Ordinary Axes Research Articles

Infrared Optical Anisotropy in Quasi‐1D Hexagonal Chalcogenide BaTiSe3

AbstractPolarimetric infrared (IR) detection bolsters IR thermography by leveraging the polarization of light. Optical anisotropy, i.e., birefringence and dichroism, can be leveraged to achieve polarimetric detection. Recently, giant optical anisotropy is discovered in quasi‐1D narrow‐bandgap hexagonal perovskite sulfides, A1+xTiS3, specifically BaTiS3 and Sr9/8TiS3. In these materials, the critical role of atomic‐scale structure modulations in the unconventional electrical, optical, and thermal properties raises the broader question of the nature of other materials that belong to this family. To address this issue, for the first time, high‐quality single crystals of a largely unexplored member of the A1+xTiX3 (X = S, Se) family, BaTiSe3 are synthesized. Single‐crystal X‐ray diffraction determined the room‐temperature structure with the P31c space group, which is a superstructure of the earlier reported P63/mmc structure. The crystal structure of BaTiSe3 features antiparallel c‐axis displacements similar to but of lower symmetry than BaTiS3, verified by the polarization dependent Raman spectroscopy. Fourier transform infrared (FTIR) spectroscopy is used to characterize the optical anisotropy of BaTiSe3, whose refractive index along the ordinary (E ⊥ c) and extraordinary (E ‖ c) optical axes is quantitatively determined by combining ellipsometry studies with FTIR. With a giant birefringence Δn ∼ 0.9, BaTiSe3 emerges as a new candidate for miniaturized birefringent optics for mid‐wave infrared to long‐wave infrared imaging.

Intra-pulse difference frequency generation in ZnGeP2 for high-frequency terahertz radiation generation

The highly-nonlinear chalcopyrite crystal family has experienced remarkable success as source crystals in the mid-infrared spectral range, such that these crystals are primary candidates for producing high terahertz frequency (i.e., gtrsim 10 THz) electric fields. A phase-resolved terahertz electric field pulse is produced via intra-pulse difference frequency generation in a chalcopyrite (110) ZnGeP2 crystal, with phase-matching being satisfied by the excitation electric field pulse having polarizations along both the ordinary and extraordinary crystal axes. While maximum spectral power is observed at the frequency of 24.5 THz (in agreement with intra-pulse phase-matching calculations), generation nonetheless occurs across the wide spectral range of 23–30 THz. To our knowledge, this is the first time a chalcopyrite ZnGeP2 crystal has been used for the generation of phase-resolved high-frequency terahertz electric fields.

BATTLE AXES OF AMAZONS OF EUROPEAN SCYTHIA

Weapons are one of the most important elements of the material culture of the North Pontic nomads. Archaeological finds from the steppe kurhans testify that the Scythians were armed with bows and arrows, spears and javelins, slings, swords and daggers, battle axes, horseman’s picks (pick axe), hammers and maces. However, not all types of weapons were equally common, and battle axes were less popular.
 Relatively few battle axes came from burial assemblages on the territory of European Scythia — from 50 to 100 items, according to the data of various researchers. By morphological features, two groups are distinguished: battle axes (three divisions) and axes with hammers (two divisions). The length of the wooden handles in most cases is about 50―70 cm. Battle axes are known in Scythian burial sites from the 7th to the 2nd century BC. Finds of early specimens are correlated mainly with antiquities of the Forest Steppe, while later specimens are concentrated in the central part of the territories of European Scythia. Until recently, it was believed that this type of weapon marked only male Scythian burials, however, the presence of axes in several female burials proves otherwise.
 The use of axes by the Amazons is mentioned in the works of several ancient authors, the works of ancient art demonstrate this phenomenon as well. According to archaeological materials, battle axes were found in only six (2 %) women’s graves: two in the Lower Dnipro Steppe Group and four in the Lower Dniester Steppe Group. An examination of the burial complexes of Scythian female warriors with axes made it possible to note several characteristic features.
 
 All axes are iron. Five of them have a single blade, from 16.5 to 22 cm long. And only one axe has a double blade. It is also stand out by its small size — 14.6 cm. Typologically and in terms of size, all these axes fully correspond to samples from other Scythian graves of European Scythia.
 An examination of the placement of axes in the graves showed a variety of its options. This means that there were no clear canons for the location of axes regarding the dead.
 The nature and size of the burials, as well as the assortment and number of grave goods testify that Scythian female warriors armed with axes were mainly representatives of the middle class of nomadic society.
 The age of women who were buried with axes is determined to be between 20 and 35 years old. This means that we are talking about the most active members of military units.
 Only ordinary iron axes were found in women’s graves, usually in sets with other weapons, mainly arrows. Gala and artistically decorated pick axes or sceptre axes, which served as symbols of high social status and power, are not known in women’s graves.
 Axes from women’s graves typologically and chronologically do not differ from those found in men’s graves.
 
