Properties of plasmonpolariton waveguide on silver nanowires W'M'Saj Information Optics Group Warsaw

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Properties of plasmon-polariton waveguide on
silver nanowires W.M.Saj Information Optics
Group Warsaw University
SPIE International Congress on Optics and
Optoelectronics Conference on MetamaterialsWarsa
w University of Technology, 28 Aug 2 Sep 2005
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Outline

• Properties of a waveguide on silver nanowires
• Its possible application in net medium
  construction
• Conclusions

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Plasmon polariton waveguides

• Guide energy with surface plasmons or coupling
  between surface/particle plasmons
• Exhibit high confinement of light in space (cross
  section far less than wavelength)
• Have moderate losses in dielectric channel
  structures
• Are fabricated of noble metals (low losses on
  absorption in optical range)
• Developed for highly integrated optical
  nanocircuits

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Waveguide on hexagonal lattice of silver nanorods

• Its a 2D structure, waveguiding energy because
  of coupling between surface plasmons excited on
  neighbor silver rods. Two free parameters of the
  structure are diameter of rods d and lattice
  constant ? . The refractive index of surrounding
  medium is also important as it modifies plasmon
  properties.

For calculations we assume d100 nm, ?150 nm and
refractive index of surrounding medium n 1 . We
use FDTD method and describe silver with Drude
model. Morever we examine only interaction with H
polarized light in the visible range.
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Band structure of the waveguide

• FDTD with complex representation of fields and
  with UPML and Bloch boundary conditions is used
  for the analysis of modes. The value of
  propagation constant k is a parameter of the
  simulation. Modes frequencies ? are find from
  position of peaks in time spectrum of initial
  field evolution. Modes fields are obtained by
  Fourier transform of the same evolution at found
  frequencies.

Scheme of computational area
Band structure of the waveguide (first BZ) for H
polarization and intensity distributions of
modes
Simulation time step ?t 8.37 attoseconds, space
step ?r5 nm, computational grid size 70 x 500
(without UPML) , time steps 10 000 20 000 are
used for the analysis
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Transmission through the waveguide
For FDTD simulations of propagation in structure
on the right we use two types of illumination
symmetrical (Gaussian source) and antisymmetrical
(Hermite Gaussian source) to excite different
modes separately. Attenuation in dB/?m is
calculated from FDTD results as a10 log(I/I0)
/ d where d 4 ?m, I and I0 are intensities
integrated over x axis (perpendicular to the
waveguide) at plane z4 ?m and at plane z0 ?m,
correspondingly.
Simulation area
Attenuation is higher than 3.6 and 10.0 dB/?m for
symmetrical and antisymmetrical ilumination,
respectively.
Simulation time step ?t 8.37 attoseconds, space
step ?r5 nm, computational grid size 1000 x 500
(without UPML) , intensity is obtained as
Poynting vector length averaged over 5 periods of
source
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Glance at mechanism of waveguiding

• Evolution of fields from FDTD results at
  ilummination wavelength 600 nm
• symmetry of source according to waveguide axis
• symmetric
  antisymmetric
• H
• P

Simulation time step ?t 8.37 attoseconds, space
step ?r5 nm, computational grid size 1000 x 500
(without UPML) , simulation area as before
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Intensity distribution in case of symmetrical
(Gaussian) illumination of 600 nm wavelength
Simulation time step ?t 8.37 attoseconds, space
step ?r5 nm, computational grid size 1000 x 500
(without UPML) , simulation area as before
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Intensity distribution in case of antisymmetrical
(Hermite - Gaussian) illumination of 600 nm
wavelength
Simulation time step ?t 8.37 attoseconds, space
step ?r5 nm, computational grid size 1000 x 500
(without UPML) , simulation area as before
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Other examples of propagation referred to modes
properties
Intensity profile in case of Gaussian source of
600 nm moved 250 nm off axis. Serpent like
beating pattern between symmetric and
antisymmetric modes appers.
Simulations time step ?t 8.37 attoseconds,
space step ?r5 nm, computational grid size 1000
x 500 (without UPML) , simulations area as before,
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Various designs of 2D and 3D metamaterials - LHM
and other media with unusual refractive index

• Resonant units e.g. wiresSRRs placed with
  different orientations generate local
  polarizations and magnetizations that determine
  effective permittivity and permeabilitty
• Photonic crystal with isotropic photonic band
  acts like a medium with refraction index
  determined by band radius
• Net medium - net of various oriented waveguides

WireSSR structures from UCSD (left) and Boeing
(right)
Figures from Notomi, Phys. Rev. B 62, 10, 696
(2000).
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Net medium

• The main idea of net medium is to use waveguides
  with desired property to construct 2D (or even
  3D) media exhibiting the same property.
• In 2003 Shvets proposed such structure, 2D LHM
  made of net of plasmonic channel waveguides.
  Waveguides were organised in square or hexagonal
  lattice.
• In net medium light propagates along waveguides,
  what defines propagation in a whole medium
• Various orientations of waveguides assure
  different directions of phase front propagation
• Different lattices (square, hexagonal, random...)
  lead to different anisotropy
• Single mode waveguides are preferred as
  construction elements (to avoid two beams
  propagating in medium) and mode field shape
  should be symmetric to be easy excited with plane
  wave
• Waveguides have to be small to construct a dense
  net with full angle isotropic propagation in a
  metamaterial

Figures from Shvets basic waveguide and
waveguides forming lattices
G. Shvets, Photonic approach to making a
material with a negative index of refraction,
Phys. Rev. B 67, 035109 (2003).
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Plasmon waveguide on silver nanords as a base for
visible range frequencies metamaterial

• Advantages
• small size
• tuneable by geometrical parameters
• existence of LH modes

Disadvantages high losses multimode non trivial
coupling between different angle oriented
waveguides (problem of nodes in net)
Intensity in FDTD simulated coupling between
waveguides of different orientation
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Conclusions

• The examined structure guides energy with
  considerable losses higher than 4 dB/?m. It
  needs tuning of geometrical parameters. Perhaps
  an active medium can be added in the structure or
  in nodes of net metamaterial?
• Net medium requires a node structure that couples
  energy between waveguides with high efficiency.
  Preservation of rods position in hexagonal
  lattice would be preferable for most fabrication
  methods?
• Detailed properties of net medium need further
  investigations.

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Thank You For Your Attention author email
saj_at_igf.fuw.edu.pl
Acknowledgments This research was sponsored by
Polish Ministry of Science and Information
Society Technologies grant 3 T08A 081 27. The
author participates in the EU 6PR Network of
Excellence METAMORPHOSE contract 500 252.