Material Dispersion

The Material Dispersion window calculates the delay added by one pass through a chosen thickness of bulk material. It separates substrate or window dispersion from coating dispersion and provides a closed-form check for the Total mode in the GD / GDD window.

For thickness d, refractive index n(ω), and angular frequency ω, the reported propagation terms are:

GD  = (d/c) [n + ω dn/dω]
GDD = (d/c) [2 dn/dω + ω d²n/dω²]
TOD = (d/c) [3 d²n/dω² + ω d³n/dω³]
CDC = GDD·2πc/λ²

Settings

Material: any material available to the active design and material catalogs.

Thickness: single-pass propagation distance. Select nm, µm, or mm to use film and substrate dimensions directly. For an opaque path, the warning badge on the control row reports the maximum thickness that keeps the full selected range evaluable.

Quantity: phase, GD, GDD, CDC, or TOD. CDC is the same group delay dispersion taken against wavelength rather than angular frequency, in fs/nm, which is how a telecommunications specification is written.

Wavelength range: the span plotted and exported. TFStudio selects the sampling automatically because each wavelength is evaluated pointwise.

Material models

Formula derivatives are exact for the stored coefficients. PCHIP derivatives are exact for the cubic piece drawn through the supplied table, but higher orders still describe that interpolation choice. PCHIP is continuous through its first derivative; GDD and TOD can jump at table knots. The plot samples each knot and draws the jump as a step through the value on each side of it, so the curve is never cut there. A gap means the opposite, that the sample has no value: a wavelength the thickness has masked, or one whose model cannot supply third-order derivatives. The window’s notice gives the reason.

Outside the material’s data range the curve is still drawn, over a shaded band naming the material and the range it does cover. A table holds the value in its last row out there, so its index has no slope and the material adds no dispersion at all: what is plotted in the band is the delay of a dispersionless slab. A formula is extrapolated past the band it was fitted over and keeps dispersing, which is a model outside its validity rather than an absence of one. A user-created smooth fit is used only inside the validity range stored with the material. The results table marks those rows with the material, so an exported number is never silently an extrapolation, and narrowing the plotted range to the covered span is one click on the notice.

For an absorbing material, k does not enter propagation phase directly. It sets how much of the direct pulse survives. TFStudio masks wavelengths where the selected thickness gives a field optical depth above 50, equivalent to internal intensity transmission below exp(-100). Reporting a delay there would describe the phase of a pulse that has been extinguished.

For reference, the bundled fused-silica Sellmeier model gives about 36.2 fs²/mm at 800 nm. This check is bulk propagation only and does not include coating-interface phase.

References

• H. A. Macleod, Thin-Film Optical Filters, 5th ed., Ch. 11.
• I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” Journal of the Optical Society of America 55, 1205-1209 (1965), doi:10.1364/JOSA.55.001205.
• OptiLayer, “Material Dispersion”, bulk-material phase and group-delay definitions.