epsilon-near-zero behavior from plasmonic dirac …epsilon-near-zero behavior from plasmonic dirac...
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Epsilon-Near-Zero behavior from Plasmonic Dirac Point: Theory and realization using 2D materials
Marios Mattheakis
APS March Meeting, APS March Meeting, March 13, 2017March 13, 2017
New Orleans, Louisiana New Orleans, Louisiana
School of Engineering &
Applied Physics (SEAS) Collaborators:
C. ValagiannopoulosE. Kaxiras
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Periodic Structures
Plasmonic Crystal:Plasmonic Crystal: Periodic arrangement of dielectric/metal slabs
Optical Bands:Optical Bands: The propagation modes form bands in k-space
Normal Refraction Negative Refraction Epsilon-Near-Zero (ENZ)
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Motivation
Can we design a structure with dynamically tunabledynamically tunable optical bands?
Can we have ENZ behaviorENZ behavior between normal and negative refraction regimes?
What the shape of ENZ bandshape of ENZ band will be?
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Structure
2D metals2D metals are embedded periodically in an anisotropic dielectric host
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Maxwell EquationsTransverse Magnetic (TM) monochromatic EM waves
EigenValue Problem
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Dispersion Relation
Dense grid λ >> d:
Plasmonic Thickness
PPlasmonic DDirac PPoint (PDP)M. Mattheakis et. al., Phys. Rev. B, 94, 201404(R), 2016.
(B.Wang et. al. PRL 109, 2012)
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A Plasmonic Dirac Point leads to ENZ
Effective medium (metamaterial) approach
M. Mattheakis et. al., Phys. Rev. B, 94, 201404(R), 2016.
,
Plasmonic Dirac Point leads to Epsilon-Near-Zero behavior
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EM wave simulations
M. Mattheakis et. al., Phys. Rev. B, 94, 201404(R), 2016.
● 40 periods structure: doped graphene layers embedded in MoS
2 host (ε
x=3.5, ε
z=13)
● 2D magnetic dipole source● λ
0 = 12 μm (f = 25 THz), ξ=20.8 nm
(R.K. Defo et. al. PRB 94, 2016)
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Tunability in terms of λ, μc & d
Combinations of μc and λ leading to PDP & ENZ (d is plotted in nm).
M. Mattheakis et. al., Phys. Rev. B, 94, 201404(R), 2016.
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Effective PermittivityCombinations of λ and μ
c at fixed period d=20nm. Dashed lines indicate ENZ regime.
M. Mattheakis et. al., Phys. Rev. B, 94, 201404(R), 2016.
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Conclusion
Relevant Publication: Relevant Publication: M. Mattheakis, C.A. Valagianopoulos and E. Kaxiras, Phys. Rev. B, 94, 201404(R), 2016.
➢ Any periodic structure of 2D plasmonic materials (e.g. doped graphene) exhibits Plasmonic Dirac Point in k-space.
➢ A Plasmonic Dirac Point leads to Epsilon-Near-Zero metamaterial.
✔ A systematic method for designing ENZ metamaterials.
➢ Optical properties can be tuned dynamically via doping and frequency.
✔ Tunable Metamaterial.
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Acknowledgment
M. Mattheakis et. al., Phys. Rev. B, 94, 201404(R), 2016.
H2020-MSCA-RISE-2015
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Plasmonic Metamaterial (simulations)
d=ξ=20,8 nm (linear) d<ξ (hyperbolic) d>ξ (elliptic)
100 periods structure is excited by a plane wave source of f=25 THz (λ=12μm).
M. Mattheakis et. al., Phys. Rev. B, 94, 201404(R), 2016.
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Dispersion Relation
Assuming a very dense grid λ >> d:
Plasmonic Thickness
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Propagation Length
Propagation length L/d for combinations of λ, d & μc leading to ENZ.
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Plasmonic Metamaterial
Doped graphene surface conductivity:
PDP is extremely sensitive to structural defects:
Stacking of 2D materials provides essentially perfect planarity.Stacking of MoS2 builds a anisotropic dielectric:
(R.K. Defo et. al. PRB 94, 2016)
M. Mattheakis et. al., Phys. Rev. B, 94, 201404(R), 2016.
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Optical Bands
M. Mattheakis et. al., Phys. Rev. B, 94, 201404(R), 2016.
Weak plasmon coupling
Strong plasmon coupling
Critical plasmon coupling
PPlasmonic DDirac PPoint (PDP)