operation principles of contemporary optical communication systems employing optical fibers and modern op ...

Description

This lecture covers the definition of the Fourier transform and its application in describing waves in single-mode fibers, including the propagation of chirped pulses and the effect on the spectrum. It also delves into the concept of propagation constants, discussing the real and imaginary parts, effective refractive index, and the linear and nonlinear contributions. The lecture further explores the linear part of the propagation constant, dispersion parameters, and the relationship between phase velocity and group velocity.

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Instructor

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

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Related concepts (32)

Group velocity

The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as a capillary wave. The expanding ring of waves is the wave group or wave packet, within which one can discern individual waves that travel faster than the group as a whole.

Phase velocity

The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ (lambda) and time period T as Equivalently, in terms of the wave's angular frequency ω, which specifies angular change per unit of time, and wavenumber (or angular wave number) k, which represent the angular change per unit of space, To gain some basic intuition for this equation, we consider a propagating (cosine) wave A cos(kx − ωt).

Dispersion relation

In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency.

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).

Propagation constant

The propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a circuit, or a field vector such as electric field strength or flux density. The propagation constant itself measures the change per unit length, but it is otherwise dimensionless. In the context of two-port networks and their cascades, propagation constant measures the change undergone by the source quantity as it propagates from one port to the next.

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