DIFFRACTION OF 3.2 CM. ELECTROMAGNETIC WAVES BY DIELECTRIC RODS: I. LUCITE AND TENITE 1 IN. DIAMETER CYLINDERS

1956 ◽  
Vol 34 (6) ◽  
pp. 546-554 ◽  
Author(s):  
M. K. Subbarao ◽  
A. B. McLay

Diffraction patterns of lucite and tenite cylindrical rods of approximately one inch diameter, in a nearly plane beam of square-wave modulated 3.2 cm. waves with electric vector parallel to the cylinder axis, have been measured in several planes transverse to the incident beam direction. Patterns are compared with theoretical ones (Froese and Wait 1954) and with ones obtained earlier, under similar experimental conditions, for brass and hard rubber cylinders (Wiles and McLay 1954). Some general marked trends in the patterns of the four rods, comprising a conductor, two nearly lossless dielectrics with different dielectric constants, and a lossier dielectric, are related to the effects of transmission and/or surface reflection expected from geometrical optics considerations.

1956 ◽  
Vol 34 (6) ◽  
pp. 555-562 ◽  
Author(s):  
A. B. McLay ◽  
M. K. Subbarao

Diffraction patterns of a lucite cylinder and a half cylinder in a nearly plane beam of square-wave modulated 3.2 cm. waves, with electric vector parallel to the cylinder axis, have been measured in several planes transverse to the incident beam direction. Patterns of the half cylinder were obtained with the plane face toward and away from the source of radiation. Marked trends in the patterns are related qualitatively to the effects of transmission and surface reflection, both external and internal, expected from geometrical optics considerations.


1954 ◽  
Vol 32 (6) ◽  
pp. 372-380 ◽  
Author(s):  
A. B. McLay ◽  
S. T. Wiles

Diffraction patterns of a brass tube and a hard rubber rod, each a cylinder of 1 in. diameter, in a nearly plane beam of square-wave modulated 3 cm. waves with electric vector parallel to the cylinder axis, have been measured in several planes transverse to the incident beam direction. Experimental results for the conducting cylinder agree closely with calculations based on scalar diffraction theory. Patterns of the dielectric rod show a pronounced central peak immediately behind the rod and other intensity effects differing from the conducting cylinder patterns, particularly in the vicinity of the shadow.


2004 ◽  
Vol 860 ◽  
Author(s):  
Jin Li ◽  
Thomas M. Horgan ◽  
Andrew J. Gatesman ◽  
Robert H. Giles ◽  
Aram S. Karakashian ◽  
...  

ABSTRACTTwo-dimensional hexagonal photonic crystals of air columns in a wax substrate were fabricated by jet-based methods. By modifying the structure of the photonic crystals (PC), electromagnetic waves can be controlled, enabling the design of novel devices for waveguides, filters, and couplers. The jet-based processing is a solid freeforming method that can fabricate complex 2D or 3D photonic structures quickly and easily as compared to micro-machining and lithographic methods. The resolution of our 3D Systems ThermoJet® solider object printer is 300 × 400 × 600 dpi (XYZ) with the layer thickness of 0.042 mm. The wax used is a thermopolymer build material, similar to production investment casting wax material. The periodicity of the lattice of our 2D PC structures was designed to form bandstop filters in the 0.1–0.3 THz range. Transmission spectra of the structures were measured with a Bruker IFS 66v FT-IR interferometer. Photonic band gaps were observed at 0.17 THz and 0.23 THz along the Γ-M direction for both the TM and TE polarized incident beam for the PC structures with lattice constant of 0.787 mm and 0.586 mm, respectively. The location and width of the bandgaps agree with theoretical calculation based on a block-iterative frequency-domain method for Maxwell's equations in a planewave basis. To the best of our knowledge, this is the first time a jet-based process has been used successfully to fabricate PC structures at these high frequencies. However, the ThermoJet® printer as well as other current available solid freeforming technologies lack the resolution to PC structures operating in the terahertz regime. To extend this technology to terahertz applications, such as terahertz lasers, waveguides, and imaging system, a 10-fold increase in machine resolution is required to produce finer structures. Engineering materials with lower electromagnetic absorption and higher dielectric constants at terahertz frequencies are also critical to developing THz photonic bandgap technology.


Author(s):  
K. Ishizuka

The technique of convergent-beam electron diffraction (CBED) has been established. However there is a distinct discrepancy concerning the CBED pattern symmetries associated with translation symmetries parallel to the incident beam direction: Buxton et al. assumed no detectable effects of translation components, while Goodman predicted no associated symmetries. In this report a procedure used by Gjønnes & Moodie1 to obtain dynamical extinction rules will be extended in order to derive the CBED pattern symmetries as well as the dynamical extinction rules.