 Therefore, iron axes from women’s graves, along with other types of weapons, were obviously used for their intended purpose. They were not part of the insignia of power but marked the belonging of women to the military state.

THz Multi-Mode Q-Plate with a Fixed Rate of Change of the Optical Axis Using Form Birefringence.

We report the design, fabrication and experimental validation of a THz all-dielectric multi-mode q-plate having a fixed rate of change of the optical axis. The device consists of space-variant birefringent slabs manufactured by 3D printing using melt-extruded Acrylonitrile Butadiene Styrene (ABS). The desired form birefringence is analytically evaluated and experimentally measured by the THz time domain spectroscopy technique. The manufactured q-plate design is characterized using a polarization-sensitive imaging setup. The full electric field spatial maps are acquired from the beam propagating through the q-plate. The device enables the realization of both radial and azimuthal vector beams at discrete frequency intervals by controlling the space-dependent orientation of the ordinary and extraordinary axes in the transverse plane with a multi-mode sequence.

A Compact Broadband Terahertz Range Quarter-Wave Plate

We detail the design and characterization of a terahertz range achromatic quarter-wave plate based on a stack of aligned variable thickness birefringent sapphire discs. The disc thicknesses and relative rotations of the discs are determined through a basin-hopping Monte Carlo thermal annealing routine. The basin-hopping scheme allows an improved refinement of the required thicknesses and rotations to give a predicted phase error from the ideal π/2 of only 0.5%, which is a factor of approximately 6 better than previous efforts. Moreover, the large contrast between extraordinary and ordinary axes of sapphire allows us to greatly decrease the overall optical path length of our wave plate design by approximately a factor of 10 over similar designs based on quartz discs. However, this very same contrast requires very precise tolerances in the milled thicknesses of the discs and their assembly. We detail a method to compensate for differences in the thickness from their calculated ideal values. We have constructed one of our designs and found it similar in performance to other configurations, but with our much more compact geometry.

The effect of anisotropy on cross section spectra of uniaxial spherical particles small compared to the wavelength

We study the effect of anisotropy on the extinction, absorption and scattering spectra of optically uniaxial spherical particles, which are small compared to the wavelength of the incident light, in the infrared spectral region. To do so we compare simulated Finite-Difference Time-Domain (FDTD) spectra of the uniaxial sphere to spectra of a corresponding isotropic materials calculated with Mie-theory, which are given the principal dielectric functions of the ordinary and extraordinary axes, respectively. Several effects of anisotropy can be observed, caused by the incident plane wave being bent around the sphere and penetrating into the sphere.

Polarization-dependent non-uniform rotation rates of rhombohedral calcite

We demonstrate the polarization-dependent torque on rhombohedral calcite in an optical trap. Our precipitate technique produces regular crystals approximately 10μm on all edges. The regularity of the crystal shape makes it possible to visually identify the optical axis as well as the orientation of the polarization axes. When a rhombohedral crystal is trapped in an elliptically polarized beam, it orients itself with its optic axis approximately parallel to the beam axis. While in this orientation, the total torque increases and decreases relative to three extraordinary and ordinary axes of the crystal. We measure this axis-dependent calcite rotation through video analysis and model the dependence of the torque on the crystal orientation. The ability to predict the motion of calcite gives an analytical tool for applications such as fluid stirring or "lab on a chip" systems.

Measurement of the real dielectric permittivity ϵr of glacial ice

Owing to their small interaction cross-section, neutrinos are unparalleled astronomical tracers. Ultra-high energy (UHE; E > 10 PeV) neutrinos probe the most distant, most explosive sources in the Universe, often obscured to optical telescopes. Radio-frequency (RF) detection of Askaryan radiation in cold polar ice is currently regarded as the best experimental measurement technique for UHE neutrinos, provided the RF properties of the ice target can be well-understood. To that end, the Askaryan Radio Array (ARA) experiment at the South Pole has used long-baseline RF propagation to extract information on the index-of-refraction (n=ϵr) in South Polar ice. Owing to the increasing ice density over the upper 150–200 m, rays are measured along two, nearly parallel paths, one of which refracts through an inflection point, with differences in both arrival time and arrival angle that can be used to constrain the neutrino properties. We also observe (first) indications for RF ice birefringence for signals propagating along predominantly horizontal trajectories, corresponding to an asymmetry of order 0.1% between the ordinary and extra-ordinary birefringent axes, numerically compatible with previous measurements of birefringent asymmetries for vertically-propagating radio-frequency signals at South Pole. Qualitatively, these effects offer the possibility of redundantly measuring the range from receiver to a neutrino interaction in Antarctic ice, if receiver antennas are deployed at shallow (z ∼ −25 m) depths. Such range information is essential in determining both the neutrino energy, as well as the incident neutrino direction.

