Showing papers on "Diffraction published in 2016"

Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

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The Scherrer equation and the dynamical theory of X-ray diffraction

Abstract: The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6 and CeO2. The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm−1 the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm.

Three-dimensional control of the helical axis of a chiral nematic liquid crystal by light

Abstract: Chiral nematic liquid crystals--otherwise referred to as cholesteric liquid crystals (CLCs)--are self-organized helical superstructures that find practical application in, for example, thermography, reflective displays, tuneable colour filters and mirrorless lasing. Dynamic, remote and three-dimensional control over the helical axis of CLCs is desirable, but challenging. For example, the orientation of the helical axis relative to the substrate can be changed from perpendicular to parallel by applying an alternating-current electric field, by changing the anchoring conditions of the substrate, or by altering the topography of the substrate's surface; separately, in-plane rotation of the helical axis parallel to the substrate can be driven by a direct-current field. Here we report three-dimensional manipulation of the helical axis of a CLC, together with inversion of its handedness, achieved solely with a light stimulus. We use this technique to carry out light-activated, wide-area, reversible two-dimensional beam steering--previously accomplished using complex integrated systems and optical phased arrays. During the three-dimensional manipulation by light, the helical axis undergoes, in sequence, a reversible transition from perpendicular to parallel, followed by in-plane rotation on the substrate surface. Such reversible manipulation depends on experimental parameters such as cell thickness, surface anchoring condition, and pitch length. Because there is no thermal relaxation, the system can be driven either forwards or backwards from any light-activated intermediate state. We also describe reversible photocontrol between a two-dimensional diffraction state, a one-dimensional diffraction state and a diffraction 'off' state in a bilayer cell.

Fourier-Transform Ghost Imaging with Hard X Rays

Abstract: Knowledge gained through x-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. However, it is only applied to crystalline structures and cannot resolve noncrystalline materials. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudothermal hard x rays that extends x-ray crystallography to noncrystalline samples. By measuring the second-order intensity correlation function of the light, Fourier-transform diffraction pattern of a complex amplitude sample is achieved at the Fresnel region in our experiment and the amplitude and phase distributions of the sample in the spatial domain are retrieved successfully. For the first time, ghost imaging is experimentally realized with x rays. Since a highly coherent x-ray source is not required, the method can be implemented with laboratory x-ray sources and it also provides a potential solution for lensless diffraction imaging with fermions, such as neutrons and electrons where intensive coherent sources usually are not available.

Ultra-precise holographic beam shaping for microscopic quantum control.

Abstract: High-resolution addressing of individual ultracold atoms, trapped ions or solid state emitters allows for exquisite control in quantum optics experiments. This becomes possible through large aperture magnifying optics that project microscopic light patterns with diffraction limited performance. We use programmable amplitude holograms generated on a digital micromirror device to create arbitrary microscopic beam shapes with full phase and amplitude control. The system self-corrects for aberrations of up to several λ and reduces them to λ/50, leading to light patterns with a precision on the 10-4 level. We demonstrate aberration-compensated beam shaping in an optical lattice experiment and perform single-site addressing in a quantum gas microscope for 87Rb.

Diffraction gratings: from principles to applications in high-intensity lasers

Abstract: Diffraction gratings were discovered during the 18th century, and they are now widely used in spectrometry analysis, with outstanding achievements spanning from the probing of single molecules in biological samples to the analysis of solar systems in astronomy. The fabrication of high-quality diffraction gratings requires precise control of the period at a nanometer scale. The discovery of lasers in the 1960s gave birth to optical beam lithography in the 1970s. This technology revolutionized the fabrication of diffraction gratings by offering highly precise control of the grating period over very large scales. It is surprising to see that a few years after, the unique spectral properties of diffraction gratings revolutionized, in turn, the field of high-energy lasers. We review in this paper the physics of diffraction gratings and detail the interest in them for pulse compression of high-power laser systems.

Diffraction-free pulsed optical beams via space-time correlations.

Abstract: Diffraction places a fundamental limitation on the distance an optical beam propagates before its size increases and spatial details blur. We show here that imposing a judicious correlation between spatial and spectral degrees of freedom of a pulsed beam can render its transverse spatial profile independent of location along the propagation axis, thereby arresting the spread of the time-averaged beam. Such correlation introduced into a beam with arbitrary spatial profile enables spatio-temporal dispersion to compensate for purely spatial dispersion that underlies diffraction. As a result, the spatio-temporal profile in the local time-frame of the pulsed beam remains invariant at all positions along the propagation axis. One-dimensional diffraction-free space-time beams are described – including non-accelerating Airy beams, despite the well-known fact that cosine waves and accelerating Airy beams are the only one-dimensional diffraction-free solutions to the monochromatic Helmholtz equation.

