Lecture

Wave Packets and Group Speed Dispersion

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In course

PHYS-317: Optics I

L'optique est un vieux domaine qui touche à beaucoup de sujets modernes, des techniques expérimentales aux applications courantes. Ce premier cours traite plusieurs aspects de base de l'optique: propagation, dispersion, interférence, diffraction, polarisat ...

Description

This lecture covers the concept of wave packets, their relation to Fourier transforms, and the dispersion of group speed. It explains how different frequencies in wave packets result in delays, the propagation of wave packets in dispersive media, and the effects of dispersion on pulse width. The instructor discusses the transformation of wave packets in series, the impact of frequency modulation on wave packets, and the potential for superluminal group speeds. The lecture also delves into interference phenomena, coherence effects on intensity, and the conditions for correct interference. Additionally, it explores diffraction of light, Young's experiment, and the principles of interferometry.

Instructor

Benjamin Dwir

Academic title: Dr. Birth date: 24.10.1959 Nationality: Swiss At EPFL since: 1988

Official source

Related concepts (32)

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.

Frequency modulation

Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing. In analog frequency modulation, such as radio broadcasting, of an audio signal representing voice or music, the instantaneous frequency deviation, i.e. the difference between the frequency of the carrier and its center frequency, has a functional relation to the modulating signal amplitude.

Fourier transform

In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

Modulation

In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a separate signal called the modulation signal that typically contains information to be transmitted. For example, the modulation signal might be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal representing a sequence of binary digits, a bitstream from a computer.

Wave packet

In physics, a wave packet (also known as a wave train or wave group) is a short burst of localized wave action that travels as a unit, outlined by an envelope. A wave packet can be analyzed into, or can be synthesized from, a potentially-infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere.

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