Effective optical constants of anisotropic silver nanoparticle films with plasmonic properties.

Mueller matrix ellipsometry has been used to determine the effective optical constants of island-like Ag films deposited by thermal evaporation. These films depart substantially from bulk silver with a prominent localized surface plasmon resonance. Moreover, despite the isotropic appearance, they exhibit uniaxial optical properties with the optical axis inclined by 83.4° from the substrate normal toward the direction of the incoming vapor flux. The uniaxial model supports the plasmon resonance peaks revealed by in-plane absorbance measurements of the films. The uniaxial behavior suggests that the resonances along the ordinary axes are weakly coupled between neighboring particles, whereas the extraordinary resonance is relatively strongly coupled. Therefore, the anisotropy should be considered in the practical applications of these plasmonic films.

Van der Waals torque and force between dielectrically anisotropic layered media.

We analyse van der Waals interactions between a pair of dielectrically anisotropic plane-layered media interacting across a dielectrically isotropic solvent medium. We develop a general formalism based on transfer matrices to investigate the van der Waals torque and force in the limit of weak birefringence and dielectric matching between the ordinary axes of the anisotropic layers and the solvent. We apply this formalism to study the following systems: (i) a pair of single anisotropic layers, (ii) a single anisotropic layer interacting with a multilayered slab consisting of alternating anisotropic and isotropic layers, and (iii) a pair of multilayered slabs each consisting of alternating anisotropic and isotropic layers, looking at the cases where the optic axes lie parallel and/or perpendicular to the plane of the layers. For the first case, the optic axes of the oppositely facing anisotropic layers of the two interacting slabs generally possess an angular mismatch, and within each multilayered slab the optic axes may either be the same or undergo constant angular increments across the anisotropic layers. In particular, we examine how the behaviors of the van der Waals torque and force can be "tuned" by adjusting the layer thicknesses, the relative angular increment within each slab, and the angular mismatch between the slabs.

Simple spectral technique to identify the ordinary and extraordinary axes of a liquid crystal retarder

We present a very simple method to distinguish between ordinary and extraordinary axes in an optical retarder. The method is based on inserting the retarder in between two crossed linear polarizers, oriented at 45° to the neutral axes. By tilting the retarder to obtain oblique-incidence illumination, a different behavior is observed depending on the orientation of the ordinary/extraordinary axes relative to the tilt direction. Simply using white light illumination from a tungsten lamp and spectral analysis by means of a portable spectrometer, it is possible to differentiate between ordinary and extraordinary axes. Theoretical analysis is provided, as well as the experimental verification with a liquid crystal variable retarder (LCR). A significant difference of the LCR retardance variation is obtained for different orientation of the LC director relative to the tilt direction.

Linear birefringence magnitude of artificial self-assembled DNA crystals

We determine the linear birefringence magnitude, i.e. the difference between refractive indexes along the extraordinary and ordinary axes, of artificial uniaxial DNA crystals assembled with the so-called DNA tile approach. Based on the ellipsometric measurements, the birefringence magnitude is between 0.001 and 0.0018 in the visible and near infrared range. Besides being of fundamental interest, the optical properties of DNA crystals are crucial in the design of novel photonic nanostuctures.

CONSTRUCTION OF A LATTICE KNOT WHOSE THREE SHADOWS ARE ALL TREES

It is known by few that a trivial knot can be transformed into a lattice knot whose three shadows are all trees (here, three shadows mean the projections of the lattice knot to the directions of ordinary orthogonal axes). Since a knot itself is a loop in the space, this fact may be rather astonishing. It will be interesting to ask whether a non-trivial knot has such a transformation or not. The purpose of this paper is to show that any two-bridge torus knot or link has a transformation into a lattice knot whose three shadows are all trees. The algorithm to construct such a position will be demonstrated.

