Bianisotropy

Bianisotropy is a property of materials in which the linear electromagnetic response cannot be described by separate electric permittivity and magnetic permeability tensors alone. In bianisotropic media, the electric and magnetic fields are coupled, so the electric field can induce magnetic polarization and the magnetic field can induce electric polarization.

In linear, local media the constitutive relations are typically written as D = ε E + ξ H and B = ζ E + μ H, where D is the electric displacement, B is the magnetic induction, E is the electric field, H is the magnetic field, ε and μ are the permittivity and permeability tensors, and ξ and ζ are magnetoelectric coupling tensors that encode the cross-coupling between electric and magnetic fields.

For reciprocal media, the coupling tensors satisfy ζ = -ξ^T. Breaking time-reversal symmetry, for example by applying a magnetic bias or using moving media, can lead to nonreciprocal bianisotropy, where the response depends on the direction of wave propagation.

Bianisotropy originates from the microstructure of materials, especially when their geometry or composition lacks certain symmetries. It is a common feature in metamaterials and in composites with strong near-field coupling, chiral arrangements, layered or asymmetric inclusions, and magnetoelectric effects at interfaces. Subclasses include bi-isotropic, chiral, Tellegen, and omega media, each with characteristic forms of the coupling tensors.

Applications of bianisotropy include polarization control, optical activity, handedness discrimination, and the design of materials and devices with tailored impedance and refractive properties.