Double Refraction Effect Research Articles

Новый метод поиска прямолинейного участка на экспериментальной диаграмме напряжение–деформация

Polyethylene terephthalate glycol (PETG) is characterized by a double refraction effect which is used when modeling the stress states of building structures. This paper aims to study the mechanical properties of PETG due to the need for practical approval of the modeling results. Experiments show that, for most plastics, the initial region of the stress–strain diagram significantly deviates from a straight line. However, an extended interval can be distinguished in this region, where the diagram is well approximated by a linear function. If the deviations of the diagram from the straight line are random, it is possible to test the statistical hypothesis of their correspondence. Only diagrams with valid hypothesis are applied in this study. Twelve PETG samples have been tested using the fused deposition modeling (FDM) method. For the five diagrams, the hypothesis of the presence of the linear region in interval   [0.0075; 0.0275] is confirmed at a deviation significance level of 1%. The Young's modulus determined using the diagrams is 0.047 0.027 2.044   109 Pa. This value falls within interval 2.01  109  2.11  109 Pa presented on Wikipedia. The obtained yield strength is 49.71 ± 1.81 MPa, which is consistent with the results reported in the literature and reference data.

X‐Ray White Beam Interferences on Thin Crystals

AbstractResults of white beam X‐ray interference measurements on almost perfect semiconductor wafers are presented. A specific measurement geometry allows for the investigation of diffraction effects on thin wafers down to at least 375 µm with a simple experimental setup (standard lab CT with microfocus X‐ray tube). Furthermore, the dynamic diffraction effect of double refraction has been studied in detail for thicker samples. This might lead to a new wafer testing method as the observed dynamic effects are very sensible on crystal quality.

Birefractive stereo imaging for single-shot depth acquisition

We propose a novel birefractive depth acquisition method, which allows for single-shot depth imaging by just placing a birefringent material in front of the lens. While most transmissive materials present a single refractive index per wavelength, birefringent crystals like calcite posses two, resulting in a double refraction effect. We develop an imaging model that leverages this phenomenon and the information contained in the ordinary and the extraordinary refracted rays, providing an effective formulation of the geometric relationship between scene depth and double refraction. To handle the inherent ambiguity of having two sources of information overlapped in a single image, we define and combine two different cost volume functions. We additionally present a novel calibration technique for birefringence, carefully analyze and validate our model, and demonstrate the usefulness of our approach with several image-editing applications.

Interpretation of the Nano-Electron-Diffraction Patterns along the Five-Fold Axis of Decahedral Gold Nanoparticles

The transition from 10-fold to 5-fold symmetry was observed during the analysis of nanodiffraction patterns of a gold decahedral multiple twinned nanoparticle of 15 nm in diameter. The analysis shows that as the convergence of the beam is increased, the rotational symmetry of the diffraction pattern shifts from 10- to 5-fold. The 10-fold symmetry predicted by Friedel's law is lost by the asymmetric shift of the diffraction spots, an effect that becomes more noticeable as the electron beam convergence increases. Dynamical and kinematical diffraction calculations indicate this decrease in symmetry is the result of a double refraction effect coupled with the variation of the dynamical diffraction conditions arising from a varying electron beam convergence.

Electronic double refraction due to the Rashba effect: Analytical and numerical results

By analogy with the classic effect of the double refraction of light, we investigate the relevant effect of an electron entering from the Non-Rashba region to the Rashba region in two-dimensional systems. It is shown that the effect of electronic double refraction is determined by a combined parameter γ = m*λFα/2πħ2, rather than both the Rashba coefficient α and wavelength λF of a Fermi electron, separately. For the case of normal incidence, the analytical expressions for the wavefunction of the electron are presented; it is predicted that the Rashba spin-orbit coupling can induce a current perpendicular to the normal incident direction of the electron. Moreover, the general case of incident electron with any given momentum and spin state are studied numerically in detail, including the abrupt changes of spin direction and the two-step characters for reflection.

Refractive indices determination of a small-size nonlinear biaxial crystal by use of double-refraction measurements with a laser beam

We show that it is possible to determine the magnitude of the three principal refractive indices of a biaxial crystal from the measurement of the double-refraction effect at the exit of the crystal cut as a millimetric sphere and illuminated with a laser beam. By this way, we determined the indices of a monoclinic crystal, Ca4YO(BO3)3, at λ=0.6328 μm with an accuracy of 6×10−3. The sphere method, which we implemented several years ago, is now self-sufficient for a complete characterization of the linear and nonlinear optical properties of any new biaxial crystal.

