Investigation on multilayer microstructure grating for three-port splitting

2016 ◽  
Vol 30 (16) ◽  
pp. 1650195
Author(s):  
Wenhao Shu ◽  
Bo Wang ◽  
Hao Pei ◽  
Hongtao Li ◽  
Li Chen ◽  
...  
Keyword(s):  
Beam Splitter ◽  
Single Layer ◽  
Zeroth Order ◽  
First Order ◽  
Transmission Grating ◽  
Dielectric Layers ◽  
Incident Waves ◽  
Reflection Grating ◽  
Independent Property ◽  
Polarization Independent

A new structure of microstructure reflection three-port beam splitter grating is described in this paper. The grating includes two dielectric layers and a metal slab on the substrate, where incident waves are reflected into the zeroth-order and the ± first-order with polarization-independent property. With the optimized grating profile, reflection efficiencies’ ratios between the first-order and the zeroth-order can reach 0.998 and 1.001 for TE and TM polarizations, respectively. Especially, the reflection grating can diffract efficiencies more than 30% into the ± first-order and the zeroth-order with the incident angular bandwidth of −1.9–1.9[Formula: see text] for TM polarization, which can have merits compared with single-layer transmission grating.

Angle and polarization-independent miniaturized UWB FSS design

2021 ◽  
pp. 1-9
Author(s):  
Yanning Yuan ◽  
Yuchen Zhao ◽  
Xiaoli Xi
Keyword(s):  
Design Method ◽  
Incident Angle ◽  
Stop Band ◽  
Single Layer ◽  
Wireless Systems ◽  
Frequency Selective Surface ◽  
Ultra Wideband ◽  
Band Frequency ◽  
Gain Enhancement ◽  
Polarization Independent

Abstract A single-layer ultra-wideband (UWB) stop-band frequency selective surface (FSS) has several advantages in wireless systems, including a simple design, low debugging complexity, and an appropriate thickness. This study proposes a miniaturized UWB stop-band FSS design. The proposed FSS structure consists of a square-loop and metalized vias that are arranged on a single layer substrate; it has an excellent angle and polarization-independent characteristics. At an incident angle of 60°, the polarization response frequencies of the transverse electric and magnetic modes only shifted by 0.003 f0 and 0.007 f0, respectively. The equivalent circuit models of the square-loop and metallized vias structure are analysed and the accuracy of the calculation is evaluated by comparing the electromagnetic simulation. The 20 × 20 array constitutes an FSS reflector with a unit size of 4.2 mm × 4.2 mm (less than one-twentieth of the wavelength of 3 GHz), which realizes an UWB quasi-constant gain enhancement (in-band flatness is <0.5 dB). Finally, the simulation results were verified through sample processing and measurement; consistent results were obtained. The FSS miniaturization design method proposed in this study could be applied to the design of passband FSS (complementary structure), antennas and filters, among other applications.

scholarly journals Perturbation Solution for One-Dimensional Flow to a Constant-Pressure Boundary in a Stress-Sensitive Reservoir

2021 ◽  
Author(s):  
Amarjot Singh Bhullar ◽  
Gospel Ezekiel Stewart ◽  
Robert W. Zimmerman
Keyword(s):  
Approximate Solution ◽  
Pore Pressure ◽  
Constant Pressure ◽  
Initial Permeability ◽  
Order Perturbation ◽  
Zeroth Order ◽  
One Dimensional ◽  
First Order ◽  
Outflow Boundary ◽  
Perturbation Solutions

