Analysis of the Propagation of Light along an Array of Nanorods Using the Generalized Multipole Technique

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Analysis of the Propagation of Light along an Array of Nanorods Using the Generalized Multipole Technique

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Nahid Talebi

and

Mahmoud Shahabadi

Photonics Research Lab., School of Electrical and Computer Engineering, University of Tehran

July 9, 2007

- Introduction: Plasmonic waveguides
- Why plasmonic waveguides?
- Different kinds of Plasmonic waveguides

- Modal analysis of a plasmonic waveguide (a periodic array comprised of nanorods)
- Analysis of a finite chain array
- Conclusion

Why

?

Plasmonic Waveguides

- Guiding the electromagnetic energy below the diffraction limit and routing of energy around sharp corners
- Engineering the plasmonic resonances of coupled structures leads to confined propagating modes in comparison with dielectric waveguides

Different Kinds of

- Metallic wires1
- Chains of metallic nanoparticles:
- A chain array of cubes 2
- A chain array of spheres 3
- A chain array of nanorods (here)

- Channel plasmon-polariton waveguides
- Wedge plasmon-polariton waveguides

Green’s dyadic

technique

Dipole estimation

technique

3. M. Brongersma, J. Hartman, and H. Atwater, Phys. Rev. B 62, 356, (2000)

2. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet,

phys. Rev. lett. 82, 2590 (1999)

1. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, Opt. Lett. 22, 475 (1997)

D3

D2

R

D1

L

D4

1. P. B. Johnson and R. W. Christy, Phys. Rev. B, 6, 4370, (1972).

Periodic boundary conditions

N =3

N =5

Fictitious excitation:

A monopole

h

Rayleigh expansion center

Excitation

The unknown amplitudes

The impedance matrix

We search for the maximum of the residue function

at each frequency, in the complex plane.

very time consuming

We propose an iterative procedure

Using R, find β

L

N

y

R

L

R=25 nm

L=55 nm

R

R=25 nm

L=55 nm

L

Single mode region

3 dB/71.8 µm

Gaussian Incident Field:

Rayleigh length

5th mode:

4th mode:

- The iterative procedure introduced here is an efficient method for computing the complex propagation constants.
- Single mode propagation with group velocity near to the group velocity of the light and the attenuation constant of as low as 3 dB/71.8 µm.
- An array comprised of a number of nanorods can be used as a plasmonic waveguide.

Thank you!

- Excitation of the computed modes in a finite array of nanorods with plane wave

N =6

N =3

Both longitudinal and transverse modes

are propagating.

This excitation results

in the propagation of

just Longitudinal mode

5th mode

4th mode

- The method is based on thermal evaporation of gold onto aporous alumina (PA) membrane used as a template. The gold films wereobtained after removing the template and characterized using scanningelectron microscopy, atomic force microscopy and ultraviolet–visiblespectrophotometry.

Dusan Losic, et. al, Nanotechnology 16 (2005) 2275–2281