Academic literature on the topic 'Diffractive Bragg Reflector'
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Journal articles on the topic "Diffractive Bragg Reflector"
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Schuster, M., and H. Göbel. "Application of Graded Multilayer Optics in X-Ray Diffraction." Advances in X-ray Analysis 39 (1995): 57–71. http://dx.doi.org/10.1154/s037603080002245x.
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Periodic multilayers are ideally suited as high-reflectivity and wide-bandwidth Bragg reflectors. Their period can be matched laterally to the incidence angle so that for all points on the reflector, Bragg reflection is obtained for the same wavelength. Three major types of laterally graded multilayer optics were appJied to X-ray diffraction: (i) Parabolically curved multilayer mirrors were used to convert divergent radiation emerging from an X-ray source into a parallel beam. The parallel beam was applied in powder diffraction, grazing incidence diffraction, reflectometry, high-resolution diffraction, and protein crystallography, (ii) Elliptically curved multilayer mirrors focused the divergent radiation from the source into a line on the sample or detector. The high brilliance and small dimension of the focused beam make this mirror type suited for transmission diffractometry of capillary and fiber specimens, (iii) Planar multilayer mirrors were employed in divergent-beam optics. In Bragg-Brentano diffractometers, this mirror type can serve as a compact incident-beam monochromator for removing Kβ lines and Bremsstrahlung.
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Batigun, C. M., and R. M. Brugger. "Mirror and Bragg reflections of neutrons at a nuclear resonance." Journal of Applied Crystallography 21, no. 1 (1988): 54–59. http://dx.doi.org/10.1107/s0021889887009579.
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A set of experiments has observed the mirror reflection and Bragg diffraction of neutrons at the energy of a low-lying nuclear resonance of 115In. The reflector was a mirror of In metal with the resonance at 1.457 eV. The mirror reflection for different angles of incidence was measured and sets of data showing the relative reflectivities were obtained. For the Bragg diffraction experiment the crystal was a wafer of InP and several examples of Bragg reflections near 1.456 eV were measured.
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Yao, Nan, and John M. Cowley. "Characterization of Surface Resonance Conditions for Surface Imaging." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 1 (1990): 332–33. http://dx.doi.org/10.1017/s0424820100180410.
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In order to increase intensity and contrast in the image of a surface, the surface resonance conditions have been widely used to enhance the Bragg reflection for image formation in REM (Reflection Electron Microscopy). However, detailed studies of how the resonance conditions relate to the imaging contrast have not been reported. This paper will concentrate on the general properties of the different resonance conditions, as well as the resulting image contrast.Figure 1 shows a series of RHEED (Reflection High Energy Electron Diffraction) patterns and REM images from the same region of a Pt(l11) surface with the incident electron beam in a direction close to the [112] zone axis at 200 KeV, with a glancing incident angle of about 24 mrad which corresponds to the (555) Bragg reflection condition inside the crystal. For the purpose of convenience in discussion, the four different diffraction conditions shown in figures l(al)-(dl) have been named as D1-D4. With Dl, the specular reflected spot falls in an intersection of a parallel Kikuchi line with a parabola; with D2, the specular reflected spot coincides with an intersection of the Kikuchi lines running parallel to and inclined to the crystal surface; with D3, the specular reflected spot crosses only the parallel Kikuchi line; and with D4, the specular reflected spot intersects only with a parabola. It was found that the diffraction conditions Dl and D2 can not be considered as identical, although the specular reflected spots for both cases are commonly regarded as (555) Bragg reflection in the RHEED pattern. Detailed inspection indicates that for Dl, both the Bragg reflection and the electron surface channelling wave are excited, and for D2, the excitement of simultaneous Bragg reflection occurs closely associated with the properties of three-dimensional dynamical diffraction for a bulk crystal.
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Huang, Yihe. "Some imaging properties of volume reflection holography." Canadian Journal of Physics 63, no. 12 (1985): 1518–24. http://dx.doi.org/10.1139/p85-253.
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Morelhão, S. L., and E. Abramof. "Investigation of Bragg surface diffraction in semiconductors and epitaxic structures by reciprocal-space analysis." Journal of Applied Crystallography 32, no. 5 (1999): 871–77. http://dx.doi.org/10.1107/s0021889899007013.
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Bragg surface diffraction (BSD) is a special case of three-beam diffraction, where the secondary beam is scattered in the surface-parallel direction. Under the BSD condition, the surface-detour reflection (secondary plus coupling reflections) transfers some of the secondary-beam intensity into the monitored primary beam. The extinction regime in which such transfer takes place depends on the crystalline perfection of the surface. Based on this fact, the mapping of the BSD profile, in an ω:φ scan technique, has been proposed [Morelhão & Cardoso (1996).J. Appl. Cryst.29, 446–456] as a method to obtain information on the in-plane crystalline quality of the surface. With the X-ray optics for BSD mapping, the diffracting surface thickness that defines the profile could not be measured or compared with those under conventional Bragg diffraction. In this report, the BSD using a triple-axis diffractometer is investigated. Reciprocal-space mapping of the Bragg reflection (primary reflection) was performedinandoutof the BSD condition. It reveals the diffracting surface thickness of BSD in GaAs and Si substrates. The triple axis was also used to investigate the BSD in the SiGe multiple quantum well, and it has demonstrated the existence of effective satellite peaks for such structures.
