Wavelength vs Angle

Wavelength vs Angle answers how far the coating drifts when the light stops arriving straight on. It computes one quantity over a wavelength range and an angle range together and draws the result as a colour map, so a passband edge that walks 30 nm between 0° and 45° is one picture rather than ten overlaid spectra.

The map recomputes whenever the design changes. There is nothing to press.

Settings

Quantity: T, R or A, on the control row.

Polarization: avg, s or p. At normal incidence the three agree; they separate as the angle grows, and the s / p split is often the thing being looked for.

Render: Heatmap draws the map flat, which is the easier one to read a number off. 3D draws the same grid as a rotatable surface, which shows the shape of a peak better than a colour ramp does.

In the settings panel:

λ: the wavelength range and the step between columns.

Angle: the angle-of-incidence range and the step between rows. The window opens on 0 to 60°, and takes anything up to 89°.

Colors: the colorscale. Turbo by default, with Jet, Viridis, Cividis and others to pick from.

The grid size is shown under the ranges. Both step sizes are yours to set, and a fine grid over a thick stack takes longer, so start coarse and tighten once the region of interest is clear.

The map is computed for the surface mode set in the Design Editor, shown as a badge next to the results.

How to read it

Read across a row for the spectrum at one angle, and down a column for how one wavelength behaves as the light tilts. Anything that runs diagonally is a feature moving with angle; anything vertical is a feature that stays put.

Features move toward shorter wavelengths as the angle grows. A layer’s phase thickness at oblique incidence is 2π·nd·cos θ/λ, where θ is the angle inside the layer rather than the angle of incidence. That leaves an apparent optical thickness of nd·cos θ, so the stack looks thinner the further it is tilted, and every wavelength-dependent feature in it shifts down with it. That is why an edge filter specified at normal incidence lands short of its target in a converging beam, and why a bandpass filter is often designed slightly long so a tilt brings it onto wavelength.

The Results strip below the plot holds the grid as numbers, one row per wavelength and angle pair, and Export writes it to CSV. The chart’s own toolbar exports the picture as PNG or SVG.

For a single angle at full spectral detail, use Optical Evaluation; for a map over something other than angle, such as a layer thickness, use the Plot Engine surface, which this window is built on.

References

• H. A. Macleod, Thin-Film Optical Filters, 5th ed., §9.2 (Eq. 9.2, tilted thicknesses).