Diffraction from one- and two-dimensional quasicrystalline gratings (original) (raw)
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Periodic Diffraction Patterns for 1D Quasicrystals
Acta Physica Polonica B, 2005
A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction patterns are calculated analytically both using ``cut and project'' and ``average unit cell'' method, taking advantage of the physical space properties of the structure.
A rigorous approach for the analysis of diffraction from quasicrystalline gratings is presented. Previous methods for determining the diffraction properties of quasicrystalline gratings have relied on periodic supercell approximations. Our method exploits the cut-and-project method, which constructs quasicrystals as irrational slices of higher-dimensional periodic structures onto the physical space. The periodicity in the higher-dimensional space allows for the application of Floquet's theorem. The solutions can then be obtained by solving Maxwell's equations in the higher-dimensional space and projecting the results to the lower dimensional physical space. As an example, the method is applied to a one-dimensional aperiodic grating based on a Fibonacci quasicrystal (QC) where the results that were generated are shown to be in near-perfect agreement with those obtained using the supercell approximations.
Periodic Series of Peaks in Diffraction Patterns of Aperiodic Structures
Acta Physica Polonica A, 2014
Quasicrystals are aperiodic structures with no periodicity both in direct and reciprocal space. The diraction pattern of quasicrystals consists however of the periodic series of peaks in the scattering vector space. The intensities of the peaks of all series reduced in a proper way build up the so-called envelope function common for the whole pattern. The Fourier transformed envelope gives the average unit cell which is the statistical distribution of atomic positions in physical space. The distributions lifted to high dimensions correspond to atomic surfaces the basic concept of structural quasicrystals modeling within higher-dimensional approach.
Numerical Example Of Aperiodic Diffraction Grating
2017
Diffraction grating is periodic module used in many<br> engineering fields, its geometrical conception gives interesting<br> properties of diffraction and interferences, a uniform and periodic<br> diffraction grating consists of a number of identical apertures that are<br> equally spaced, in this case, the amplitude of intensity distribution<br> in the far field region is generally modulated by diffraction pattern<br> of single aperture. In this paper, we study the case of aperiodic<br> diffraction grating with identical rectangular apertures where theirs<br> coordinates are modeled by square root function, we elaborate a<br> computer simulation comparatively to the periodic array with same<br> length and we discuss the numerical results.
Development of the theory of quasi-periodic diffraction grating systems
Journal of the Optical Society of America, 1988
Characteristics of the Fresnel field of a quasi-linear grating system illuminated by a coherent, quasi-spherical wave front are studied. The considerations are based on the analyses of changes of the Fourier spectrum during the field propagation through the gratings. The treatment given simplifies the problem to the case of a single diffraction grating illuminated by a wave front that contains complex information about the preceding gratings and the input aberrated beam. It also furnishes a straightforward explanation for the variations in the output field distribution caused by any change of parameters in the system.
Diffraction from metallic gratings with locally varying profile forms
Optics Letters, 1999
Measurements of the diffraction characteristics of one-dimensional surface-relief gratings of locally varying prof ile are compared with rigorous diffraction theory. These gratings result from the superposition of two linear sinusoidal gratings of uniform depth for which the relative phase between the two gratings varies slowly with position. The resultant surface prof ile exhibits a relatively large-period variation in prof ile form. The periodic variation in diffraction efficiency that results yields a visual moiré pattern that has interesting asymmetry and polarization properties that alter as the viewing conditions are changed; the gratings can be exploited by diffractive optically variable devices for document security.
Diffraction from quasi-one-dimensional crystals
Physical Review B, 2009
General expressions of diffraction intensity distribution of quasi-one-dimensional crystals are evaluated within kinematical approximation. In order to gain the generality, diffraction intensity has been derived for each of the fifteen conformation classes. Characteristic features of the diffraction patterns are discussed and it is shown how the symmetry can be fully determined from the diffraction intensity distribution. General results are tabulated and their application is illustrated on the ͑10,10͒ molybdenum disulfide nanotube.
Optoelectronics Letters, 2011
We report a numerical method to analyze the fractal characteristics of far-field diffraction patterns for two-dimensional Thue-Morse (2-D TM) structures. The far-field diffraction patterns of the 2-D TM structures can be obtained by the numerical method, and they have a good agreement with the experimental ones. The analysis shows that the fractal characteristics of far-field diffraction patterns for the 2-D TM structures are determined by the inflation rule, which have potential applications in the design of optical diffraction devices.
Distortion and Peak Broadening in Quasicrystal Diffraction Patterns
Physical Review Letters, 1986
In this paper, we discuss how quenched strains in phonon and phason variables andlor quenched dislocations can lead to peak broadening and distortion in quasicrystal diffraction patterns. %e argue that high-resolution electron micrographs and observations of distortions in electron diffraction patterns indicate the presence of anisotropic strains in the phason variable in the icosahedral phase of Al-Mn and related alloys. Such strains also contribute to the x-ray peak widths and line shapes. PACS numbers: 61.50.Em, 61.5S.HI Recently, an "icosahedral phase" which diffracts electrons in an icosahedrally symmetric pattern consisting of rather sharp spots has been observed in rapidly cooled aluminum-manganese and related alloys. '