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
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)
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