Bi-isotropic material

In

(or simply, light) interact in an unusual way.

Definition

For most materials, the

. Crystals typically have D fields which are not aligned with the E fields, while the B and H fields remain related by a constant. Materials where either pair of fields is not parallel are called anisotropic.

In bi-isotropic media, the

are

${\displaystyle D=\varepsilon E+\xi H\,}$

${\displaystyle B=\mu H+\zeta E\,}$

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.

This can be generalized to the case where ε, μ, ξ and ζ are

Coupling constant

ξ and ζ can be further related to the

chirality

κ parameter

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

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

after substitution of the above equations into the constitutive relations, gives

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

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

Classification

	non-chiral ${\displaystyle \kappa =0\,}$	chiral ${\displaystyle \kappa \neq 0}$
reciprocal ${\displaystyle \chi =0\,}$	simple isotropic medium	Pasteur Medium
non-reciprocal ${\displaystyle \chi \neq 0}$	Tellegen Medium	General bi-isotropic medium

Examples

Pasteur media can be made by mixing metal

[3]

The magnetoelectric effect can be understood from the helix as it is exposed to the electromagnetic field. The helix geometry can be considered as an inductor. For such a structure the magnetic component of an EM wave induces a current on the wire and further influences the electric component of the same EM wave.

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

${\displaystyle D=\varepsilon E-i\kappa {\sqrt {\varepsilon \mu }}H.}$

Hence, the D field is delayed by a phase i due to the response from the H field.

Tellegen media is the opposite of Pasteur media, which is electromagnetic: the electric component will cause the magnetic component to change. Such a medium is not as straightforward as the concept of handedness.

bonded with magnets belong to this kind of media. When the dipoles align themselves to the electric field component of the EM wave, the magnets will also respond, as they are bounded together. The change in direction of the magnets will therefore change the magnetic component of the EM wave, and so on.

From the constitutive relations, for Tellegen media, κ = 0,

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

This implies that the B field responds in phase with the H field.

See also

• Anisotropy
• Chirality (electromagnetism)
• Metamaterial
• Reciprocity (electromagnetism)
• Maxwell's_equations#Constitutive_relations

References