Wave Propagation in Multiferroic Materials (2013)

Based on an idea that using novel materials could be useful for antenna applications, we began looking at the use of multiferroics. These novel materials exhibit a cross-coupling between electric and magnetic ordering parameters, which technically is saying that an electric field applied to one these materials can turn the material into a magnet (i.e. - it produces magnetization in the material). The converse of this statement, that a magnetic field applied to the material can produce an electric polarization is also true. The notion that an applied voltage can drive the intrinsic magnetization in a material to produce a controlled magnetic field, not relying on current-driven-coupling through Ampere's Law, is a very powerful one and the potential of this coupling phenomena for use in electromagnetic devices is enormous. The focus of the work contained herein is to help assess if and how that potential can be utilized.My dissertation concentrates on modeling linear multiferroic (MF) materials and examines the potential for their use in electromagnetic (EM) wave ``processing'' applications. In the interest of pursuing various applications of magneotelectic (ME) materials a fundamental understanding of the nature of waves in these materials is required. The wave equation for a general linear ME material system is developed and presented here with a discussion of the unique features of ME waves. This discussion is on wave transmission in extended mediums; interface behavior of ME composites and phase matching issues with transmission/reflection characteristics of the MF materials are discussed. Further, single phase ME materials have been known to exist for about 50 years, but the cross-coupling of these materials is too weak to be of interest for most applications. To enhance cross-coupling effects, strain coupled materials have been developed. While these strain coupled materials show enhanced cross-coupling, typical coefficients reported in the literature are two to three orders of magnitude lower than desired for significant influence on EM waves. To assess the feasibility of strain coupled materials in EM applications, a homogenization model is developed that accommodates the effects of elastic coupling in multi-phase composite materials and predicts the resultant constitutive parameters of the material. The resulting homogenization model produces constitutive parameters for a material which is magnetoelectroelastic (MEE), extending the complexity of the original magnetoelectric coupling in the material. The additional coupling reflects the additional ``predominately acoustic'' modes which exist in the combined material system. To understand the wave behavior of this extended system a wave equation is developed for the solution of the propagation modes and phase velocities of the MEE system. While MEE systems are of significant in their own right, it is desirable to have effective properties of an MEE material that resemble the EM system so that the computational and physical complexity can be reduced. This facilitates design codes and a functional understanding of the ``purely electromagnetic'' properties of an MEE system in device implementations. To address this properly, the MEE system is reduced to an effective ME system. This is more involved than simply looking at the effective permeability, permittivity and magnetoelectric coupling terms in the MEE constitutive form as is commonly done. The importance of the mechanical coupling is demonstrated. Finally, an application of multiferroic coupling principles is applied to the design of an extreme sub-wavelength receive antenna. The complexity and computational size of the antenna concept requires numerical simulation. The three step FEM modeling process used to design the receive antenna is discussed in detail as well as suggestions for improved performance in future devices.