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Pateras, Anastasios, Ross Harder, Wonsuk Cha, et al. "Combining Laue diffraction with Bragg coherent diffraction imaging at 34-ID-C." Journal of Synchrotron Radiation 27, no. 5 (2020): 1430–37. http://dx.doi.org/10.1107/s1600577520009844.
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Measurement modalities in Bragg coherent diffraction imaging (BCDI) rely on finding a signal from a single nanoscale crystal object which satisfies the Bragg condition among a large number of arbitrarily oriented nanocrystals. However, even when the signal from a single Bragg reflection with (hkl) Miller indices is found, the crystallographic axes on the retrieved three-dimensional (3D) image of the crystal remain unknown, and thus localizing in reciprocal space other Bragg reflections becomes time-consuming or requires good knowledge of the orientation of the crystal. Here, the commissioning of a movable double-bounce Si (111) monochromator at the 34-ID-C endstation of the Advanced Photon Source is reported, which aims at delivering multi-reflection BCDI as a standard tool in a single beamline instrument. The new instrument enables, through rapid switching from monochromatic to broadband (pink) beam, the use of Laue diffraction to determine crystal orientation. With a proper orientation matrix determined for the lattice, one can measure coherent diffraction patterns near multiple Bragg peaks, thus providing sufficient information to image the full strain tensor in 3D. The design, concept of operation, the developed procedures for indexing Laue patterns, and automated measuring of Bragg coherent diffraction data from multiple reflections of the same nanocrystal are discussed.
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Balyan, Minas K. "X-ray third-order nonlinear plane-wave Bragg-case dynamical diffraction effects in a perfect crystal." Journal of Synchrotron Radiation 22, no. 6 (2015): 1410–18. http://dx.doi.org/10.1107/s1600577515017804.
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Two-wave symmetric Bragg-case dynamical diffraction of a plane X-ray wave in a crystal with third-order nonlinear response to the electric field is considered theoretically. For certain diffraction conditions for a non-absorbing perfect semi-infinite crystal in the total reflection region an analytical solution is found. For the width and for the center of the total reflection region expressions on the intensity of the incidence wave are established. It is shown that in the nonlinear case the total reflection region exists below a maximal intensity of the incidence wave. With increasing intensity of the incidence wave the total reflection region's center moves to low angles and the width decreases. Using numerical calculations for an absorbing semi-infinite crystal, the behavior of the reflected wave as a function of the intensity of the incidence wave and of the deviation parameter from the Bragg condition is analyzed. The results of numerical calculations are compared with the obtained analytical solution.
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Lauraux, Florian, Stéphane Labat, Sarah Yehya, et al. "Simultaneous Multi-Bragg Peak Coherent X-ray Diffraction Imaging." Crystals 11, no. 3 (2021): 312. http://dx.doi.org/10.3390/cryst11030312.
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The simultaneous measurement of two Bragg reflections by Bragg coherent X-ray diffraction is demonstrated on a twinned Au crystal, which was prepared by the solid-state dewetting of a 30 nm thin gold film on a sapphire substrate. The crystal was oriented on a goniometer so that two lattice planes fulfill the Bragg condition at the same time. The Au 111 and Au 200 Bragg peaks were measured simultaneously by scanning the energy of the incident X-ray beam and recording the diffraction patterns with two two-dimensional detectors. While the former Bragg reflection is not sensitive to the twin boundary, which is oriented parallel to the crystal–substrate interface, the latter reflection is only sensitive to one part of the crystal. The volume ratio between the two parts of the twinned crystal is about 1:9, which is also confirmed by Laue microdiffraction of the same crystal. The parallel measurement of multiple Bragg reflections is essential for future in situ and operando studies, which are so far limited to either a single Bragg reflection or several in series, to facilitate the precise monitoring of both the strain field and defects during the application of external stimuli.
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Wimpory, Robert C., Uwe Wasmuth, Joana Rebelo-Kornmeier, and Michael Hofmann. "The Effect of Grain Size on Strain Determination Using a Neutron Diffractometer." Materials Science Forum 638-642 (January 2010): 2405–10. http://dx.doi.org/10.4028/www.scientific.net/msf.638-642.2405.
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The determination of strain from neutron diffraction data is normally based upon the fit of a Gaussian function to a Bragg reflection. The error in the fit is assumed to be that based on ‘counting statistics’ and this error propagates through the analyses until the final stress evaluation. This relies on there being a big enough number of diffracting grains/crystallites within the gauge volume to ‘approximate’ to counting statistics. The number of grains however depends on the gauge volume size chosen and the average size of the grains (and hence diffracting grains) within the gauge volume and this should be taken into account. The aim of this work is to give an estimate of the uncertainty due to these ‘grain-size statistics’ due to grain size, gauge volume, FWHM of the Bragg reflection (for angular dispersive diffractometers), scattering angle (2), size of detector (and hence number of diffracting grains ‘seen’ on the detector), hkl multiplicity (m) and eventually texture.
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Medvedev, V. V., A. J. R. van den Boogaard, R. van der Meer, et al. "Infrared diffractive filtering for extreme ultraviolet multilayer Bragg reflectors." Optics Express 21, no. 14 (2013): 16964. http://dx.doi.org/10.1364/oe.21.016964.
