Negative Refraction

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Negative Refraction
RijksUniversiteit GroningenNanoscience TopMaster
2006 Symposium

• Asem Ampoumogli
• 1582542

Groningen June 2006
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Refraction

• Refraction is one of the fundamental phenomena
  in the interaction of matter and radiation along
  with reflection, absorption and scattering.
• When a ray of light traveling through medium A
  (e.g. air) of refractive index n1 arrives at a
  medium B (e.g. glass) of refractive index n2, it
  is refracted at the interface.
• All kinds of waves refract i.e. acoustic waves,
  seismic waves, even sea waves!

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Index of refraction

• The refractive index n is defined by the
  equation

• Where
• er is the relative electrical permittivity,
  defined as ere/e0
• µr is the relative magnetic permeability, defined
  as µr µ/µ0

Both these constants are generally positive
numbers.
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Index of refraction

• In 1621 the Dutch mathematician Willebrord Snell
  arrived at the sin? form of the law of refraction.

• Upon entering medium B, the radiations phase
  velocity will change to

The refractive index is always positive.
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Veselagos classic paper
In 1968 the Russian physicist Victor Veselago
published a paper in which he studied the
interaction of electromagnetic radiation with a
(hypothetical) material for which both e and µ
are simultaneously negative.
V.G. Veselago, Soviet Physics USPEKHI, 10, 509
(1968).

• He arrived at some interesting conclusions
• A planar slab of this material will focus light
  (not parallel rays though).
• The vector set k, E, H will be left handed,
  which means the group and the phase velocities in
  this material will be in opposite directions.
• The energy flow EH of an electromagnetic wave
  will be in the opposite direction to the wave
  vector because the permeability is negative.

http//sagar.physics.neu. .edu/lhm-intro-1.html
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Veselagos classic paper
Most importantly, Veselago was able to show that
this material would have a negative index of
refraction.

• This has some more interesting consequences
• The Doppler shift will be reversed.
• The Cerenkov radiation will be reversed.
• Snells law will be reversed.

How can this happen? What does it mean? Why are
there no materials readily found that exhibit a
negative refractive index?
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The Drude Lorentz model and negative response
In the Drude-Lorentz atomic model, the atoms are
modeled as oscillators (the electrons are bound
to the nucleus with a spring) with a resonant
frequency ?0. An electric field of frequency ?
will drive the oscillations of the system at
?. If the frequency of the radiation is near the
resonant frequency the induced polarization
becomes very large. In the classical analogue
(mass on an ideal spring), below the resonant
frequency, the mass is displaced in the same
direction as the driving force (analogy
massdipole moment). However, above the resonant
frequency, the mass is displaced in a direction
opposite to the driving force. In the case of
resonance with the electric field, the material
will exhibit a negative permittivity e (as is the
case with metals at optical frequencies). At
resonance with a driving magnetic field, the
material will exhibit a negative permeability .
So, the negative index of refraction will be
observed when the material is in resonance with
both the electric field and the magnetic field.
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Negative Index materials
Can we create materials that will have a negative
index even for a narrow frequency window?
In 1999 Professor J. Pendry of the London
Imperial college published a paper proposing
structures that, was predicted, would feature the
needed electromagnetic properties to have a
measurable negative refractive index.
J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J.
Stewart, IEEE transactions on microwave theory
and techniques, 47, 2075 (1999).
The proposed structures are to be created with
two elements Cut wires (designed to have a
specific electrical resonance frequency)
and Split ring resonators (SRRs) (designed to
have a specific magnetic resonance frequency).
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Negative Index materials
Because the radiation that will be used has a
wavelength hundreds of times larger than the
atomic units in our material, the atomic details
lose importance in describing how the material
will interact with it.
It was further argued that we can define an
effective permittivity and an effective
permeability to macroscopically describe our
materials.
From this point of view we will have created a
meta-material whose unique properties are not
determined by the fundamental physical properties
of its constituents but by the shape and the
distribution of the specific patterns included in
them.
What would something like that look like?
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Permittivity
The resonant frequency can be set to virtually
any value in this kind of materials, so the
negative e can be reproduced at low frequencies
rather than just the optical region.
Above ?0 and below ?p the effective permittivity
is negative.
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Permeability
The split ring resonator (SRR) will feature a
magnetic response without being inherently
magnetic. We will have the meta-material
equivalent of a magnetic atom.
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Other designs
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Experimental verification
R. A. Shelby, D. R. Smith, S. Schultz, Science
292, 77-79 (2001).
The experiment was carried out at a frequency of
10.5 GHZ. The control sample was made of Teflon,
cut with a step pattern identical to that of the
LHM sample Results NIM n - 2.7 Teflon n 1.4
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Applications
The most prominent application of refractive
materials is in the manufacturing of
lenses. Veselago (as well as Pendry) have shown
that NIM lenses would not require curved surfaces
to focus radiation (but would not focus parallel
rays and will have a magnification of unity).
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Applications
One of the most dramatic and controversial-
prediction for the NIMs was that by Pendry in
1999 which stated that a thin negative-index film
should behave as a superlens, providing image
detail with a resolution beyond the diffraction
limit, to which all positive-index lenses are
subject.
This restriction is a significant problem.
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Applications
Magnetic Resonance Imaging (MRI) Large
quasi-static fields cause the nuclear spins in
the patients body to align. The spins are
resonant at the local Larmor frequency, so a
second magnetic field (an RF field) will excite
them causing them to precess around the magnetic
field. Images are constructed by observing the
time dependent signal resulting from the
precession of the spins.