Diffraction by a wide slit and complementary strip. I

1958 ◽  
Vol 54 (4) ◽  
pp. 479-496 ◽  
Author(s):  
R. F. Millar
Keyword(s):  
Asymptotic Expression ◽  
Normal Incidence ◽  
Present Theory ◽  
Slit Width ◽  
Simple Problem ◽  
Far Field ◽  
Angle Of Incidence ◽  
Current Densities ◽  
Aperture Distribution ◽  
Wide Slit

ABSTRACTIn recent years much attention has been directed towards the asymptotic solution of diffraction problems. In the present work, consideration is given to the relatively simple problem of the diffraction of an E-polarized plane wave by an infinite slit. The solution takes the form of a series in inverse powers of the ratio of slit-width to wavelength of the incident wave, and is based on the solution by successive substitutions of a pair of integral equations. The current densities induced on both halves of the screen are calculated, from which is deduced the electric field in the slit. The far-field is determined from the aperture distribution, and an asymptotic expression is found for the transmission coefficient as a function of the angle of incidence and the ratio of slit-width to wavelength.While most previous work has been confined to near-normal incidence, the present theory is uniformly valid for all angles of incidence.

Diffraction by a wide slit and complementary strip. II

1958 ◽  
Vol 54 (4) ◽  
pp. 497-511 ◽  
Author(s):  
R. F. Millar
Keyword(s):  
Transmission Coefficient ◽  
Infinite Series ◽  
Present Method ◽  
Detailed Comparison ◽  
Slit Width ◽  
Accurate Information ◽  
Induced Current ◽  
Transmission Coefficients ◽  
Current Densities ◽  
Wide Slit

ABSTRACTThe notions developed in Part I in connexion with the diffraction of an E-polar-ized wave are here applied to the case of H-polarization. Induced current densities, aperture and far fields, and the transmission coefficient are again found in the form of infinite series in inverse powers of the slit-width to wavelength ratio. By means of Babinet's principle, the solution for diffraction by a strip is obtained.A detailed comparison is made with values of the transmission coefficients for both polarizations found previously and by the present method. It appears that this theory provides accurate information when the slit-width is greater than about a wavelength.

On resolving fine periodic microstructures in the optical microscope

1989 ◽  
Vol 47 ◽  
pp. 364-365
Author(s):  
W.S. Putnam ◽  
C. Viney
Keyword(s):  
Liquid Crystalline ◽  
Numerical Aperture ◽  
Polarized Light ◽  
Normal Incidence ◽  
Optical Microscope ◽  
Angle Of Incidence ◽  
Resolution Limit ◽  
Crystalline Materials ◽  
Periodic Microstructures ◽  
Liquid Crystalline Materials

Many sheared liquid crystalline materials (fibers, films and moldings) exhibit a fine banded microstructure when observed in the polarized light microscope. In some cases, for example Kevlar® fiber, the periodicity is close to the resolution limit of even the highest numerical aperture objectives. The periodic microstructure reflects a non-uniform alignment of the constituent molecules, and consequently is an indication that the mechanical properties will be less than optimal. Thus it is necessary to obtain quality micrographs for characterization, which in turn requires that fine detail should contribute significantly to image formation.It is textbook knowledge that the resolution achievable with a given microscope objective (numerical aperture NA) and a given wavelength of light (λ) increases as the angle of incidence of light at the specimen surface is increased. Stated in terms of the Abbe resolution criterion, resolution improves from λ/NA to λ/2NA with increasing departure from normal incidence.

scholarly journals Stabilizing electrodeposition in elastic solid electrolytes containing immobilized anions

2016 ◽  
Vol 2 (7) ◽  
pp. e1600320 ◽  
Author(s):  
Mukul D. Tikekar ◽  
Lynden A. Archer ◽  
Donald L. Koch
Keyword(s):  
Elastic Solid ◽  
Present Theory ◽  
Metal Electrode ◽  
Mitigation Strategies ◽  
Factors Affecting ◽  
Wide Range ◽  
Current Densities ◽  
Morphological Instabilities ◽  
The Stability

Ion transport–driven instabilities in electrodeposition of metals that lead to morphological instabilities and dendrites are receiving renewed attention because mitigation strategies are needed for improving rechargeability and safety of lithium batteries. The growth rate of these morphological instabilities can be slowed by immobilizing a fraction of anions within the electrolyte to reduce the electric field at the metal electrode. We analyze the role of elastic deformation of the solid electrolyte with immobilized anions and present theory combining the roles of separator elasticity and modified transport to evaluate the factors affecting the stability of planar deposition over a wide range of current densities. We find that stable electrodeposition can be easily achieved even at relatively high current densities in electrolytes/separators with moderate polymer-like mechanical moduli, provided a small fraction of anions are immobilized in the separator.

Tiny impacts for far-field focusing by plasmonic lens with a free slit-width design

2017 ◽  
Vol 56 (11) ◽  
pp. 1 ◽  
Author(s):  
Tingzhao Fu ◽  
Shaohui Cui ◽  
Huan Wang ◽  
Yang Xia ◽  
Chaobo Li
Keyword(s):  
Slit Width ◽  
Far Field ◽  
Plasmonic Lens

THE INFLUENCE OF A CRITICAL ANGLE ON AN ORIENTATION OF RADIATION OF A SHEAR WAVE THE ANGLE BEAM PROBE

2019 ◽  
pp. 14-25
Author(s):  
V. N. Danilov
Keyword(s):  
Shear Wave ◽  
Critical Angle ◽  
Asymptotic Expression ◽  
Shear Waves ◽  
Far Field ◽  
Directivity Characteristic ◽  
The Third ◽  
Working Frequency