Conical Diffraction and Composite Lieb Bosons in Photonic Lattices.

Abstract: Pseudospin describes how waves are distributed between different "internal" degrees of freedom or microscopic states, such as polarizations, sublattices, or layers. Here, we experimentally demonstrate and explain wave dynamics in a photonic Lieb lattice, which hosts an integer pseudospin s=1 conical intersection. We study the most striking differences displayed by integer pseudospin states: pseudospin-dependent conical diffraction and the generation of higher charged optical vortices.

Self-Referenced Coherent Diffraction X-Ray Movie of Ångstrom- and Femtosecond-Scale Atomic Motion

Abstract: Time-resolved femtosecond x-ray diffraction patterns from laser-excited molecular iodine are used to create a movie of intramolecular motion with a temporal and spatial resolution of 30 fs and 0.3 A. This high fidelity is due to interference between the nonstationary excitation and the stationary initial charge distribution. The initial state is used as the local oscillator for heterodyne amplification of the excited charge distribution to retrieve real-space movies of atomic motion on angstrom and femtosecond scales. This x-ray interference has not been employed to image internal motion in molecules before. In conclusion, coherent vibrational motion and dispersion, dissociation, and rotational dephasing are all clearly visible in the data, thereby demonstrating the stunning sensitivity of heterodyne methods.

Macromolecular diffractive imaging using imperfect crystals

Abstract: The three-dimensional structures of macromolecules and their complexes are mainly elucidated by X-ray protein crystallography. A major limitation of this method is access to high-quality crystals, which is necessary to ensure X-ray diffraction extends to sufficiently large scattering angles and hence yields information of sufficiently high resolution with which to solve the crystal structure. The observation that crystals with reduced unit-cell volumes and tighter macromolecular packing often produce higher-resolution Bragg peaks suggests that crystallographic resolution for some macromolecules may be limited not by their heterogeneity, but by a deviation of strict positional ordering of the crystalline lattice. Such displacements of molecules from the ideal lattice give rise to a continuous diffraction pattern that is equal to the incoherent sum of diffraction from rigid individual molecular complexes aligned along several discrete crystallographic orientations and that, consequently, contains more information than Bragg peaks alone. Although such continuous diffraction patterns have long been observed--and are of interest as a source of information about the dynamics of proteins--they have not been used for structure determination. Here we show for crystals of the integral membrane protein complex photosystem II that lattice disorder increases the information content and the resolution of the diffraction pattern well beyond the 4.5-angstrom limit of measurable Bragg peaks, which allows us to phase the pattern directly. Using the molecular envelope conventionally determined at 4.5 angstroms as a constraint, we obtain a static image of the photosystem II dimer at a resolution of 3.5 angstroms. This result shows that continuous diffraction can be used to overcome what have long been supposed to be the resolution limits of macromolecular crystallography, using a method that exploits commonly encountered imperfect crystals and enables model-free phasing.

X-ray diffraction (XRD) techniques for materials characterization

Abstract: Since the discovery of X-rays at the end of the 19th century and the first works on diffraction of X-rays by crystals, huge developments were achieved in the application of these methods for material characterization. In particular, in the field of materials science and engineering, several applications were developed to become state of the art techniques. This chapter first presents a condensed overview of the production of X-rays as well as of the theory of diffraction of X-rays by crystals. A short survey of the hardware for X-ray diffraction (XRD) measurements is given. The methods of phase analysis, residual stress measurements, and texture investigations of polycrystalline materials are then described with examples, and finally, special methods and future trends are presented.

Theory of metascreen-based acoustic passive phased array

Abstract: The metascreen-based acoustic passive phased array provides a new degree of freedom for manipulating acoustic waves due to their fascinating properties, such as a fully shifting phase, keeping impedance matching, and holding subwavelength spatial resolution. We develop acoustic theories to analyze the transmission/reflection spectra and the refracted pressure fields of a metascreen composed of elements with four Helmholtz resonators (HRs) in series and a straight pipe. We find that these properties are also valid under oblique incidence with large angles, with the underlying physics stemming from the hybrid resonances between the HRs and the straight pipe. By imposing the desired phase profiles, the refracted fields can be tailored in an anomalous yet controllable manner. In particular, two types of negative refraction are exhibited, based on two distinct mechanisms: one is formed from classical diffraction theory and the other is dominated by the periodicity of the metascreen. Positive (normal) and negative refractions can be converted by simply changing the incident angle, with the coexistence of two types of refraction in a certain range of incident angles.

