Derivation Of Dispersion Coupling Permittivity/Permeability Of Magnetoelectric Composite Materials

The piezoelectric and piezomagnetic properties of the magnetoelectric composite materials can be described by their constitutive relation. However, the dispersion features of the material parameters are not reflected in the constitutive relation. It is necessary to construct a new constitutive relation involving dispersion coupling permittivity and permeability. We establish the constitutive relation exhibiting spatial dispersion and temporal dispersion by coupling the Maxwell's Equations with the previous constitutive relation. In fact, the linear relation of the magnetic field with the magnetic flux density, as well as the electric displacement and the electric field are obtained to replace the previous constitutive relation. The constitutive relation is generally suitable for magnetoelectric composite materials, which is helpful to understand the wave propagation mechanism inside the materials and can reduce the computational resources when the dispersion of the permittivity and permeability occurs in materials.