Material Library

Where optical constants come from

The optics experiments here need two numbers for each material: how much it slows light down and how much it absorbs. For an ideal glass you can type 1.5 and move on. For silicon or gold the numbers change with wavelength, depend on how the sample was made, and were measured by somebody over a limited range. This page holds six such datasets from the refractiveindex.info database and keeps each one attached to its source, its conditions and the wavelengths it actually covers.

What n and k describe

The site uses the time dependence $\exp(-i\omega t)$ and a complex refractive index $\tilde n=n+ik$. A plane wave travelling along $+z$ is then

with $\lambda$ the vacuum wavelength. The real part $n$ sets the phase velocity $c/n$ and shortens the wavelength inside the material to $\lambda/n$. The imaginary part $k$ makes the wave decay; with this sign convention a passive material has $k\ge 0$. Intensity goes as $|E|^2$, so it falls by a factor of $e$ over

which is the inverse of the absorption coefficient $\alpha=4\pi k/\lambda$. The solvers work with permittivity instead. For a nonmagnetic material

The Optical quantity menu below shows all four. The three metals here have $k$ larger than $n$ in the visible, so their real permittivity is negative. Silver at 550 nm has $n=0.06$, which puts its phase velocity far above $c$. That breaks nothing; phase velocity carries no signal.

Tables and formulas

A table lists $n$ and $k$ at discrete wavelengths. Gold from Johnson and Christy has 49 points between 187.9 and 1937 nm; silicon from Green has 121, every 10 nm from 250 to 1450 nm. Between points this page interpolates $n$ and $k$ linearly. Beyond the first and last point it refuses. A table also records choices: the TiO₂ film table lists $k=0$ exactly for its last 198 points, from 1014.7 to 1689.8 nm. The file does not say why; the step from $10^{-6}$ to zero looks like rounding or a model cut-off. Read them as no reported loss, not as a measurement of perfect transparency.

Two tables are reconstructions rather than direct measurements. Green's silicon combines datasets while enforcing Kramers–Kronig consistency, the causality relation that ties $n$ to $k$ (see Kramers–Kronig). Rakić's aluminium comes from an iterative, self-consistent algorithm that combines Kramers–Kronig analysis with a semiquantum model, applied to optical and electron-energy-loss data for evaporated films. The source records keep those labels.

A formula stores a few coefficients. The fused silica record has the Sellmeier form

with $B_i=0.6961663,\ 0.4079426,\ 0.8974794$ and $C_i=0.0684043,\ 0.1162414,\ 9.896161\ \mu\text{m}$. Each term behaves like a fitted resonance at $\lambda=C_i$: two in the vacuum ultraviolet (68 and 116 nm), one in the infrared (9.9 µm). A formula will return a number almost anywhere you ask, which is the problem. Malitson fitted it between 0.21 and 3.71 µm, and the source record says Tan verified it up to 6.7 µm. Evaluated at 9 µm, next to the infrared term, the same coefficients give $n^2=-2.2$. The page only evaluates it from 210 to 6700 nm.

The formula also has no $k$. That does not make silica lossless; loss was simply not part of the fit. Malitson's index is relative to air and his wavelengths are in air. Polyanskiy's 2024 descriptor uses this record as its example of the fields $\texttt{n\_is\_absolute: false}$ and $\texttt{wavelength\_is\_vacuum: false}$; the pinned file bundled here has neither. The page does not convert. Multiplying by the index of dry standard air at 15 °C from Ciddor's equation, $n_\text{air}\approx1.00028$, gives an absolute index about 0.03% higher: 1.4589 instead of 1.4585 at 587.6 nm. Malitson measured at 20 °C; warmer air or the small wavelength correction changes that by less than $10^{-5}$, too little to show in the film results here.

Three things to try

Silica without a k. The page opens on fused silica. It gives $n=1.4585$ at 587.6 nm and 1.4440 at 1550 nm. The film buttons stay disabled until you tick the transparent-band model, because $k=0$ is your assumption, not the source's. With it, the 100 nm film sent to the thin-film page (air above, a substrate of index 1.5, normal incidence) reflects 3.0% at 550 nm.

Silicon across the visible. Uncheck silica and select silicon, then switch to $k$ (the record's $k$ covers band-to-band absorption only). It drops from 0.296 at 400 nm to 0.0280 at 550 nm and 0.0054 at 800 nm. The decay lengths are 108 nm, 1.6 µm and 11.8 µm. Sent to the thin-film page, the 100 nm film absorbs 37.7% at 400 nm (set the wavelength on the thin-film page), 3.0% at 550 nm and 1.0% at 800 nm. That is not simply $1-e^{-d/\ell}$ (60%, 6.2% and 0.85%), with $d$ the film thickness: the front surface reflects part of the light first, and interference between passes redistributes the rest. At 800 nm the film absorbs slightly more than one pass would.

Three metals. Untick every selected dataset, then select gold, silver and aluminium, in that order. The chart uses their common range, 187.9–1937 nm, even though the aluminium table runs from 0.124 nm to 200 µm. Switch to real permittivity: at 550 nm (interpolated between table points) it is −5.9 for gold, −12.9 for silver and −42.9 for aluminium. The intensity decay lengths there are 17.7, 12.2 and 6.6 nm, so a 100 nm film is effectively opaque. Send gold, the first selection, to the thin-film page: at 550 nm the 100 nm film reflects 78.6%, absorbs 20.7% and transmits 0.7%, and at 400 nm it absorbs 59%. Come back to this page, untick everything, select silver on its own and send it: it reflects 98.3%.