Full textDissertations / Theses on the topic "Diffractive Bragg Reflector"
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Wang, Songzhe. "Etched diffraction grating demultiplexer with distributed Bragg reflector facets on Silicon-on-insulator." Thesis, McGill University, 2014. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=123076.
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Multiplexers and demultiplexers are essential components of a wavelength division multiplexing (WDM) system which allows for the multiplication of data transmission capacity based on existing telecom infrastructure. In this master thesis, a distributed etched diffraction grating (DEDG), which finds its application as the wavelength demultiplexer, is studied. The device is designed and built based on the platform of silicon on insulator (SOI). A center-fled reflective grating configuration is used for the design of the layout. Distributed Bragg grating reflectors are incorporated at the back of the diffraction grating facets for the purpose of enhancing the Fresnel reflection, as the insufficient reflectivity is the general problem encountered by this type of devices. Taking advantage of the high refractive index contrast of the SOI, the Bragg reflectors are fabricated with shallow etching, greatly easing the fabrication difficulty while preserving the reflectivity performance.The device is first designed with several layout and modeling software. As for a CWDM design, 4 output channels with a 20nm wavelength spacing centered at 1550nm are proposed. By simulation the inter-channel crosstalk is less than -30dB . Furthermore, 8 output channels with 10nm wavelength spacing centered at 1550nm are proposed and simulated as well. Then a bi-layer lift off fabrication process is designed and. Electron beam lithography (EBL) is used for defining the patterns of the input/output waveguides, with a width of 500nm, and the first order Bragg grating reflectors, which have features as small as 100nm. The choice of incorporating first order Bragg reflector is to maximize the reflectivity performance and minimize the device footprint. Reactive ion etching (RIE), which has the capability of providing near vertical sidewalls, is used for the etching process.<br>Les multiplexeurs et les démultiplexeurs sont des composantes essentielles pour les systèmes à multiplexage par répartition en longueur d'onde qui permettent de multiplier la capacité de transmission de données sur les infrastructures de télécommunication existantes. Dans cette thèse de maîtrise, un réseau de diffraction gravé et réparti servant de démultiplexeur à longueur d'onde est examiné. Le dispositif est conçu et fabriqué sur une plateforme de silicium sur isolant. Une configuration de réseau réflecteur est utilisée pour la conception du plan d'ensemble. La faiblesse des réflexions sur les réseaux de diffraction étant un problème connu et important, des réflecteurs de Bragg distribués sont incorporés à l'arrière des facettes du réseau afin d'augmenter les réflexions de Fresnel. Les réflecteurs de Bragg sont fabriqués par une gravure peu profonde grâce au large contraste de l'indice de réfraction du silicium sur isolant ce qui permet de diminuer les difficultés lors de la fabrication tout en préservant la performance du dispositif.Le dispositif est d'abord conçu selon plusieurs plans par l'entremise d'un logiciel de modélisation. Pour le multiplexage par répartition approximative en longueur d'onde, nous proposons quatre canaux espacés par 20 nm en longueur d'onde et centrés à 1550 nm. Par simulation de la diaphonie inter-canaux est inférieur à-30dB. De plus, nous proposons et simulons 8 canaux de sortie espacés par 10 nm en longueur d'onde et centrés à 1550 nm. Par la suite, nous élaborons un procédé de fabrication de soulèvement par bi-couche. Nous utilisons la lithographie par faisceau d'électrons pour créer les guides d'onde d'entrée et de sortie avec une largeur de 500 nm ainsi que les réflecteurs de Bragg de premier ordre qui ont des éléments aussi petits que 100 nm. Les réflecteurs de Bragg de premier ordre sont incorporés afin de maximiser la réflexion tout en minimisant la surface utilisée par le dispositif. La gravure par ions réactifs est utilisée pour la gravure puisqu'elle permet la fabrication de murs quasi verticaux.
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Tsyier, Sergei. "Caractérisation des profils d'indice de réseaux de Bragg innovants en module et phase." Thesis, Paris, ENST, 2013. http://www.theses.fr/2013ENST0022/document.
