Mie scattering

[1] A modern formulation of the Mie solution to the scattering problem on a sphere can be found in many books, e.g., J.

By enforcing the boundary condition on the spherical surface, the expansion coefficients of the scattered field can be computed.

For particles much larger or much smaller than the wavelength of the scattered light there are simple and accurate approximations that suffice to describe the behavior of the system.

Danish physicist Ludvig Lorenz and others independently developed the theory of electromagnetic plane wave scattering by a dielectric sphere.

The notable features of these results are the Mie resonances, sizes that scatter particularly strongly or weakly.

The Rayleigh scattering model breaks down when the particle size becomes larger than around 10% of the wavelength of the incident radiation.

The intensity of Mie scattered radiation is given by the summation of an infinite series of terms rather than by a simple mathematical expression.

The blue colour of the sky results from Rayleigh scattering, as the size of the gas particles in the atmosphere is much smaller than the wavelength of visible light.

Rayleigh scattering is much greater for blue light than for other colours due to its shorter wavelength.

In contrast, the water droplets that make up clouds are of a comparable size to the wavelengths in visible light, and the scattering is described by Mie's model rather than that of Rayleigh.

Here, all wavelengths of visible light are scattered approximately identically, and the clouds therefore appear to be white or grey.

[3] The anomalous diffraction approximation is valid for large (compared to wavelength) and optically soft spheres; soft in the context of optics implies that the refractive index of the particle (m) differs only slightly from the refractive index of the environment, and the particle subjects the wave to only a small phase shift.

In order to solve the scattering problem,[3] we write first the solutions of the vector Helmholtz equation in spherical coordinates, since the fields inside and outside the particles must satisfy it.

Then the following conditions are imposed: Scattered fields are written in terms of a vector harmonic expansion as Here the superscript

For metal particles, the peak visible in the scattering cross-section is also called localized plasmon resonance.

In the limit of small particles or long wavelengths, the electric dipole contribution dominates in the scattering cross-section.

, corresponds to the minimum in backscattering (magnetic and electric dipoles are equal in magnitude and are in phase, this is also called first Kerker or zero-backward intensity condition[14]).

The sum of the electric and magnetic dipoles forms Huygens source [16] For dielectric particles, maximum forward scattering is observed at wavelengths longer than the wavelength of magnetic dipole resonance, and maximum backward scattering at shorter ones.

) : coefficients: Mie solutions are implemented in a number of programs written in different computer languages such as Fortran, MATLAB, and Mathematica.

Mie theory is very important in meteorological optics, where diameter-to-wavelength ratios of the order of unity and larger are characteristic for many problems regarding haze and cloud scattering.

The Mie solution is also important for understanding the appearance of common materials like milk, biological tissue and latex paint.

Mie scattering occurs when the diameters of atmospheric particulates are similar to or larger than the wavelengths of the light.

Dust, pollen, smoke and microscopic water droplets that form clouds are common causes of Mie scattering.

Mie scattering occurs mostly in the lower portions of the atmosphere, where larger particles are more abundant, and dominates in cloudy conditions.

Mie theory has been used to determine whether scattered light from tissue corresponds to healthy or cancerous cell nuclei using angle-resolved low-coherence interferometry.

Mie theory is a central principle in the application of nephelometric based assays, widely used in medicine to measure various plasma proteins.

They usually consist of three-dimensional composites of metal or non-metallic inclusions periodically or randomly embedded in a low-permittivity matrix.

In such a scheme, the negative constitutive parameters are designed to appear around the Mie resonances of the inclusions: the negative effective permittivity is designed around the resonance of the Mie electric dipole scattering coefficient, whereas negative effective permeability is designed around the resonance of the Mie magnetic dipole scattering coefficient, and doubly negative material (DNG) is designed around the overlap of resonances of Mie electric and magnetic dipole scattering coefficients.

To meet the criteria of homogenization, which may be stated in the form that the lattice constant is much smaller than the operating wavelength, the relative permittivity of the dielectric particles should be much greater than 1, e.g.

[25][26][27] Mie theory is often applied in laser diffraction analysis to inspect the particle sizing effect.