Light scattering by particles

Light scattering by particles - describes light scattering and absorption by small particles. Light scattering by ice crystals, dust, planetary dust, blood cells are all examples of light scattering. Observable phenomena due to light scattering by particles range from rainbow, color of the sky, halo.

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 spherica 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

$x={\frac {2\pi r}{\lambda }}.$

Exact Computational methods

Mie approximation

Main article: Mie theory

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).

For more complex shapes such as coated spheres, multispheres, spheroids, and infinite cylinders there are extensions which express the solution in terms of infinite series.

Discrete dipole approximation

Main article: 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.

T-matrix

Main article: T-matrix_method

The technique is also known as null field method and extended boundary technique method (EBCM). Matrix elements are obtained by matching boundary conditions for solution of Maxwell equations. The incident, transmitted, and scattered field are expanded into spherical vector wave functions.

Finite-difference time-domain method

Main article: 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 $x<<1$.

Light rays enter a raindrop from one direction (typically a straight line from the Sun), reflect off the back of the raindrop, and fan out as they leave the raindrop. The light leaving the rainbow is spread over a wide angle, with a maximum intensity at 40.89–42°.

Geometric optics

Main article: Geometric optics

See also

• Codes for electromagnetic scattering by spheres
• Codes for electromagnetic scattering by cylinders
• Discrete dipole approximation codes
• Mie theory
• Finite-difference time-domain method
• Scattering

References

• 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 9971508133, ISBN 997150832X (pbk.)

• Bohren, Craig F. and Donald R. Huffman, Title Absorption and scattering of light by small particles, New York : Wiley, 1998, 530 p., ISBN 0471293407, ISBN 9780471293408

• Hulst, H. C. van de, Light scattering by small particles, New York, Dover Publications, 1981, 470 p., ISBN 0486642283.

• 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 0124986609.

• Stratton, Julius Adams, Electromagnetic theory, New York, London, McGraw-Hill book company, inc., 1941. 615 p.