Author(s):  
N. J. Zaluzec

The ultimate sensitivity of microchemical analysis using x-ray emission rests in selecting those experimental conditions which will maximize the measured peak-to-background (P/B) ratio. This paper presents the results of calculations aimed at determining the influence of incident beam energy, detector/specimen geometry and specimen composition on the P/B ratio for ideally thin samples (i.e., the effects of scattering and absorption are considered negligible). As such it is assumed that the complications resulting from system peaks, bremsstrahlung fluorescence, electron tails and specimen contamination have been eliminated and that one needs only to consider the physics of the generation/emission process.The number of characteristic x-ray photons (Ip) emitted from a thin foil of thickness dt into the solid angle dΩ is given by the well-known equation


Author(s):  
Z. L. Wang

A new dynamical theory has been developed based on Yoshioka's coupled equations for describing inelastic electron scattering in thin crystals. Compared to existing theories, the primary advantage of this theory is that the incoherent summation of the diffracted intensities contributed by electrons after exciting vast numbers of different excited states has been evaluated before any numerical calculation. An additional advantage is that the phase correlations of atomic vibrations are considered, so that full lattice dynamics can be combined in the phonon scattering calculation. The new theory has been proven to be equivalent to the inelastic multislice theory, and has been applied to calculate energy-filtered diffraction patterns and images formed by phonon, single electron and valence scattered electrons.A calculated diffraction pattern of elastic and phonon scattered electrons for a parallel incident beam case is in agreement with the one observed (Fig. 1), showing thermal diffuse scattering (TDS) streaks and Kikuchi pattern.


Author(s):  
M.A. Gribelyuk ◽  
M. Rühle

A new method is suggested for the accurate determination of the incident beam direction K, crystal thickness t and the coordinates of the basic reciprocal lattice vectors V1 and V2 (Fig. 1) of the ZOLZ plans in pixels of the digitized 2-D CBED pattern. For a given structure model and some estimated values Vest and Kest of some point O in the CBED pattern a set of line scans AkBk is chosen so that all the scans are located within CBED disks.The points on line scans AkBk are conjugate to those on A0B0 since they are shifted by the reciprocal vector gk with respect to each other. As many conjugate scans are considered as CBED disks fall into the energy filtered region of the experimental pattern. Electron intensities of the transmitted beam I0 and diffracted beams Igk for all points on conjugate scans are found as a function of crystal thickness t on the basis of the full dynamical calculation.


Author(s):  
K. Ishizuka ◽  
K. Shirota

In a conventional alignment for high-resolution electron microscopy, the specimen point imaged at the viewing-screen center is made dispersion-free against a voltage fluctuation by adjusting the incident beam direction using the beam deflector. For high-resolution works the voltage-center alignment is important, since this alignment reduces the chromatic aberration. On the other hand, the coma-free alignment is also indispensable for high-resolution electron microscopy. This is because even a small misalignment of the incident beam direction induces wave aberrations and affects the appearance of high resolution electron micrographs. Some alignment procedures which cancel out the coma by changing the incident beam direction have been proposed. Most recently, the effect of a three-fold astigmatism on the coma-free alignment has been revealed, and new algorithms of coma-free alignment have been proposed.However, the voltage-center and the coma-free alignments as well as the current-center alignment in general do not coincide to each other because of beam deflection due to a leakage field within the objective lens, even if the main magnetic-field of the objective lens is rotationally symmetric. Since all the proposed procedures for the coma-free alignment also use the same beam deflector above the objective lens that is used for the voltage-center alignment, the coma-free alignment is only attained at the sacrifice of the voltage-center alignment.


Author(s):  
Kazuo Ishizuka

It is well known that taking into account spacial and temporal coherency of illumination as well as the wave aberration is important to interpret an image of a high-resolution electron microscope (HREM). This occues, because coherency of incident electrons restricts transmission of image information. Due to its large spherical and chromatic aberrations, the electron microscope requires higher coherency than the optical microscope. On an application of HREM for a strong scattering object, we have to estimate the contribution of the interference between the diffracted waves on an image formation. The contribution of each pair of diffracted waves may be properly represented by the transmission cross coefficients (TCC) between these waves. In this report, we will show an improved form of the TCC including second order derivatives, and compare it with the first order TCC.In the electron microscope the specimen is illuminated by quasi monochromatic electrons having a small range of illumination directions. Thus, the image intensity for each energy and each incident direction should be summed to give an intensity to be observed. However, this is a time consuming process, if the ranges of incident energy and/or illumination direction are large. To avoid this difficulty, we can use the TCC by assuming that a transmission function of the specimen does not depend on the incident beam direction. This is not always true, because dynamical scattering is important owing to strong interactions of electrons with the specimen. However, in the case of HREM, both the specimen thickness and the illumination angle should be small. Therefore we may neglect the dependency of the transmission function on the incident beam direction.


Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.


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