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Récemment, de nouvelles techniques ont été développées pour la fabrication des réseaux de Bragg à profil complexe. Ces composants photoniques sont utilisés dans plusieurs applications émergentes telles que la compensation de la dispersion pour les systèmes de communication de longue portée, les lasers à fibre, multiplexeurs et détecteurs optiques. Le diagnostic après inscription devrait fournir les informations nécessaires pour l’amélioration de la fabrication des réseaux de Bragg. Nous savons que les propriétés spectrales du réseau de Bragg sont liées au profil d’indice Δn. Les techniques de mesure directes, telles que la diffraction latérale de Krug, permettent de retrouver l’amplitude de modulation d’indice le long du réseau. Cependant, ces techniques sont insensibles aux fluctuations de phase. Une méthode alternative de caractérisation indirecte fondée sur l’algorithme de Layer-Peeling (LP) a été proposée. Toutefois elle ne peut pas être appliquée à la caractérisation des réseaux longs en raison de la propagation du bruit de calcul. Dans cette thèse nous avons présenté une nouvelle technique pour la mesure directe de l’amplitude et de la phase du profil d’indice le long du réseau de Bragg fondée sur la luminescence bleue (LB) induite par l’irradiation UV. Nos résultats expérimentaux de la mesure du profil de modulation d’indice sont en bonne correspondance avec la méthode de Krug. La méthode que nous proposons peut être appliquée à la caractérisation des réseaux longs. Elle permet de retrouver simultanément l’amplitude de modulation d’indice Δnac(z), la fonction du chirp et détecter le changement de l’indice moyen Δndc(z)<br>N the last decade new techniques were developed for fabrication of sophisticated Fiber Bragg Gratings (FGBs). This has been motivated by the emergence of many applications such as dispersion compensation for long-haul communication systems, DFB fiber lasers, optical add/drop multiplexers, and optical sensors. Post-fabrication diagnostics should provide relevant information to enhance the FBG fabrication process. It is well known that the FBG spectral properties are related to the index profile Δn. Direct measurement techniques, such as the side diffraction method reported by P. Krug, allow determining the index modulation amplitude along the FBG. Nevertheless, these techniques provide no information about phase fluctuations. An alternative method of indirect characterization, based on the Layer-Peeling (LP) algorithm, consists in Bragg grating profile reconstruction from its complex reflectivity. However, the LP method is unstable when applied to characterize long FBGs (>1mm) due to the error propagation effect. In this thesis we have shown the principle of a novel technique for the direct measurement of amplitude and phase variations of the index modulation along an FBG based on the blue luminescence (BL). Our experimental results are in a good agreement with the according Krug characterization. The proposed method of FBG characterization in amplitude and phase using the UV induced BL can be applied to long gratings (up to tens of centimeters) having complex index modulation profiles. It allows retrieving simultaneously the index profile modulation Δnac(z) and the chirp function, localizing phase shifts, and also detecting the mean index change Δndc(z)
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Matsouli, Ioanna. "Study of magneto-acoustic effects in FeBOâ†3 by synchrotron radiation diffraction imaging." Thesis, University of Warwick, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.310013.
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Mokhov, Sergiy V. "Theoretical study of beam transformations by volume diffraction." Doctoral diss., University of Central Florida, 2011. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4986.
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Laser beams can be manipulated by volume diffractive elements in addition to conventional optical elements like mirrors, lenses, and beam splitters. Conventional optical elements can be described by applying the basic laws of reflection and refraction at the surfaces of the elements. Even diffraction by surface gratings utilizes relatively simple mathematics. This is to be contrasted with the volume diffraction, which requires coupled wave theory in the slowly varying envelope approximation (SVEA) to obtain accurate results. Efficient spatially distributed diffraction of laser beams is possible due to the high coherence of laser light, and it occurs at specific resonant Bragg conditions. This research work is inspired and driven by the successful development of recording technology for robust, high-efficiency volume Bragg gratings (VBGs) in photo-thermo-refractive (PTR) glass. Mostly VBGs of the reflective type are discussed in this dissertation. Starting with an analysis of electro-magnetic wave propagation in layered media, we have reformulated Fresnel and volume reflection phenomena in terms of a convenient parameter--strength of reflection. The influence that the different non-uniformities inside a VBG have on its spectral properties has been examined. One important result of this work is the proposal of moire VBG and the derivation of an analytical expression for its bandwidth. A multiplexed VBG used as a coherent combiner is discussed as well. Beam distortion via transmission through and/or reflection by a heated VBG due to residual absorption is analyzed.<br>ID: 030423243; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Thesis (Ph.D.)--University of Central Florida, 2011.; Includes bibliographical references (p. 114-127).<br>Ph.D.<br>Doctorate<br>Optics and Photonics
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Zippel, Jan. "Gepulste Laserabscheidung und Charakterisierung funktionaler oxidischer Dünnfilme und Heterostrukturen." Doctoral thesis, Universitätsbibliothek Leipzig, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-100358.
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In der vorliegenden Arbeit wird das Hauptaugenmerk auf die Untersuchung der Auswirkungen einer Modifikation der zugänglichen Prozessparameter auf die funktionalen Eigenschaften oxidischer Dünnfilme während der gepulsten Laserabscheidung (PLD) gelegt.
Der erste Teil der Arbeit stellt die Herstellung von BaTiO3/SrTiO3-Mehrfach-Heterostrukturen auf thermisch und chemisch vorbehandelten SrTiO3-Substraten mittels gepulster Laserabscheidung (PLD) vor. Die zugängliche in-situ Wachstumskontrolle durch ein reflection high-energy electron diffraction (RHEED)-System ermöglicht es die Wachstumsprozesse in Echtzeit zu überwachen. Angestrebt wird ein stabiler zwei-dimensionaler Wachstumsmodus, der neben glatten Grenzflächen auch eine hohe Dünnfilmqualität ermöglicht. Es wird erstmals die prinzipielle Anwendbarkeit von BaTiO3/SrTiO3-Heterostrukturen als Bragg-Spiegel aufgezeigt. Für BaTiO3- sowie SrTiO3-Dünnfilme wurden die PLD-Parameter Substrattemperatur, Sauerstoffpartialdruck, Energiedichte des Lasers sowie Flussdichte der Teilchen variiert und die Auswirkungen auf die strukturellen, optischen und Oberflächeneigenschaften mittels Röntgendiffraktometrie (XRD), spektraler Ellipsometrie (SE) und Rasterkraftmikroskopie (AFM) beleuchtet.
