Mie theory

Mie theory

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.

The term "Mie theory" is misleading, since it does not refer to an independent physical theory or law. The phrase "the Mie solution (to Maxwell's equations)" is therefore preferable. Currently, the term "Mie solution" is also used in broader contexts, for example when discussing solutions of Maxwell's equations for scattering by stratified spheres or by infinite cylinders, or generally when dealing with scattering problems solved using the exact Maxwell equations in cases where one can write separate equations for the radial and angular dependence of solutions.

In contrast to Rayleigh scattering, the Mie solution to the scattering problem is valid for all possible ratios of diameter to wavelength, although the technique results in numerical summation of infinite sums. In its original formulation it assumed an , isotropic and optically linear material irradiated by an infinitely extending plane wave. However, solutions for layered spheres are 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. A further application is in the characterization of particles via optical scattering measurements. The Mie solution is also important for understanding the appearance of common materials like milk, biological tissue and latex paint.

The Mie theory has been used in the detection of oil concentration in polluted waters.

A modern formulation of the Mie solution to the scattering problem on a sphere can be found in 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 FORTRAN program to compute the Mie solution for a sphere and an infinite cylinder can be found in the book by Bohren and Huffman on light scattering by small particles. A useful alternative is provided by Mishchenko, Travis and Lacis in their book Scattering, Absorption, and Emission of Light by Small Particles.

ee also

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

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).Link to translation of original article: http://diogenes.iwt.uni-bremen.de/vt/laser/papers/RAE-LT1873-1976-Mie-1908-translation.pdf
* M. Mishchenko, L. Travis, A. Lacis: "Scattering, Absorption, and Emission of Light by Small Particles", Cambridge University Press, 2002.
* J. Frisvad, N. Christensen, H. Jensen: "Computing the Scattering Properties of Participating Media using Lorenz-Mie Theory", SIGGRAPH 2007

External links

* [http://atol.ucsd.edu/scatlib Collection of light scattering codes]
* [http://www.T-Matrix.de www.T-Matrix.de] . Implementations of Mie solutions in FORTRAN, C++, IDL, PASCAL, Mathematica and Mathcad
* [http://www.scatlab.com ScatLab] . Mie scattering software for Windows.
* [http://www.lightscattering.de/MieCalc/ on line Mie solution calculator] is available, with documentation in German and English.
* [http://omlc.ogi.edu/calc/mie_calc.html on line Mie scattering calculator] produces beautiful graphs over a range of parameters.
* [http://luxrerum.icmm.csic.es/?q=node/research/PG_material Mie resonance mediated light diffusion and random lasing]


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Mie — may refer to: KMIE, the ICAO code for the Delaware County Airport near Muncie, Indiana Mie Prefecture, Japan Mie District, Mie, a district of Japan Mie, Ōita, a town of Japan Mie University, a university in Tsu, Mie, Japan Mie (pose), a pose in… …   Wikipedia

  • Mie scattering — 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 the wavelength, the normalized… …   Wikipedia

  • Mie-Streuung — 3D Darstellung der Mie Streuung von rotem Licht (633 nm) an einem sphärischen Partikel mit 2 µm Durchmesser. Das Partikel befindet sich in der Mitte bei x = y = z = 0, das Licht wird von links eingestrahlt. Die unterschiedliche… …   Deutsch Wikipedia

  • Difusión de Mie — La Teoría de Mie, también llamada teoría de Lorenz Mie o teoría de Lorenz Mie Debye, es una solución completamente analítica a las ecuaciones de Maxwell para la dispersión de la radiación electromagnética por partículas esféricas. La solución es… …   Wikipedia Español

  • Diffusion de Mie — Théorie de Mie En physique optique ondulatoire, la théorie de Mie, aussi appelée théorie de Lorenz Mie, est une théorie de la diffraction de la lumière par des particules sphériques. Elle tire son nom du physicien danois Ludvig Lorenz et du… …   Wikipédia en Français

  • Theorie de Mie — Théorie de Mie En physique optique ondulatoire, la théorie de Mie, aussi appelée théorie de Lorenz Mie, est une théorie de la diffraction de la lumière par des particules sphériques. Elle tire son nom du physicien danois Ludvig Lorenz et du… …   Wikipédia en Français

  • Théorie de Lorenz-Mie — Théorie de Mie En physique optique ondulatoire, la théorie de Mie, aussi appelée théorie de Lorenz Mie, est une théorie de la diffraction de la lumière par des particules sphériques. Elle tire son nom du physicien danois Ludvig Lorenz et du… …   Wikipédia en Français

  • Théorie de Mie — En physique optique ondulatoire, la théorie de Mie, ou plus justement solution de Mie ou solution de Lorenz Mie, est une solution particulière des équations de Maxwell décrivant la diffusion de la lumière par des particules sphériques. Elle tire… …   Wikipédia en Français

  • Théorie de mie — En physique optique ondulatoire, la théorie de Mie, aussi appelée théorie de Lorenz Mie, est une théorie de la diffraction de la lumière par des particules sphériques. Elle tire son nom du physicien danois Ludvig Lorenz et du physicien allemand… …   Wikipédia en Français

  • Gans theory — or Mie Gans theory is the extension of Mie theory for the case of spheroidal particles. It gives the scattering characteristics of both oblate and prolate spheroidal particles much smaller than the excitation wavelength.Since it is a solution of… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”