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In optics, group-velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium affects the duration of an optical pulse traveling through it. Formally, GVD is defined as the derivative of the inverse of group velocity of light in a material with respect to angular frequency , [ 1 ] [ 2 ]
The RP Photonics Encyclopedia (formerly Encyclopedia of Laser Physics and Technology) is an encyclopedia of optics and optoelectronics, laser technology, optical fibers, nonlinear optics, optical communications, imaging science, optical metrology, spectroscopy and ultrashort pulse physics. [1] It is available online as a free resource.
Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. [1] Sometimes the term chromatic dispersion is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common property may be termed a dispersive medium.
The introduced dispersion by such a compressor is often described in dispersion orders: the group delay dispersion (GGD), third order of dispersion (TOD) etc. Figure 2 shows the dispersion orders for a grating compressor with a groove density of = /, an incidence angle of =, and a normal grating separation of =, as described in the original ...
The Gaussian function has a 1/e 2 diameter (2w as used in the text) about 1.7 times the FWHM.. At a position z along the beam (measured from the focus), the spot size parameter w is given by a hyperbolic relation: [1] = + (), where [1] = is called the Rayleigh range as further discussed below, and is the refractive index of the medium.
Although the birefringence Δn may vary slightly due to dispersion, this is negligible compared to the variation in phase difference according to the wavelength of the light due to the fixed path difference (λ 0 in the denominator in the above equation). Waveplates are thus manufactured to work for a particular range of wavelengths.
The term in is the group velocity dispersion (GVD) or second-order dispersion; it increases the pulse duration and chirps the pulse as it propagates through the medium. The term in β 3 {\displaystyle \beta _{3}} is a third-order dispersion term that can further increase the pulse duration, even if β 2 {\displaystyle \beta _{2}} vanishes.
This dispersion relation is vitally dependent on the sign of the term within the square root, as if positive, the wavenumber will be real, corresponding to mere oscillations around the unperturbed solution, whilst if negative, the wavenumber will become imaginary, corresponding to exponential growth and thus instability. Therefore, instability ...