Im zweiten Teil werden ZnO/MgxZn1−xO-Quantengrabenstrukturen hetero- und homoepitaktisch auf thermisch vorbehandelten a-Saphir- respektive m- und a-orientierten ZnO-Einkristallen vorgestellt. Die Realisierung eines zwei-dimensionalen „layer-by-layer“ Wachstumsmodus wird für die Quantengrabenstrukturen aufgezeigt. Die Quantengrabenbreite lässt sich aus beobachteten RHEED-Oszillationen exakt bestimmen. Ein Vergleich zwischen, mittels Photolumineszenz gemessenen Quantengrabenübergangsenergien als Funktion der Grabenbreite mit theoretisch ermittelten Werten wird vorgestellt, wobei der Unterschied zwischen polaren und nicht-polaren Strukturen mit Blick auf eine Anwendung aufgezeigt wird. Für c-orientierte ZnO-Dünnfilme wird das Wachstum im Detail untersucht und ein alternativer Abscheideprozess im so genannten Intervall PLD-Verfahren vorgestellt.
Die Verifizierung der theoretischen Prognose einer ferromagnetischen Ordnung mit einer Curie-Temperatur oberhalb Raumtemperatur (RT) für kubische, Mangan stabilisierte Zirkondioxid (MnSZ)-Dünnfilme stellt den dritten Teil der Arbeit dar. Die strukturellen Eigenschaften der Dünnfilme werden mittels XRD, AFM sowie Transmissionselektronenmikroskopie (TEM) untersucht. Die Bedingungen einer erfolgreichen Stabilisierung der kubischen Kristallphase durch den Einbau von Mn wird aufgezeigt. Mittels Röntgenphotoelektronenspektroskopie (XPS) sowie Elektronenspinresonanz (EPR) wird der Ladungszustand der, in der Zirkondioxidmatrix eingebauten, Mn-Ionen ermittelt. Die elektrischen Eigenschaftenwerden durch Strom-Spannungsmessungen(IU) sowie der Leitungstyp durch Seebeck-Effekt Messungen charakterisiert. Zur Erhöhung der Leitfähigkeit werden die MnSZ Dünnfilme in verschiedenen Atmosphären thermisch behandelt und Veränderungen durch IU-Messungen aufgezeigt. Ergebnisse von optischen Untersuchungen mittels Transmissionsmessungen und KL werden
präsentiert. Superconducting quantum interference device (SQUID)-Magnetometrie wird zur
Charakterisierung der magnetischen Eigenschaften genutzt. Magnetische Ordnungen im Bereich zwischen 5 K ≤ T ≤ 300 K werden untersucht und der Einfluss von Defekten sowie einer thermischen Behandlung in verschiedenen Atmosphären auf die magnetischen Eigenschaften diskutiert.
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Alnakhli, Zahrah J. "Broadband Reflective Metalens in Visible Band Based on Bragg Reflector Multilayers for VECSEL Applications." Thesis, 2020. http://hdl.handle.net/10754/664908.
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In conventional optics, curved lenses focus light rays to a focal point after light passes through them. These lenses have been designed to shape the wavefront of the incident beam as it emerges from the curved surface of the lens. Conventional lenses suffer from many limitations, such as limited optical quality for imaging and integration difficulties with other optical components due to their large size, huge thickness, as well as being difficult to manufacture. Using subwavelength structure, it is possible to fabricate flat, thin lenses (metalenses) with new optical properties not found in nature, in which many fundamental properties of light (like polarization, focal point, and phase) can be controlled with high accuracy. This results in high resolution and high quality of optical imaging.
This thesis demonstrates a new design of reflective metalens, in which the metalens structure is integrated with another optical component: Distributed Bragg Reflector (DBR). The metalens planer is a two-dimensional ultrathin planer arranged as an array with subwavelength separation distance. In recent works, a metalens was integrated with (metal/dielectric)-mirrors to form reflective metalenses. Simulation results show that, high-focusing efficiency is obtained for the lens (> 60%) with the ability to
reflect96% of total incident optical power. In comparison, the new metalens-DBR design - processes maintain the same high-focusing efficiency, but with a reflectance of 99.99%, which makes it promising for optoelectronic integration and perfectly suitable for integration with Vertical Cavity Surface Emitting Lasers (VCSEL) technology. This study of the optical properties: focal length; optical aberration; insensitivity to light polarization; and focusing efficiency of demonstrated metalens was done mainly by Finite Difference Time Domaine (FDTD) by using Lumerical FDTD solution.
Book chapters on the topic "Diffractive Bragg Reflector"
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Von Dreele, R. B., and J. Rodriguez-Carvajal. "Chapter 3. The Intensity of a Bragg Reflection." In Powder Diffraction. Royal Society of Chemistry, 2008. http://dx.doi.org/10.1039/9781847558237-00058.
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Bail, Armel Le. "Chapter 5. The Profile of a Bragg Reflection for Extracting Intensities." In Powder Diffraction. Royal Society of Chemistry, 2008. http://dx.doi.org/10.1039/9781847558237-00134.
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Glusker, Jenny Pickworth, and Kenneth N. Trueblood. "Diffraction." In Crystal Structure Analysis. Oxford University Press, 2010. http://dx.doi.org/10.1093/oso/9780199576340.003.0011.