Beam deflector using double-refraction in ferroelectric liquid crystal waveguides

Confined SmC* liquid crystals layers have particularly advantageous properties which can be used to produce fast light modulators, with various applications in optical signal processing and optical communication systems. Although usually used in a spatial configuration (e.g. spatial light modulators), other configurations use FLC in waveguide applications. The advantageous properties of FLC, allow it however to be used as the guiding core of waveguides. In this context, we present the design, fabrication and experimental characterization of an optical deflector based on the double-refraction effect in a FLC waveguide.

Double refraction in coherent media

A new effect of double refraction in a coherent medium with a double-Λ scheme of excitation is analysed theoretically. It arises if usual phase conditions on coherent population trapping in a quantum system with closed interaction contour are satisfied. The value of the refractive index of such a medium is different for matched and antimatched (by amplitude) parts of a bichromatic laser radiation. Therefore the matched part can be separated spatially from the antimatched one using the optically thin coherent medium as a birefringent prism. A possible scheme for experimental observation of this effect is discussed.

Polarization device employing the combination effect of double refraction and diffraction

Upon the combination of double refraction and diffraction effects, a new kind of polarization device is proposed, which is made of the birefringent plate with the grooves of a sawtooth profile on its surface. This device may separate an incident light beam into two polarized beams spatially with a high extinction ratio and large beam-splitting angle, moreover it has a sheet form, large aperture, and low cost, thus being suitable for practical use.

Dynamical tensor polarizability in the ground state of the hydrogen atom

The dynamical tensor polarizability in the ground state of hydrogen is calculated. It arises in the third order of perturbation theory with respect to operators of hyperfine and electric dipole interaction. The obtained analytical expression is a sum of linear and squared combinations of Gauss hypergeometric functions 2F1. It is pointed out that the double refraction effect can be observed in polarized atomic hydrogen.

Effect of double refraction on type II phase matched second harmonic generation

The results of a typical analysis of the effect of double refraction on type II phase matched second harmonic generation are presented. It is shoen that walk-off results in a more severe reduction in conversion efficiency compared to the case of type I phase matching. A scheme for type II second harmonic generation involving non-collinear phase matching is discussed in which the walk-off can be substantially reduced.

Oblique transmission of electromagnetic waves through a magnetized ferrite slab

New transmission properties of a magnetized ferrite slab are investigated theoretically for an oblique incident H plane wave. When the direction of magnetization is normal to the plane of incidence, there is single refraction. For magnetization parallel to the plane of incidence, then double refraction leads to a double beam of microwaves at the exit surface. If the electromagnetic field vectors of these two beams can be made orthogonal then after the beams exit the ferrite slab they can be independently modulated and subsequently analyzed and demodulated at a remote receiver. It was found that the two transmitted beams are contrarotating and elliptically polarized. The required interrelationship of the transmission coefficients was determined for cross polarization. The analysis not only explains the double refraction effect but also defines new transmission coefficients that can be used to evaluate the components of the transmitted waves.

Morphology and coalescence growth of metal oxide smoke particles prepared by gas evaporation technique

The crystal habit and growth of metal oxide smoke particles which were prepared by burning component metals in a mixture gas of 80 % Ar and 20 % O2 at a pressure of 100 Torr are studied by electron microscopy.Figure 1 shows SEM and TEM images and ED patterns of a single-crystal In2O3 particle, which grew in an octahedron bounded by eight {111} planes of the cubic bixbyite structure. The particle in (a) and (b) is oriented with the [001] and directions parallel to the incident electron beam, respectively. The determination of crystal habit has so far been done only by TEM observations of a single particle which is placed in different orientations with a tilting goniometer stage, considering thickness contours in the images and fine structures due to double refraction effect as shown in the ED patterns. It is, however, laboursome and sometimes ambiguous. Since the SEM images reveal not only the crystal external form but also surface structure, SEM observations are very useful for the study of fine particles whose sizes are several tens of nanometers or less.

Resonant optical second harmonic generation and mixing

Experimental and theoretical results are described on the enhancement of optical second harmonic generation (SHG) and mixing in KDP by the use of optical resonance. Both resonance of the harmonic and of the fundamental are considered. Large enhancements are possible for resonators with low loss. Using a planoconcave harmonic resonator containing 1.23 cm of KDP, the authors achieved a loss < 4 percent per pass. This resulted in an enhancement of ∼ 500 times the harmonic power internal to the resonator and ∼ 10 times external to the resonator. When resonating, the fundamental enhancements of ∼ 5 were observed. The theory includes the effect of double refraction. This results in a coupling coefficient of the generated harmonic power to the transverse modes of the harmonic resonator. The experimental results are in substantial agreement with the theory.

