Mie scattering calculator

COMSOL Multiphysics, Lumerical and other FDTD or finite-element tools solve any shape but need meshing, boundary settings and minutes to hours per run. For spheres and layered spheres, Mie theory is exact and takes about a second, so this calculator is the fastest way to get the answer and a reference to validate full-wave nanoparticle models.

The extinction, scattering and absorption cross-sections (and efficiencies) of a sphere versus wavelength, for a solid sphere or a core with up to three shells, from exact Mie theory. Pick materials from the built-in database of measured optical constants (gold, silver, copper, aluminum, platinum, silicon, TiO₂, silica, polystyrene…) or enter your own refractive index, choose the medium, and press Calculate.

Absorption is the light the particle turns into heat, scattering the light it redirects, and extinction their sum: everything removed from the beam, which is what a UV-vis spectrometer measures. Each is given as a cross-section, an area; divided by the particle's geometric cross-section it becomes an efficiency.

Choose gold or silver, set the diameter and the solvent, and calculate: the extinction curve is the UV-vis spectrum. The gold and silver pages also list the plasmon peak and extinction coefficient for every common size.

Yes: add up to three shells, each with its own material and thickness. Gold nanoshells on silica, silica-coated gold, ligand layers and oxide skins are all layered spheres, solved exactly.

Yes. Choose Custom for the particle, a shell or the medium and enter n and k; otherwise the data come from published measurements (the source is shown and can be changed).

Mie theory is exact for spheres, and the series is summed with numerically stable recursions to convergence; the results have been checked against independent solvers. The only approximations are in the inputs: ideal spheres and the chosen optical constants.