Introductory Fourier transform spectroscopy

A method and system for spectroscopic ellipsometry employing reflective optics to measure a small region of a sample by reflecting radiation (preferably broadband UV, visible, and near infrared radiation) from the region. The system preferably has an autofocus assembly and a processor programmed to determine from the measurements the thickness and/or complex refractive index of a thin film on the sample. Preferably, only reflective optics are employed along the optical path between the polarizer and analyzer, a sample beam reflects with low incidence angle from each component of the reflective optics, the beam is reflectively focused to a small, compact spot on the sample at a range of high incidence angles, and an incidence angle selection element is provided for selecting for measurement only radiation reflected from the sample at a single, selected angle (or narrow range of angles). The focusing mirror preferably has an elliptical shape to reduce off-axis aberrations in the focused beam. Some embodiments include both a spectrophotometer and an ellipsometer integrated together as a single instrument. In such instrument, the spectrophotometer and ellipsometer share a radiation source, and radiation from the source can be focused by either the spectrophotometer or the ellipsometer to the same focal point on a sample. Preferred embodiments of the ellipsometer employ a rotating, minimal-length Rochon prism as a polarizer, and include a spectrometer with an intensified photodiode array to measure reflected radiation from the sample, and a reference channel (in addition to a sample channel which detects radiation reflected from the sample).

Focused beam spectroscopic ellipsometry method and system

Homogeneous composites, or metamaterials, made of dielectric or metallic particles are known to show magnetic properties that contradict arguments by Landau and Lifshitz [Landau LD, Lifshitz EM (1960) Electrodynamics of Continuous Media (Pergamon, Oxford, UK), p 251], indicating that the magnetization and, thus, the permeability, loses its meaning at relatively low frequencies. Here, we show that these arguments do not apply to composites made of substances with Im e S eS ≫ λ/l or Re e S eS ∼ λ/l (eS and l are the complex permittivity and the characteristic length of the particles, and λ ≫ l is the vacuum wavelength). Our general analysis is supported by studies of split rings, one of the most common constituents of electromagnetic metamaterials, and spherical inclusions. An analytical solution is given to the problem of scattering by a small and thin split ring of arbitrary permittivity. Results reveal a close relationship between eS and the dynamic magnetic properties of metamaterials. For | e S eS | ≪ λ/a (a is the ring cross-sectional radius), the composites exhibit very weak magnetic activity, consistent with the Landau–Lifshitz argument and similar to that of molecular crystals. In contrast, large values of the permittivity lead to strong diamagnetic or paramagnetic behavior characterized by susceptibilities whose magnitude is significantly larger than that of natural substances. We compiled from the literature a list of materials that show high permittivity at wavelengths in the range 0.3–3000 μm. Calculations for a system of spherical inclusions made of these materials, using the magnetic counterpart to Lorentz–Lorenz formula, uncover large magnetic effects the strength of which diminishes with decreasing wavelength.

/pdf/metamaterials-and-the-landau-lifshitz-permeability-argument-1p6xq87o3m.pdf

Metamaterials and the Landau–Lifshitz permeability argument: Large permittivity begets high-frequency magnetism

Ultrawide range dielectric spectra from the kilohertz to terahertz range of BaTiO3 (BT), Ba(Zr0.25Ti0.75)O3 (BZT), (Ba0.6Sr0.4)TiO3 (BST), and SrTiO3 ceramics were presented by analyzing dielectric permittivity and IR reflectivity data. It was found that the permittivity of the ST was determined only by the ionic polarization while that of the BT was determined by the ionic polarization as well as the dipole polarization due to the domain contribution. The high permittivity of the BZT ceramics was attributed to the dipole polarization of polar nanoregions in the relaxors. The dipole and ionic polarizations overlapped in the BST.

Ultrawide range dielectric spectroscopy of BaTiO3-based perovskite dielectrics

Doped strontium titanate becomes superconducting at a density as low as $n=5\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, where the Fermi energy is orders of magnitude smaller than the longitudinal-optical-phonon frequencies. In this limit, the only optical mode with a frequency which is smaller than the Fermi energy is the plasmon. In contrast to metals, the interaction strength is weak due to screening by the crystal, which allows the construction of a controllable theory of plasmon superconductivity. We show that plasma mediated pairing alone can account for the observed transition temperatures only if the dielectric screening by the crystal is reduced in the slightly doped samples compared with the insulating ones. We also discuss unique features of the plasmon mechanism, which appear in the tunneling density of states above the gap.

https://link.aps.org/accepted/10.1103/PhysRevB.94.224515

Superconductivity at very low density: The case of strontium titanate

By combining reflectance spectroscopy and spectroscopic ellipsometry, the complex dielectric function of SrTiO3 in the frequency range 40–5000 cm−1 at 20, 100, 200, and 300 K has been determined. Using a factorized description, analytical expressions for the optical quantities were derived, giving excellent agreement with the experimental data. These can be used for two‐layer fits of films on SrTiO3, e.g., of high‐Tc superconductors. The fit parameters complement very well those found at higher temperatures.

/pdf/the-low-temperature-infrared-optical-functions-of-srtio3-3ofn2dtxx2.pdf

K.-L. Barth

Papers

The low-temperature infrared optical functions of SrTIO3 determined by reflectance spectroscopy and spectroscopic ellipsometry

Far-IR spectroscopic ellipsometer