Generalized effective medium theories and numerical verification

First developed to explain the refractive index of natural materials which are weka- or non-magnetic, effective medium theory nowadays faces challenges to facilitate designing, synthesizing, and mixing of various media responding to both electric and magnetic fields, such as metamaterials, periodic composites, magnetoelectric multiferroics, nanoparticles, metasurfaces, and mesocrystals. To generalize the effective medium theory for materials with also magnetic responses and boundary effects, the three projects below are undertaken. Firstly, the Clausius-Mossotti relation is reviewed and reexamined in conditions where material responds to both electric and magnetic fields. Surprisingly, materials with indices near zero and with real parts less than zero, that is the real part of both the permeability and permittivity are negative, are found to emerge from the interaction of electric and magnetic responses in a self-consistent theory. The new results point the way to artificial and natural materials with exotic responses. A simulation with 10-billion-level particles shows good agreement with the analytical results. The second part reviews a numerical verification of the effective medium theory. The Foldy-Lax equation is generalized for a medium that consists of particles with both electric and magnetic responses. The result is used to compute fields scattered from ensembles of particles. The computational complexity is reduced by hierarchical clustering techniques to enable simulations with on the order of 10 billion particles. With so many particles, we are able to see the transition to bulk media behavior of the fields. For non-magnetic materials, the observable index, permittivity, and permeability of the effective bulk medium are in good agreement with the Clausius-Mossotti relation. The fields simulated for particles with both electric and magnetic responses are in good agreement with the analytical results in the first part. Finally, we derive a modified Clausius-Mossotti relation for the effective dielectric permittivity of a medium in a half-space geometry. A first-principles derivation shows that the polarizability of the medium constituents should take into account the impact of an inhomogeneous environment. In particular, we take into account the interaction of constituent molecules with a nearby conductor which leads to an effective molecular polarizability and thus an effective dielectric permittivity in the medium that is both inhomogeneous and anisotropic. In the region very close to the boundary, the index of refraction dramatically changes from the bulk value. The three projects expand the effective medium theory to broader range of materials and mixtures including metamaterials, ferromagnetic materials, and magnetoelectric multiferroics, thus with more potential applications.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Wang, Lang

Contributors dc:contributor

• Carney, Paul S.
• Jin, Jianming
• Dragic, Peter
• Dallesasse, John

• Effective medium theory
• Clausius-Mossotti relation
• diffused particle method
• magnetic susceptibility
• permeability
• magnetoelectric effect

Statement dc:rights

• I declare that this thesis is my own original work and, to the best of my knowledge and belief, it does not: Breach the copyright or other intellectual property rights of a third party.

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/116160

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F116160