Bending Back Light: The Science of Negative Index Materials

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Bending Back Light The Science of Negative Index
Materials
C. M. Soukoulis Ames Lab. and Physics Dept. Iowa
State University, Ames, Iowa, USA
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Collaborators
P. Markos (Ames Slovakia), Th. Koschny (Ames)
E. N. Economou, M. Kafesaki, N. Katsarakis
(Crete, Greece) S. Foteinopoulou (Crete Ames)
J. Dong (China Ames) E. Ozbays group (Bilkent,
Turkey) Lei Zhang, J. Zhou, R. Moussa G. Tuttle
(Ames, USA) D. R. Smith (Duke, USA) J. B.
Pendry (Imperial, UK) V. Sandoghdar (ETH,
Zurich) M. Wegeners group, K. Busch (Karlsruhe,
Germany) Boeings group (Seattle, USA)
DOE, DARPA, MURI, ONR, EU, EU-ENSEMBLE,
EU-PHOME
http//cmpweb.ameslab.gov/personnel/soukoulis
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Outline of Talk

• Brief history of left-handed materials
• Losses are high gt 20dB/??? ?/a approaches 2 at
  high f
• Total thickness/l much less than one! No 3d or
  even bulk.
• Upper limits of the SRRs? Simulation results and
  their interpretation by a LC model. Experiments.
• Breaking of scaling. Negative m without magnetic
  materials
• Strongly coupled fishnet structures.
• No negative n with only cut wires. Losses can
  give a negative n, without LH propagation.
• Negative n at optical frequencies! Fishnet
  structure.
• New designs (Chiral, 3d structures with DLW).
• Concluding Remarks (EIT, Reducing losses)

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µ
elt0, µgt0 imaginary extinction metals
egt0, µgt0 real propagation transparent materials
e
egt0, µlt0 imaginary extinction magnets for ?1lt
? lt ?2
elt0, µlt0 propagation opposite phase group
velocities negative refraction opposite Doppler
effect opposite Cerenkov radiation flat
lenses perfect lenses zero index of
refraction zero reflection
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A dream comes true Prof. Pendry suggests
structures with elt0 and µlt0

• Basic idea behind RESONANCES
• For e lt 0 A wire medium. It can yield e lt 0 in a
  tunable frequency range (Pendry et al., PRL
  1996). Artificial dielectrics using metals!!
• For µ lt 0 Split ring resonators. They yield µ lt
  0 in a tunable frequency range (Pendry et al.,
  IEEE, 1999). Artificial magnetic materials using
  non-magnetic metals!!
• A combined medium can yield both e lt 0 and µ lt
  0 simultaneously.
• A medium with negative index
• of refraction should be possible
• by using these suggested structures?

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Science Jan 5, 2007
Solid symbol nlt0
Open symbol ?lt0
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A Brief History of Left-handed Metamaterials
Since the first demonstration of an artificial
LHM in 2000, there has been rapid development of
metamaterials over a broad range of frequencies.
Science 315, 47 (2007)
nlt0 for 780 nm (AL/Crete Karlsruhe) Opt. Lett.
32, 53 (2007)
nlt0 for 1.5 µm (AL/Crete Karlsruhe) Science
312, 892 (2006)
µlt0 for 6 THz (Ames Crete) Opt. Lett. 30, 1348
(2005)
nlt0 for 4 GHz (AL/Crete Bilkent ) Opt. Lett.
29, 2623 (2004)
Open symbol µlt0
Solid symbol nlt0
Ames Laboratory (AL) and Crete involved in
designing, fabrication and testing of LHMs from
GHz to optical frequencies 4,6,7,10,11,13,14.
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Metamaterials structures shown in these
split-ring resonators are amenable to
manufacture by common planar lithography.
It has a magnetic response perpendicular to the
plane, which is difficult to detect by direct
incidence measurements.
Use of multilayer processing can been used to
fabricate metamaterials that give both negative
? and ?, as well as n for perpendicular
propagation.
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Towards optical frequencies Increase of losses
Overview of the current experiments
Losses in the metallic parts become more important
Experiments
Orange Double-ring SRR based structures Green
single-ring SRR based structures Blue
slab-pair-based structures Violet fishnet
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Towards optical frequencies Subwavelength
operation?
Overview of the current experiments
Orange double-ring SRRs based structures Green
single-ring SRR based structures Blue
slab-pair-based structures Violet fishnet
Optical structures are less subwavelength
Solid symbols nlt0
Open symbols µlt0
Photonic Crystals ??
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Total thickness/wavelength Experiments
1. Smith D R, et.al PRL 84 4184 (2000)
2. Bayindir M, et.al , APL. 81 120 (2002)
3. Aydin K, et.al, Opt. Lett. 29 2623 (2004)
4. Katsarakis N, et. al, APL, 84 2943 (2004)
5. Yen T J, et.al, Science 303 1494 (2004)
6. Linden S, et.al, Science 306 1351 (2004)
7. S. Zhang, et al PRL 94, 037402 (2005)
8. G. Dolling, et al OL 30, 3198 (2005)
9. V. Shalaev, et al OL 30, 3356 (2005)
10. Enkrich C, et. al, PRL. 95 203901 (2005)
11. Katsarakis N,et. al, OL, 30,1348 (2005)
12. J. Zhou, PRB, 73, 041101, 2006
13. J. Zhou, APL, 88,221103(2006)
14. Gokkavas M, et.al, PRB, 73 193103 (2006)
15. Klein M W, et.al, OL, 31 1259 (2006)
16. G. Dolling, et al OL 31, 1800 (2006)
17. G. Dolling, et al, OL, 32, 5 (2007)
18. Katsarakis et.al, Photon. Nanostruct. 5 149, (2007)
19. G. Dolling, et al OL 32, 53 (2007)
20. Liu N, et.al, Nat. Matt., 7, 31, 2008
21. J. Valentine, et al Nature August 11, (2008)
Its premature to call these metamaterials 3d!
Red Multiple layers Blue single
layers Hollow parallel incident Solid Normal
incident Square SRRs, Triangle Fishnet, Circle
cut-wires
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Applications of Metamaterials

