 Transit and pulse evolution

Taking $L=1.00\mathrm{cm}$ as the distance travelled in the medium, the narrowband group delay isIf $1\mathrm{cm}$ denotes a slab thickness measured normal to the interface instead, the central ray travels $L/\cos 17.80^{\circ }$, giving about $92.1\mathrm{ps}$. The coordinate-mixed velocity above would give $89.3\mathrm{ps}$ for a $1\mathrm{cm}$ path; it should not replace the consistent calculation silently.

The pulse envelope travels at the local group velocity, while individual carrier crests move at the phase velocity. In general, variation of group velocity across the pulse spectrum produces different delays, temporal broadening and chirp. Absorption can reshape the spectrum and envelope as well. The refraction data also show wavelength-dependent angles, so a finite-width incident beam acquires spatial separation of its spectral components. The supplied first derivative determines the central delay but does not specify a pulse duration, absorption spectrum or reliable second derivative of the dispersion relation; it therefore does not determine a numerical broadening, or its sign. If propagation phase is effectively linear across a sufficiently narrow spectrum, the leading approximation is a delayed pulse with unchanged shape.