Theoretical investigations on
Optical Metamaterials
Jianji Yang
Supervisor : Christophe Sauvan
Nanophotonics and Electromagnetism Group
Laboratoire Charles Fabry de l’Institut d’Optique
Collaborators: Stéphane Collin, Jean Luc Pelouard
Laboratoire de Photonique et de Nanostructures (LPN)
Metamaterials (MMs)
MMs:
Engineered materials possessing properties that are not available in
nature, especially negative permeability and negative refractive index.
Potential applications :
Imaging, Invisibility Cloaking, Sensors , Photon Management, Nonlinear
Optics, Antennas, Wave Absorber…
Example:
Negative Index
“Perfect” Lens
J. Pendry, " Negative Refraction
Makes a Perfect Lens ", Phys.
Rev. Lett. 85, 3966 (2000).
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Concept of Effective Parameters
Effective Parameters:
It is a significant challenge to homogenize metamaterials, i.e. to
determine the effective material parameters.
Crucial Parameters:
effective refractive index neff , effective permittivity ɛeff and
effective permittivity µeff …
r
metamaterial
r
homogenization
neff, ɛeff , µeff
ɛeff <0, µeff <0
t
neff <0
t
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Negative index in the microwaves
Magnetic Response
Split Ring
Resonator (SRR)
H
μeff
Electric Response
Metallic Wires
Collection of SRR
forms effective
magnetic medium.
εm<0
Collection of conducting
wires forms an effective
metal with a controllable
plasma frequency.
Fω2
= 1- 2
ω - ω02 + iωΓ
Γ: dissipation factor F: fractional factor
 eff
ωP2
= 1- 2
ω
ωP: controllable plasma frequency
Pendry, J. B., et al., 47, 2075, IEEE Trans. Microw. Theory Tech. (1999)
Pendry, J. B., et al., 76, 4773 , Phys. Rev. Lett. (1996)
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Negative index in the microwaves
5mm
Split-ring resonators (SRRs) based
metamaterial, functioning in
microwave spectrum.
R. A. Shelby et al., Vol. 292, pp. 77 - 79,
Science (2001).
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Moving to Optical Spectrum
Conceptual Difficulties: high dissipation of metals, saturation of magnetic resonance…
Fabrication Difficulties: difficulty of scaling-down and stacking-up…
Fishnet
Metamaterial
1mm
Fishnet metamaterials, functioning
in near-infrared spectrum.
J. Valentine et al., 455, 376-379, Nature (2008).
Current Loop
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Fishnet: important fundamental mode
Prism Measurement
Air
Fishnet
Prism
α
n<0
measurement
Output
Beam
fundamental
Bloch mode
Quartz
Incident Beam
Measurement agrees well with
calculated fundamental Bloch mode.
J. Valentine et al., 455, 376-379, Nature (2008).
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Fishnet: important fundamental mode
Single Bloch Mode
Approximation (SBMA)
fundamental Bloch mode
mediates the light transport
in fishnet metamaterials.
r
air
0.8
T
0.6
0.4
0.2
SBMA
0
Rigorous
0.8
R
0.6
Fundamental
Bloch Mode
neff
0.2
Fishnet
t
0.4
0
1.4
1.8
2.2
λ (μm)
J. Yang et al., Appl. Phys. Lett. 97, 061102 (2010)8
Microscopic Model: basic waveguide modes
TE01
Metal layer
Dielectric
layer
gap-SPP
TE01 : least attenuated mode of a rectangular hole
gap-SPP : least attenuated mode of a planar SPP waveguide
J. Yang et al., (submitted)
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Elementary Scattering Coefficients
Incident
TE01
Incident
gap-SPP
ρ
α
gap-SPP
α
α
τ
TE01
tsp
rsp
α
gap-SPP
ρ , τ : reflectivity and transmissivity of TE01
rsp , tsp : reflectivity and transmissivity of gap-SPP
α : coupling coefficient between gap-SPP and TE01
H.T. Liu and P. Lalanne, 452, 728-731, Nature (2008)
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Coupled Mode Formalism
Am B m
Cn
Cn+1
Dn
Dn+1
Am+1 Bm+1
Am = τAm+1 + ρBm
Bm = τBm-1 + ρAm
Cn = tspCn+1 + rspDn
Dn = tspDn+1 + rspCn
+ αCn + αDn+1
+ αCn + αDn+1
+ αBm+1 + αAm
+ αBm+1 + αAm
s
Dispersion
relation
Analytical Model
(   )2  (   )2  1
cos (k 0neff a z ) 
2(   )
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Microscopic Model
Am B m
Cn
Cn+1
Dn
Dn+1
Am+1 Bm+1
Microscopic model
Fishnet mode (exact)
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Resonance of gap-SPP
Gap-SPP mode shows resonance
around 2mm, via the coupling
with TE01 mode, this resonance
influences the light transport
significantly.
Current Loop
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Conclusion:
We have studied the optical fishnet metamaterials theoretically. In
particular we investigate the important fundamental Bloch mode of
fishnet structure, and we also formulate the construction of this mode
from a relatively microscopic point of view.
In the future, we will investigate other types of plasmonic structures,
especially some potentially applicable designs.
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Thank you !
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