• The losses are large for THz and optical
  frequencies FOM Ren/Imn 0.1-3.0
• So only thin-film applications for metamaterials
• Optical switching and bistability
• Zero reflectance.
• Modulators (phase, electro-optic, etc)
• Zero index of refraction (beaming,
  concentrators)
• Thin-film optical isolators (Chirality)
• Diamagnetic response. Magnetic levitation
• Miniaturization of devices for RF applications.

Key idea is the direct control of the magnetic
component of EM waves. Magnetism at THz and
Optical frequencies
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Breaking of the scaling low and saturation of ?m
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Frequency dependence of real part of ????
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Slab-pairs and wires scaling
Al metal Glass substrate
600 THz
ak u.c. size
Fishnet higher saturation frequency Due to neck
inductance
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Metamaterials structures shown in these
split-ring resonators are amenable to manufacture
by common planar lithography.
It has a magnetic response perpendicular to the
plane, which is difficult to detect by direct
incidence measurements.
Use of multilayer processing can been used to
fabricate metamaterials that give both negative
? and ?, as well as n for perpendicular
propagation.
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Weakly and strongly coupled fishnet-structures
Zhang et al, Nature 2008
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Weakly coupled
Strongly coupled
Photonic crystal Superlattice metal/dielectric/met
al
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Weakly and strongly coupled fishnet-structures
aza/15
az2a/15
az4a/15
Solid lines 2 coupled fishnets Dashed lines
single fishnet
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5 layers
Anti-symmetric Mode Weak resonance, n0 (ngt0 for
this case, induced B is completely canceled)
J
B'
B''
B' B'' 0
B'
Diamagnetic response
J
Symmetric Mode Strong resonance, nlt0
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Inversion of S-parameters Homogeneous effective
medium (HEM) approach
Lifting ambiguities using causality arguments
d
PRB, 65, 195103 (2002)
Phys. Rev. B 71, 245105 (2005)
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T and R of a homogeneous slab
d
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Weakly coupled fishnet-structures
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7 (2d0) , 11 (3d0) and 19 (5d0) layers
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19 (5d0) and 27 (7d0) layers
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Strongly coupled fishnet-structures
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Strongly coupled fishnet-structures
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Strongly coupled fishnet-structures
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FOM is large for strongly coupled
fishnet-structures
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Weakly coupled fishnet-structures Periodic
effects I
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Weakly coupled fishnet-structures Periodic
effects II
FOM is large too!
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3D metamaterials
Neither truly 3D nor isotropic photonic
meta- materials can be fabricated with e-beam
lithography. Idea Use DLW and CVD of metals
(e.g., Ag).
EU PHOME, KARLRUHE
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Michael S. Rill
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Direct laser writing (DLW)
For DLW-technique see S. Kawata et al., Nature
412, 697 (2001)
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Direct laser writing (DLW)
Markus Deubel
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3D SU-8 template via DLW
2 µm
Michael Thiel
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Fabricated structures
a 1 µm
M.S. Rill et al., Nature Mater., online (2008)
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Fabricated structures
a 1 µm
SU-8 SiO2 Ag
M.S. Rill et al., Nature Mater., online (2008)
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Fabricated structures
? 4 a
M.S. Rill et al., Nature Mater., online (2008)
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Fabricated structures
? 4 a
M.S. Rill et al., Nature Mater., online (2008)
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1d Designs for Direct Laser Writing
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2d Designs for Direct Laser Writing
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Direct laser Writing
M. S. Rill, Karlsruhe
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A chiral metamaterialof the cut-wire pair type
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Negative refraction index in chiral media
?chiral parameter

• A chiral object has no mirror symmetry in its
  geometric structure.
• Optical properties polarization plane
  rotation(rotatory power) and circular dichroism.