Fine Structure due to Refraction Effect in Electron Diffraction Pattern of Powder Sample Part II. Multiple Structures due to Double Refraction given by Randomly Oriented Smoke Particles of Magnesium and Cadmium Oxide

Fine structures composed of sets of doublets as expected by the double refraction effect, an effect concluded by the dynamical theory of electron diffraction, are studied in details for reflexions given by individual smoke particles of magnesium and cadmium oxides having random orientations. The configurations of doublets vary according not only to the azimuths of the crystallites but also to the angles of deviations from Bragg condition, namely, the errors of resonance of Bragg reflexions. By determining these two parameters from the configuration, the mean and periodic terms of the Fourier expansion of the inner potentials of the crystals are obtained from the inter-doublets and intra-doublets separations in the fine structures. The results show a reasonable agreement with the theoretical values. The intensity anomaly of the double refraction effect, suggested in Part I, are found to be a general phenomenon. It is observed that between the two spots of a doublet, that of larger deviation is always weake...

Fine Structure Due to Refraction Effect in Electron Diffraction Pattern of Powder Sample Part I. Fine Structure given by Magnesium and Cadmium Oxide Smoke having a Fibrous Orientation

Fine structures due to refraction effect in electron diffraction patterns of cubic magnesium and cadmium oxides are studied when the sample have a fibrous orientation around [001] axis and the electron incidence is nearly perpendicular to the axis. In the case of magnesium oxide, most of the reflexions split into doublets corresponding to the ordinary refraction effect due to a mean inner potential of about 15∼16 volts; (002) reflexion, however, splits into quartet corresponding to the double refraction effect, which was formerly pointed out by Sturkey, the separation of which is also in accordance with the theoretical expectation. The intensities of the two spots corresponding to a double refraction are found to be remarkably different; the spot of larger deviation is weaker than that of smaller deviation. In the.case of cadmium oxide, though the fine structures of the fibrous reflexion are less apparent than in the case of magnesium oxide, it is noted the fact that the (111) reflexion splits only into d...

Multiple Scattering and Radiation Damping. II

The analysis of multiple elastic scattering by a system of fixed scatterers in terms of two-body collision matrices is extended to large bodies. The dynamical theory of particle propagation in crystals is formulated and discussed from this viewpoint, as an extension of Ewald's theory to scatterers of finite size. A theory of propagation in a random medium, including disordered crystals, is obtained as the limiting case for a crystal with infinite unit cell. Contrary to the usual approach, this analysis considers a definite frozen configuration of the medium; statistical averaging over configurations may be used on the intensities obtained.In crystals and dense liquids, radiation damping is compensated by the reaction of surrounding scatterers. Therefore, it is found convenient to restate the basic equations of multiple scattering in terms of a matrix $\ensuremath{\beta}$ which is essentially the Green's function for the single scattering event, with standing wave rather than outgoing wave boundary conditions. This has the advantage of eliminating the spurious radiation damping terms at the outset; one obtains nonattenuated waves in nondissipative crystals or dense liquids by a simple expansion method.Application is made to the following problems: the equivalent of the Lorentz-Lorenz formula for matter waves; index of refraction for an interaction of the form of a one-level Breit-Wigner formula; attenuation of long waves in a disordered crystal containing protons with random spins; double refraction effect in a liquid or crystal containing protons with partially oriented spin.

Aeolotrophy and Seismology

THE mathematical problem of the seismological implications of aeolotrophy in continental structure has been discussed by Robert Stoneley (Mon. Not. Roy. Astro Soc., Geophysical Supplement, 5, No. 8, 343 ; 1949). He finds that for near earthquakes, erronemous values of the focal depth and thickness of layer might be found from the observations if the continental material had been thought to be isotropic. Further, for a transversely isotropic continent, SH waves would travel with a different velocity from that of S V, and the law of variation of velocity with direction would be different. With body waves, the sharp distinction into compressional and distortional waves would not hold, and an explosion would generate an S wave as well as a P wave ; an apparent difference in the instant of generation of P and S might arise. Stoneley has also proved that waves of the Rayleigh type can be propagated over the surface of a transversely isotropic body in which the axis of circular symmetry is normal to the free surface, supposed plane ; in such waves the diminution of amplitude with depth is shown to be different from that in an isotropic body, so that the amplitudes of the surface waves generated by a source at a given depth will be different from that which they would be in an isotropic medium. Love waves can be propagated as in isotropic media. Byerly noted a possible double refraction effect on the crust of the earth for waves from the earthquake of July 6, 1934 (Butt. Seism. Soc. Amer., 28, 12 ; 1938). Miss I. Lehmann may also have noted a similar effect (Pub. Bur. Cent. Seism. Int., A, No. 12, 109 ; 1935).