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

  The thickness Jacobian, the thickness Hessian and the needle P-function, computed exactly rather than by finite differences.

• Phase dispersion

  Group delay, GDD and TOD as exact frequency derivatives, so they do not depend on the wavelength grid. Their thickness derivatives come from the same call.

• Node and the browser

  JavaScript with no dependencies, and an optional WebAssembly build of the C.

• Python

  The same C kernel as a wheel for your platform, with numpy arrays in and out. See Python.

• C99

  The kernel needs only libm and compiles as one file.

• Checkable

  Four commands, needing only Node, rerun the accuracy checks in Validation.

Install

npm install tmmcore

The WebAssembly binary ships prebuilt, so nothing is compiled at install time. For Python, pip install tmmcore.

A first calculation

import { rta } from 'tmmcore';

// A quarter-wave MgF2 layer on glass, at 550 nm, normal incidence.
const stack = {
    incident: 1.0,                                // ñ = n, or { n, k }
    substrate: 1.52,
    layers: [{ n: 1.38, d: 550 / (4 * 1.38) }],   // quarter wave, thickness in nm
};

const { R, T, A } = rta(stack, 550);

console.log(R);   // 0.012600790214630274

That value has a closed form, \(R = \left(\frac{n_0 n_s - n_1^2}{n_0 n_s + n_1^2}\right)^2\); Validation compares the two.

Implementations

JavaScript	The reference implementation. No dependencies.
C	A line-by-line port of the JavaScript. C99, libm only.
WebAssembly	The C, compiled. Opt-in, and over a wavelength grid about an order of magnitude faster than the JavaScript.
Python	The C, compiled for your platform and called through ctypes.

The C matches the JavaScript to float64 round-off, and npm test checks it.

Scope

tmmcore computes coherent stacks. An incoherent substrate, ellipsometric \(\Psi\) and \(\Delta\), and material data are left to the caller; the examples build the first two on its calls. For a full design environment, see TFStudio.

Licence

MIT.