A relationship between the far field diffraction pattern and the axial pressure radiating from a two-dimensional aperture

2010 ◽  
Vol 127 (3) ◽  
pp. 1381-1390 ◽  
Author(s):  
Edward H. Pees
Keyword(s):  
Diffraction Pattern ◽  
Far Field ◽  
Two Dimensional ◽  
Axial Pressure

scholarly journals Far-Field Focus and Dispersionless Anticrossing Bands in Two-Dimensional Photonic Crystals

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Xiaoshuang Chen ◽  
Renlong Zhou ◽  
Yong Zeng ◽  
Hongbo Chen ◽  
Wei Lu
Keyword(s):  
Photonic Crystal ◽  
Photonic Crystals ◽  
Negative Refraction ◽  
Far Field ◽  
Two Dimensional ◽  
Surface Polaritons ◽  
Concave Lens ◽  
Bloch Mode ◽  
Two Dimensional Photonic Crystal ◽  
Photonic Band

We review the simulation work for the far-field focus and dispersionless anticrossing bands in two-dimensional (2D) photonic crystals. In a two-dimensional photonic-crystal-based concave lens, the far-field focus of a plane wave is given by the distance between the focusing point and the lens. Strong and good-quality far-field focusing of a transmitted wave, explicitly following the well-known wave-beam negative refraction law, can be achieved. The spatial frequency information of the Bloch mode in multiple Brillouin zones (BZs) is investigated in order to indicate the wave propagation in two different regions. When considering the photonic transmission in a 2D photonic crystal composed of a negative phase-velocity medium (NPVM), it is shown that the dispersionless anticrossing bands are generated by the couplings among the localized surface polaritons of the NPVM rods. The photonic band structures of the NPVM photonic crystals are characterized by a topographical continuous dispersion relationship accompanied by many anticrossing bands.

scholarly journals NEGATIVE REFRACTION AND SUBWAVELENGTH FOCUSING USING PHOTONIC CRYSTALS

2004 ◽  
Vol 18 (25) ◽  
pp. 1275-1291 ◽  
Author(s):  
EKMEL OZBAY ◽  
KAAN GUVEN ◽  
ERTUGRUL CUBUKCU ◽  
KORAY AYDIN ◽  
B. KAMIL ALICI
Keyword(s):  
Optical Properties ◽  
Photonic Crystals ◽  
Negative Refraction ◽  
Numerical Study ◽  
Effective Index ◽  
Index Of Refraction ◽  
Far Field ◽  
Two Dimensional ◽  
Flat Lens ◽  
Effective Index Of Refraction

In this article, we present an experimental and numerical study of novel optical properties of two-dimensional dielectric photonic crystals (PCs) which exhibit negative refraction. We investigate two mechanisms which utilize the band structure of the PC to generate a negative effective index of refraction (n eff <0) and demonstrate the negative refraction experimentally. To the isotropic extend of n eff , different PC slab structures are employed to focus the radiation of a point source. It is shown experimentally that the PC can generate an image of the source with subwavelength resolution in the vicinity of the PC interface. Using a different PC, one can also obtain a far field focusing. In the latter case, we explicitly show the flat lens behavior of the structure. These examples indicate that PC-based lenses can surpass limitations of conventional lenses and lead to novel optics applications.

scholarly journals Διάδοση κυμάτων σε ανομοιογενή μέσα

2007 ◽  
Author(s):  
Κωνσταντίνος Αναγνωστόπουλος
Keyword(s):  
Field Equation ◽  
Plane Wave ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Field Operator ◽  
Sampling Point ◽  
Far Field ◽  
Two Dimensional ◽  
Time Harmonic

