# Group Velocity And Phase Velocity Ppt To Pdf

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According to quantum physics, particles sometimes behave like waves. In some cases, waves behave like particles. This property of particles and waves is known as the wave- particle duality.

## group velocity dispersion ppt

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 , within which one can discern individual wavelets of differing wavelengths traveling at different speeds. The shorter waves travel faster than the group as a whole, [ citation needed ] [ dubious — discuss ] but their amplitudes diminish as they approach the leading edge of the group. The longer waves travel more slowly, and their amplitudes diminish as they emerge from the trailing boundary of the group. The group velocity v g is defined by the equation: [2] [3] [4] [5].

## group velocity dispersion ppt

The parametric interaction of optical wave pulses in metamaterials is considered in the first approximation of the theory of dispersion. The interaction between the quasi-monochromatic pump wave and the wave pulse at the total frequency with quadratic phase modulation is assumed. The results of calculation of the shape of the spectrum of an excited signal wave at a difference frequency are presented for low frequency pumping. It is shown that the effects of group mismatch in metamaterials lead to a narrowing of the spectrum of the excited wave. With an increase in the modulation degree of a weak exciting wave, the spectrum of the excited wave broadens. Metamaterials are artificial materials formed from microstructures metaatoms , whose properties can be controlled. Such media are made from natural materials with a positive refractive index.

Wave packet, phase velocity and group velocity. The velocities of the individual waves which superpose to produce the wave packet representing the particle.

## Optics Express

Note: this box searches only for keywords in the titles of encyclopedia articles. For full-text searches on the whole website, use our search page. Note: the article keyword search field and some other of the site's functionality would require Javascript, which however is turned off in your browser. Group velocity dispersion is the phenomenon that the group velocity of light in a transparent medium depends on the optical frequency or wavelength. The term can also be used as a precisely defined quantity, namely the derivative of the inverse group velocity with respect to the angular frequency or sometimes the wavelength :.

In Alford and Zhao , henceforth Part I , time series of depth-integrated energy E and flux F were computed at 80 historical moorings for the first two baroclinic modes. They describe a globally propagating field of near-inertial and semidiurnal internal waves. Knowledge of the group velocity proves very powerful, because it yields internal-wave intrinsic frequency via the dispersion relation—enabling, for example, estimation of horizontal wavenumber from single-point measurements.

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### Phase Velocity and Group Velocity Civil Engineering (CE) Notes | EduRev

Wave:de-localized spread out in space and time How do we associate a wave nature to a particle? What could represent both wave and particle? Find a description of a particle which is consistent with our notion of both particles and waves Fits the wave description Localized in space A Wave Packet 3 of the group envelope is non-zero only in the neighbourhood of the particle A wave packet is localized a good representation for a particle!

Phase velocity and Group velocity Phase velocity: The velocity with which a wave travels is called Phase velocity or wave velocity. It is denoted by v p. It is given by. The above equation gives the relationship between the phase velocity and particle velocity.

#### Conversion of Chromatic Dispersion Values

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