In a far field it is received asymptotic expression of displacement of the shear waves transmitted in the elastic environment by the angle beam probe in view of features of radiation of such waves under a angle of probe, coming nearer to the third critical. At sufficient remoteness from a critical corner this expression passes in received earlier in geometroacustical approximation. The estimations carried out for steel have shown, that for converters with nominal angles of probe 37 – 40 influence of this critical angle causes increase of an angle of registration of a maximum of the signal, observed earlier experimentally. This feature is influenced as distance up to points of registration of a shear wave, and with working frequency of the angle beam probe and its size piezoplate (width of the directivity characteristic).

scholarly journals Enhanced harmonic generation by propagation of two-color p-polarized laser beams in plasma

2017 ◽  
Vol 35 (1) ◽  
pp. 182-189 ◽  
Author(s):  
E. Agrawal ◽  
N.K. Verma ◽  
P. Jha
Keyword(s):  
Plasma Density ◽  
Normal Incidence ◽  
Laser Beams ◽  
Angle Of Incidence ◽  
Arbitrary Integer ◽  
Third Harmonic ◽  
Harmonic Radiation ◽  
Fundamental Frequencies ◽  
Order Of Magnitude ◽  
Spatially Varying

AbstractA theoretical model is developed for studying the generation of third-harmonic radiation by the interaction of obliquely incident, two-color p-polarized laser beams with spatially varying plasma density. The ratio of the fundamental frequencies of the two laser beams are considered to be an arbitrary integer. The amplitude of harmonic radiation obtained by oblique incidence of two-color laser fields propagating in homogeneous plasma is enhanced in comparison with that obtained by normal incidence of two-color laser beams. The periodicity of the plasma density allows the harmonic radiation to be phase-matched, leading to further increase in the amplitude of phase-matched harmonic radiation by an order of magnitude. The amplitude of the generated harmonic radiation increases with the increase in angle of incidence.

EFFECTS OF ANGLE OF INCIDENCE OF SH-WAVE AT THE BASIN-EDGE ON THE CHARACTRISTICS OF BASIN-EDGE INDUCED LOVE WAVE

2012 ◽  
Vol 06 (01) ◽  
pp. 1250006 ◽  
Author(s):  
J. P. NARAYAN
Keyword(s):  
Soil Column ◽  
Normal Incidence ◽  
Love Waves ◽  
Angle Of Incidence ◽  
Percentage Increase ◽  
Sh Wave ◽  
Order Accuracy ◽  
Fundamental Wavelength ◽  
Aggravation Factor ◽  
Basin Edge

This paper presents the effects of angle of incidence of SH-wave at the basin-edge on the characteristics of basin-edge induced Love waves and associated strain and aggravation factor (aggravation factor is simply the extra spectral amplification due to complex 2D site effects over the 1D response of the soil column). The linear seismic responses of basin-edge model with various edge-slopes were computed using SH-wave finite difference algorithm with second-order accuracy in time and fourth-order accuracy in space. The analysis of simulated results revealed an increase of amplitude of induced Love waves, differential ground motion (strain), and aggravation factor with decrease of basin-edge slope and increase of angle of incidence of SH-wave at the basin-edge. Maximum strain of the order of 9.23 × 10-4 (for 1.0 cm peak ground displacement at the bedrock) was obtained at an offset of 60.0 m (0.47λF0, where λF0 is the fundamental wavelength), in case of 84.4° angle of incidence of SH-wave. Further, the percentage increase of strain with respect to the strain in case of normal incidence of SH-wave was almost equal to the angle of incidence of SH-wave at the basin-edge.

Collimated Sputtering of Titanium and Titanium Nitride Films

MRS Bulletin ◽  
1995 ◽  
Vol 20 (11) ◽  
pp. 42-45 ◽  
Author(s):  
James G. Ryan ◽  
Stephen B. Brodsky ◽  
Tomio Katata ◽  
Makoto Honda ◽  
Naohiro Shoda ◽  
...  
Keyword(s):  
Physical Vapor Deposition ◽  
Normal Incidence ◽  
Angle Of Incidence ◽  
Tin Films ◽  
Sputtered Films ◽  
Obliquely Incident ◽  
Grain Structures ◽  
Pass Through ◽  
Full Face ◽  
Contact Adhesion

Collimated sputtering is a physical vapor deposition (PVD) method where a collimator is inserted between a conventional “full-face-erosion” sputtering target and a substrate (Figure 1). The collimator is a plate of hexagonal cells that acts as a filter to remove obliquely incident atoms before they arrive at the substrate. Only material with a nearly normal incidence trajectory may pass through the collimator and deposit on the substrate. Collimated sputtering was initially evaluated for conductor-level depositions in order to improve the filling of recessed features. Although the method has been successfully used to fill damascene structures, depositing thick conductor films is inefficient because most of the sputtered material is captured by the collimator, causing the collimator to clog quickly, necessitating frequent replacement.A more common use of collimated sputtering is associated with the deposition of thin “liner” films. For example, thin, collimated aluminum alloy films have been used as underlayers for aluminum reflow processes. Also, collimated Ti/TiN films are used as contact/adhesion layers for chemically vapor-deposited (CVD) W metallization. Collimation provides better bottom and sidewall coverage for small, high aspect-ratio features than conventionally sputtered films do.Coliimated sputtered films often exhibit unique properties because the angle of incidence of depositing atoms is controlled. Collimated AlMg alloys have superior electromigration resistance compared to noncollimated AlMg films. Collimated TiN films appear to exhibit denser grain structures when compared to films deposited with higher amounts of obliquely incident flux (Figure 2).

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