The scope of this doctoral thesis is, first, to develop an analytical, in principle, method for the solution of the two-dimensional scattering problem of time-harmonic elastic plane waves by a homogeneous orthotropic scatterer, second, to establish the complete theoretical framework, which is necessary for the application of the Linear Sampling Method (LSM) to the problem of reconstructing the support of twodimensional elastic anisotropic inclusions embedded in isotropic media and, third, to derive an extension of the Factorization Method (FM) to the inverse elastic scattering problem by penetrable isotropic bodies for time-harmonic plane wave incidence. Aconcise description of the contents of the thesis is outlined below. Chapter one contains a detailed bibliographical search, which is related to the analytical and numerical methods (with emphasis on the former) usually employed for the solution of the direct scattering problem by anisotropic elastic bodies as well as to those inverse scattering techniques, which are usually referred to as sampling and probe methods and, in particular, the LSM and the FM. Chapter two commences with a brief discussion of some fundamental results from the linearized theory of dynamic elasticity. The problem of a rigorous analysis of the elasticity equation governing the elastic behaviour of an orthotropic material in two dimensions is then addressed. This analysis, which is based on a suitable diagonalization applied to the underlying differential system and a plane wave expansion of the sought field, results in a Fourier series expansion for the displacement field describing the elastic deformations of the orthotropic medium and is complemented by the results of appendix A. A mathematical model for the solution of the associated transmission scattering problem, taking advantage of the aforementioned expansion, is also settled and analyzed. The details of its numerical treatment can be found in appendix B. Finally, numerical results for several inclusion geometries and a system thereof with material properties characterized by the cubic symmetryclass -a special case of the orthotropic class of symmetry- are presented. In chapter three, the LSM is extended to the case of a two-dimensional homogeneous anisotropic inclusion embedded in an isotropic background medium. The concepts of the elastic Herglotz function, the elastic far-field operator and the corresponding far-field equation, on which the formulation of the LSM heavily relies, are first introduced. Then, the proposed inverse scattering scheme is introduced and discussed in detail. By means of an appropriate operator decomposition of the far-field operator,the main theorem of the method, concerning the characterization of the behaviour of an approximate solution to the far-field equation at the boundary of the scatterer, is proved. In the end of the third chapter, the performance of the LSM is examined by applying it to a set of different geometric configurations of the elastic inclusion, filled with a cubic anisotropic material. An investigation of the effect of the various parameters entering the problem, such as the scatterer’s degree of anisotropy, the polarization of the elastic point source located at the sampling point and the noise level in the synthetic far-field data, on the reconstructed geometric profiles’ quality,is carried out. In the fourth chapter, the FM is elaborated for the shape reconstruction of a penetrable isotropic elastic body from the knowledge of the far-field pattern of the scattered fields for plane incident waves. The theoretical analysis is conducted in three dimensions and focuses on deriving a factorization of the far-field operator, which is the cornerstone for the applicability of the particular inversion scheme, and investigating thorougly the properties of the involved operators. This investigation gave birth to a number of interesting by-products and one of them, namely, a regularity estimate for the solution of a particular form of the corresponding interior transmission problem, is the subject matter of appendix C. By means of the proposed factorization, a series of theorems, which finally lead to an explicit characterization of the scattering obstacle, is then proved. In the end of the chapter, the performance of the investigated inverse scattering technique is demonstrated by applying it to specific two-dimensional elastic scatterer reconstruction problems involving different scatterer configurations and various choices for their constitutive parameters. The effect of using different levels of additive random noise in the forward synthetic data and combining results obtained for different polarizations of the elastic point source located at the sampling point, on the quality of the reconstructed profiles, is also examined. Finally, chapter five draws the conclusions that flow from the foregoing chapters and discusses the contribution of this doctoral thesis. A brief discussion about possible future studies is also included.

scholarly journals Crystallinity fitting using cellulose crystallite models

2014 ◽  
Vol 70 (a1) ◽  
pp. C1135-C1135
Author(s):  
Patrik Ahvenainen ◽  
Ritva Serimaa
Keyword(s):  
Diffraction Pattern ◽  
Cell Structure ◽  
Unit Cell ◽  
Scattering Data ◽  
Crystalline Cellulose ◽  
Two Dimensional ◽  
Cellulose Crystallite ◽  
Cellulose Iβ ◽  
Diffraction Peaks ◽  
Unit Cell Structure

