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A Theoretical study on Negative
Refractive Index Metamaterials (Review)
Madhurrya P. Talukdar
Tezpur University
Contents
• Introduction
• Negative refraction
• Electromagnetic Wave propagation
• How to make NIM
• Conclusion
Introduction
Invisibility
Camouflage
Stealth
technology
Vacuum property
(most effective)
Possible types of materials:
•μ>0, Є>0, being most known materials, natural or otherwise.
•μ>0, Є<0, being materials not well investigated.
•μ<0, Є>0, also being materials not well investigated
•μ<0, Є<0, where these materials do not exist naturally(Metamaterials)
Metamaterials
Man-made materials
First introduced theoretically by Victor Veselago in
1967
Consists of Artificially structured units (meta-atoms)
Meta atoms composed of two or more conventional
materials
Negative refraction:
empty glass
regular water,
n = 1.3
“negative” water,
n = -1.3
Group velocity vg is in the opposite direction to
the wave (or phase) velocity, vp
The structural array of metamaterials must be
smaller than the EM wavelength used.
To achieve negative refraction MM’s must
interact with the magnetic component of light.
* ‘Probing the Magnetic Field of Light at Optical Frequencies’ Brussi et.al VOL
326
SCIENCE
Electromagnetic wave propagation and cloaking
Theory
Transformation optics is a simple
approach to design MM’s (Pendry et.al)
What happens to light in NIM?
Light enters n > 0
material  deflection
Light enters n < 0
material  focusing
(“Veselago Lens”)
Cloaking
Fermat’s principle states light rays take the shortest optical paths in
dielectric media
When n is spatially varying shortest optical paths are usually
curved.
Fig: bending of light around a cloaked object
(Leonhart 2006)
W. Cai et al., “Optical cloaking with metamaterial,” Nat. Photonics 1, 224 (2007).
T. Ebbesen et al., Nature 391, 667 (1998).
G. Gay et al., Phys. Rev. Lett. 96,
213901 (2006).
G. Abajo et al., “Tunneling mechanism of
light transmission through metallic films,”
Phys. Rev. Lett. 95, 067403 (2005).
W. Barnes et al., Phys. Rev. Lett. 92,
107401 (2004).
A. Alu & N. Engheta, Phys. Rev. E 72,
016623 (2005).
How to make NIM?
In microwave range: use “perfectly” conducting components to
simulate e < 0 and m < 0, Smith et.al., (2000)
Metal poles: e = 1 – wp2/w2 < 0
Split-ring resonators, Pendry’99:
“geometric” resonance at wM
c  2
w p  
D  log(D/r)
1/ 2



FwM2
m  1 2
0
2
w  wM
Split Ring Resonators
At frequency> resonant frequency the real part
of μ of the SRR becomes negative.
Combining the negative permeability with
negative dielectric constant of another material
to produce negative refractive index
metamaterials.
Challenges:
(a) moving to optical frequencies (infrared, visible, UV)
(b) simplifying the structure (e < 0 and m < 0 from same element)
Conclusion
Optical meta-materials have been shown to have remarkable
applications:
Can be used to engineer exotic meta-media: Negative Index
Materials  plasmonic approach to making a sub-l NIM
NIMs and negative e materials can be used to overcome
diffraction limit and construct a super-lens
A super-lens enables ultra-deep sub-surface imaging
Very new field  lots of work to do (theory and
experiments)
References
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