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1. Generation of over 1000 Diffraction Spots from 2D Graded Photonic Super-Crystals

   https://doi.org/10.3390/photonics7020027  

   Hassan, Safaa; Jiang, Yan; Alnasser, Khadijah; Hurley, Noah; Zhang, Hualiang; Philipose, Usha; Lin, Yuankun (June 2020, Photonics)

   For the first time, we are able to generate over 1000 diffraction spots from a graded photonic super-crystal with a unit super-cell size of 12a × 12a where a is the lattice constant and hole radii are gradually changed in dual directions. The diffraction pattern from the graded photonic super-crystal reveals unique diffraction properties. The first order diffractions of (±1,0) or (0,±1) disappear. Fractional diffraction orders are observed in the diffraction pattern inside a square with vertices of (1,1), (1,−1), (−1,−1) and (−1,−1). The fractional diffraction can be understood from lattices with a period of a. However, a dual-lattice model is considered in order to explain higher-order diffractions. E-field intensity simulations show a coupling and re-distribution among fractional orders of Bloch waves. There are a total of 12 × 12 spots in E-field intensity in the unit supercell corresponding to 12 × 12 fractional diffraction orders in the diffraction pattern and 12 × 12 fractional orders of momentum in the first Brillouin zone in k-space. 

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2. Laser Diffraction Zones and Spots from Three-Dimensional Graded Photonic Super-Crystals and Moiré Photonic Crystals

   https://doi.org/10.3390/photonics9060395  

   Hurley, Noah; Kamau, Steve; Alnasser, Khadijah; Philipose, Usha; Cui, Jingbiao; Lin, Yuankun (June 2022, Photonics)

   The laser diffraction from periodic structures typically shows isolated and sharp point patterns at zeroth and ±nth orders. Diffraction from 2D graded photonic super-crystals (GPSCs) has demonstrated over 1000 spots due to the fractional diffractions. Here, we report the holographic fabrication of three types of 3D GPSCs through nine beam interferences and their characteristic diffraction patterns. The diffraction spots due to the fractional orders are merged into large-area diffraction zones for these three types of GPSCs. Three distinguishable diffraction patterns have been observed: (a) 3 × 3 Diffraction zones for GPSCs with a weak gradient in unit super-cell, (b) 5 × 5 non-uniform diffraction zones for GPSCs with a strong modulation in long period and a strong gradient in unit super-cell, (c) more than 5 × 5 uniform diffraction zones for GPSCs with a medium gradient in unit super-cell and a medium modulation in long period. The GPSCs with a strong modulation appear as moiré photonic crystals. The diffraction zone pattern not only demonstrates a characterization method for the fabricated 3D GPSCs, but also proves their unique optical properties of the coupling of light from zones with 360° azimuthal angles and broad zenith angles. 

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3. Diffraction-Based Multiscale Residual Strain Measurements

   https://doi.org/10.1093/mam/ozae011  

   Pai, Namit; Manda, Sanjay; Sudhalkar, Bhargav; Syphus, Bethany; Fullwood, David; de_Kloe, René; Wright, Stuart; Patra, Anirban; Samajdar, Indradev (March 2024, Microscopy and Microanalysis)

   Abstract Modern analytical tools, from microfocus X-ray diffraction (XRD) to electron microscopy-based microtexture measurements, offer exciting possibilities of diffraction-based multiscale residual strain measurements. The different techniques differ in scale and resolution, but may also yield significantly different strain values. This study, for example, clearly established that high-resolution electron backscattered diffraction (HR-EBSD) and high-resolution transmission Kikuchi diffraction (HR-TKD) [sensitive to changes in interplanar angle (Δθθ)], provide quantitatively higher residual strains than micro-Laue XRD and transmission electron microscope (TEM) based precession electron diffraction (PED) [sensitive to changes in interplanar spacing (Δdd)]. Even after correcting key known factors affecting the accuracy of HR-EBSD strain measurements, a scaling factor of ∼1.57 (between HR-EBSD and micro-Laue) emerged. We have then conducted “virtual” experiments by systematically deforming an ideal lattice by either changing an interplanar angle (α) or a lattice parameter (a). The patterns were kinematically and dynamically simulated, and corresponding strains were measured by HR-EBSD. These strains showed consistently higher values for lattice(s) distorted by α, than those altered by a. The differences in strain measurements were further emphasized by mapping identical location with HR-TKD and TEM-PED. These measurements exhibited different spatial resolution, but when scaled (with ∼1.57) provided similar lattice distortions numerically. 

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4. A review and reassessment of diffraction, scattering, and shadows in electrodynamics

   Berg, M. J.; Sorensen, C. M. (January 2018, Journal of Quantitative Spectroscopy & Radiative Transfer)

   The concepts of diffraction and scattering are well known and considered fundamental in optics and other wave phenomena. For any type of wave, one way to define diffraction is the spreading of waves, i.e., no change in the average propagation direction, while scattering is the deflection of waves with a clear change of propagation direction. However, the terms “diffraction”and “scattering”are often used interchangeably, and hence, a clear distinction between the two is difficult to find. This review considers electromagnetic waves and retains the simple definition that diffraction is the spreading of waves but demonstrates that all diffraction patterns are the result of scattering. It is shown that for electromagnetic waves, the “diffracted”wave from an object is the Ewald–Oseen extinction wave in the far-field zone. The intensity distribution of this wave yields what is commonly called the diffraction pattern. Moreover, this is the same Ewald–Oseen wave that cancels the incident wave inside the object and thereafter continues to do so immediately behind the object to create a shadow. If the object is much wider than the beam but has a hole, e.g., a screen with an aperture, the Ewald–Oseen extinction wave creates the shadow behind the screen and the incident light that passes through the aperture creates the diffraction pattern. This point of view also illustrates Babinet’s principle. Thus, it is the Ewald–Oseen extinction theorem that binds together diffraction, scattering, and shadows. 

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5. SPIND : a reference-based auto-indexing algorithm for sparse serial crystallography data

   https://doi.org/10.1107/s2052252518014951  

   Li, Chufeng; Li, Xuanxuan; Kirian, Richard; Spence, John_C H; Liu, Haiguang; Zatsepin, Nadia A (January 2019, IUCrJ)

   SPIND(sparse-pattern indexing) is an auto-indexing algorithm for sparse snapshot diffraction patterns (`stills') that requires the positions of only five Bragg peaks in a single pattern, when provided with unit-cell parameters. The capability ofSPINDis demonstrated for the orientation determination of sparse diffraction patterns using simulated data from microcrystals of a small inorganic molecule containing three iodines, 5-amino-2,4,6-triiodoisophthalic acid monohydrate (I3C) [Beck & Sheldrick (2008),Acta Cryst.E64, o1286], which is challenging for commonly used indexing algorithms.SPIND, integrated withCrystFEL[Whiteet al.(2012),J. Appl. Cryst.45, 335–341], is then shown to improve the indexing rate and quality of merged serial femtosecond crystallography data from two membrane proteins, the human δ-opioid receptor in complex with a bi-functional peptide ligand DIPP-NH₂and the NTQ chloride-pumping rhodopsin (CIR). The study demonstrates the suitability ofSPINDfor indexing sparse inorganic crystal data with smaller unit cells, and for improving the quality of serial femtosecond protein crystallography data, significantly reducing the amount of sample and beam time required by making better use of limited data sets.SPINDis written in Python and is publicly available under the GNU General Public License from https://github.com/LiuLab-CSRC/SPIND. 

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