Polarized Reflectivity Measurements Research Articles

Reflection spectroscopy for anisotropic materials: Direct determination of phase differences; validity of Fresnel formulas

The reflectance of an anisotropic crystal is generally a tensor quantity even at normal incidence. Phase differences among the tensor components can be obtained from polarized reflectance measurements. A simple method for doing so is described and tested here. Possible applications of phase-difference information range from checking Kramers-Kronig evaluations of absolute phases to substituting for the Kramers-Kronig procedure. In addition, the following is proved, subject to some simple assumptions: If reflection extinction directions exist, the standard Fresnel equations may be used to derive optical constants ($n$'s and $k$'s), regardless of the anisotropy of the crystal. Moreover, extinction directions come in perpendicular pairs.

Single crystal optical properties of two forms of tetrathiafulvalenium iodide (TTF−In)

Polarized specular reflectance measurements over the energy range 0.6-5 eV are reported for two crystalline forms of tetrathiafulvalenium iodide ($\mathrm{TTF}\ensuremath{-}{\mathrm{I}}_{n}$). Since the plane of each TTF molecule is either approximately parallel or perpendicular to an external face of each crystal, polarized reflectance measurements can sample the various symmetry-allowed electronic transitions of the TTF molecule. The optical constants have been determined by means of a Lorentzian oscillator fit. A Drude-like edge is seen for light polarized along the conducting axis of monoclinic $\mathrm{TTF}\ensuremath{-}{\mathrm{I}}_{n}$ ($n\ensuremath{\sim}0.7$). Structure in the reflectance data for light polarized perpendicular to the stacking axes in both forms of $\mathrm{TTF}\ensuremath{-}{\mathrm{I}}_{n}$ is interpreted as being primarily due to in-plane transitions of the ${\mathrm{TTF}}^{+}$ ion. Transitions polarized along the long and short axes of the ${\mathrm{TTF}}^{+}$ ion in orthorhombic $\mathrm{TTF}\ensuremath{-}{\mathrm{I}}_{n}$ ($n=2$) can be resolved to aid in the assignment of the transitions for the ${\mathrm{TTF}}^{+}$ ion.

Optical Properties of Polymeric Sulfur Nitride,(SN)x

We report polarized reflectivity measurements on crystalline ${(\mathrm{SN})}_{x}$ in the range of 0.25-6.0 eV. Our analysis of the data gives $\ensuremath{\hbar}{\ensuremath{\omega}}_{p}=4.6$ eV and ${m}^{*}=2{m}_{e}$,, values considerably different from those previously reported by other workers. The data also suggest that ${(\mathrm{SN})}_{x}$ has sufficient electronic dimensionality to suppress a Peierls distortion.

Far-infrared reflectivity spectra of BiSI

Abstract The soft mode behavior in the paraelectric phase has been investigated in BiSI crystals by means of far-infrared polarized reflection measurements in the wave number region 4–400 cm−1. Four Bu modes for E⊊ Cand two Au modes for E ∥ C are observed in good agreement with group theoretical predictions according to the simplified C2/2h space group. A very low frequency mode shifts from ∼39 cm−1 at room temperature to ∼12 cm−1 at -152°C and accounts for the large static dielectric constant of the crystal.

Restrictions on the Inversion of the Fresnel Reflectance Equations

The regions for which the Fresnel equations can be inverted to determine the optical constants, n and K, from polarized reflection measurements of a plane electromagnetic wave are presented for different angles of incidence. The surface upon which this wave is incident is assumed to be a large, smooth, planar surface of a conducting medium that is linear, homogeneous, and isotropic. The sensitivity of the inversion procedure to +/-1% error in the measured reflectances is presented graphically. Such a small error in reflectances could produce a large error, more than 20%, in the determined optical constants n and K with K being the more erroneous. Angles of incidence in the neighborhood of 10 degrees and 80 degrees produce the largest acceptable regions for inversion.