This document discusses plasmonic chain waveguides. Plasmonic chain waveguides use linear chains of plasmonic nanoparticles to concentrate optical beams below the diffraction limit and guide electromagnetic energy. Each nanoparticle acts as a dipole that interacts with the nearest neighboring nanoparticles. This coupling supports localized surface plasmons and guided wave propagation along the chain. Both the particle size and distance between particles impact the coupling strength and guided modes. Plasmonic chain waveguides have applications in nanophotonics due to their ability to squeeze optical signals into subwavelength confinement.

1. Plasmonic chain waveguides
R.Gandhimathi

2. ▪A structure which guides light wave by limiting it to travel along a desired path
▪Waveguide contains a region of increased refractive index(core), compared with the
surrounding medium (cladding)
▪An electromagnetic energy to be carried by a waveguide is injected into one end of the
waveguide
▪The electric and magnetic fields associated with the signal bounce off inside walls back
and forth as it progresses down the waveguide
Optical wave guide
Guided waves
Insulation CoreCladding
Core
Refractive index
ncladding < ncore
Light entering is trapped
as long as
cladding
core
n
sin
n
 

3. ▪ Plasmonics deals with coupling Light to Nanoscale via Surface Plasmons (SPs)
▪ SPs are identified as optical modes at metal/dielectric interface and are characterized in
terms of dispersion and spatial profile
▪ Both surface plasmon polaritons and localized surface plasmon modes support low-loss
light wave propagation at subwavelength size
▪ Surface plasmonic waveguides have the ability to confine light at sub-wavelength scale
▪ Plasmon Waveguide can squeeze the optical signal by shrinking its wavelength by a
factor of 10 or more and have a large number of applications in the field of nanocircuits,
nanophotonics devices, biological and chemical sensors, holography, and other
applications
Plasmonic Waveguide

4. Different plasmonic waveguide structures
▪ Layered structures
▪ Metallic nanowires
▪ Metallic nanoparticle arrays
▪ Metallic nano particles chain
▪ Channel plasmon polariton waveguides
▪ Wedge plasmon-polariton waveguides
Plasmonic waveguide structures
Metallic nanowires and nano-grooves support guided plasmonic modes and can be used as
subwavelength waveguides of optical signal.

5. ▪ Nanoscale plasmonic waveguides composed of metallic nanoparticles are capable of
guiding electromagnetic energy below the optical diffraction limit
▪ Linear chains of plasmonic (silver or gold) nanoparticles concentrate the optical beam
in a narrow region of space, in large part filled by lossy metal
▪ Energy transfer via dipolar interactions between closely spaced metal nano particles
supports localized surface plasmons (LSP) and leads to the formation of a waveguide
▪ The coupling among the guided modes may improve the guidance performance
Plasmonic Chain Waveguide
Coupled mode theory is used
in order to study systems of
interacting plasmonic spheres

6. Factors to be considered
▪ Dynamic interaction among the infinite number of nanoparticles composing the linear
arrays
▪ Realistic presence of losses and the frequency dispersion of the involved plasmonic
materials
Advantages
▪ longer propagation lengths
▪ More confined beams
▪ Design flexibility
▪ Easy construction within current nanotechnology
▪ the realization of such ultracompact waveguides
▪ operating analogously to transmission-line segments at lower frequencies
Disadvantages
▪ strong sensitivity to material and radiation losses

7. Field enhancementField enhancement
➢ In assembled metal nanoparticles, plasmons on the particles interact with each
other to give characteristic spatial distributions of the electric field.
➢ Interparticle coupling associated with a strong induced charge in the hotspot
enhance the field in the gap many times and this enhancement is much larger than
the field enhancement close to a single nanoparticle.
Nano particle dimer

8. • If the size of nanoparticles is much smaller than the wavelength of the incident
electromagnetic radiation, particles will behave as point dipoles
• The excitations in nano particle dimer are recognized using dipole approximations.
I.e. transverse and longitudinal modes
• Depending on the polarization direction of the exciting light, it leads to a blue-shift of the
plasmon resonance for the excitation of transverse modes, and a red-shift for longitudinal
modes
Dipole moments perpendicular to x-axis
Transverse modes
Dipole moments along the x-axis.
longitudinal modes

9. E12 -Field generated by the dipole 2 at the point dipole 1
E21 -Field generated by the dipole 1 at the point dipole 2
1, 2-Polarizability of the two nanoparticles
1 1 2
2 2 1
( )
( )
T
T
P g P
P g P
 
 
=
=
3
0
1
4
Tg
a
= −Coupling constant
gT -Inverse cube of distance between the dipoles
1 1 12
2 2 21
( )
( )
P E
P E
 
 
=
=
Induced Dipole moment
21 1TE g P= 12 2TE g P=&Where
➢Particle size and the distance between the
particles are less than incident light
wavelength
➢Dipoles interaction with each other and the
incident field, giving rise dipole polarizations
➢All Scattering quantities can be obtained
from these polarizations
Interaction of dipole moments

10. T+
P1=P2 - symmetric
High frequency Mode
Low frequency Mode
T+
T−
Eigen frequencies of the modes &
P1= -P2-antisymmetric modes T−
0 01T Tg  
= 
The eigen states or polarization states
3
0 3T
R
g
a
 =
3
0 3
1T
R
a
 
= 
3
0 3
2
L
R
g
a
 =
3
0 3
2
1L
R
a
 
= 
gL=2gT
Dipole
moments
in same
direction
Opposite
direction
Transverse modes Longitudinal mode
Frequency vs distance between he two metal nanoparticles
Longer the distance between the
particles, then weaker coupling
gL –two times the transverse field

11. , 1 , 1
1 10 12
, 1 1
, 1 1
1 1
( )( )
1
( )( )
( ) ( )
n n n n n
n n T n
n n T n
n T n n
P E E
n
P E E
E g P
E g P
P g P P
 
 
 
− +
− −
+ +
− +
= +
=
= +
=
=
= +
Nanoparticle chain
➢ Each metal nanoparticle acts a dipole
➢ Only nearest neighbor interaction is considered . i.e.,
➢ Particle n interacts with (n+1) and (n-1) particles only two particles
➢ The dipole moment of nth particle is defined by the fields generated by (n+1) & (n-1)
particles
n-1 n n+1
Guided wave propagation along linear arrays of
plasmonic nanoparticles

12. ➢ When metal nanoparticles are assembled, interaction between plasmons on each one
of the particles, through the electromagnetic field, becomes prominent.
➢ Interference between the plasmon-induced electric field also occurs.
➢ As a result, the assembled system shows totally different optical characteristics from
isolated nanoparticles.
➢ Direct imaging of the electric-field distribution in such assembled nano particles gives
the understanding of behavior of plasmons and a guiding principle to design and
control plasmonic systems

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Odom, “The rich photonic world of plasmonic nanoparticle arrays”, Materials Today d Volume 21, Number
3 d April 2018
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Andrea Alù1,*, Pavel A. Belov2,3, and Nader Engheta, “Coupling and Guided Propagation along Parallel
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References

14. Thnk you