Ab initio structure determination from prion nanocrystals at atomic resolution by MicroED

Abstract: Electrons, because of their strong interaction with matter, produce high-resolution diffraction patterns from tiny 3D crystals only a few hundred nanometers thick in a frozen-hydrated state. This discovery offers the prospect of facile structure determination of complex biological macromolecules, which cannot be coaxed to form crystals large enough for conventional crystallography or cannot easily be produced in sufficient quantities. Two potential obstacles stand in the way. The first is a phenomenon known as dynamical scattering, in which multiple scattering events scramble the recorded electron diffraction intensities so that they are no longer informative of the crystallized molecule. The second obstacle is the lack of a proven means of de novo phase determination, as is required if the molecule crystallized is insufficiently similar to one that has been previously determined. We show with four structures of the amyloid core of the Sup35 prion protein that, if the diffraction resolution is high enough, sufficiently accurate phases can be obtained by direct methods with the cryo-EM method microelectron diffraction (MicroED), just as in X-ray diffraction. The success of these four experiments dispels the concern that dynamical scattering is an obstacle to ab initio phasing by MicroED and suggests that structures of novel macromolecules can also be determined by direct methods.

Beam steering for virtual/augmented reality displays with a cycloidal diffractive waveplate.

Abstract: We proposed a switchable beam steering device with cycloidal diffractive waveplate (CDW) for eye tracking in a virtual reality (VR) or augmented reality (AR) display system. Such a CDW diffracts the incident circularly polarized light to the first order with over 95% efficiency. To convert the input linearly polarized light to right-handed or left-handed circular polarization, we developed a broadband polarization switch consisting of a twisted nematic liquid crystal cell and an achromatic quarter-wave retardation film. By cascading 2-3 CDWs together, multiple diffraction angles can be achieved. To suppress the color dispersion, we proposed two approaches to obtain the same diffraction angle for red, green, and blue LEDs-based full color displays. Our device exhibits several advantages, such as high diffraction efficiency, fast response time, low power consumption, and low cost. It holds promise for the emerging VR/AR displays.

Diffraction-free beams in fractional Schrödinger equation.

Abstract: We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrodinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories z = ±2(x - x0), which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone z = 2√(x(2) + y(2)) and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE.

Polarization volume grating with high efficiency and large diffraction angle.

Abstract: We propose a polarization volume grating (PVG), which exhibits nearly 100% diffraction efficiency and large diffraction angle. Both reflective and transmissive PVGs can be configured depending on application preference. Such a PVG is polarization-sensitive so that it can split an incident unpolarized beam into two well-separated yet polarized beams. These outstanding features make PVG a strong candidate for photonic and display applications. To investigate and optimize the diffraction properties, we build a rigorous simulation model based on finite element method. To illustrate its potential applications, we propose a simple 2D/3D wearable display using a planar waveguide comprising of two reflective PVGs.

$\mathcal{PT}$ symmetry in a fractional Schr\"odinger equation

Abstract: We investigate the fractional Schr\"odinger equation with a periodic $\mathcal{PT}$-symmetric potential. In the inverse space, the problem transfers into a first-order nonlocal frequency-delay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the one-dimensional case, which results in a nondiffracting propagation and conical diffraction of input beams. If only one channel in the periodic potential is excited, adjacent channels become uniformly excited along the propagation direction, which can be used to generate laser beams of high power and narrow width. In the two-dimensional case, there appears conical diffraction that depends on the competition between the fractional Laplacian operator and the $\mathcal{PT}$-symmetric potential. This investigation may find applications in novel on-chip optical devices.

