I think it is implicitly assumed that the specified index of refraction n_0 is valid for the central wavelength of the laser pulse.
In the presence of chirp, it is necessary to vary the index of refraction correctly.
This can be a perturbative calculation, as the chirp is small relative to the central wavelength.
The same needs to be done with the n2 (aka dn/dT) component of the index of refraction.
I think it is implicitly assumed that the specified index of refraction n_0 is valid for the central wavelength of the laser pulse. In the presence of chirp, it is necessary to vary the index of refraction correctly. This can be a perturbative calculation, as the chirp is small relative to the central wavelength.
The same needs to be done with the n2 (aka dn/dT) component of the index of refraction.