Transfer-matrix method for multilayer thin-film optics, with exact analytic derivatives.

Documentation · Getting started · API · Validation

Takes a stack of layers and returns reflectance, transmittance and absorptance for absorbing and dispersive materials, at any angle of incidence, in s and p polarization. Alongside the spectra it returns the exact thickness Jacobian, the exact thickness Hessian, and the needle-insertion P-function, computed analytically rather than by finite differences.

Ships as JavaScript, as C, and as a WebAssembly build of the C. The JavaScript has no dependencies and works on import. WebAssembly is opt-in and roughly an order of magnitude faster.

npm install tmmcore

The .wasm is prebuilt and included, so no Emscripten toolchain is required.

import { tmm } from 'tmmcore';

// A quarter-wave MgF2 layer on glass, at 550 nm, normal incidence.
const { R, T, A } = tmm(
    550,            // wavelength, nm
    0,              // angle of incidence, degrees from normal
    's',            // polarization: 's' or 'p'
    [1.0, 0],       // incident medium, ñ = [n, k]
    [1.52, 0],      // substrate
    [{ n: [1.38, 0], d: 550 / (4 * 1.38) }]   // quarter wave, thickness in nm
);

console.log(R);   // 0.012600790214630274

Layers run from the incident medium toward the substrate.

Mismatched conventions are the most common cause of two TMM codes disagreeing, so check these first.

This is the complex conjugate of Macleod's convention. R, T and A are identical under conjugation; phase-sensitive quantities are not.

Two commands, neither needing anything but Node:

npm test        # the JavaScript and the C agree, to float64 round-off
npm run compare # and both agree with an independent implementation

The first drives both implementations with identical inputs across absorbing, dispersive and oblique-incidence cases and compares every returned quantity. 64,416 comparisons, worst disagreement 4.4e-16.

The second checks them against Steven Byrnes' tmm, written independently in Python under the same complex-index convention, so only the mathematics is under test. 12,352 values, worst disagreement 8.6e-14, which is float64 accumulation noise over a forty-layer matrix product.

Timing comparisons against four other packages are in the documentation, and need a Python environment.

• Getting started
• API reference
• Examples
• Validation
• Comparison with other TMM packages

src/tmm_kernel.c is C99 with no dependencies beyond libm. Drop it into a project and compile:

cc -std=c99 -O2 -c src/tmm_kernel.c

MIT © Andrey Achapovsky

Built for and used by TFStudio, an open-source optical coating design application.