Phase Wedge Research Articles

Simple digital technique for high-accuracy measurement of focal length based on Fresnel diffraction from a phase wedge

An accurate and simple technique based on Fresnel diffraction of light from a phase wedge is described to measure the effective focal lengths (EFLs) of optical imaging systems. When the neighbourhood of a transparent wedge is illuminated by a monochromatic parallel beam of light, the Fresnel diffraction occurs as a result of sharp change in phase at the wedge boundary. The wedge with small apex angle imposes a linearly varying phase change that causes periodic diffraction fringes in the direction parallel to the wedge boundary. The EFL is determined by measuring the fringe spacing of the Fresnel diffraction both before and after installing the test lens in the setup. The method is easy to apply and it is less sensitive to vibration compared to interferometric methods. It covers a wide range of both positive and negative focal lengths. Experimental results for several different lenses are quite consistent with the values indicated by the lens manufacturer.

Intermediate phase cone growth kinetics along dislocation pipes inside polycrystal grains

Dislocation-pipe diffusion (DPD) becomes a major contribution to device failure in microelectronic components at working temperatures. Usually, the simple random walk law for diffusion (Type C kinetics t1/2) is employed to calculate of DPD coefficients. The article presents an analytically solvable model of describing the diffusion phase cone growth along dislocation pipes inside polycrystal grains involving outflow from dislocation lines (Type B kinetics). Correlative analytical method to solve differential diffusion equations for such model is suggested. Competition between phase cone growth along dislocation lines involving outflow and phase wedge growth along grain boundaries (GBs) involving outflow is analyzed. It is shown that while phase wedge growth law along GBs is the Fisher regime t1/4, phase cone growth law along dislocation lines is another diffusion regime t1/6. Real experimental data are analyzed using such diffusion regime. It is shown that it is possible to calculate DPD coefficients not only for the phase cone formation, but for migration of atoms along dislocations and self-diffusion along dislocation pipes too.

Investigation of Kerr effect in a blue phase liquid crystal using wedge-cell technique

In this work an alternative method for refractive index measurement of blue phase liquid crystal in the Kerr effect has been described. The proposed wedge method uses simple goniometric setup, allowing for direct index measurements for any wavelengths and index values. This is significant advantage comparing to other methods, usually having limitations of the measurement range as well as necessity complicated calculation to obtain refractive indices values. The results are reliable and agree well with the subject literature. Full Text: PDF ReferencesW. Cao et al., "Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II", Nat. Mater. 1, 111-113 (2002). CrossRef S. Meiboom, M. Sammon, W.F. Brinkman, "Lattice of disclinations: The structure of the blue phases of cholesteric liquid crystals", Phys. Rev. A. 27, 438 (1983). CrossRef S. Tanaka et al., "Double-twist cylinders in liquid crystalline cholesteric blue phases observed by transmission electron microscopy", Sci. Rep. 5, 16180 (2015). CrossRef Y. Li and S.-T. Wu, "Polarization independent adaptive microlens with a blue-phase liquid crystal", Opt. Express 19(9), 8045-8050 (2011). CrossRef N. Rong et al., "Polymer-Stabilized Blue-Phase Liquid Crystal Fresnel Lens Cured With Patterned Light Using a Spatial Light Modulator", J. of Disp. Technol. 12(10), 1008-1012 (2016). CrossRef J.-D. Lin et al., "Spatially tunable photonic bandgap of wide spectral range and lasing emission based on a blue phase wedge cell", Opt. Express 22(24), 29479-29492 (2014). CrossRef P. Joshi et al., "Tunable light beam steering device using polymer stabilized blue phase liquid crystals", Photon. Lett. Poland 9(1), 11-13 (2017). CrossRef Ch.-W. Chen et al., "Temperature dependence of refractive index in blue phase liquid crystals", Opt. Mater. Express 3(5), 527-532 (2013). CrossRef Y.-H. Lin et al., "Measuring electric-field-induced birefringence in polymer stabilized blue-phase liquid crystals based on phase shift measurements", J. Appl. Phys. 109, 104503 (2011). CrossRef J. Yan et al., "Direct measurement of electric-field-induced birefringence in a polymer-stabilized blue-phase liquid crystal composite", Opt. Express 18(11), 11450-11455 (2010). CrossRef K.A. Rutkowska, K. Orzechowski, M. Sierakowski, "Wedge-cell technique as a simple and effective method for chromatic dispersion determination of liquid crystals", Photon. Lett. Poland 8(2), 51-53 (2016). CrossRef O. Chojnowska et al., "Electro-optical properties of photochemically stable polymer-stabilized blue-phase material", J. Appl. Phys. 116, 213505 (2014). CrossRef J. Yan et al., "Extended Kerr effect of polymer-stabilized blue-phase liquid crystals", Appl. Phys. Lett. 96, 071105 (2010). CrossRef M. Chen et al., "Electrically assisting crystal growth of blue phase liquid crystals", Opt. Mater. Express 4(5), 953-959 (2014). CrossRef J. Kerr, Philos. Mag. 50, 337 (1875).

