Theoretical investigations on Optical Metamaterials

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Theoretical investigations on Optical
Metamaterials

• Jianji Yang
• Supervisor Christophe Sauvan

Nanophotonics and Electromagnetism Group
Laboratoire Charles Fabry de lInstitut dOptique
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
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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 ?eff and effective
permittivity µeff
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Negative index in the microwaves
?P controllable plasma frequency
G dissipation factor F fractional factor
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 Fabricat
ion Difficulties difficulty of scaling-down and
stacking-up
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
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.
J. Yang et al., Appl. Phys. Lett. 97, 061102
(2010)
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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 gap-SPP
?
TE01
a
tsp
rsp
a
gap-SPP
? , t reflectivity and transmissivity of
TE01 rsp , tsp reflectivity and transmissivity
of gap-SPP a 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 tAm1 ?Bm aCn aDn1 Bm tBm-1
?Am s aCn aDn1 Cn tspCn1
rspDn aBm1 aAm Dn tspDn1 rspCn
aBm1 aAm
Dispersion relation
Analytical Model
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Microscopic Model
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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.
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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 !