Isotropy

Isotropy (the opposite of anisotropy) is the property of being independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.

• Mathematics: Isotropy is also a concept in mathematics. Some manifolds are isotropic, meaning that the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. A manifold can be homogeneous without being isotropic.

• Radio broadcasting: In radio, an isotropic antenna is an idealized "radiating element" used as a reference; an antenna that broadcasts power equally (calculated by the poynting vector) in all directions. In practice, an isotropic antenna cannot exist, as equal radiation in all directions would be a violation of the Helmholtz Wave Equation. The gain of an arbitrary antenna is usually reported in Decibels relative to an isotropic antenna, and is expressed as dBi or dB(i).

• Physiology: In skeletal muscle cells (a.k.a. muscle fibers), the term "isotropic" refers to the light bands (I bands) that contribute to the striated pattern of the cells.

• Materials: In the study of mechanical properties of materials, "isotropic" means having identical values of a property in all crystallographic directions.

• Optics: Optical isotropy is usually seen as equivalent to the fact that the dielectric tensor is a scalar or is reduced to a scalar in case of polydomain materials. The latter is not correct, however, if the domains can not be considered as small compared to the wavelength.

Helmholtz Equation: