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Analysis of the Propagation of Light along an Array of Nanorods Using the Generalized Multipole Technique. Nahid Talebi and Mahmoud Shahabadi Photonics Research Lab., School of Electrical and Computer Engineering, University of Tehran July 9, 2007. Outline.

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Slide1 l.jpg

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

Nahid Talebi

and

Mahmoud Shahabadi

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

July 9, 2007


Outline l.jpg
Outline Nanorods Using the Generalized Multipole Technique

  • 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


Plasmonic waveguides l.jpg
Plasmonic Waveguides Nanorods Using the Generalized Multipole Technique

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


Plasmonic waveguide l.jpg
Plasmonic Waveguide Nanorods Using the Generalized Multipole Technique

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)


Modal analysis of a periodic array comprised of metallic nanorods using gmt l.jpg
Modal Analysis of a Periodic Array Comprised of Metallic Nanorods Using GMT

D3

D2

R

D1

L

D4

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


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Periodic boundary conditions Nanorods Using GMT

N =3

N =5

Fictitious excitation:

A monopole

h

Rayleigh expansion center


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Excitation Nanorods Using GMT

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


The iterative procedure l.jpg
The Iterative Procedure Nanorods Using GMT

Using R, find β

L

N

y


Convergence of the iterative procedure l.jpg
Convergence of the Iterative Procedure Nanorods Using GMT

R

L

R=25 nm

L=55 nm


Propagation constant l.jpg
Propagation Constant Nanorods Using GMT

R

R=25 nm

L=55 nm

L

Single mode region

3 dB/71.8 µm


Longitudinal mode l.jpg
Longitudinal Mode Nanorods Using GMT


Transverse mode l.jpg
Transverse Mode Nanorods Using GMT


Higher order modes l.jpg
Higher Order Modes Nanorods Using GMT


Analysis of a finite chain array l.jpg
Analysis of a finite chain array Nanorods Using GMT

Gaussian Incident Field:

Rayleigh length


Array in the bandgap l.jpg
Array in the Bandgap Nanorods Using GMT


Longitudinal mode16 l.jpg
Longitudinal mode Nanorods Using GMT


Higher order modes17 l.jpg
Higher Order modes Nanorods Using GMT

5th mode:

4th mode:


Conclusion l.jpg
Conclusion Nanorods Using GMT

  • 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.


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Thank you! Nanorods Using GMT


Analysis of a finite chain array20 l.jpg
Analysis of a finite chain array Nanorods Using GMT

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

N =6

N =3


Longitudinal mode22 l.jpg
Longitudinal Mode Nanorods Using GMT

Both longitudinal and transverse modes

are propagating.

This excitation results

in the propagation of

just Longitudinal mode


Higher order modes23 l.jpg
Higher Order Modes Nanorods Using GMT


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5 Nanorods Using GMTth mode

4th mode


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  • The method is based on thermal evaporation of gold onto a Nanorods Using GMTporous 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


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