Mie theory

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Mie theory, also called Lorenz-Mie theory or Lorenz-Mie-Debye theory, is a complete analytical solution of Maxwell's equations for the scattering of electromagnetic radiation by spherical particles (also called Mie scattering). Mie solution is named after its developer German physicist Gustav Mie. However, Danish physicist Ludvig Lorenz and others independently developed the theory of electromagnetic plane wave scattering by a dielectric sphere.

Mie theory is not a correct name because it is not a theory per se, rather Mie solution to Maxwell's equations should be used. Currently, Mie solution is also used in broader context, for example when discussing solution to scattering by stratified spheres or by infinite cylinders, or in general when dealing with scattering problems solved using exact Maxwell equations in cases where one can separate equations for the radial and angular dependence of solutions.

In contrast to Rayleigh scattering Mie solutions to scattering embraces all possible ratios of diameter to wavelength, although the technique results in numerical summation of infinite sums. In its original formulation it assumed an homogeneous, isotropic and optically linear material irradiated by an infinitely extending plane wave. However, solutions for layered spheres is also possible.

Mie theory is very important in meteorological optics, where diameter-to-wavelength ratios of the order of unity and larger are characteristic of many problems regarding haze and cloud scattering. Scattering of radar energy by raindrops constitutes another significant application of the Mie solution. A further application is optical particle characterization. Mie solution is also important for understanding the appearance of common materials like milk, biological tissue and latex paint.

The modern way to formulate the Mie solutions to scattering problems on a sphere was outlined also by J. A. Stratton (Electromagnetic Theory, New York: McGraw-Hill, 1941). In this formulation the incident plane wave as well as the scattering field is expanded into radiating spherical vector wave functions. The internal field is expanded into regular spherical vector wave functions. By enforcing the boundary condition on the spherical surface, the expansion coefficients of the scattered field can be computed. A basic FORTRAN program of the Mie solution for sphere and infinite cylinder can be found in the book by Bohren and Huffman on light scattering by small particles.

[edit] See also

Discrete dipole approximation - a technique to solve light scattering on non-spherical particles.

[edit] References

A. Stratton: Electromagnetic Theory, New York: McGraw-Hill, 1941.
H. C. van de Hulst: Light scattering by small particles, New York, Dover, 1981.
M. Kerker: The scattering of light and other electromagnetic radiation. New York, Academic, 1969.
C. F. Bohren, D. R. Huffmann: Absorption and scattering of light by small particles. New York, Wiley-Interscience, 1983.
P. W. Barber, S. S. Hill: Light scattering by particles: Computational methods. Singapore, World Scientific, 1990.
G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Leipzig, Ann. Phys. 330, 377–445 (1908).