The GD/GDD window computes the spectral phase of a coating and its derivatives with respect to frequency: the group delay (GD), group-delay dispersion (GDD), and third-order dispersion (TOD). These are the quantities you tune when designing mirrors and coatings for ultrafast lasers, where controlling how different frequencies are delayed is as important as controlling reflectance.

The phase is taken from the complex reflection or transmission coefficient, and the derivatives follow as:

φ(ω) = arg(r)  or  arg(t)
GD  = −dφ/dω     [fs]
GDD = −d²φ/dω²   [fs²]
TOD = −d³φ/dω³   [fs³]

Settings

Quantity — choose which curve to plot: phase φ, GD, GDD, or TOD.

Reflection / Transmission — take the phase from the reflected (R) or transmitted (T) wave.

Polarization — s or p.

Side — take the phase from the front coating or the back coating. Each coating is evaluated on its own, so a part with a chirped mirror on one face and a different coating on the other can be inspected one side at a time.

Wavelength range and step — the span and sampling interval of the plot, in nm. Use a fine step (0.2 nm or smaller) before trusting GDD and TOD near sharp spectral features, because each higher derivative amplifies sampling noise.

AOI — the angle of incidence in degrees.

Reference wavelength — when shown, the phase curve is shifted so it reads zero at this wavelength. This is a constant offset and only affects the phase plot; GD, GDD and TOD are derivatives and are unchanged.

How to read it

For a chirped mirror, GD should follow the target ramp across the band and GDD should hold the intended (usually negative) value to compensate pulse dispersion. A clean, smooth curve indicates a well-resolved phase; if GDD or TOD shows unphysical spikes near a sharp feature, the wavelength step is too coarse — refine it until the spikes disappear.

The data table lists the phase and its derivatives against wavelength for export.

References

• H. A. Macleod, Thin-Film Optical Filters, 5th ed., Ch. 11 (Eq. 11.17) — ultrafast coatings.
• S. Diddams & J.-C. Diels, J. Opt. Soc. Am. B 13, 1120 (1996).