# Energy Flow in a Negative-Index Material

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This Demonstration shows the energy flows from a dipole source ("object") near a slab made of negative index material (NIM) or left-handed material (LHM). In contrast to the conventional picture of energy flows from a source to an image [1,2] ( from left to right in our case), we show that for small distances between the dipole and the NIM slab (regime of a "perfect" lens), the energy in such systems does not go from the object to its "image", but from the object and its "image" to an intersection point inside a metamaterial layer, or in the opposite direction. This Demonstration is based on an analytical solution of Maxwell's equations for an ‐oriented dipole ("object") placed at a distance from a NIM slab of width [3,4]. The solution is a combination of fields of three ‐oriented dipoles. Two of them are sources of energy while third dipole is sink of energy.

Contributed by: Vasily Klimov (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: energy flows when the dipole is far from the slab ()

Snapshot 2: energy flows in critical geometry, where a pair of source-sink dipoles appear at

Snapshot 3: energy flows in a regime of a "perfect" lens ()

Snapshots 1-3 show the transformation of energy flows from a conventional picture to the highly nontrivial picture of a "perfect lens".

References:

[1] V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of and ," *Sov. Phys. Usp.*, 10, 1968 p. 509.

[2] J. B. Pendry, " Negative Refraction Makes a Perfect Lens," *Phys. Rev. Lett.*, 85, 2000 p. 3966.

[3] V. Klimov, "Novel Approach to a Perfect Lens," http://arxiv.org/abs/0811.4381.

[4] V. Klimov, "Novel Approach to a Perfect Lens," *JETP Letters*, 89(5), 2009.

## Permanent Citation

"Energy Flow in a Negative-Index Material"

http://demonstrations.wolfram.com/EnergyFlowInANegativeIndexMaterial/

Wolfram Demonstrations Project

Published: March 7 2011