1. 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

2. Outline 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

3. Why Plasmonic Waveguides ? 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

4. Plasmonic Waveguide 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)
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phys. Rev. lett. 82, 2590 (1999)

5. Modal Analysis of a Periodic Array Comprised of Metallic Nanorods Using GMT
1. P. B. Johnson and R. W. Christy, Phys. Rev. B, 6, 4370, (1972).

6. Periodic boundary conditions
Fictitious excitation:
A monopole h
Rayleigh expansion center

7. 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

8. The Iterative Procedure
Using R, find β L N y

9. Convergence of the Iterative ProcedureL
R=25 nm
L=55 nm

10. Propagation Constant R R=25 nm L=55 nm L Single mode region
3 dB/71.8 µm

11. Longitudinal Mode

12. Transverse Mode

13. Higher Order Modes

14. Analysis of a finite chain array
Gaussian Incident Field:
Rayleigh length

15. Array in the Bandgap

16. Longitudinal mode

17. Higher Order modes
5th mode:
4th mode:

18. Conclusion
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.

19. Thank you!

20. Analysis of a finite chain array
Excitation of the computed modes in a finite array of nanorods with plane wave
N =6
N =3

22. Longitudinal Mode Both longitudinal and transverse modes
are propagating.
This excitation results
in the propagation of
just Longitudinal mode

23. Higher Order Modes

24. 5th mode
4th mode

25. The method is based on thermal evaporation of gold onto a porous alumina (PA) membrane used as a template. The gold films were obtained after removing the template and characterized using scanning electron microscopy, atomic force microscopy and ultraviolet–visible spectrophotometry.
Dusan Losic, et. al, Nanotechnology 16 (2005) 2275–2281