Optical anisotropy and charge-transfer transition energies in BiFeO3from 1.0 to 5.5 eV

We discuss uniaxial optical anisotropy in single-crystal BiFeO${}_{3}$ determined by spectroscopic ellipsometry from 1.0 to 5.5 eV. The dielectric function \ensuremath{\varepsilon} $=$ \ensuremath{\varepsilon}${}_{1}$ $+$ i\ensuremath{\varepsilon}${}_{2}$ and refractive index $N$ $=$ $n$ $+$ $\mathit{ik}$ spectra of BiFeO${}_{3}$ are extracted for the tensor components along its ordinary and extraordinary principal axes. Using the standard line-shape analysis, we also obtain the energies of the major optical structures associated with the charge-transfer transitions in BiFeO${}_{3}$.

Tunable Defect Mode in One-Dimensional Photonic Crystal with Liquid Crystal Defect Layer

ABSTRACT Electrical tuning of defect modes in a one-dimensional (1D) photonic crystal (PC) has been demonstrated using a ferroelectric liquid crystal (FLC) and a nematic liquid crystal (NLC) defect layers in the periodic structure. The transmission peak intensities for defect mode depends on the angle between LC molecular axis and polarization direction of the incident light. At defect mode wavelength, the 1D PC with LC defect layer transmits only the light with the polarization direction determined by the direction of extraordinary or ordinary optical axes in LC defect. Polarization direction of the light propargating through the 1D PC with in-plane NLC defect can be controlled based on field-induced in-plane realignment of NLC molecules.

Refractive-index measurements of zinc germanium diphosphide at 300 and 77 K by use of a modified Michelson interferometer.

A method to determine the absolute refractive index of materials available in the shape of flat wafers with parallel sides by using interferometric techniques is presented. With this method, nondestructive, sample-specific measurements can be made. The method is tested by using silicon, germanium and zinc selenide, and measurements for both the ordinary and extraordinary axes of ZnGeP2 for temperatures of 300 and 77 K are reported.

Dielectric constant and loss tangent in LiNbO3 crystals from 90 to 147 GHz

The complex dielectric constant ε(ω) of poled LiNbO3 crystals has been measured from 90 to 147 GHz using a reflectometer bridge. Electric field polarizations in both the ordinary and extraordinary axes were studied. The real part of ε(ω) differs only slightly from its value near 10 GHz, while the imaginary part is significantly larger than reported at lower frequencies. The data are used to model the dissipative losses of a gold co-planar waveguide on LiNbO3.

Transverse-electric/transverse-magnetic polarization converter using twisted optic–axis waveguides in poled polymers

Polymeric passive TE/TM polarization converters are fabricated based on an adiabatic following in twisted optic–axis waveguides. Waveguides are formed by a reactive ion etching, and the optic axis of the waveguide is twisted by 90° with specially designed poling electrodes. Both TE and TM modes confined in the waveguides are converted to their counterparts by following the twisted ordinary and extraordinary axes, respectively. Conversion efficiency better than 20 dB and polarization-dependent loss less than 0.5 dB are obtained. The device provides wavelength insensitive operations and has large fabrication tolerances.

Optical fibre Babinet compensator

The author reports a new kind of birefringent compensator made of a bent single-mode optical fibre. Birefringent properties result from variation of the geometry of a fibre coil including 20 loops. The ompensator introduces up to 14 pi adjustable phaseshift between the ordinary and extraordinary axes without significant losses.

Bivariate allometry: Interval estimation of the slopes of the ordinary and standardized normal major axes and structural relationship

An exact confidence set for the slope of a linear bivariate normal structural relationship consists of a pair of conjugate intervals; the primary interval contains the maximum likelihood estimate and is used alone as an approximate confidence interval; the secondary interval is discarded because it would assign to the slope of the relationship a sign opposite to that of the sample correlation. New simulations confirm that, in small samples from populations having low correlations, the inaccuracy of the significance level due to discarding the secondary interval is negligible for the ordinary major axis, where the ratio of residual variances equals unity, but considerable for the standardized major axis, where residual variances are proportional to total (marginal) variances. The inaccuracy of the significance level for the standardized major axis can be reduced but cannot be eliminated by computing a conditional confidence interval only when the sample correlation is significant. A recent proposal by Rayner (1985, J. Zool. Lond. (A) 206 , 415–439) and a recent claim by McArdle (1988, Can. J. Zool. 66, 2329–2339), concerning the interval estimation of the slope of the standardized major axis, are shown to be erroneous. Because many biological data are non-negative, have positively-skewed and heteroscedastic distributions, and are related by power functions, and because the covariance matrix of logarithmically-transformed data is dimensionless, the ordinary major axis of logarithms is often suitable in biology.