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In physics, engineering and materials science, bi-isotropics (or biisotropics) are any of a class of materials having the special optical property that it can twist the polarization of light in either refraction or transmission. This does not mean all materials with twist effect fall in the Bi isotropic class. The twist effect of the class of Bi isotropic materials is caused by the chirality and non-reciprocity of the structure of the media, in which the electric and magnetic field of an electromagnetic wave (or simply, light) interact in an unusual way.

[edit] Definition

Bi-isotropic refers to a kind of media in which the E-field and B-field are coupled.

the constitutive relations is

D = ε E + ξ H

B = μ H + ζ E

D, E, B , H , $ε$ and $μ$ are corresponding to usual electromagnetic qualities. $ξ$ and $ζ$ are the coupling constants, which is the intrinsic constant of each media.

[edit] Coupling Constant

$ξ$ and $ζ$ can be further related to the Tellegen (refer to as reciprocity) $χ$ and chirality $κ$ parameter

$\chi +i \kappa = \frac{\zeta }{\sqrt{\epsilon \mu }}$

$\chi -i \kappa = \frac{\xi }{\sqrt{\epsilon \mu }}$

after substitute the above equations into the constitutive relations, gives

$D=\epsilon E+ (\chi - i \kappa) \sqrt{\epsilon \mu } H$

$B= \mu H + (\chi + i \kappa) \sqrt{\epsilon \mu } E$

[edit] Classification

	non-chiral $κ = 0$	chiral $\kappa \neq 0$
reciprocal $χ = 0$	simple isotropic medium	Pasteur Medium
non-reciprocal $\chi \neq 0$	Tellegen Medium	General Bi isotropic medium

[edit] Example Media

Pasteur Media can be made by mixing metal helices of one handedness into a resin. Care has been exercised to secure isotropy: the helices must be randomly oriented so that there is no special direction. [1]

The megnetoelectric effect can be understood from the helix as it is exposed to the electromagnetic field. the helix geometry is a sort of inductor. The magnetic component of a EM wave will induces a current on the wire and further influence the electric component of the same EM wave.

From the constitutive relations, for Pasteur media, $χ = 0$ ,

$D=\epsilon E - i \kappa \sqrt{\epsilon \mu } H$

the D field was delayed the respond from the H-field by a phase i.

Tellegen Media is an opposite of Pasteur media, which is electromagnetic : the electric component will cause change to the magnetic component. such a medium is not as straightforward as the concept of handedness. Electric dipoles bonded with magnets is belong to this kind. when the dipoles turned by the electric part of a EM wave, the magnets will also be changed, due to they bounded together. The change of magnets direction will change the magnetic component of the same EM wave.

from the constitutive relations, for Pasteur media, $κ = 0$ ,

$B= \mu H + \chi \sqrt{\epsilon \mu } E$

The D field was responded immediately from the H-field.

[edit] See also

[edit] References

[1] Electromagnetic Waves in Chiral and Bi-isotropic Media, I.V. Lindell, A.H. Shivola, S.A. Tretyakov, A.J. Viitanen