Fast Li-Ion-Conducting Garnet-Related Li7–3xFexLa3Zr2O12 with Uncommon I4̅3d Structure

Abstract: Fast Li-ion-conducting Li oxide garnets receive a great deal of attention as they are suitable candidates for solid-state Li electrolytes. It was recently shown that Ga-stabilized Li7La3Zr2O12 crystallizes in the acentric cubic space group I43d. This structure can be derived by a symmetry reduction of the garnet-type Ia3d structure, which is the most commonly found space group of Li oxide garnets and garnets in general. In this study, single-crystal X-ray diffraction confirms the presence of space group I43d also for Li7–3xFexLa3Zr2O12. The crystal structure was characterized by X-ray powder diffraction, single-crystal X-ray diffraction, neutron powder diffraction, and Mosbauer spectroscopy. The crystal–chemical behavior of Fe3+ in Li7La3Zr2O12 is very similar to that of Ga3+. The symmetry reduction seems to be initiated by the ordering of Fe3+ onto the tetrahedral Li1 (12a) site of space group I43d. Electrochemical impedance spectroscopy measurements showed a Li-ion bulk conductivity of up to 1.38 × ...

Diffraction and single-crystal elastic constants of Inconel 625 at room and elevated temperatures determined by neutron diffraction

Abstract: In this work, diffraction and single-crystal elastic constants of Inconel 625 have been determined by means of in situ loading at room and elevated temperatures using time-of-flight neutron diffraction. Theoretical models proposed by Voigt, Reuss, and Kroner were used to determine single-crystal elastic constants from measured diffraction elastic constants, with the Kroner model having the best ability to capture experimental data. The magnitude of single-crystal elastic moduli, computed from single-crystal elastic constants, decreases and the single crystal anisotropy increases as temperature increases, indicating the importance of texture in affecting macroscopic stress at elevated temperatures. The experimental data reported here are of great importance in understanding additive manufacturing of metallic components as: diffraction elastic constants are required for computing residual stresses from residual lattice strains measured using neutron diffraction, which can be used to validate thermomechanical models of additive manufacturing, while single-crystal elastic constants can be used in crystal plasticity modeling, for example, to understand mechanical deformation behavior of additively manufactured components.

Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT.

Abstract: We present a plane-scanning RESOLFT [reversible saturable/switchable optical (fluorescence) transitions] light-sheet (LS) nanoscope, which fundamentally overcomes the diffraction barrier in the axial direction via confinement of the fluorescent molecular state to a sheet of subdiffraction thickness around the focal plane. To this end, reversibly switchable fluorophores located right above and below the focal plane are transferred to a nonfluorescent state at each scanning step. LS-RESOLFT nanoscopy offers wide-field 3D imaging of living biological specimens with low light dose and axial resolution far beyond the diffraction barrier. We demonstrate optical sections that are thinner by 5–12-fold compared with their conventional diffraction-limited LS analogs.

Light Modes of Free Space

Abstract: A surprisingly large number of known distinct sets of light patterns propagate in free space essentially unchanged. These sets of light patterns (intensity distributions of the electric–magnetic fields) can be divided into two groups: light Waves and light Beams. Wave sets are solutions of the exact Helmholtz equation (HE). Beam sets are solutions of the paraxial HE. The sets of Waves and Beams can be further classified according to the coordinate system to which they belong. All sets are complete and orthogonal such that any square integrable input field can be decomposed into a linear superposition of the set's functions. We classify the patterns, present the solution equations and display sample patterns for each of 4 Wave sets and each of 14 Beam sets.

Perfect optical vortex array with controllable diffraction order and topological charge.

Abstract: We have demonstrated a holographic grating, the far-field diffraction pattern of which is a perfect optical vortex (POV) array. The diffraction order, as well as the topological charge of each spot in the array, is controllable. By setting different parameters when designing the hologram, the spot in different diffraction orders will be changed, resulting in the variance of the POV array. During the experiment, we uploaded holograms of different design on a phase-only spatial light modulator. We then observed POV arrays with different dimensions and topological charges using a CCD camera, which fit well with the simulation. This technique provides the possibility to generate multiple POVs simultaneously, and can be used in domains where multiple POVs are of high interest such as orbital angular momentum multiplexed fiber data transmission systems.

Imaging of sub-wavelength structures radiating coherently near microspheres

Abstract: Using a two-dimensional model, we show that the optical images of a sub-wavelength object depend strongly on the excitation of its electromagnetic modes. There exist modes that enable the resolution of the object features smaller than the classical diffraction limit, in particular, due to the destructive interference. We propose to use such modes for super-resolution of resonant structures such as coupled cavities, metal dimers, or bowties. A dielectric microsphere in contact with the object forms its magnified image in a wide range of the virtual image plane positions. It is also suggested that the resonances may significantly affect the resolution quantification in recent experimental studies.