Abstract Most analyses of fluid flow in porous media are conducted under the assumption that the permeability is constant. In some “stress-sensitive” rock formations, however, the variation of permeability with pore fluid pressure is sufficiently large that it needs to be accounted for in the analysis. Accounting for the variation of permeability with pore pressure renders the pressure diffusion equation nonlinear and not amenable to exact analytical solutions. In this paper, the regular perturbation approach is used to develop an approximate solution to the problem of flow to a linear constant-pressure boundary, in a formation whose permeability varies exponentially with pore pressure. The perturbation parameter αD is defined to be the natural logarithm of the ratio of the initial permeability to the permeability at the outflow boundary. The zeroth-order and first-order perturbation solutions are computed, from which the flux at the outflow boundary is found. An effective permeability is then determined such that, when inserted into the analytical solution for the mathematically linear problem, it yields a flux that is exact to at least first order in αD. When compared to numerical solutions of the problem, the result has 5% accuracy out to values of αD of about 2—a much larger range of accuracy than is usually achieved in similar problems. Finally, an explanation is given of why the change of variables proposed by Kikani and Pedrosa, which leads to highly accurate zeroth-order perturbation solutions in radial flow problems, does not yield an accurate result for one-dimensional flow. Article Highlights Approximate solution for flow to a constant-pressure boundary in a porous medium whose permeability varies exponentially with pressure. The predicted flowrate is accurate to within 5% for a wide range of permeability variations. If permeability at boundary is 30% less than initial permeability, flowrate will be 10% less than predicted by constant-permeability model.

Analysis of a first‐order reflection grating with second‐harmonic generation

1991 ◽  
Vol 69 (3) ◽  
pp. 1201-1204 ◽  
Author(s):  
Z. Weissman ◽  
A. Hardy ◽  
E. Marom ◽  
S. R. J. Brueck
Keyword(s):  
Second Harmonic Generation ◽  
Harmonic Generation ◽  
Second Harmonic ◽  
First Order ◽  
Reflection Grating ◽  
Order Reflection

scholarly journals ANISOTROPIC NULL STRING COSMOLOGIES

1998 ◽  
Vol 13 (39) ◽  
pp. 3169-3177 ◽  
Author(s):  
IOANNIS GIANNAKIS ◽  
K. KLEIDIS ◽  
A. KUIROUKIDIS ◽  
D. PAPADOPOULOS
Keyword(s):  
Equations Of Motion ◽  
String Tension ◽  
Perturbative Expansion ◽  
Speed Of Light ◽  
Zeroth Order ◽  
First Order ◽  
Cosmological Background ◽  
String Propagation ◽  
Analytical Expressions ◽  
Null String

We study string propagation in an anisotropic, cosmological background. We solve the equations of motion and the constraints by performing a perturbative expansion of the string coordinates in powers if c2 — the worldsheet speed of light. To zeroth order the string is approximated by a tensionless string (since c is proportional to the string tension T). We obtain exact, analytical expressions for the zeroth- and first-order solutions and we discuss some cosmological implications.

A Slender-Ship Theory of Wave Resistance

1983 ◽  
Vol 27 (01) ◽  
pp. 13-33
Author(s):  
Francis Noblesse
Keyword(s):  
Froude Number ◽  
Wave Resistance ◽  
Successive Approximations ◽  
Zeroth Order ◽  
Remarkable Effect ◽  
Ship Wave ◽  
First Order ◽  
Wigley Hull ◽  
Low Froude Number ◽  
The Waves

A new slender-ship theory of wave resistance is presented. Specifically, a sequence of explicit slender-ship wave-resistance approximations is obtained. These approximations are associated with successive approximations in a slender-ship iterative procedure for solving a new (nonlinear integro-differential) equation for the velocity potential of the flow caused by the ship. The zeroth, first, and second-order slender-ship approximations are given explicitly and examined in some detail. The zeroth-order slender-ship wave-resistance approximation, r(0) is obtained by simply taking the (disturbance) potential, ϕ, as the trivial zeroth-order slender-ship approximation ϕ(0) = 0 in the expression for the Kochin free-wave amplitude function; the classical wave-resistance formulas of Michell [1]2 and Hogner [2] correspond to particular cases of this simple approximation. The low-speed wave-resistance formulas proposed by Guevel [3], Baba [4], Maruo [5], and Kayo [6] are essentially equivalent (for most practical purposes) to the first-order slender-ship low-Froude-number approximation, rlF(1), which is a particular case of the first-order slender-ship approximation r(1): specifically, the first-order slender-ship wave-resistance approximation r(1) is obtained by approximating the potential ϕ in the expression for the Kochin function by the first-order slender-ship potential ϕ1 whereas the low-Froude-number approximation rlF(1) is associated with the zero-Froude-number limit ϕ0(1) of the potentialϕ(1). A major difference between the first-order slender-ship potential ϕ(1) and its zero-Froude-number limit ϕ0(1) resides in the waves that are included in the potential ϕ(1) but are ignored in the zero-Froude-number potential ϕ0(1). Results of calculations by C. Y. Chen for the Wigley hull show that the waves in the potential ϕ(1) have a remarkable effect upon the wave resistance, in particular causing a large phase shift of the wave-resistance curve toward higher values of the Froude number. As a result, the first-order slender-ship wave-resistance approximation in significantly better agreement with experimental data than the low-Froude-number approximation rlF(1) and the approximations r(0) and rM.

