An introduction to Metamaterials and their applications

1. Metamaterials
Physics and Applications
Shuvan Prashant,
Taishi Zhang,
Kain Lu Low,
Naomi Nandakumar
Zhao Wenwen

2. Talk Outline
What is a metamaterial?
How to get negative µ and ε
Technical Challenges
Applications
3D Metamaterials
Slow Light
Superlens
Chiral Metamaterials
Metamaterial Cloak

3. Classifying Materials
based on electromagnetic response (µ,ε)
ε<0, µ>0
Metals ,Doped
Semiconductors
Evanescent waves
ε>0, µ> 0
Most Dielectrics
Propagating Waves
ε<0, µ<0
No natural
Materials
Propagating Waves
ε>0, µ<0
Some ferrites
Evanescent waves
ε
µ III
III IV

4. What is a metamaterial ?
‘Meta’ means Beyond
Metamaterial is an artificially engineered composite of
periodic or non-periodic structures with exotic
macroscopic properties that are not found in Nature.

5. Where do metamaterials fit
in Optical Engineering ?
a<< λ
Effective medium
Approximation with
Maxwell Equations
a~λ
Structure dominates
Properties
determined by
diffraction and
interference
a>>λ
Properties
described by
geometrical optics
and ray tracing
Examples
Optical Crystals
Metamaterials
Examples
Photonic Crystals
X Ray diffraction
Radar Systems
Examples
Lens Systems
Shadows
a/λ0 1 ∞

6. )1)(1(   iin )()1(   i





 

2
)(
1
i
t
D
jHD
t
B
EB






,.
,0.

In 1968,
Victor Veselago theoretically proved that we can have material
with
Maxwell’s equations
2
n
  i
  i
Real part is negative,
Generally imaginary parts are >0
since they characterizes light absorption
Imaginary part of n has to be positive for any passive material.
Therefore minus sign must be chosen
Both ε´ < 0 and μ´ < 0 is possible ,
But not the only approach to achieving a negative n
Equation ε´|μ| + μ´|ε| < 0 must be obeyed to get negative n
Simultaneously negative ε and μ

7. Negative Refraction

8. Poynting Vector S: The direction of the
energy is determined by the real part of
the vector
Reversed
Doppler shift






EHk
HEk


ε<0,μ<0
E,H,K form a left-
handed triplet
ε>0,μ>0
E,H,K form a right-
handed triplet
HES 
2
1
Left or Right ?

9. How to Get ε<0  Noble metals
Assuming Drude Model for permittivity Silver parameters
Plasma frequency
depends on geometry
rather than on material
properties
A periodic array of thin
metal wires with
r<<a<<λ
can acts as a low
frequency plasma
ε<0

10. How to get μ < 0 : Split Ring Resonator
Bulk metal has
no magnetism
in optics
A metal ring : weak
magnetic response
Current induced by H
A Split ring : magnetic
resonance due to LC
Double Split ring :
Enhanced magnetic
resonance
L
C
LC
res
1

Hind
Hext

11. Negative Index MM at GHz
ε<0
μ<0

12. Technical Challenges
Optical Metamaterials
3D Metamaterials
Loss Compensation in Metamaterials
Incorporate Gain Media
Coupling Effects in Meta-atoms 
Metamolecules?
Slow Light
Fano Resonances

13. Technical Challenges
Polarization Control
Chiral Metamaterials
Tunability and Gain
Active Metamaterials
Superfocusing
Superlens (Negative index lens)
Transformation Optics
Cloaking

14. What we will focus on…
 Optical Metamaterials
 3D Metamaterials
 Slow Light
 Cloaks
 Chiral Metamaterials
 Superlens

15. How low can you go ? Scaling Limit of SRRs
• Saturation of resonance frequency with scaling
• Reason  Loss in metal giving rise to kinetic inductance
• Finite electron mobility
;coilL size
1
kineticL
size

;total coil kineticL L L 
total sizeC 
2
1 1 1
( . / ).( . )total total
res
L C A size A size C size size const
   
  

16. Fishnet Structure : ε<0, μ<0
Nanostrip pair (TM):
Magnetic field applied along the
nanostrip. µ < 0 (resonant)
Nanostrip pair (TE):
Electric field applied along the
nanostrip. ε < 0 (non-resonant)
Fishnet - Combination of
Nanostrip pair in TM and TE:
µ < 0 and ε < 0
H
E
K
Nanostrip consists of 2 layers of
metal separated by a dielectric
spacer layer.
Dielectric Metal

17. The Rise of Metamaterials

18. 3D Metamaterials: Making them Bulky

19. App1.Slow Light in MMs

20. App 2. Metamaterial Cloaks
Transform geometry variation into
index variation to hide objects

21. App 3. Superlens : Perfect Focusing
PropertyLens Normal Lens Superlens
Structure Structural RI Varitation
for focusing
Negative index
metamaterial slab
Diffraction Limited Yes No
Evanescent Waves Decay exponentially Get Enhanced

22. Experimental verification of SuperLens

23. App 4. Controlling Polarization : Chiral MMs
Mirror Plane
/L R r rn    
Rosette Structure
Giant Optical Activity
Circular Dichroism
Broadband Polarizers

24. In conclusion
• Traditionally Question: Which material has
desired optical properties ?
• New Question: How to engineer/design
materials to achieve desired optical
properties ?
– Answer: Metamaterials
• Dispersion engineering(Tamper ε and μ)
– Change how light interacts with matter
– Slow Light, Cloaking, Superlensing,
Thank You ALL, Q?A!

25. Divide and Rule
• Kain Lu LowChiral
• Zhang Taishi Slow light
• Shuvan Prashant3D Meta
• Zhao WenWen Cloak
• Naomi
Nandakumar
Super
Lens

26. References
• General
– Veselago, Soviet Physics Uspekhi 10 509, (1968)
– Liu & Zhang, Chem. Soc. Rev ., 40, 2 494–2507, (2011)
– Optical Metamaterials, Wenshan Cai and Vladimir Shalaev, 1st Edition,
Springer.(2010) and references therein.
– Shalaev, Nature Photonics, 1 ,41(2007)
• 3D Metamaterials
– Soukoulis and Wegener, Nature Photonics Published online, doi:
10.1038/nphoton.2011.154, (2011) and references therein
• Slow Light and Fano Resonances
– Lukyanchuk et al , Nature Materials, doi: 10.1038/nmat2810, (2010)
– Papasimakis et al, Optics and Photonics News, 20(10), 22-27 (2009)
• Cloaks
– Chen et al, Nature Materials, doi: 10.1038/nmat2743 2010
– Tolga, Ergin et al Science 328, 337(2010)
• Chiral Metamaterials
– Gansel et al, Science 325, 1513(2009)
– Plum et al, Physical Review B 79, 035407 (2009)
– Radke et al, Advanced Materials23(27), 3018-3021, (2011)
• Superlens
– Zhang & Liu, Nature Materials 7,435, (2008)

27. 3D Metamaterials
• To make bulk metamaterials ~order of λ is
important

28. Loss Compensation in MMs
Incorporate Gain
media to counter the
losses