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Related Concept Videos

Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
Maxwell's Equation Of Electromagnetism01:29

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James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is represented by...
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Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
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The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
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Related Experiment Video

Updated: Jun 9, 2026

Fabrication and Operation of a Nano-Optical Conveyor Belt
11:10

Fabrication and Operation of a Nano-Optical Conveyor Belt

Published on: August 26, 2015

Electromagnetic concentrators with arbitrary geometries based on Laplace's equation.

Chengfu Yang1, Jingjing Yang, Ming Huang

  • 1School of Information Science and Engineering, Yunnan University, Kunming 650091, China.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|September 3, 2010
PubMed
Summary

A new numerical method designs arbitrary concentrators by solving Laplace's equation. This approach yields effective scattering and concentrating properties, confirmed by simulations, offering a flexible design tool.

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Area of Science:

  • Physics
  • Materials Science
  • Applied Mathematics

Background:

  • Designing electromagnetic concentrators often relies on analytical methods requiring coordinate transformations.
  • Arbitrary geometries present challenges for traditional design approaches.

Purpose of the Study:

  • To develop a general and flexible numerical method for designing concentrators with arbitrary geometries.
  • To independently obtain material parameters without coordinate transformations.

Main Methods:

  • Numerical solution of Laplace's equation to determine material parameters.
  • Design of concentrators based on numerical results.
  • Validation through full-wave simulations.

Main Results:

  • Concentrators designed using the numerical method exhibit comparable scattering and concentrating properties to those from analytical methods.
  • A slight difference in the stretching region was observed but did not impact overall design.
  • The numerical method proved general and flexible for arbitrary concentrator designs.

Conclusions:

  • The developed numerical method provides a valid and effective approach for designing arbitrary concentrators.
  • Full-wave simulations confirm the method's validity and the concentrating effects achieved.
  • This approach offers an alternative to analytical methods, simplifying the design process.