Mie scattering

Mie scattering refers to the electromagnetic scattering of an incident wave by a sphere, described by solving Maxwell's equations with the appropriate electromagnetic boundary conditions at the sphere's surface. The solution accounts for both the field scattered outside the particle and the field within it. It can be used to calculate quantities such as scattering and absorption cross-sections, angular distribution and polarization of scattered light. The result depends on particle radius, wavelength and the optical properties of the particle and surrounding medium.

A useful dimensionless measure is the size parameter, conventionally written x = 2πr/λ for a sphere of radius r and wavelength λ in the surrounding medium. When particles are much smaller than the wavelength, Rayleigh scattering gives a useful small-particle limit. When particles are comparable to or larger than the wavelength, the angular and spectral behavior can be more complex; Mie theory provides a spherical-particle solution beyond the small-particle approximation. For very large particles, geometrical-optics approximations may be useful, but they are approximations rather than the same calculation as the exact spherical-wave solution.

The theory is named for German physicist Gustav Mie, whose 1908 paper treated electromagnetic-wave scattering by a sphere. The mathematical formulation is often called Lorenz–Mie theory, reflecting earlier related work by Ludvig Lorenz. In its classical form, Mie theory concerns homogeneous spheres and a specified incident electromagnetic field. A real particle that is irregular, internally layered, or part of a strongly interacting cluster may require other methods or an extension of the spherical model; the unmodified classical solution should not be assumed to describe every particle shape.

Atmospheric researchers use spherical-particle scattering calculations to interpret how aerosols and cloud droplets interact with sunlight, including effects on atmospheric radiation and observed optical signals. The theory is also useful in particle-sizing instruments and in the study of colloids and optical materials, where scattering changes with particle size and wavelength. For ensembles of particles, calculations commonly combine the responses of individual particles using their size distribution and optical properties; the accuracy of a prediction therefore depends not only on the scattering model but also on how well the particle population is characterized.