Light scattering by particles
Light scattering by particles is the process by which small particles scatter light causing optical phenomena such as the blue 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 particle geometries, 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, 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.
The relative size of a scattering particle is defined by its size parameter, which is the ratio of its characteristic dimension to its wavelength:
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 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. 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. 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.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.
There are codes available to study light scattering in Mie approximation for spheres, layered spheres, and multiple spheres and cylinders.
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.There are DDA codes available to calculate light scattering properties in DDA approximation.