Mueller matrices for anisotropic metamaterials generated using 4×4 matrix formalism

Abstract

Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor 1 µ ≠ are studied. 4 4 × matrix formalism is employed to produce general solutions for the complex reflection coefficients and MMs of dielectric-magnetic materials having arbitrary crystal symmetry and arbitrary laboratory orientation. For certain orientations of materials with simultaneously diagonalizable ε and µ tensors (with coincident principal axes), analytic solutions to the Berreman equation are available. For the single layer thin film configuration of these materials, analytic formulas for the complex reflection and transmission coefficients are derived for orthorhombic or higher crystal symmetry. The separation of the magnetic and dielectric contributions to the optical properties of a material are demonstrated using measurements of the MM at varying angles of incidence.

Synchrotron radiation-based far-infrared spectroscopic ellipsometer with full Mueller-matrix capability

“…Preparing large, high quality samples can be challenging, so effectively all farinfrared ellipsometry measurements have very low throughput. As demonstrated by Kircher et al, 7 high brightness synchrotron radiation overcomes this throughput limit and allows for relatively quick ellipsometric measurements of the samples with a modest cross section area of a few mm 2 . This capability has become increasingly important for researching complex oxides where competing orders drive new physical phenomena (e.g., superconductivity, colossal magnetoresistance, multiferroicity).…”

“…Several sets of rotating retarders enable a full Muller matrix analysis of anisotropic and bianisotropic samples. The typical spot-size of about 3 × 3 mm 2 at the sample position for the slowly focused synchrotron radiation with f # = 20 allows studying relatively small samples with the surface area of about 1 × 1 mm 2 . In this paper we will describe the instrument in details and will present several examples of the measured rotating analyzer ellipsometry (RAE) and MM spectra of magnetic and ME materials such as Dy 3 Fe 5 O 12 and TbMnO 3 single crystals.…”

“…The related activity of our team in theory of the data analysis and simulations in materials with μ = 1 is published in Ref. 2. The principles of the rotatable broadband optical retarders are published in Ref.…”

Far-infrared spectra of the magnetic exchange resonances and optical phonons and their connection to magnetic and dielectric properties of Dy3Fe5OKang1, Standard2, Rogers3 et al. 2012Phys. Rev. B17150View full textAdd to dashboardCite

“…36 For the spectra measured at low temperatures, the maximum number of the oscillators used in the fit was N=27. This number does not include the numerous CF and LF transitions below 80 cm -1 that were already described in the previous Section.…”

Spectroscopic ellipsometry for active nano- and meta-materials

“…In this case, if the material can be considered as an effective medium, its electromagnetic properties shall be described by several tensors: dielectric permittivity [ε eff ], magnetic permeability [μ eff ], chirality [γ eff ] and [ζ eff ], which have to be retrieved from fitting of the measured SE data (using the Berreman multilayer matrix formalism). Also, it has been suggested that Mueller matrix SE on an effective medium material displaying optical magnetism (i.e., with a nonzero magnetic permeability tensor) is required for separating the magnetic and dielectric contributions to its effective response and recording necessary information for evidencing negative refraction [32]. Note that the effective medium description of metamaterials (and of rough surfaces) is not always legitimate, as evoked in Section 7.…”