Eigenwaves in chiral medium right circularly
polarized (RCP) and left circularly polarized
(LCP), whose wavenumber and effective index
If chirality parameter is very large,
then
Pendry, Science 2004
refractive index of LCP eigenwave is negative.
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Chiral Metamaterial designs
omega praticle S. Tretyakov, Photon.
Nanostruc.Fundam. Appl.,3,107 (2005)
Bi-layer rosette design A.V. Rogacheva, PRL, 97,
177401 (2006)
Twisted Swiss-role J.B. Pendry, Science, 306,1353
(2004)
3D chiral Photonic crystal M. Thiel, OPL, 32,
2547 (2007)
Bi-layer swastika design M. Decker, OPL, 32,
586 (2007)
Chiral SRR L. Jelinek, PRB, 77,205110 (2008)
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Chiral cut-wire pair type structures Rossettes
and cross-wires
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These chiral materials give negative n!
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These chiral materials give negative n!
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Bi-isotropic retrieval procedure
Maxwells Equation
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Negative refraction index in chiral media
N. Zheludev, Univ. of Sathoumpton
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Rotatory power
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• Significant contributions to the development of
  LHMs by our group
• Electric response of SRRs
• Electric excitation of the magnetic resonance
• Retrieval calculations for e, µ
• Closed rings for distinguishing LH from RH peaks
• Negative µ at THz and visible.
• Negative n at 1.5 µ and 780 nm.
• Upper frequency limit of the SRRs. Diamagnetic
  response of SRRs.
• Negative n at GHz and THz. Negative phase and
  group velocities.
• Designs for 3d isotropic LHMs.
• Future directions
• Understanding and reducing losses. Introduce
  gain to reduce losses.
• Fabrication of 3d LHMs. Direct laser writing.
  (Karlsruhe)
• Electromagnetic induced transparency. Slow
  light, low losses.
• Non-linear effects. Chirality effects.
• Anisotropic metamaterials. Pseudo-focusing.
• Applications

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April 5-9, 2009 Dockside, Cockle Bay
Wharf Sydney, Australia
The 8th International Photonic Electromagnetic
Crystal Structures Meeting
Convenor Professor Ben Eggleton Co-Convenor
Professor Yuri Kivshar
More info at http//pecs8.mtci.com.au/ or
http//www.pecsconference.org/
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8th International Conference onElectrical,
Transport and Optical Properties of Inhomogeneous
MediaETOPIM 8 June 7-12, 2009
Aquila Rithymna Beach Hotel, Rethymnon,
Crete Convenors Costas Soukoulis,AMES Lab
USA/FORTH, Crete Maria Kafesaki, FORTH,
Crete  http//etopim8.mtci.com.au
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Functional cloaking device !
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Strongly coupled fishnet-structures
?2230nm Re(n)-0.17 Anti-symmetric
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Strongly coupled fishnet-structures
?1859nm Re(n)-2.50 Symmetric
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Strongly coupled fishnet-structures
Symmetric mode, n0
Anti-Symmetric mode, nlt0
Induced B parallel, strong n
Induced B anti-parallel, n0
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5 layers
Anti-symmetric Mode Weak resonance, n0 (ngt0 for
this case, induced B is completely canceled)
Symmetric Mode Strong resonance, nlt0
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Diamagnetic response of SRRs Magnetic levitation
according to
µ(?) should return to unity below and above the
resonance?
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Diamagnetic response of Metamaterials
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Diamagnetic Resonant currents
100nm SRR Skin depth currents penetrate deeper
into ring
L100nm f116THz
L100nm f30THz
below resonance
at resonance (note scale is 30x larger)
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Two types of diamagnetic response
below resonance B eliminated from area of ring
metal
above resonance B eliminated from all enclosed
area
at resonance
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Diamagnetic Resonant currents
we describe metal by Drude model
permittivity then current density is available as
L10µm f300GHz
L10µm f3.2THz
below resonance
at resonance (note scale is 10x larger)
Skin-depth
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Negative n with ?gt0 and ?lt0