scholarly journals OPTIMAL FOCUSING FOR MONOCHROMATIC SCALAR AND ELECTROMAGNETIC WAVES

2011 ◽  
Vol 23 (08) ◽  
pp. 839-863
Author(s):  
JEFFREY RAUCH
Keyword(s):  
Wave Equation ◽  
Electric Field ◽  
Electromagnetic Waves ◽  
Field Energy ◽  
Scalar Case ◽  
Far Field ◽  
Maxwell’S Equation ◽  
Maximum Field ◽  
Optimal Focusing ◽  
Maxwell's Equation

For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in the scalar case is radial. In the case of Maxwell's equation, the electric field maximizing the value at the origin follows longitude lines on the sphere at infinity. In dimension d = 3, the highest electric field for Maxwell's equation is smaller by a factor 2/3 than the highest corresponding scalar waves. The highest electric field densities on the balls BR(0) occur as R → 0. The density dips to half max at R approximately equal to one third the wavelength. For these small R, the extremizing fields are identical to those that attain the maximum field intensity at the origin.

The Electric Field in Maxwell's Equations

1978 ◽  
Vol 15 (2) ◽  
pp. 169-171 ◽  
Author(s):  
Z. L. Budrikis
Keyword(s):  
Electric Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Coulomb Force ◽  
Maxwell’S Equation ◽  
Ohm’S Law ◽  
Ohm's Law ◽  
Maxwell's Equation

The field E in Maxwell's equation curl E = – δB/δ t is limited to induction and Coulomb force. It does not extend to all phenomena that are included in E of Ohm's law, J = σE. Maxwell's equation would need another term to account for additional vorticity of the E in Ohm's law.

scholarly journals Bunch Expansion as a Cause for Pulsar Radio Emissions

2021 ◽  
Vol 923 (1) ◽  
pp. 99
Author(s):  
Jan Benáček ◽  
Patricio A. Muñoz ◽  
Jörg Büchner
Keyword(s):  
Electric Field ◽  
Electromagnetic Waves ◽  
Plasma Heating ◽  
Plasma Temperature ◽  
Weighting Factor ◽  
Field Energy ◽  
Initial Kinetic Energy ◽  
Pulsar Radio ◽  
Electron Positron ◽  
Pic Code

Abstract Electromagnetic waves due to electron–positron clouds (bunches), created by cascading processes in pulsar magnetospheres, have been proposed to explain the pulsar radio emission. In order to verify this hypothesis, we utilized for the first time Particle-in-Cell (PIC) code simulations to study the nonlinear evolution of electron–positron bunches dependant on the initial relative drift speeds of electrons and positrons, plasma temperature, and distance between the bunches. For this sake, we utilized the PIC code ACRONYM with a high-order field solver and particle weighting factor, appropriate to describe relativistic pair plasmas. We found that the bunch expansion is mainly determined by the relative electron–positron drift speed. Finite drift speeds were found to cause the generation of strong electrostatic superluminal waves at the bunch density gradients that reach up to E ∼ 7.5 × 105 V cm−1 (E/(m e c ω p e −1) ∼ 4.4) and strong plasma heating. As a result, up to 15% of the initial kinetic energy is transformed into the electric field energy. Assuming the same electron and positron distributions, we found that the fastest (in the bunch reference frame) particles of consecutively emitted bunches eventually overlap in momentum (velocity) space. This overlap causes two-stream instabilities that generate electrostatic subluminal waves with electric field amplitudes reaching up to E ∼ 1.9 × 104 V cm−1 (E/(m e c ω p e −1) ∼ 0.11). We found that in all simulations the evolution of electron–positron bunches may lead to the generation of electrostatic superluminal or subluminal waves, which, in principle, can be behind the observed electromagnetic emissions of pulsars in the radio wave range.

MUTUAL NONLINEAR INTERACTION OF A NUMBER OF ELECTROMAGNETIC WAVES IN A PLASMA

1963 ◽  
Vol 41 (10) ◽  
pp. 1702-1711 ◽  
Author(s):  
Mahendra Singh Sodha ◽  
Carl J. Palumbo
Keyword(s):  
Wave Equation ◽  
Electric Fields ◽  
Current Density ◽  
Nonlinear Interaction ◽  
Electromagnetic Waves ◽  
Physical Significance ◽  
Mutual Interaction ◽  
Modulated Waves ◽  
Boltzmann's Equation ◽  
Uniform Plasma

In this communication the authors have obtained an expression for current density in a slightly ionized uniform plasma in the presence of a number of electric fields of different frequencies by solving the appropriate Boltzmann's equation. This expression along with the wave equation has been used to investigate the nonlinear mutual interaction of a number of electromagnetic waves, propagating in a plasma. Limitations of the present analysis have also been indicated and the physical significance of the results has been discussed. The technique has also been applied to investigate the mutual interaction of amplitude-modulated waves, and the results express a generalization of Luxembourg effect to a number of strong modulated waves.

Transmissive 2-bit anisotropic coding metasurface

2022 ◽  
Author(s):  
Pengtao Lai ◽  
Zenglin Li ◽  
Wei Wang ◽  
Jia Qu ◽  
Liang Wei Wu ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Electromagnetic Wave ◽  
Circular Polarization ◽  
Orbital Angular Momentum ◽  
Electromagnetic Waves ◽  
Beam Splitter ◽  
Far Field ◽  
Polarization Conversion ◽  
Field Patterns ◽  
Phase Profile

Abstract Coding metasurfaces have attracted tremendous interests due to unique capabilities of manipulating electromagnetic wave. However, archiving transmissive coding metasurface is still challenging. Here we propose a transmissive anisotropic coding metasurface that enables the independent control of two orthogonal polarizations. The polarization beam splitter and the OAM generator have been studied as typical applications of anisotropic 2-bit coding metasurface. The simulated far field patterns illustrate that the x and y polarized electromagnetic waves are deflected into two different directions, respectively. The anisotropic coding metasurface has been experimentally verified to realize an orbital angular momentum (OAM) beam with l = 2 of right-handed polarized wave, resulting from both contributions from linear-to-circular polarization conversion and the phase profile modulation. This work is beneficial to enrich the polarization manipulation field and develop transmissive coding metasurfaces.

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