Mie scattering

Mie scattering representations

Mie scattering as particle diameter changes from 0.1 to 1 wavelength. The sphere's refractive index is 1.5.

Mie scattering, artistic view: Linearly polarized incident plane wave scattered by octupolar resonance.

Mie resonances vs. radius.

Monostatic radar cross section (RCS) of a perfectly conducting metal sphere as a function of frequency (calculated by Mie theory). In the low-frequency Rayleigh scattering limit, where the circumference is less than wavelength, the normalized RCS is ${\displaystyle {\tfrac {\sigma }{\pi R^{2}}}\sim 9(kR)^{4}}$. In the high-frequency optical limit, ${\displaystyle {\tfrac {\sigma }{\pi R^{2}}}\sim 1}$.

In electromagnetism, the Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the form of an infinite series of spherical multipole partial waves. It is named after German physicist Gustav Mie.

The term Mie solution is also used for solutions of Maxwell's equations for scattering by stratified spheres or by infinite cylinders, or other geometries where one can write separate equations for the radial and angular dependence of solutions. The term Mie theory is sometimes used for this collection of solutions and methods; it does not refer to an independent physical theory or law. More broadly, the "Mie scattering" formulas are most useful in situations where the size of the scattering particles is comparable to the wavelength of the light, rather than much smaller or much larger.

Mie scattering (sometimes referred to as a non-molecular scattering or aerosol particle scattering) takes place in the lower 4,500 m (15,000 ft) of the atmosphere, where many essentially spherical particles with diameters approximately equal to the wavelength of the incident ray may be present. Mie scattering theory has no upper size limitation, and converges to the limit of geometric optics for large particles.^[1]