A Very Tentative Metaskeptical Endorsement of Eliminativism about Moral Responsibility

2012 ◽  
Author(s):  
Tamler Sommers
Keyword(s):  
Moral Responsibility ◽  
Historical Period ◽  
First Order ◽  
Practical Implications ◽  
Independent Property

This chapter argues that moral responsibility is not a mind-independent property like “transparent” that can be assigned objectively or universally when certain conditions are met. The answer to the question of whether we can be morally responsible boils down to a subjective all-things-considered judgment that takes many factors into account, including the ethical and practical consequences of each alternative. It examines the case for first-order skepticism or eliminativism about moral responsibility, and offers a very tentative endorsement of this position in the context of our environment, historical period, and circumstances. It begins by examining the moral and practical implications of denying moral responsibility and adopting the objective attitude on an exclusive basis. Next, it considers arguments that attempt to explain away or debunk the intuition that people can be morally responsible for their behavior. Finally, it discusses an important concession to compatibilism, one that prevents the author from arriving at a more confident endorsement of the eliminativist conclusion.

Synthesis, Properties and Application in Optical Memory of a Photochromic Diarylethene Bearing Pyrimidine and Pyridine Ring

2012 ◽  
Vol 490-495 ◽  
pp. 3733-3737
Author(s):  
Shu Hong Jing ◽  
Shou Zhi Pu ◽  
Shi Qiang Cui
Keyword(s):  
Uv Light ◽  
Optical Memory ◽  
Order Reaction ◽  
Pmma Film ◽  
Zeroth Order ◽  
First Order ◽  
Synthesis Properties ◽  
Fluorescence Switching ◽  
Photochromic Reaction ◽  
Hexane Solution

A new photochromic diarylethene compound, 1-(2,4-dimethoxy-5-pyrimidine)-2-[2-methyl-5-(3-pyridine)-3-thienyl]perfluorocyclopentene(1a), was synthesized, and its photochromic reactivity, fluorescent and electrochemical property were also investigated. Diarylethene 1a changed the color from colorless to pink upon irradiation with UV light, in which absorption maxima were observed at 520 and 519 nm in hexane and PMMA film, respectively. The the photochromic reaction kinetics indicated that the cyclization processes of 1 belong to the zeroth order reaction and the cycloreversion process belong to the first order reaction. This new photochromic system also exhibited remarkable fluorescence switching in hexane solution and this new photochromic system also exhibited remarkable optical storage character.

Theory & Performance of Holographically-Formed Stigmatic X-Ray Gratings

1975 ◽  
Vol 19 ◽  
pp. 643-656
Author(s):  
R. J. Speer
Keyword(s):  
Fringe Pattern ◽  
Optical Design ◽  
Grazing Incidence ◽  
Laser Fusion ◽  
Molecular Chemistry ◽  
X Ray ◽  
First Order ◽  
Imaging Theory ◽  
Reflection Grating ◽  
Aberration Corrected

Holographically-formed X-ray reflection grating scan now be constructed with competitive groove efficiency to classically ruled types, down to a short wavelength diffracting limit of several angstroms.The gratings can be generated on any surface capable of intersecting the interference fringe pattern without shadowing. This fact alone brings several new X-ray optical design possibilities within reach, for example, by combining plane construction waves with steep aspheric substrates. The first order imaging theory of the grazing incidence mounting is discussed and compared to measured performance for aberration corrected stigmatic types.A new 5 meter spectrograph has also been constructed with applications in molecular chemistry, laser fusion research and synchro tronspectroscopy. The unit is available with fully prefocussed holographic and classical X-ray grating optics, and uses the precision miniature camera principle of fully interchangeable lenses, but applied, in this case to the entrance slit, grating and detector modules.

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