Dispersion

Dispersion is the dependence of a wave’s propagation speed or a medium’s refractive index on frequency or wavelength. It causes different spectral components to travel at different speeds.

Group velocity: The speed at which a wave packet’s envelope or modulation propagates through a medium. Its frequency dependence determines how quickly a pulse envelope travels through a dispersive medium.
Wavenumber: A measure of spatial frequency, equal to the phase change per unit distance. Its dependence on angular frequency encodes a wave’s dispersion relation.
Chromatic aberration: An optical imaging defect in which different wavelengths focus at different positions or magnifications. Wavelength-dependent refraction spreads colors out of focus in lenses.
Absorption: The transfer of electromagnetic-wave energy into matter, reducing the wave’s intensity as it propagates. Absorption attenuates spectral components, while dispersion changes their propagation phase and speed.
Phase velocity: The speed at which a fixed phase point, such as a crest, moves through a wave. Dispersion makes this speed vary with frequency, changing the spacing of wave crests.
Angular frequency: The rate of phase rotation of a periodic signal, measured in radians per unit time. Dispersion describes how propagation changes as angular frequency changes.
Optical fiber communication: The transmission of information as light signals through optical fibers. Fiber dispersion broadens pulses and can cause neighboring data symbols to overlap.
Scattering: The redirection of waves by variations or objects in a medium. Scattering redirects waves; dispersion changes propagation according to frequency even in a uniform medium.
Refractive index: A dimensionless measure of how much slower light travels in a material than in vacuum. Its variation with wavelength is the optical form of dispersion.
Dispersion relation: A relation connecting a wave’s angular frequency to its wavenumber in a specified medium or system. It states directly how frequency and propagation characteristics are linked.

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