Spatially tunable photonic bandgap of wide spectral range and lasing emission based on a blue phase wedge cell

This study demonstrates for the first time a continuously tunable photonic bandgap (PBG) of wide spectral range based on a blue phase (BP) wedge cell. A continuously shifting PBG of the BP wedge cell occurs due to the thickness gradient of the wedge cell at a fixed temperature. The wedge cell provides a gradient of boundary force on the LCs and thus forms a distribution of BP crystal structure with a gradient lattice. Additionally, a spatially tunable lasing emission based on a dye-doped BP (DDBP) wedge cell is also demonstrated. The tunable band of the PBG and lasing emission is about 130 nm and 70 nm, respectively, which tuning spectral ranges are significantly wider than those of CLC and DDCLC wedge cells, respectively. Such a BP device has a significant potential in applications of tunable photonic devices and displays.

Hot deformation behavior and globularization mechanism of Ti-6Al-4V-0.1B alloy with lamellar microstructure

Hot deformation behavior and globularization mechanism of Ti-6Al-4V-0.1B alloy with lamellar microstructure were quantitatively studied through isothermal compression tests with the temperature range of 850–950 °C and strain rate range of 0.01–1.00 s−1. The results show that the peak flow stress and steady stress are sensitive to the strain rate and temperature. The value of deformation activation energy is 890.49 kJ·mol−1 in (α + β) region. Dynamic recrystallization is the major deformation mechanism. Flow softening is dominated by dynamic recrystallization at 850–950 °C. TiB particles promote the recrystallization of α laths. Globularization processes consist of four steps: formation of subgrain after dynamic recovery in α plates; subgrain boundary migration caused by α/β interfacial instability; interfacial migration promoting β phase wedge into α phase; disintegrating of α laths by diffusion processes; and grain-boundary sliding. Globularization mechanisms during hot deformation processes of the Ti-6Al-4V-0.1B alloy with lamellar structure are continuous dynamic recrystallization.

Optical refractometry based on Fresnel diffraction from a phase wedge

A method that utilizes the Fresnel diffraction of light from the phase step formed by a transparent wedge is introduced for measuring the refractive indices of transparent solids, liquids, and solutions. It is shown that, as a transparent wedge of small apex angle is illuminated perpendicular to its surface by a monochromatic parallel beam of light, the Fresnel fringes, caused by abrupt change in refractive index at the wedge lateral boundary, are formed on a screen held perpendicular to the beam propagation direction. The visibility of the fringes varies periodically between zero and 1 in the direction normal to the wedge apex. For a known or measured apex angle, the wedge refractive index is obtained by measuring the period length by a CCD. To measure the refractive index of a transparent liquid or solution, the wedge is installed in a transparent rectangle cell containing the sample. Then, the cell is illuminated perpendicularly and the visibility period is measured. By using modest optics, one can measure the refractive index at a relative uncertainty level of 10(-5). There is no limitation on the refractive index range. The method can be applied easily with no mechanical manipulation. The measuring apparatus can be very compact with low mechanical and optical noises.

