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

Nahid TalebiandMahmoud Shahabadi

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

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 WaveguidesWhy

?

Plasmonic Waveguide 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

Different Kinds of

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

Green’s dyadictechnique

Dipole estimation technique

2. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, phys. Rev. lett. 82, 2590 (1999) 3. M. Brongersma, J. Hartman, and H. Atwater, Phys. Rev. B 62, 356, (2000)

Modal Analysis of a Periodic Array Comprised of Metallic Nanorods Using GMT

L

RD1

D2

D3

D4

1

0

( )r

0

0

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

Rayleigh expansion center

Periodic boundary conditions

N =5

N =3

Fictitious excitation:A monopole

h

( ) ( ) xj Lx L x e

, , ,f f f Z U EXC

The unknown amplitudes

The impedance matrix

Excitation

2

, . , ,R f f f Z U EXC

i

We search for the maximum of the residue function at each frequency, in the complex plane.

We propose an iterative procedure

very time consuming

The Iterative Procedure0

0

0

f f

Using R, find β

n

1n n

n

y

N

n

n

11

1

1ln

2 2nr loss n

P

L P P P

L

2 1 exp 2P P L

1 2 2 r lossP P P P

Convergence of the Iterative Procedure

R=25 nmL=55 nm

L

R

Propagation Constant

Single mode region

3 dB/71.8 µm

R=25 nmL=55 nm

L

R

Longitudinal Mode

470nm

Transverse Mode

426nm

Higher Order Modes

2 2

2 ( arctan )2 ( )( )0

0

22 0

0

2

( , )( )

( ) 1 ( ) ,

( ) 1

R

r z kri kz

z R zw z

RR

R

wE r x E e e

w z

wzw z w z

z

zR z z

z

Analysis of a finite chain array

Gaussian Incident Field:

Rayleigh length

Array in the Bandgap

r328.275nm -0.085074387+i0.6117195

Longitudinal mode

384.975nm -3.501285+i0.187184r

Higher Order modes

4th mode: 370.8nm -2.742645+i0.231894r 5th mode: 358.2nm -2.059943+i0.280605r

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.

Thank you!

Analysis of a finite chain array Excitation of the computed modes in a finite array of

nanorods with plane wave

N =6

N =3

328nm

Longitudinal Mode

388 nm

369nm

Both longitudinal and transverse modesare propagating.

This excitation results in the propagation of just Longitudinal mode

Higher Order Modes

358nm

4th mode

5th 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