tmmcore

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

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.

• Analytic derivatives

  Exact thickness Jacobian, exact thickness Hessian, and the needle P-function, computed analytically rather than by finite differences or autodiff. The reason to pick tmmcore if you are building an optimizer.

• Runs in a browser

  JavaScript and WebAssembly, working in Node and on the web. The JavaScript path has no dependencies and works on import.

• Portable C99

  The kernel is a single C file needing nothing beyond libm. Drop it into a C or C++ project and compile it.

• Checkable

  Two commands reproduce the accuracy claims on your machine.

Install

npm install tmmcore

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

A first calculation

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
    's',                            // polarization
    [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

That value has a closed form, \(R = \left(\frac{n_0 n_s - n_1^2}{n_0 n_s + n_1^2}\right)^2\), and tmmcore reproduces it to \(1.4\times10^{-17}\). See Validation.

Implementations

JavaScript	The reference implementation. No dependencies, works everywhere.
C	A line-by-line port of the JavaScript. C99, libm only.
WebAssembly	The C, compiled. Opt-in, roughly an order of magnitude faster.

The JavaScript is the behavioural reference and the C must match it to float64 round-off. npm test checks that agreement.

Scope

Incoherent layers, ellipsometric parameters, and material databases are out of scope. tmmcore is the calculation kernel; those belong in the application above it. For a full design environment, see TFStudio.

Licence

MIT.