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Related Concept Videos

Gauss's Law: Spherical Symmetry01:26

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...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Spherical and Cylindrical Capacitor01:26

Spherical and Cylindrical Capacitor

A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...
Spherical Coordinates01:23

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...

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Agarose-based Tissue Mimicking Optical Phantoms for Diffuse Reflectance Spectroscopy
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Spherical cloaking with homogeneous isotropic multilayered structures.

Cheng-Wei Qiu1, Li Hu, Xiaofei Xu

  • 1Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore. eleqc@nus.edu.sg

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

We demonstrate practical spherical cloaking using layered isotropic materials. This method mimics anisotropic cloaks, enabling invisibility through effective medium theory and multilayer dielectric coatings.

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Area of Science:

  • Electromagnetism
  • Materials Science
  • Optics

Background:

  • Electromagnetic cloaking aims to render objects invisible to electromagnetic waves.
  • Traditional cloaking often relies on complex anisotropic materials.
  • Practical realization of cloaking devices remains a significant challenge.

Purpose of the Study:

  • To propose a practical method for achieving spherical electromagnetic cloaking.
  • To utilize layered structures of homogeneous isotropic materials for cloaking.
  • To simplify the modeling and fabrication of cloaking devices.

Main Methods:

  • Mimicking anisotropic cloaks using alternating thin layers of isotropic dielectrics.
  • Applying effective medium theory to determine material properties (permittivity and permeability) for each layer.
  • Utilizing Mie theory for simplified modeling.
  • Performing eigenmode analysis to understand discretization effects in multilayers.

Main Results:

  • A practical design for spherical electromagnetic cloaking using layered isotropic dielectrics is proposed.
  • The effective medium theory provides a pathway to achieve desired electromagnetic properties.
  • Mie theory facilitates efficient modeling of the cloaked object.
  • Eigenmode analysis offers insights into the discretization process.

Conclusions:

  • Layered isotropic materials offer a feasible approach to spherical electromagnetic cloaking.
  • The proposed method simplifies both the theoretical modeling and practical fabrication of cloaking devices.
  • This work paves the way for more accessible invisibility technologies.