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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]

Settings

Section titled “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, or TOD.

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

Material models

Section titled “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 leaves gaps at those jumps instead of connecting unrelated one-sided values. A user-created smooth fit is used only inside the validity range stored with the material. Points outside a model range are blank and the window reports how many were omitted.

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

Section titled “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.