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Negative Refraction of Electromagnetic Waves
Negative index medium
(NIM) has very unusual properties. For this material, both the permittivity
ε and permeability μ are negative. The index of refraction is thus negative.
From Maxwell's equation, we have k×H=ωεE and
k×E=-ωμH. Thus for the elctromagnetic waves inside
NIM, the electric field E, magnetic field H and wave vector
k will form a left-handed triplet, so the light inside NIM is left-handed.
The energy flow in NIM which can be represented by the Poynting vector S=E×H
is always opposite to the direction of the wave vector k. For any localized wave packet, the refraction between PIM and NIM is
always negative.
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A Gaussian wave packet moving through the PIM-NIM interface. Click on the picture to see the movie. |
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A Gaussian beam moving through the PIM-NIM interface. Click on the picture to see the movie. |
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A group of 3 plane waves moving through the PIM-NIM interface. Clike on the image to see the animated gif file. |
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A Gaussian beam moving through slab of NIM. Clike on the image to see the animated gif file.
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Pendry at Imperial College proposed the idea of super lens made of a slab of NIM. He also pointed out that for near field imaging, n=-1 is not necessarily required. Instead for P-polarized evanescent waves, only ε=-1 suffices.
Far Field
In the far field imaging, the super lens is perfect only at n=-1. If the index of refraction is away from this value, caustics and aberration will be present.
Wave Optics for n=-0.95 |
Geometric optics for n=-0.95 |
Wave Optics for n=-1 |
Geometric optics for n=-1 |
Wave Optics for n=-1.05 |
Geometric optics for n=-1.05 |
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