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physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
,
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
and materials science, bi-isotropic materials have the special optical property that they can rotate the polarization of light in either
refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenome ...
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 In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
(or simply, light) interact in an unusual way.


Definition

For most materials, the electric field ''E'' and electric displacement field ''D'' (as well as the magnetic field ''B'' and inductive magnetic field ''H'') are parallel to one another. These simple mediums are called isotropic, and the relationships between the fields can be expressed using constants. For more complex materials, such as crystals and many metamaterials, these fields are not necessarily parallel. When one set of the fields are parallel, and one set are not, the material is called anisotropic. 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
electric Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...
and magnetic fields are coupled. The
constitutive relation In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and app ...
s are :D = \varepsilon E + \xi H\, :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
tensors In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
(i.e. they depend on the direction within the material), in which case the media is referred to as ''bi-anisotropic''.


Coupling constant

''ξ'' and ''ζ'' can be further related to the Tellegen (referred to as reciprocity) ''χ'' and chirality ''κ'' parameter :\chi - i \kappa = \frac :\chi + i \kappa = \frac after substitution of the above equations into the constitutive relations, gives :D = \varepsilon E+ (\chi - i \kappa) \sqrt H :B = \mu H + (\chi + i \kappa) \sqrt E


Classification


Examples

''Pasteur media'' can be made by mixing metal
helices A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, ...
of one handedness into a resin. Care must be exercised to secure isotropy: the helices must be randomly oriented so that there is no special direction. 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 An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
. 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, :D = \varepsilon E - i \kappa \sqrt 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.
Electric dipole The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb- meter (C⋅m). T ...
s 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, :B = \mu H + \chi \sqrt{\varepsilon \mu} E This implies that the ''B'' field responds in phase with the ''H'' field.


See also

*
Anisotropy Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
*
Chirality (electromagnetism) 300px, The direction of current flow and induced magnetic flux follow a "handness" relationship The term chiral describes an object, especially a molecule, which has or produces a non-superposable mirror image of itself. In chemistry, such a m ...
*
Metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...
*
Reciprocity (electromagnetism) In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources) and the resulting electromagnetic fields in Maxwell's equations for time-invariant ...
* Maxwell's_equations#Constitutive_relations


References

Orientation (geometry) Materials science