Ultrathin Absorbing Interference Coatings

Nanometre optical coatings based on strong interference effects in highly absorbing media Authors: M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso Journal: Nature Materials 12, 20–24 (2013) · Comparison target: Figure 2c https://doi.org/10.1038/nmat3443

Put a few to a few tens of nanometres of germanium on a gold mirror and the reflection dip moves steadily with thickness, changing the colour you see — at thicknesses far below the quarter-wave the textbook asks for.

This case deposits Ge on 150 nm of Au, sweeps the Ge thickness, and computes 7° reflection spectra and reflected colour for comparison with paper Figure 2c.

Note

The published figure is not reproduced here: Figure 2 is copyright Nature Materials (Springer Nature) and commercial reuse permission has not been granted. Open the original through DOI 10.1038/nmat3443 to view it; access may require a subscription or institutional login. Every value labelled “paper” below is a data point read off the original independently; the figure itself is neither copied nor redrawn.

The dip of each of the five traces moves monotonically to the red as Ge thickens, and none of them falls below the gold baseline.

Note

Prerequisite: complete Quick Start, and read Parameter Sweep and Spectrum and Color Analysis.

Background

Conventional thin-film design assumes interference requires transparent or weakly absorbing layers. Kats et al. formalize a different regime: a few to a few tens of nanometres of a highly absorbing film on a metal produces non-trivial reflection-phase shifts at both interfaces, so an absorption resonance forms at thicknesses well below λ/(4n₂).

The full published Figure 2 gives the context — panel a shows the n,k inputs, panel b the measured reflection at 7°, panel c the calculated reflection that this case targets, and panel d the absorbed fraction in the Ge layer. View all four panels in the original paper.

Structure

Item	Model value	Notes
Incidence medium	Air	Matches the paper’s air-side measurement geometry
Top layer	Ge, thickness swept over 5, 10, 15, 20, 25 nm	A uniform 5 nm step is the closest uniform sweep to the paper’s 7/10/15/20/25 sequence
Bottom layer	Au, 150 nm	The paper deposits Ge on 150 nm of e-beam Au, optically thick across the visible
Transmission medium	Air	The 150 nm Au is opaque across the visible, so the through-substrate contribution is negligible
Ge optical data	Built-in Aspnes database entry	The paper instead uses ellipsometry on its own deposited films
Au optical data	Built-in Johnson database entry	—

Only two layers are needed: a top Ge layer at 15 nm (the sweep supplies the rest) with the Ge entry from the database, and an Au layer at 150 nm, with a semi-infinite backing to suppress transmission.

Choosing the Ge optical constants from the built-in database:

The resulting two-layer structure page:

Optical Settings

Setting	Value
Wavelength range	400–824 nm, step 2 nm
Incidence angle	7°
Polarization	pRatio = 0.5 (unpolarized), matching the paper’s measurement convention
Detector	Reflectance
Sweep variable	Top-layer thickness, from = 5, to = 25, step = 5

The 824 nm upper limit comes from the built-in Ge dataset, which reaches only 826.6 nm.

Note

This case does not use Optimize. If a notice related only to Optimize appears at the bottom of the page, continue with Sweep.

Simulation Results and Comparison with Figure 2c

Paper Figure 2c is in the original article.

The same sweep in the app, five traces ordered by Ge thickness:

Three features match the paper: the dip walks monotonically toward the red as Ge thickens; no trace collapses below the Au baseline, since the metal mirror keeps every curve reflection-dominated; and the two thinnest films show a defined dip inside 500–600 nm before climbing back at long wavelengths.

Switching the same stack to Reflection Color turns that thickness-driven spectral shift into a continuous colour sequence:

The Reflection Spectrum page reads the local spectral detail of a single thickness:

Deviation Notes

The thinnest trace uses 5 nm in place of the paper’s 7 nm: the sweep supports only uniform steps, and 5 nm is the closest uniform value to the published sequence, so its dip sits slightly bluer.

Both materials use published database data, while the paper uses ellipsometry on its own films, so absolute dip depth and crossover wavelength shift as a whole; a different Au dataset would also redistribute the interface phase and relocate the dips slightly.

The model contains no surface roughness, no native oxide on the Ge, and no Au–Ge interfacial reaction.

Going further

These tutorials cover the operating steps only. The physics behind them, the full parameter reference for each feature, how to read the results, and the algorithm validation all live on the documentation site:

• Transfer-Matrix Method — the physics and formulas behind these tutorials
• Feature Guide — complete reference for every screen and parameter
• Results — how to read each kind of output
• Open Dreapex TMM — build and simulate in the browser