Light scattering by particles
Light scattering by particles is the process by which small particles such as ice crystals, dust, planetary dust, and blood cells cause observable phenomena such as rainbows, the color of the sky, and halos.
Maxwell's equations are the basis of theoretical and computational methods describing light scattering but since exact solutions to Maxwell's equations are only known for selected geometries (such as spherical particle) light scattering by particles is a branch of computational electromagnetics dealing with electromagnetic radiation scattering and absorption by particles.
In case of geometries for which analytical solutions are known (such as spheres, cluster of spheres, infinite cylinders), the solutions are typically calculated in terms of infinite series. In case of more complex geometries and for inhomogeneous particles the original Maxwell's equations are discretized and solved. Multiple-scattering effects of light scattering by particles are treated by radiative transfer techniques (see, e.g. atmospheric radiative transfer codes).
Relative size of a scattering particle is defined by size parameter which is the ratio of its characteristic dimension and wavelength
Exact Computational methods 
Mie approximation 
Scattering from any spherical particles with arbitrary size parameter is explained by the 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 (Bohren and Huffman, 1998).
Discrete dipole approximation 
There are several techniques for computing scattering of radiation by particles of arbitrary shape. The discrete dipole approximation is an approximation of the continuum target by a finite array of polarizable points. The points acquire dipole moments in response to the local electric field. The dipoles of these points interact with one another via their electric fields.
The technique is also known as null field method and extended boundary technique method (EBCM). Matrix elements are obtained by matching boundary conditions for solutions of Maxwell equations. The incident, transmitted, and scattered field are expanded into spherical vector wave functions.
Finite-difference time-domain method 
The FDTD method belongs in the general class of grid-based differential time-domain numerical modeling methods. The time-dependent Maxwell's equations (in partial differential form) are discretized using central-difference approximations to the space and time partial derivatives. The resulting finite-difference equations are solved in either software or hardware in a leapfrog manner: the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic field vector components in the same spatial volume are solved at the next instant in time; and the process is repeated over and over again until the desired transient or steady-state electromagnetic field behavior is fully evolved.
Approximate methods 
|Approximation||Refractive index||Size parameter||Phase shift|
|Rayleigh scattering||abs(mx) very small||very small|
|Geometric optics||very large||very large|
|Anomalous Diffraction Theory||abs(m-1) very small||x large|
|Complex Angular Momentum||moderate m||large x|
Rayleigh scattering 
Rayleigh scattering regime is the scattering of light, or other electromagnetic radiation, by particles much smaller than the wavelength of the light. Rayleigh scattering can be defined as scattering in small size parameter regime .
Geometric optics 
See also 
- Codes for electromagnetic scattering by spheres
- Codes for electromagnetic scattering by cylinders
- Discrete dipole approximation codes
- Finite-difference time-domain method
- Barber,P.W. and S.C. Hill, Light scattering by particles : computational methods, Singapore ; Teaneck, N.J., World Scientific, c1990, 261 p.+ 2 computer disks (3½ in.), ISBN 9971-5-0813-3, ISBN 9971-5-0832-X (pbk.)
- Bohren, Craig F. and Donald R. Huffman, Title Absorption and scattering of light by small particles, New York : Wiley, 1998, 530 p., ISBN 0-471-29340-7, ISBN 978-0-471-29340-8
- Hulst, H. C. van de, Light scattering by small particles, New York, Dover Publications, 1981, 470 p., ISBN 0-486-64228-3.
- Kerker, Milton, The scattering of light, and other electromagnetic radiation, New York, Academic Press, 1969, 666 p.
- Mishchenko, Michael I., Joop W. Hovenier, Larry D. Travis, Light scattering by nonspherical particles: theory, measurements, and applications, San Diego : Academic Press, 2000, 690 p., ISBN 0-12-498660-9.
- Stratton, Julius Adams, Electromagnetic theory, New York, London, McGraw-Hill book company, inc., 1941. 615 p.