Theoretical investigations on Theoretical investigations on
Optical MetamaterialsOptical Metamaterials
Jianji YangSupervisor : 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)
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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
homogenization
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 …
metamaterial
r
t
r
t
neff, ɛeff , µeff
ɛeff <0, µeff <0 neff <0
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Negative index in the microwaves
Magnetic Response
H
Split Ring Resonator
(SRR)Collection of SRR forms effective magnetic medium.
Electric Response
Metallic Wires
εm<0Collection of conducting wires forms an effective metal with a 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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eff 2 20
Fωμ = 1 -
ω - ω + iωΓ
2P
eff 2
ω= 1 -
ω
Γ: dissipation factor F: fractional factor ωP: controllable plasma frequency
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Split-ring resonators (SRRs) based metamaterial, functioning in microwave spectrum. R. A. Shelby et al., Vol. 292, pp. 77 - 79, Science (2001).
5mm
Negative index in the microwaves
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Moving to Optical Spectrum
Fishnet metamaterials, functioning in near-infrared spectrum.
J. Valentine et al., 455, 376-379, Nature (2008).
Fishnet Metamaterial
Conceptual Difficulties: high dissipation of metals, saturation of magnetic resonance…Fabrication Difficulties: difficulty of scaling-down and stacking-up…
Current Loop
1m
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Fishnet: important fundamental mode
Measurement agrees well with calculated fundamental Bloch mode.J. Valentine et al., 455, 376-379, Nature (2008).
measurement
fundamental Bloch mode
Quartz
FishnetPrism
Air
Incident Beam
Output Beam
n<0α
Prism Measurement
8J. Yang et al., Appl. Phys. Lett. 97, 061102 (2010)
Fishnet: important fundamental mode
Single Bloch Mode Approximation
(SBMA)
fundamental Bloch mode mediates the light transport in fishnet metamaterials.
SBMA
Rigorous
TT0.8
0.6
0.4
0.2
0
λ (μm)
RR
1.4 1.8 2.2
0.8
0.6
0.4
0.2
0
t
Fishnet
r air
neff
Fundamental Bloch Mode
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Microscopic Model: basic waveguide modes
TE01 : least attenuated mode of a rectangular hole
gap-SPP : least attenuated mode of a planar SPP waveguide
gap-SPP
TE01
Metal layer
Dielectriclayer
J. Yang et al., (submitted)
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Elementary Scattering Coefficients
ρ
gap-SPP
αα
τ
Incident TE01
H.T. Liu and P. Lalanne, 452, 728-731, Nature (2008)
α
αtsp
rsp
TE01
gap-SPP
Incidentgap-SPP
ρ , τ : reflectivity and transmissivity of TE01
rsp , tsp : reflectivity and transmissivity of gap-SPP
α : coupling coefficient between gap-SPP and TE01
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Coupled Mode Formalism
Analytical ModelAnalytical Model eff
2 2
0 z ( ) ( ) 1
cos (k a )n2( )
Dispersion relation
Am = τAm+1 + ρBm + αCn + αDn+1
Bm = τBm-1 + ρAm s+ αCn + αDn+1
Cn = tspCn+1 + rspDn + αBm+1 + αAm
Dn = tspDn+1 + rspCn + αBm+1 + αAmAm+1 Bm+1
Am Bm
Cn+1
Dn+1
Cn
Dn
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Resonance of gap-SPP
Current Loop
Gap-SPP mode shows resonance around 2m, via the coupling with TE01 mode, this resonance influences the light transport significantly.
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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.