Optimal linear phase mask for the singular beam synthesis from a Gaussian beam and the scheme of its experimental realisation

The functions of phase wedge and symmetric phase mask for optical vortex synthesised from a Gaussian beam are carefully analysed. The optimal linear phase dependence in the cross-section of a Gaussian beam for the singular beam with a single charge synthesis is found. The similarity of the obtained beam phase and intensity distributions in the singular beam depending on the distance of the resulting field observation is investigated. The simple original technique of the experimental realisation of the necessary phase mask for the singular beam synthesis with the help of two inclined mirrors is offered.

Two-coordinate electrically controlled liquid-crystal optical phase wedge

Based on the capacity of a parallel-oriented layer of nematic liquid crystal to alter its birefringence under the influence of an applied electric field, a two-coordinate electrically controlled optical phase wedge has been developed.

Selective generation of high-order optical vortices from a single phase wedge

We demonstrate that it is possible to generate high-order optical vortices from a single phase wedge by applying an incident beam with an annular intensity distribution. Various topological charges of optical vortices are realized by a static phase wedge when the position and radius of the annular illumination are changed accordingly.

X-ray investigation, high-resolution electron holography, and density functional calculations of single-crystallineBaTiO3

Single crystal x-ray diffraction (XRD), high-resolution electron holography and density functional calculations (DFT) are employed to investigate single-crystalline ${\mathrm{BaTiO}}_{3}$ in the noncentrosymmetric tetragonal phase. From XRD and DFT the structure parameters, the electron density and corresponding properties, such as atomic charges and the dipole moment are determined. For this purpose the maximum-entropy method was utilized to get accurate electron densities in the case of XRD, whereas all-electron calculations were performed in the framework of DFT. A comparison of experimental results and density functional calculations yield a rather good agreement. The electron density distributions are used to determine the ``natural'' unit cell corresponding to the neutral boundary cells of the whole crystal and its dipole moment, providing the boundary conditions necessary for calculating the electrostatic potential within the unit cell through the Poisson equation. The electrostatic potential was then utilized to perform electron scattering simulations within the framework of the Multislice formalism, resembling unique features of experimentally recorded electron holograms. It is shown that the phase wedge in the scattered wave, which is due to the polarization field within the specimen, is essential for the image reconstruction. This essential feature has not been included in simulations before.

Last interglacial stratigraphy in the burg El-Arab region of the northwestern coast of Egypt

Abstract The northwestern coast of Egypt, a stable carbonate platform, is characterized by the presence of successive coastal ridges that extend parallel to the present shoreline. Study of marine deposits at the bottom of Gebel Maryut ridge from the drain cut of Bahig, together with analyses of core samples raised from four boreholes drilled in the El-Dekheilla depression to the depths of 10–15 m, reveal the presence of two phases of beach boulders. The lower older phase (B.B.1) wedge eolianites (E.1) at an elevation of 3–4 m and show an average δ18O of −0.82‰. The upper younger phase (B.B.II) wedge eolianites (E.2) at 6–7 m a.s.l., with an average δ18O of −1.5‰. These beach boulders are overlained by thick fossiliferous limestones and geosoils. They record the last interglacial high sea level (isotope substage 5e and aminozone E, with an interpolated age of 125 ka) which was globally 6–8 m higher than present sea level, with characteristic warm wet tropical climatic conditions. A bed composed of marine molluscs and foraminifera shells with ooids and pellets below the loamy calcareous and evaporites of the El-Dekheilla depression was also examined. This bed is located 1–4 m b.s.l., with an average δ18O of −0.25‰. It is related to aminozone C (isotope substage 5c/5a) with an interpolated age of 110 ka, and related to a transgressive sea with a mean sea level possibly equal to or slightly lower than the present one with evidence for less warm climatic conditions.