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A common approach to crystal structure analysis by X-ray diffraction presented in texts that have been written for nonspecialists involves the Bragg equation, and a discussion in terms of “reflection” of X rays from crystal lattice planes (Bragg, 1913). While the Bragg equation, which implies this “reflection,” has proved extremely useful, it does not really help in understanding the process of X-ray diffraction. Therefore we will proceed instead by way of an elementary consideration of diffraction phenomena generally, and then diffraction from periodic structures (such as crystals), making use of optical analogies (Jenkins and White, 1957; Taylor and Lipson, 1964; Harburn et al., 1975). The eyes of most animals, including humans, comprise efficient optical systems for forming images of objects by the recombination of visible radiation scattered by these objects. Many things are, of course, too small to be detected by the unaided human eye, but an enlarged image of some of them can be formed with a microscope—using visible light for objects with dimensions comparable to or larger than the wavelength of this light (about 6 × 10−7 m), or using electrons of high energy (and thus short wavelength) in an electron microscope. In order to “see” the fine details of molecular structure (with dimensions 10−8 to 10−10 m), it is necessary to use radiation of a wavelength comparable to, or smaller than, the dimensions of the distances between atoms. Such radiation is readily available (1) in the X rays produced by bombarding a target composed of an element of intermediate atomic number (for example, between Cr and Mo in the Periodic Table) with fast electrons, or from a synchrotron source, (2) in neutrons from a nuclear reactor or spallation source, or (3) in electrons with energies of 10–50 keV. Each of these kinds of radiation is scattered by the atoms of the sample, just as is ordinary light, and if we could recombine this scattered radiation, as a microscope can, we could form an image of the scattering matter.
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Glusker, Jenny Pickworth, and Kenneth N. Trueblood. "The diffraction pattern obtained." In Crystal Structure Analysis. Oxford University Press, 2010. http://dx.doi.org/10.1093/oso/9780199576340.003.0014.
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In this chapter we will describe those factors that control the intensities of Bragg reflections and how to express them mathematically so that we can calculate an electron-density map. The Bragg reflections have intensities that depend on the arrangement of atoms in the unit cell and how X rays scattered by these atoms interfere with each other. Therefore the diffraction pattern has a wide variety of intensities in it. Measured X-ray diffraction data consist of a list of the relative intensity I (hkl), its indices (h, k, and l), and the scattering angle 2θ, for each Bragg reflection. All the values of the intensity I (hkl) are on the same relative scale, and this entire data set describes the “diffraction pattern.” It is used as part of the input necessary to determine the crystal structure. As already indicated from a study of the diffraction patterns from slits and from various arrangements of molecules, the angular positions (2θ) at which scattered radiation is observed depend only on the dimensions of the crystal lattice and the wavelength of the radiation used, while the intensities I (hkl) of the different diffracted beams depend mainly on the nature and arrangement of the atoms within each unit cell. It is these two items, the unit-cell dimensions of the crystal and its atomic arrangement, that comprise what we mean by “the crystal structure.” Their determination is the primary object of the analysis described here. As illustrated in Figure 1.1b and the accompanying discussion, and mentioned again at the start of Chapter 3, X rays scattered by the electrons in the atoms of a crystal cannot be recombined by any known lens. Consequently, to obtain an image of the scattering matter in a crystal, the “structure” of that crystal, we need to simulate this recombination, which means that we must find a way to superimpose the scattered waves, with the proper phase relations between them, to give an image of the material that did the scattering, that is, the electrons in the atoms.
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Blow, David. "Diffraction by crystals." In Outline of Crystallography for Biologists. Oxford University Press, 2002. http://dx.doi.org/10.1093/oso/9780198510512.003.0009.
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In Chapter 4 many two-dimensional examples were shown, in which a diffraction pattern represents the Fourier transform of the scattering object. When a diffracting object is three-dimensional, a new effect arises. In diffraction by a repetitive object, rays are scattered in many directions. Each unit of the lattice scatters, but a diffracted beam arises only if the scattered rays from each unit are all in phase. Otherwise the scattering from one unit is cancelled out by another. In two dimensions, there is always a direction where the scattered rays are in phase for any order of diffraction (just as shown for a one-dimensional scatterer in Fig. 4.1). In three dimensions, it is only possible for all the points of a lattice to scatter in phase if the crystal is correctly oriented in the incident beam. The amplitudes and phases of all the scattered beams from a three-dimensional crystal still provide the Fourier transform of the three-dimensional structure. But when a crystal is at a particular angular orientation to the X-ray beam, the scattering of a monochromatic beam provides only a tiny sample of the total Fourier transform of its structure. In the next section, we are going to find what is needed to allow a diffracted beam to be generated. We shall follow a treatment invented by Lawrence Bragg in 1913. Max von Laue, who discovered X-ray diffraction in 1912, used a different scheme of analysis; and Paul Ewald introduced a new way of looking at it in 1921. These three methods are referred to as the Laue equations, Bragg’s law and the Ewald construction, and they give identical results. All three are described in many crystallographic text books. Bragg’s method is straightforward, understandable, and suffices for present needs. I had heard J.J. Thomson lecture about…X-rays as very short pulses of radiation. I worked out that such pulses…should be reflected at any angle of incidence by the sheets of atoms in the crystal as if these sheets were mirrors.…It remained to explain why certain of the atomic mirrors in the zinc blende [ZnS] crystal reflected more powerfully than others.
