Analysis of Mueller matrices of metamaterials and multiferroics
Department of Physics
Doctor of Philosophy
Federici, John Francis
Ahn, Ken Keunhyuk
Berreman matrix formalism
The optical spectra of complex materials such as magnetic-dielectric media, magnetoelectric and multiferroic crystals, materials with intrinsic chirality, and metamaterials are studied. These media are important both for: (i) their interesting optical effects, such as Negative Index of Refraction (NIR) and impedance matching; and (ii) possible device applications such as switching devices and anti-reflection coatings. Proper characterization of complex materials requires advanced spectroscopic approaches and the development of theoretical models for data analysis. Berreman’s 4´4 matrix formalism is used to derive forward models for the optical spectra of Reflectivity, Transmission, Rotating Analyzer Ellipsometry (RAE), and Mueller Matrices (MM). The forward models incorporate the relative electric permittivity tensor (ε), the relative magnetic permeability tensor (μ), the magneto-electric tensors (α and α'), and the chirality tensors (ξ and ξ'). These models can accommodate various crystal symmetries in both the semi-infinite and thin film configurations. Using non-linear least squares fitting procedures, the forward models can be fitted against experimental optical spectra to determine the tensor parameters, which describe the physical properties of the material.
In the original part of this Thesis, forward models for the Mueller Matrix components of materials with relative magnetic permeability tensor μ≠1 are studied. 4×4 matrix formalism is used to calculate the complex reflection coefficients and the MMs of dielectric-magnetic materials. For materials with simultaneously diagonalizable ε and μ tensors (with coincident principal axes), analytic solutions to the Berreman equation are derived. For the single layer thin film configuration, analytic formulas for the complex reflection and transmission coefficients are derived for orthorhombic symmetry or higher. The separation of the magnetic and dielectric contributions to the optical properties as well as the ability to distinguish materials exhibiting negative index of refraction are demonstrated using simulations of the MM at varying angles of incidence.
Far-infrared spectra of magneto-dielectric Dy3Fe5O12 garnet (DY-IG) were studied using a combination of transmittance, reflectivity, and rotating analyzer ellipsometry. In addition to purely dielectric and magnetic modes, several hybrid modes with a mixed magnetic and electric dipole activity were observed. Using 4´ 4 matrix formalism for materials with μ(ω) ≠ 1, the experimental optical spectra were modeled and the far-infrared dielectric and magnetic permeability functions were determined. The matching condition μ(ωh)*Se = ε(ωh)*Sm for the oscillator strengths Se(m) explains the observed vanishing of certain hybrid modes at ωh in reflectivity.
Electromagnetic wave propagation and the spectra of optical excitations in complex materials are modeled. Analytical expressions for the complex reflection coefficients of materials with cycloidal magnetic ordering such as REMnO3 compounds (RE=rare earth) are derived for both semi-infinite and thin film configurations. Simulations for the Negative Index of Refraction (NIR) condition are given and the effect of the magneto-electric tensor on NIR is illustrated. Finally, the MMs of various combinations of material tensor components are illustrated for the dynamic magnetoelectric and chirality states and methods to distinguish their contributions are discussed.
njit-etd2011-059 (269 pages ~ 2,491 KB pdf)
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Created July 26, 2011