Cellulose is the most abundant biopolymer on Earth and hence it has enormous potential as a source of renewable energy. The nanoscale properties of cellulose are also import for the wood and papermaking industries. The atomic level structure of naturally occurring cellulose Iβ allomorph is well known [1] and this atomistic model is employed in this study for the cellulose unit cell structure. The cellulose crystallinity cannot be measured directly with scattering methods, but the crystallinity of the sample can be estimated by fitting models of crystalline and amorphous contributions to the sample intensity profile. The crystallinity fitting can be enhanced by improving the cellulose fitting model or the amorphous model. We focus on the cellulose crystallite model. The nanoscale level organization of crystalline cellulose in different plant materials is less well established that the unit cell structure of cellulose Iβ. Information on the texture of the sample is obtained efficiently by measuring the sample with a two-dimensional detector. The two-dimensional diffraction pattern can be used to obtain a wealth of information in one measurement, including the crystallite size, crystallite orientation and the crystallinity of the sample. The small size of cellulose crystallites in the wood cell wall limits the information obtainable from the diffraction pattern as the diffraction peaks widen and overlap. The overlapping of certain diffraction peaks can be studied at least qualitatively by computing the diffraction patterns from crystallite models of varying dimensions. Different models for cellulose crystallite have been suggested in the literature, such as the 36 chain model [2]. We investigate how the crystallinity fitting is influenced by the selected cellulose crystallite model and evaluate the suitability of different models to experimental X-ray scattering data of plant material, wood and highly crystalline cellulose.

Two-Dimensional Diffraction Pattern by a Silk Cloth

2020 ◽  
Vol 58 (1) ◽  
pp. 46-47
Author(s):  
Ravi Kant Avvari
Keyword(s):  
Diffraction Pattern ◽  
Two Dimensional ◽  
Silk Cloth

Far-field focusing of acoustic waves by a two-dimensional phononic crystal with surface grating

2009 ◽  
Vol 87 (5) ◽  
pp. 57003 ◽  
Author(s):  
Zhaojian He ◽  
Xiaochun Li ◽  
Ke Deng ◽  
Jun Mei ◽  
Zhengyou Liu
Keyword(s):  
Acoustic Waves ◽  
Phononic Crystal ◽  
Far Field ◽  
Two Dimensional ◽  
Surface Grating

Flow past a rotationally oscillating cylinder

2013 ◽  
Vol 735 ◽  
pp. 307-346 ◽  
Author(s):  
S. Kumar ◽  
C. Lopez ◽  
O. Probst ◽  
G. Francisco ◽  
D. Askari ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Three Dimensional ◽  
Far Field ◽  
Two Dimensional ◽  
Flow Past ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Flow Visualizations ◽  
Hydrogen Bubble Technique

AbstractFlow past a circular cylinder executing sinusoidal rotary oscillations about its own axis is studied experimentally. The experiments are carried out at a Reynolds number of 185, oscillation amplitudes varying from $\mathrm{\pi} / 8$ to $\mathrm{\pi} $, and at non-dimensional forcing frequencies (ratio of the cylinder oscillation frequency to the vortex-shedding frequency from a stationary cylinder) varying from 0 to 5. The diagnostic is performed by extensive flow visualization using the hydrogen bubble technique, hot-wire anemometry and particle-image velocimetry. The wake structures are related to the velocity spectra at various forcing parameters and downstream distances. It is found that the phenomenon of lock-on occurs in a forcing frequency range which depends not only on the amplitude of oscillation but also the downstream location from the cylinder. The experimentally measured lock-on diagram in the forcing amplitude and frequency plane at various downstream locations ranging from 2 to 23 diameters is presented. The far-field wake decouples, after the lock-on at higher forcing frequencies and behaves more like a regular Bénard–von Kármán vortex street from a stationary cylinder with vortex-shedding frequency mostly lower than that from a stationary cylinder. The dependence of circulation values of the shed vortices on the forcing frequency reveals a decay character independent of forcing amplitude beyond forcing frequency of ${\sim }1. 0$ and a scaling behaviour with forcing amplitude at forcing frequencies ${\leq }1. 0$. The flow visualizations reveal that the far-field wake becomes two-dimensional (planar) near the forcing frequencies where the circulation of the shed vortices becomes maximum and strong three-dimensional flow is generated as mode shape changes in certain forcing parameter conditions. It is also found from flow visualizations that even at higher Reynolds number of 400, forcing the cylinder at forcing amplitudes of $\mathrm{\pi} / 4$ and $\mathrm{\pi} / 2$ can make the flow field two-dimensional at forcing frequencies greater than ${\sim }2. 5$.

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