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Krishnan, Kannan M. "X-Ray Diffraction." In Principles of Materials Characterization and Metrology. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198830252.003.0007.
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X-rays diffraction is fundamental to understanding the structure and crystallography of biological, geological, or technological materials. X-rays scatter predominantly by the electrons in solids, and have an elastic (coherent, Thompson) and an inelastic (incoherent, Compton) component. The atomic scattering factor is largest (= Z) for forward scattering, and decreases with increasing scattering angle and decreasing wavelength. The amplitude of the diffracted wave is the structure factor, F <sub>hkl</sub>, and its square gives the intensity. In practice, intensities are modified by temperature (Debye-Waller), absorption, Lorentz-polarization, and the multiplicity of the lattice planes involved in diffraction. Diffraction patterns reflect the symmetry (point group) of the crystal; however, they are centrosymmetric (Friedel law) even if the crystal is not. Systematic absences of reflections in diffraction result from glide planes and screw axes. In polycrystalline materials, the diffracted beam is affected by the lattice strain or grain size (Scherrer equation). Diffraction conditions (Bragg Law) for a given lattice spacing can be satisfied by varying θ or λ — for study of single crystals θ is fixed and λ is varied (Laue), or λ is fixed and θ varied to study powders (Debye-Scherrer), polycrystalline materials (diffractometry), and thin films (reflectivity). X-ray diffraction is widely applied.
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Glusker, Jenny Pickworth, and Kenneth N. Trueblood. "Experimental Measurements." In Crystal Structure Analysis. Oxford University Press, 2010. http://dx.doi.org/10.1093/oso/9780199576340.003.0012.
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The analysis of a crystal structure by X-ray or neutron diffraction consists of three stages: (1) Data collection. This involves experimental measurement of the directions of scatter of the diffracted beams so that a unit cell can be selected and its dimensions measured. The intensities of as many as possible of the diffracted beams (Bragg reflections) from that same crystal are then recorded. These intensities depend on the nature of the atoms present in the crystal and their relative positions within the unit cell. (2) Finding a “trial structure.” This is the deduction by some method (such as one of those described in Chapters 8 and 9) of a suggested atomic arrangement (a “trial structure”). This is listed as atomic coordinates that have been measured with respect to the unit-cell axes. The intensity of each Bragg reflection corresponding to this trial structure can then be calculated (see Chapter 5) and its value then compared with the corresponding experimentally measured intensity in order to determine whether the trial structure is “good,” meaning that it is essentially correct. (3) Refinement of the trial structure. This involves modification (refinement) of a good trial structure until the calculated and measured intensities agree with each other within the limits of any errors in the observations (see Chapter 11). This is usually done by a leastsquares refinement, although difference electron-density maps may also prove useful. The result of the refinement is information on the three-dimensional atomic coordinates in this particular crystal, together with atomic displacement parameters. This chapter is concerned with the first of these stages, the experimental measurements. This is a rapidly changing area of science as more powerful and precise equipment and detection devices become available. The experimental data that may be derived frommeasurements of an X-ray or neutron diffraction pattern include: (1) The overall appearance of the Bragg reflections at the detection system. Ideally these diffraction maxima should be sharp, well-resolved peaks. Blurred, double spots or arcs may indicate disorder or poor crystal quality. (2) The angles or directions of scattering (including 2Ë, the angular deviation from the direct beam).
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Glusker, Jenny Pickworth, and Kenneth N. Trueblood. "The phase problem and electron-density maps." In Crystal Structure Analysis. Oxford University Press, 2010. http://dx.doi.org/10.1093/oso/9780199576340.003.0015.
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In order to obtain an image of the material that has scattered X rays and given a diffraction pattern, which is the aim of these studies, one must perform a three-dimensional Fourier summation. The theorem of Jean Baptiste Joseph Fourier, a French mathematician and physicist, states that a continuous, periodic function can be represented by the summation of cosine and sine terms (Fourier, 1822). Such a set of terms, described as a Fourier series, can be used in diffraction analysis because the electron density in a crystal is a periodic distribution of scattering matter formed by the regular packing of approximately identical unit cells. The Fourier series that is used provides an equation that describes the electron density in the crystal under study. Each atom contains electrons; the higher its atomic number the greater the number of electrons in its nucleus, and therefore the higher its peak in an electrondensity map.We showed in Chapter 5 how a structure factor amplitude, |F (hkl)|, the measurable quantity in the X-ray diffraction pattern, can be determined if the arrangement of atoms in the crystal structure is known (Sommerfeld, 1921). Now we will show how we can calculate the electron density in a crystal structure if data on the structure factors, including their relative phase angles, are available. The Fourier series is described as a “synthesis” when it involves structure amplitudes and relative phases and builds up a picture of the electron density in the crystal. By contrast, a “Fourier analysis” leads to the components that make up this series. The term “relative” is used here because the phase of a Bragg reflection is described relative to that of an imaginary wave diffracted in the same direction at a chosen origin of the unit cell.
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Glusker, Jenny Pickworth, and Kenneth N. Trueblood. "Symmetry and space Groups." In Crystal Structure Analysis. Oxford University Press, 2010. http://dx.doi.org/10.1093/oso/9780199576340.003.0016.
