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A closely related yet independent quantity is the group-delay dispersion (GDD), defined such that group-velocity dispersion is the group-delay dispersion per unit length. GDD is commonly used as a parameter in characterizing layered mirrors, where the group-velocity dispersion is not particularly well-defined, yet the chirp induced after ...
The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
Consequently, for frequencies within the sweep range of the chirp, it is the square-law phase term Φ 1(ω) and its group delay function ( = -d Φ 1/d(ω) ) that are of most interest. There is a plot of the group delay shown below. Both this function and the phase Φ 1(ω) are independent of the value of the time-bandwidth product.
Group-velocity dispersion is quantified as the derivative of the reciprocal of the group velocity with respect to angular frequency, which results in group-velocity dispersion = d 2 k/dω 2. If a light pulse is propagated through a material with positive group-velocity dispersion, then the shorter-wavelength components travel slower than the ...
For a sufficiently large delay (from 10 to 1000 times the Fourier transform limited [FTL] pulse duration), the interference of the two time-delayed fields results in a cosine modulation with a nominal spacing of /; and any dispersion of the pulse results in minor deviations in the nominal fringe spacing. Effectively it is these deviations in ...
However, these can only measure the pulse characteristics but not correct for defects in order to make the pulse as short as possible. For instance, the pulse could be linearly chirped or present higher order group delay dispersion (GDD) so that its duration is longer than a bandwidth-limited pulse having the same intensity spectrum. It is ...
Now we let this pulse propagate through a fibre with >, it will be affected by group velocity dispersion. For this sign of D, the dispersion is anomalous, so that the higher frequency components will propagate a little bit faster than the lower frequencies, thus arriving before at the end of the fiber. The overall signal we get is a wider ...
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 ...