Ultrathin Absorbing Interference Coatings

This case reproduces the thickness effect of an ultrathin Ge/Au absorbing coating. You will place a Ge film on an Au reflector, sweep the Ge thickness, calculate the reflection spectrum and color, and compare the results with Figure 2c.

After reading, you can understand why a strongly absorbing film can still produce pronounced interference changes below a quarter-wave thickness, track the redshift of the reflection dip as thickness increases, and use spectrum and color results to check the reproduction.

Background

Conventional thin-film design assumes interference requires transparent or weakly absorbing layers. The Kats paper formalizes a different regime: a few to a few tens of nanometres of a highly absorbing film on a metal can produce non-trivial reflection-phase shifts at both interfaces, so an absorption resonance forms at thicknesses well below λ/(4n₂) instead of the textbook quarter-wave value.

The relevant observables are reflectance and the in-Ge absorption fraction. Both stay within 1D layered optics, which makes the case a clean TMM benchmark.

Paper Details

• Paper: Nanometre optical coatings based on strong interference effects in highly absorbing media
• Authors: M. A. Kats, R. Blanchard, P. Genevet, F. Capasso
• Journal: Nature Materials 12, 20-24 (2013)
• DOI: 10.1038/nmat3443
• Comparison target: Figure 2c (calculated reflection spectra for 7/10/15/20/25 nm Ge on thick Au at near-normal incidence)

The full Figure 2 below provides context — panel a shows the n,k inputs, panel b the experimental reflection at 7° incidence, panel c the calculated reflection (the TMM-equivalent target), and panel d the absorbed fraction in the Ge layer.

Mapping the Paper to the TMM Model

The configuration file recipes/ultrathin-absorbing-coatings.json in this repository encodes the exact stack and sweep above, so the run is replayable end-to-end through the standard front end.

Reproduction Target and Acceptance Criteria

The reproduction is considered successful when:

1. A clear reflectance dip walks from short wavelength (~500 nm for 5 nm Ge) toward long wavelength (beyond 800 nm for 25 nm Ge).
2. Trace ordering follows Ge thickness monotonically across the visible band.
3. All five curves stay reflection-dominated (no curve crashes to zero across the full band); the metal mirror remains the dominant boundary.
4. The 10 nm trace shows a dip near 600-650 nm and the 15 nm trace near 700 nm, matching the Fig. 2c spectral positions.

Not required in this pass: exact dip-depth match, exact crossover wavelengths, or the experimental Fig. 2b agreement (which depends on the paper's own ellipsometry-extracted optical constants).

Modeling Path in Dreapex TMM

Structure

1. In Structure, add a top Ge layer with thickness 15 nm (sweep handles the others).
2. Set its material to main/Ge/nk/Aspnes.yml from the built-in database.
3. Add an Au layer with thickness 150 nm, material main/Au/nk/Johnson.yml.
4. Keep the transmission medium as Au-backing (semi-infinite) so transmission is suppressed.

Optical settings

• Wavelength range: 400-824 nm, step 2 nm
• Incidence angle: 7°
• Polarization: pRatio = 0.5 (unpolarized)
• Detector: Reflectance
• Sweep variable: top-layer thickness, from = 5, to = 25, step = 5 (values [5, 10, 15, 20, 25] nm)

Simulation Results and Comparison with Figure 2c

The Dreapex TMM result page is placed directly next to the paper panel. Both should show five reflectance traces ordered by Ge thickness.

Read the comparison along three axes:

• Dip migration. The minimum should walk monotonically from blue toward red as Ge thickness grows from 7 nm to 25 nm, matching the paper's central design lever.
• Reflection envelope. No trace should collapse below the Au baseline; the metal mirror keeps every curve reflection-dominated.
• Short-wavelength shape. The thinnest two films (7 nm, 10 nm) should show a defined dip inside 500-600 nm, then climb back at long wavelengths.

For application-facing interpretation, the same stack can also be inspected through Reflection Color. The thickness-driven spectral shift translates into a visually consistent color sequence:

Deviation Analysis

Expected deviations from the paper panel:

1. The TMM run uses Ge thicknesses [5, 10, 15, 20, 25] nm instead of the paper's [7, 10, 15, 20, 25] nm, because the engine's sweep widget supports only uniform from/to/step. The 5 nm curve replaces the paper's 7 nm curve and shows a slightly bluer dip — the dip-migration trend is identical.
2. Wavelength is capped at 824 nm instead of the paper's 850 nm because the built-in Aspnes Ge dataset only covers 206.6-826.6 nm. The reflection trends in the missing 826-850 nm window are continuous extensions of the visible curves.
3. This case uses the built-in Aspnes Ge dataset, while the paper uses VASE-extracted optical constants from its own e-beam-evaporated films. Absolute dip depth and exact crossover wavelength can therefore shift.
4. This case uses the built-in Johnson Au dataset; substituting Rakic-BB Au will redistribute the interface phase and slightly relocate the dips.
5. Transmission medium is Air; the 150 nm Au is opaque enough across the visible that this is equivalent to the paper's optically thick assumption.
6. The model does not include surface roughness, native oxide on Ge, or Au-Ge interfacial reactions.

These factors affect line shape, not the central conclusion: the thickness-driven dip migration survives unchanged.

Further Extensions

1. Sweep Ge thickness in 1 nm increments inside 5-20 nm to map the most sensitive region for color design.
2. Add an Absorptance detector and verify that >80% of incident light is absorbed inside the 15 nm Ge layer near 670 nm (Kats Fig. 2d claim).
3. Compare Aspnes Ge with another mid-visible Ge dataset to quantify the dip-depth uncertainty driven by optical-constant choice.
4. Repeat the sweep at 30° and 60° and compare the angular maps against Figure 3a-d.