Double Bragg Interferometry.

Abstract: We employ light-induced double Bragg diffraction of delta-kick collimated Bose-Einstein condensates to create three symmetric Mach-Zehnder interferometers. They rely on (i) first-order, (ii) two successive first-order, and (iii) second-order processes which demonstrate the scalability of the corresponding momentum transfer. With respect to devices based on conventional Bragg scattering, these symmetric interferometers double the scale factor and feature a better suppression of noise and systematic uncertainties intrinsic to the diffraction process. Moreover, we utilize these interferometers as tiltmeters for monitoring their inclination with respect to gravity.

Kirigami Nanocomposites as Wide-Angle Diffraction Gratings

Abstract: Beam steering devices represent an essential part of an advanced optics toolbox and are needed in a spectrum of technologies ranging from astronomy and agriculture to biosensing and networked vehicles. Diffraction gratings with strain-tunable periodicity simplify beam steering and can serve as a foundation for light/laser radar (LIDAR/LADAR) components of robotic systems. However, the mechanical properties of traditional materials severely limit the beam steering angle and cycle life. The large strain applied to gratings can severely impair the device performance both in respect of longevity and diffraction pattern fidelity. Here, we show that this problem can be resolved using micromanufactured kirigami patterns from thin film nanocomposites based on high-performance stiff plastics, metals, and carbon nanotubes, etc. The kirigami pattern of microscale slits reduces the stochastic concentration of strain in stiff nanocomposites including those made by layer-by-layer assembly (LBL). The slit patterning aff...

Observation of Quantum Interferences via Light-Induced Conical Intersections in Diatomic Molecules.

Abstract: We observe energy-dependent angle-resolved diffraction patterns in protons from strong-field dissociation of the molecular hydrogen ion H_{2}^{+}. The interference is a characteristic of dissociation around a laser-induced conical intersection (LICI), which is a point of contact between two surfaces in the dressed two-dimensional Born-Oppenheimer potential energy landscape of a diatomic molecule in a strong laser field. The interference magnitude and angular period depend strongly on the energy difference between the initial state and the LICI, consistent with coherent diffraction around a cone-shaped potential barrier whose width and thickness depend on the relative energy of the initial state and the cone apex. These findings are supported by numerical solutions of the time-dependent Schrodinger equation for similar experimental conditions.

Creation of Sub-diffraction Longitudinally Polarized Spot by Focusing Radially Polarized Light with Binary Phase Lens.

Abstract: The generation of a sub-diffraction longitudinally polarized spot is of great interest in various applications, such as optical tweezers, super-resolution microscopy, high-resolution Raman spectroscopy, and high-density optical data storage. Many theoretical investigations have been conducted into the tight focusing of a longitudinally polarized spot with high-numerical-aperture aplanatic lenses in combination with optical filters. Optical super-oscillation provides a new approach to focusing light beyond the diffraction limit. Here, we propose a planar binary phase lens and experimentally demonstrate the generation of a longitudinally polarized sub-diffraction focal spot by focusing radially polarized light. The lens has a numerical aperture of 0.93 and a long focal length of 200λ for wavelength λ = 632.8 nm, and the generated focal spot has a full-width-at-half-maximum of about 0.456λ, which is smaller than the diffraction limit, 0.54λ. A 5λ-long longitudinally polarized optical needle with sub-diffraction size is also observed near the designed focal point.

A facile grating approach towards broadband, wide-angle and high-efficiency holographic metasurfaces.

Abstract: We analytically show that an incident light can be almost completely diffracted into the -1(st) order in wide-angle and broadband by suitably designed thin metallic nano-gratings with simple rectangular cross sections. Such extraordinary optical diffraction results from the excitation of localized cavity modes and exists even when the grating period is modulated in a broad range. By modulating the period with binary holography techniques, we can shape an incident wave into arbitrary wavefronts with near-unity conversion efficiencies. To show the efficacy of this approach, we demonstrate three reflection-type metasurfaces for achieving near-complete conversions from a Gaussian beam into a focused beam, Bessel beam, and vortex beam, respectively, with the complete suppression of the undesired specular reflection. Our findings provide a facile approach to build arbitrary wavefront-shaping metasurfaces with wide-angle, broadband, and high efficiency performance.