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A certain degree of symmetry is apparent in much of the natural world, as well as in many of our creations in art, architecture, and technology. Objects with high symmetry are generally regarded with pleasure. Symmetry is perhaps the most fundamental property of the crystalline state and is a reason that gemstones have been so appreciated throughout the ages. This chapter introduces some of the fundamental concepts of symmetry—symmetry operations, symmetry elements, and the combinations of these characteristics of finite objects (point symmetry) and infinite objects (space symmetry)—as well as the way these concepts are applied in the study of crystals. An object is said to be symmetrical if after some movement, real or imagined, it is or would be indistinguishable (in appearance and other discernible properties) from the way it was initially. The movement, which might be, for example, a rotation about some fixed axis or a mirror-like reflection through some plane or a translation of the entire object in a given direction, is called a symmetry operation. The geometrical entity with respect to which the symmetry operation is performed, an axis or a plane in the examples cited, is called a symmetry element. Symmetry operations are actions that can be carried out, while symmetry elements are descriptions of possible symmetry operations. The difference between these two symmetry terms is important. It is possible not only to determine the crystal system of a given crystalline specimen by analysis of the intensities of the Bragg reflections in the diffraction pattern of the crystal, but also to learn much more about its symmetry, including its Bravais lattice and the probable space group. As indicated in Chapter 2, the 230 space groups represent the distinct ways of arranging identical objects on one of the 14 Bravais lattices by the use of certain symmetry operations to be described below. The determination of the space group of a crystal is important because it may reveal some symmetry within the contents of the unit cell.
Conference papers on the topic "Diffractive Bragg Reflector"
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Toga, Shinji, and Takatsune Narumi. "Flow Induced Crystallization of Colloidal Dispersion." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-14021.
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In this study, we have examined a crystallization effect of colloidal dispersion induced by the various elongational flows. Extremely strong electrostatic repulsion makes a crystal structure called ‘colloid crystal’. A colloid crystal has hundreds of nano-meters in grating scale and it reflects the visible light due to the Bragg diffraction. It has the potential to become different photonic devices such as an inexpensive photonic device and a planar laser source, but it requires the evolution of the process of making a single-crystal with external stimulus. The methods using flow operation described in this study are expected to the crystallization action of a colloidal dispersion. In the experiment, 2 types of the flow have been examined. The flows have a contraction or an expansion part between two parallel plates separated by 0.1 mm gap and it cause deformations of a contraction or an extension for the colloid. We have evaluated the crystallization effects by a spectroscopic observation of visible-lights reflection on the flow region. As a result, while expansion flows have no crystallization effect, contraction flows have shown it.
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Takenaka, Hisataka, and Yoshikazu Ishii. "Lateral-periodicity evaluation of multilayer Bragg reflector surface roughness using x-ray diffraction." In San Diego '90, 8-13 July, edited by James P. Knauer and Gopal K. Shenoy. SPIE, 1991. http://dx.doi.org/10.1117/12.23313.
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Kral, Zdenek, Josep Ferre-Borrull, Lluis F. Marsal, et al. "Reflection Analysis of 2D-photonic Crystal Lattice Using Bragg-diffraction phenomena." In 2007 Spanish Conference on Electron Devices. IEEE, 2007. http://dx.doi.org/10.1109/sced.2007.384050.
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Nazarov, Maxim M., Alexander P. Shkurinov, and Jean-Louis Coutaz. "Bragg reflection of THz surface plasmon propagating over a diffraction grating." In 2011 36th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz 2011). IEEE, 2011. http://dx.doi.org/10.1109/irmmw-thz.2011.6105165.
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Muller, Andre, Jorg Fricke, Olaf Brox, Gotz Erbert, and Bernd Sumpf. "Influence of lateral waveguide and grating layouts on the diffraction efficiency of distributed Bragg reflectors." In 2017 Conference on Lasers and Electro-Optics Europe (CLEO/Europe) & European Quantum Electronics Conference (EQEC). IEEE, 2017. http://dx.doi.org/10.1109/cleoe-eqec.2017.8086390.
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Nikulin, Andrei Y., and Alexei Y. Souvorov. "Gaussian-like shaping of coherent synchrotron x-rays: 3D diffraction at a 90-degree Bragg reflection." In Optical Engineering + Applications, edited by Katherine Creath. SPIE, 2008. http://dx.doi.org/10.1117/12.795954.
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Fedotov, V. G., T. A. Ukleev, A. Y. Men'shikova, N. N. Shevchenko, and A. V. Sel'kin. "Multiple Bragg diffraction effects in angle-resolved reflection and transmission spectra of opaline photonic crystal films." In SPIE Photonics Europe, edited by Hernán R. Míguez, Sergei G. Romanov, Lucio C. Andreani, and Christian Seassal. SPIE, 2012. http://dx.doi.org/10.1117/12.922803.
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Kwon, Yun-Young, Kun-Yul Kim, Joo-Youn Park, and Jong-Yong Park. "Study for Bragg detuning effect and asymmetry of diffraction efficiency on the transmission and the reflection hologram." In Integrated Optoelectronic Devices 2007, edited by Roger A. Lessard and Hans I. Bjelkhagen. SPIE, 2007. http://dx.doi.org/10.1117/12.704567.
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