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 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 ? 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 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) 1. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, Opt. Lett. 22, 475 (1997) 2. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, phys. Rev. lett. 82, 2590 (1999)

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).

Periodic boundary conditions 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

The Iterative Procedure Using R, find β L N y

Convergence of the Iterative Procedure L R=25 nm L=55 nm

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

Longitudinal Mode

Transverse Mode

Higher Order Modes

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

Array in the Bandgap

Longitudinal mode

Higher Order modes 5th mode: 4th mode:

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.

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

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

Higher Order Modes

5th mode 4th mode

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