Determination of the Optical Properties of Individual Gold Nanorods through Numerical

Modeling and Experiment

Y. Davletshin, J. C. Kumaradas

Ryerson University

Toronto, Canada

1 Excerpt from the Proceedings of the 2012 COMSOL Conference in Boston

The Lycurgus Cup. Late Roman Empire 4th Century AD.

www.britishmuseum.org 2

Optimization of Optical Properties of GNPs through FE

Modeling

Optical properties to optimize:

• Absorption

• Scattering

• E field Enhancement

• Etc.

3

Solving Wave Equation for Arbitrary Shape Objects

0E2

2~2B

t

Johnson P.B. & Christy R.W.\Phys. Rev. B, 1972

James Clerk Maxwell (1831–1879)

21B

~ i

4

size correction to needed

Dielectric Function of Small Clusters

Size~~~

B

,

eff

FS

L

A ,4

eff SVL

For nanoparticles where LLeff

Sonnichsen, C.,\PhD thesis, 2001

,R

V

,~

RSD

2

2

p

D

2

2

pSize

ii

s

L/1 1410094.1F

D

B

~

317 nmfs10)5.15.5(

A - unknown nm/fs 41.1p

Novo et. al.\Phys. Chem. Chem. Phys., 2006 5

A=0

A=0.5

(2R<40 nm)

(40<2R<150 nm)

Experimental Approach: Spatial Modulation Spectroscopy

with TEM on a Single Particle

6

Modeling SMS Experimental Setup

Davletshin Y. et. al.\ACS Nano., 2012

SMS FEM (COMSOL 3.5a)

The medium inside the domain was air, and the GNR support layer on

the TEM grid was modelled as a 40 nm thick silica substrate. In the

computational model a = 2.4 um, b = 0.4 um, c = 1.4 um, and d = 40

nm. The domain in the front-to-back direction had a size equal to c.

Mesh: 540k tetrahedral elements, 4M degrees of freedom

7

Results: Silica Coated GNRs

8

Fitting procedure: • GNR dimension within TEM uncertainty (+/- 0.5 nm)

• A parameter to obtain longitudinal SPR FWHM within 1%

of experimental value

A=0.47

A=0.46

A=0.55

Results: Bare GNRs

Davletshin Y. et. al.\ACS Nano., 2012

Environmental factors:

water, humidity, surfactant molecules

9

Discussions

• Realistic FE model of experimental SMS setup

* Silica substrate

* GNR geometry

* GNR dimensions

* Size corrected dielectric function of gold

• Determination of A (broadening parameter),

consistent values for 3 silica coated GNRs

Remaining questions:

• FE model didn’t work for bare GNRs

(environmental factors)

• Will A parameter work for other GNR sizes

• Dependence of Leff=4V/S not tested.

10

Acknowledgments:

Université Claude Bernard Lyon – 1, Laboratoire de Spectrométrie Ionique et Moléculaire

FemtoNanoOptics Group

Dr. Natalia Del Fatti

Dr. Fabrice Vallee

Dr. Paolo Maioli

Dr. Aurelien Crut

Dr. Vincent Juve

Anna Lombardi

Unidad Asociada CSIC – Universidade de Vigo, Departamento de Quimica Fisica

Dr. Luis M. Liz-Marzán

Dr. María Fernanda Cardinal

11