Light scattering by particles is the process by which small particles (e.g.

ice crystals Ice crystals are solid ice exhibiting atomic ordering on various length scales and include hexagonal columns, hexagonal plates, dendritic crystals, and diamond dust. Formation The hugely symmetric shapes are due to depositional growth, na ...

dust Dust is made of fine particles of solid matter. On Earth, it generally consists of particles in the atmosphere that come from various sources such as soil lifted by wind (an aeolian process), volcanic eruptions, and pollution. Dust in homes ...

, atmospheric

particulates Particulates – also known as atmospheric aerosol particles, atmospheric particulate matter, particulate matter (PM) or suspended particulate matter (SPM) – are microscopic particles of solid or liquid matter suspended in the air. The ter ...

cosmic dust Cosmic dust, also called extraterrestrial dust, star dust or space dust, is dust which exists in outer space, or has fallen on Earth. Most cosmic dust particles measure between a few molecules and 0.1 mm (100 micrometers). Larger particles are c ...

, and

blood cell A blood cell, also called a hematopoietic cell, hemocyte, or hematocyte, is a cell produced through hematopoiesis and found mainly in the blood. Major types of blood cells include red blood cells (erythrocytes), white blood cells (leukocytes), ...

s) scatter light causing

optical phenomena Optical phenomena are any observable events that result from the interaction of light and matter. All optics, optical phenomena coincide with Quantum mechanics, quantum phenomena. Common optical phenomena are often due to the interaction of ligh ...

such as the blue color of the

sky The sky is an unobstructed view upward from the surface of the Earth. It includes the atmosphere and outer space. It may also be considered a place between the ground and outer space, thus distinct from outer space. In the field of astronomy, ...

, and halos.

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...

are the basis of theoretical and computational methods describing light

scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...

, but since exact solutions to Maxwell's equations are only known for selected particle geometries (such as spherical), light scattering by particles is a branch of

computational electromagnetics Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment. It typically involves using computer ...

dealing with electromagnetic radiation scattering and absorption by particles. In case of

geometries This is a list of geometry topics. Types, methodologies, and terminologies of geometry. * Absolute geometry * Affine geometry * Algebraic geometry * Analytic geometry * Archimedes' use of infinitesimals * Birational geometry * Complex geometry ...

for which

analytical solution Generally speaking, analytic (from el, ἀναλυτικός, ''analytikos'') refers to the "having the ability to analyze" or "division into elements or principles". Analytic or analytical can also have the following meanings: Chemistry * A ...

s are known (such as

sphere A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

s, cluster of spheres, infinite

cylinders A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infini ...

), the solutions are typically calculated in terms of

infinite series In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, math ...

. In case of more complex geometries and for inhomogeneous particles the original Maxwell's equations are

discretized In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical ...

and solved. Multiple-scattering effects of light scattering by particles are treated by radiative transfer techniques (see, e.g.

atmospheric radiative transfer codes An atmospheric radiative transfer model, code, or simulator calculates radiative transfer of electromagnetic radiation through a planetary atmosphere. Methods At the core of a radiative transfer model lies the radiative transfer equation that ...

). The relative size of a scattering particle is defined by its size parameter , which is the ratio of its

characteristic dimension In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by ...

to its

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...

Exact computational methods

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.

T-matrix

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.

Computational approximations

Mie approximation

Scattering from any spherical particles with arbitrary size parameter is explained by the

Mie theory The Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the f ...

. 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,

spheroid A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has cir ...

s, and infinite cylinders there are extensions which express the solution in terms of infinite series. There are codes available to study light scattering in Mie approximation for spheres, layered spheres, and multiple spheres and

Discrete dipole approximation

There are several techniques for computing scattering of radiation by particles of arbitrary shape. The

discrete dipole approximation Discrete dipole approximation (DDA), also known as coupled dipole approximation, is a method for computing scattering of radiation by particles of arbitrary shape and by periodic structures. Given a target of arbitrary geometry, one seeks to calcul ...

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. There are DDA codes available to calculate light scattering properties in DDA approximation.

Approximate methods

Rayleigh scattering

Rayleigh scattering Rayleigh scattering ( ), named after the 19th-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the ...

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 \ll 1

Geometric optics (ray-tracing)

Ray tracing techniques can approximate light scattering by not only spherical particles but ones of any specified shape (and orientation) so long as the size and critical dimensions of a particle are much larger than the wavelength of light. The light can be considered as a collection of rays whose widths are much larger than the wavelength but small compared to the particle itself. Each ray hitting the particle may undergo (partial) reflection and/or refraction. These rays exit in directions thereby computed with their full power or (when partial reflection is involved) with the incident power divided among two (or more) exiting rays. Just as with lenses and other optical components, ray tracing determines the light emanating from a single scatterer, and combining that result statistically for a large number of randomly oriented and positioned scatterers, one can describe atmospheric optical phenomena such as

rainbows A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows cau ...

due to water droplets and

halo Halo, halos or haloes usually refer to: * Halo (optical phenomenon) * Halo (religious iconography), a ring of light around the image of a head HALO, halo, halos or haloes may also refer to: Arts and entertainment Video games * ''Halo'' (franch ...

s due to ice crystals. There are atmospheric optics ray-tracing codes available.

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.), , (pbk.) *Bohren, Craig F. and Donald R. Huffman, Title Absorption and scattering of light by small particles, New York : Wiley, 1998, 530 p., , *Hulst, H. C. van de, Light scattering by small particles, New York, Dover Publications, 1981, 470 p., . * 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., . *Stratton, Julius Adams, Electromagnetic theory, New York, London, McGraw-Hill book company, inc., 1941. 615 p. {{DEFAULTSORT:Light Scattering By Particles Scattering, absorption and radiative transfer (optics)