Effective medium properties of a ferromagnetic microwire grid

Abstract

The work presented in this paper involves the analysis of effective permittivity and permeability of a ferromagnetic microwire grid consisting of an infinite number of ferromagnetic microwires. Analytical solution is obtained through satisfying the tangential boundary conditions at the surface of a reference microwire. Subsequently, the local and average fields and hence, effective permittivity and permeability are obtained within a unit cell. The analysis reported in the literature allows to calculate only ${ϵ}_{zz}$ and ${\mu }_{\varphi \varphi }$ components of the effective permittivity and permeability for the case of $T{M}_z$ polarization with normal incidence. Proposed analysis provides a most generalized solution for the three diagonal elements of the effective permittivity and permeability tensors for the case of arbitrary polarization with arbitrarily incident uniform plane wave. Numerical results are obtained through MATLAB to show the impact of frequency, radius of the microwires, periodicity and applied external magnetization $H_0$ on the effective permittivity and permeability for $T{M}_z$ and $T{E}_z$ polarization. A comparative analysis is also done with the numerical results available in the literature to validate the proposed method of analysis.

Keywords:

• Effective medium
• ferrite
• ferromagnetic resonance
• metamaterial
• scattering
• tangential boundary conditions

Disclosure statement

No potential conflict of interest was reported by the author(s).