@galihru/mnp-mie

Rayleigh quasi-static scattering formulas for spherical metallic nanoparticles in a homogeneous dielectric medium. Computes complex polarizability and electromagnetic cross sections -- extinction, scattering, and absorption -- within the electric-dipole approximation, valid for particle radius a << lambda.

Physical Background

In the Rayleigh (quasi-static) limit, the electromagnetic response of a small sphere is fully characterised by its induced electric dipole moment. The key quantity is the complex polarizability alpha, which encodes both radiative (scattering) and non-radiative (absorption) optical losses. This framework underpins localized surface plasmon resonance (LSPR) spectroscopy, photothermal therapy, and surface-enhanced sensing.

Implemented Formulations

1. Quasi-static Polarizability (Clausius-Mossotti)

For a sphere of radius a with permittivity eps_p in an embedding medium with permittivity eps_m:

The Frohlich resonance (LSPR condition) occurs when:

2. Wave Number in the Embedding Medium

where lambda is the free-space wavelength in nanometres.

3. Electromagnetic Cross Sections

Extinction cross section -- total power removed from the incident beam:

Scattering cross section -- power re-radiated as scattered light:

Absorption cross section -- power dissipated as Ohmic heat:

Install

npm install @galihru/mnp-mie

API Reference

rayleighPolarizability(radiusNm, epsParticle, epsMedium)

Returns the complex polarizability alpha of a sphere.

import { complex, rayleighPolarizability } from "@galihru/mnp-mie";

const epsParticle = complex(-7.45, 1.23);  // Au at 548 nm
const epsMedium   = complex(1.769, 0.0);   // water

const alpha = rayleighPolarizability(50, epsParticle, epsMedium);
// -> { re: ..., im: ... }   [nm^3]

rayleighCrossSections(wavelengthNm, radiusNm, epsParticle, epsMedium)

Returns extinction, scattering, and absorption cross sections in nm^2.

import { complex, rayleighCrossSections } from "@galihru/mnp-mie";

const epsParticle = complex(-7.45, 1.23);
const epsMedium   = complex(1.769, 0.0);

// Single wavelength
const cs = rayleighCrossSections(548.1, 50, epsParticle, epsMedium);
// -> { cExt: ..., cSca: ..., cAbs: ... }   [nm^2]

// Spectral scan (array input)
const scan = rayleighCrossSections(
  [400, 450, 500, 548, 600, 700],
  50,
  [eps400, eps450, eps500, eps548, eps600, eps700],
  [em400,  em450,  em500,  em548,  em600,  em700]
);
// -> [{ cExt, cSca, cAbs }, ...]

complex(re, im)

Constructs a complex number { re, im }.

import { complex } from "@galihru/mnp-mie";

const z = complex(-5.2, 2.1);
// -> { re: -5.2, im: 2.1 }

Author

GALIH RIDHO UTOMO | [email protected] Universitas Negeri Semarang (UNNES) License: GPL-2.0-only