Gans theory or Mie-Gans theory is the extension of

Mie theory In electromagnetism, 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 sol ...

for the case of spheroidal particles. It gives the scattering characteristics of both

oblate In Christianity (specifically the Roman Catholic, Orthodox, Lutheran, Anglican and Methodist traditions), an oblate is a person associated with a Benedictine monastery or convent who is specifically dedicated to God and service. Oblates are i ...

and

prolate 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 circu ...

spheroidal particles much smaller than the excitation wavelength. Since it is a solution of the

Maxwell 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, electric and magnetic c ...

it should technically not be called a theory. The theory is named after

Richard Gans __NOTOC__ Richard Martin Gans (7 March 1880 – 27 June 1954), German of Jewish origin, born in Hamburg, was the physicist who founded the Physics Institute of the National University of La Plata, Argentina. He was its Director in two different ...

who first published the solution for gold particles in 1912 in an article entitled "Über die Form ultramikroskopischer Goldteilchen". A subsequent article in 1915 discussed the case of silver particles. In Gans theory, the

absorption Absorption may refer to: Chemistry and biology *Absorption (biology), digestion **Absorption (small intestine) *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which su ...

is only dependent on the aspect ratio of the particles and not on the absolute dimensions. This dependence is introduced through so called polarization- or shape factors related to the three dimensions of the particle. For the case of spheroids, this reduces to only two different factors since the particle is rotational symmetric around one axis. It is currently being applied in the field of

nanotechnology Nanotechnology is the manipulation of matter with at least one dimension sized from 1 to 100 nanometers (nm). At this scale, commonly known as the nanoscale, surface area and quantum mechanical effects become important in describing propertie ...

to characterize silver and gold

nanorod In nanotechnology, nanorods are one morphology of nanoscale objects. Each of their dimensions range from 1–100 nm. They may be synthesized from metals or semiconducting materials. Standard aspect ratios (length divided by width) are 3-5. Nan ...

s. A popular alternative for this is 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 ...

(DDA) method. Gans theory gives the exact solution for spheroidal particles; real nanorods, however, have a more cylindrical shape. Using DDA, it is possible to better model the exact shape of the particles. As the name suggests, this will only give an approximation.

References

Scattering Scattering, absorption and radiative transfer (optics) {{scattering-stub

See also

References