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The term Group Delay in optics is the relative amount of time light of different frequencies is delayed as it travels through a transmitting medium (like an optic made of glass) or it rattles around inside the many layers of a thin-film coating.  At some frequencies (or wavelengths), it takes light longer to emerge from the medium or thin-film coating than at other frequencies.  Mathematically Group Delay is the rate of change of the total phase shift of light with respect to angular frequency, and therefore it has units of time.  Group Delay Dispersion (GDD) describes how rapidly the Group Delay varies with the frequency or wavelength of light.  When you transmit the pulses from an ultrafast laser source through an optic or reflect them off of a thin-film coated mirror, the pulse width may increase and the peak power may decrease.  Physically, this “broadening and squishing” occurs because each short pulse is made up of a nonzero range of light frequencies (the shorter the pulse the wider the range), and these different frequency components are delayed by different amounts, thus resulting in the pulse being “chirped” such that the frequency varies along the length of the pulse.  Pulse broadening and squishing is undesirable for applications which rely on high peak power, such as multiphoton and other nonlinear optical processes which depend nonlinearly on peak power.  In these systems a reduction in peak power of say a factor of 2 results in a reduction in signal of much more than a factor of 2 (typically 4 or more).   Mathematically GDD it is the rate of change of the Group Delay with respect to angular frequency, and thus GDD has units of time squared.  Usually it is expressed in units of femtoseconds (fs) squared.  Many system optics, like microscope objectives, contribute positive GDD and necessarily cause pulse chirping.  Chirp compensation optics (such as specially designed mirrors) are frequently described as providing “negative chirp” and are used to pre-condition the pulse before it arrives at the objective or other positive GDD optics.  Removing sources of GDD is not as important as having a consistent, manageable amount of GDD. This way, the system can maintain the desired narrow width and high peak power of the ultrafast laser pulses without the need for continual or large compensation adjustments.