Mie theory

Mie theory, also called Lorenz-Mie theory, is a complete analytical solution of Maxwell's equations for the scattering of electromagnetic radiation by spherical particles (also called Mie scattering). Mie theory is named after its developer German physicist Gustav Mie (1868 Rostock - 1957 Freiburg im Breisgau) and Danish physicist Ludvig Lorenz (1829-1891) who independently developed the theory of electromagnetic plane wave scattering by a dielectric sphere in 1908.

In contrast to Rayleigh scattering or Dipole scattering, Mie scattering embraces all possible ratios of diameter to wavelength. It assumes an homogeneous, isotropic and optically linear material irradiated by an infinitely extending plane wave.

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 theory. A further application is optical particle characterization. Mie theory is also important for understanding the appearance of common materials like milk, biological tissue and latex paint.

The modern way to formulate the Mie theory has been outlined by physicist J. A. Stratton (Electromagnetic Theory, New York: McGraw-Hill, 1941). In this theory 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 profound description and a basic FORTRAN program of the Mie theory can be found in the book by Bohren and Huffman.The differences between the various formulations of Mie theory are explained in the book by Barber and Hill, which also includes FORTRAN programs.

External links

* More recent implementations of Mie theory in FORTRAN, C++, IDL, PASCAL, Maple, Mathematica and Mathcad can be found at the web site www.T-Matrix.de. An implementation in IDL can also be found at the web site gwest.gats-inc.com/software/software_page.html.
* An online Mie theory calculator is available, with documentation in German and English.

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," Ann. Phys. Leipzig 25, 377â€"445 (1908).
* Hong Du, "Mie-scattering calculation," Applied Optics 43 (9), 1951-1956 (2004).