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Concept
Mie scattering
Summary
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 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 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.
A modern formulation of the Mie solution to the scattering problem on a sphere can be found in many books, e.g., J. A. Stratton's Electromagnetic Theory. In this formulation, the incident plane wave, as well as the scattering field, is expanded into radiating spherical vector spherical harmonics. The internal field is expanded into regular vector spherical harmonics. By enforcing the boundary condition on the spherical surface, the expansion coefficients of the scattered field can be computed.
For particles much larger or much smaller than the wavelength of the scattered light there are simple and accurate approximations that suffice to describe the behavior of the system. But for objects whose size is within a few orders of magnitude of the wavelength, e.
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