Getting started¶

Install¶

npm install tmmcore

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

Conventions¶

Check these before comparing results with another code.


Refractive index	\(\tilde n = n + ik\), with \(k \ge 0\) for absorbing media
Time factor	\(\exp(-i\omega t)\), so a wave \(\exp(i(kz - \omega t))\) decays for \(k > 0\)
p-polarized amplitudes	from the tilted admittance \(n/\cos\theta\), so \(r_p = r_s\) at normal incidence
Wavelength, thickness	nanometres
Angle of incidence	degrees from normal
Complex numbers	`[re, im]` pairs, in jets and the primitives
Layer order	incident medium first, substrate last
Absorbing incident medium	every angle follows from the real invariant \(n_0 \sin\theta_0\) of Macleod's Eq. 2.85, with \(n_0\) the real part of the index, as Essential Macleod takes it; the incident wave decays along the normal only, and \(A\) is what the layers absorb, so \(R + T + A\) is not one

This is the complex conjugate of the convention in Macleod's Thin-Film Optical Filters (\(\tilde n = n - ik\), \(\exp(+i\omega t)\)). Reflectance, transmittance and absorptance are the same under conjugation. Phase is not: the phase calls report it in Macleod's convention, as Units and signs explains.

The p amplitudes follow thin-film practice, as Macleod's do, rather than the Fresnel coefficients of Born and Wolf. Byrnes' tmm takes the Fresnel sign, and the ellipsometric convention flips the reflected p direction to the same effect: \(r_p = -r_s\) at normal incidence. Their \(r_p\) is the negative of tmmcore's at every angle, and a \(\Delta\) from \(r_p/r_s\) differs by 180°. Macleod amends \(\Delta\) by \(\pm\pi\) in reflection for this reason (§9.7.1, Eq. 9.36). The cross-library check compares both coefficients with Byrnes' at 0°, 30° and 60°.

k is positive for loss

Some codes and datasets use \(\tilde n = n - ik\). A negative \(k\) given to tmmcore describes a gain medium, which gives transmittance above one rather than an error.

Describing a stack¶

A stack is the incident medium, the substrate and the layers between them, ordered from the incident medium toward the substrate. A layer is { n, k, d }, with k left out when it is 0.

import { rta } from 'tmmcore';

const stack = {
    incident: 1,
    substrate: 1.52,
    layers: [
        { n: 1.38, d: 92.4 },    // outermost, facing the incident medium
        { n: 2.20, d: 115.9 },
        { n: 1.70, d: 75.0 },    // innermost, against the substrate
    ],
};

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

The incident medium and the substrate are semi-infinite and have no thickness: each is a number, or { n, k } when it absorbs.

tmmcore has no material data: give it the index at the wavelengths you evaluate. Over a grid, any n or k can be a list with one value per wavelength.

import { rtaSpectrum } from 'tmmcore';

const wavelengths = [450, 500, 550, 600, 650];
const nSiO2 = lam => 1.46 + 3000 / (lam * lam);   // a Cauchy formula, lam in nm

const layers = [{ n: wavelengths.map(nSiO2), d: 94.2 }];
const { R } = rtaSpectrum({ incident: 1, substrate: 1.52, layers }, wavelengths);

Polarization¶

pol is 's', 'p', or 'avg', the mean of the two, which is natural light. The R/T, derivative and needle calls take 'avg' when it is left out:

rta(stack, 550, { angle: 45 }).R;              // natural light
rta(stack, 550, { angle: 45, pol: 's' }).R;

rtaSpectrum returns Rs and Rp beside R, so one call gives all three.

The phase calls take 's' or 'p'. At normal incidence, where the two are the same, pol may be left out.

Turning on WebAssembly¶

The JavaScript works on import. WebAssembly is opt-in: load the bytes, instantiate, and call the same names on the instance.

NodeBrowser

import { readFileSync } from 'node:fs';
import { createRequire } from 'node:module';
import { instantiateTmmWasm } from 'tmmcore';

const require = createRequire(import.meta.url);
const kernel = await instantiateTmmWasm(
    readFileSync(require.resolve('tmmcore/tmm_kernel.wasm'))
);

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

import { initTmmWasmFromUrl, getTmmWasm, rta } from 'tmmcore';

// Resolves false, without throwing, if the file is missing or fails to load.
const ok = await initTmmWasmFromUrl('/tmm_kernel.wasm');

const { R } = ok ? getTmmWasm().rta(stack, 550) : rta(stack, 550);

Your bundler must serve tmm_kernel.wasm as a static asset.

Instances are not shared between threads, since there is no shared memory. Each worker instantiates its own from the same bytes.

On the instance, a Spectrum call crosses from JavaScript into WebAssembly per grid rather than per wavelength. That is where the speed is.

Next¶

API reference, every call and what it returns
Examples, runnable scripts from a single layer to a needle scan
Python, the same calls from Python
Validation, how to rerun the accuracy checks