Lorenz-Mie theory

The Lorenz-Mie theory is a mathematical description of various scattering phenomena of electromagnetic waves on particles . The size of the particles can range from very small in the area of Rayleigh scattering through the area of Mie scattering to the geometrical optics of large particles. For geometric optics and Rayleigh scattering, however, the Lorenz-Mie theory is not used due to its complexity, as there are simplified descriptions in each case.

history

The Lorenz-Mie theory is named after the physicists Gustav Mie and Ludvig Lorenz . Because of the contributions by Peter Debye , the term Lorenz-Mie-Debye theory is also used. Furthermore, the short form Mie theory is common. Many other physicists made contributions to the theory.

With his work Gustav Mie made contributions to the optics of cloudy media, especially colloidal metal solutions from 1908, major contributions to theory. The work was probably written without knowledge of Lorenz's work from 1890. In 1915 Harry Bateman gave the first overview of the Lorenz-Mie theory ( The mathematical analysis of electrical and optical wave-motion on the basis of Maxwell's equations ).

Other contributions come from, among others, Lord Rayleigh (various scattering processes), Peter Debye or Joseph John Thomson .

description

The Mie theory is the exact solution of Maxwell's equations for the scattering of a plane electromagnetic wave on a spherical object of any size. The incident plane wave and the scattered electromagnetic field are described in a series of radiating spherical wave functions . The internal field is developed into regular spherical wave functions. The development coefficients of the scattered field and thus the scattered electromagnetic field in each point in space can then be calculated using the boundary conditions on the spherical surface .

In his paper from 1908, Mie succeeded in mathematically describing the color effects of a suspension of colloidal gold nanoparticles . Furthermore, the Mie theory in particle measurement technology can be used to infer the size and refractive index of a microscopic particle using simple methods . The scattered light , which fluctuates characteristically depending on the angle in space , can also be understood as the interference of the wave bent on the body . This intensity distribution of the scattering in space is recorded, from which the properties of the particle can be calculated.

For small objects (diameter ; is the wavelength of the radiation) the Mie scattering can be approximated by the Rayleigh scattering , ${\ displaystyle d <0 {,} 2 \, \ lambda}$ ${\ displaystyle \ lambda}$

For large objects (diameter ), the Mie theory approaches the classical geometric solution of refraction on a sphere. ${\ displaystyle d> 2 \ dots 10 \, \ lambda}$

If the object diameter is in the border area between Rayleigh and classical scattering , it is often referred to as Mie scattering.

{\ displaystyle (0 {,} 2 \, \ lambda <d <2 \ dots 10 \, \ lambda)}

literature

Wolfram Hergert: The Mie Theory. Basics and Applications . 2012, ISBN 978-3-642-28738-1 , pp. 27-33 .
Gustav Mie: Annalen der Physik , Volume 4, Vol. 25, 1908, pp. 377–445, doi: 10.1002 / andp.19083300302 .
Craig F. Bohren, Donald R. Huffman: Absorption and scattering of light by small particles. Wiley, 1983, ISBN 0-471-29340-7 .
MI Mishchenko, LD Travis, and AA Lacis, Absorption, and Emission of Light by Small Particles. Revised electronic edition, 2004, ISBN 0-521-78252-X