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TECHNICAL PAPERS

# Surface Plasmon Scattering by Gold Nanoparticles and Two-Dimensional Agglomerates

[+] Author and Article Information

Radiative Transfer Laboratory, Mechanical Engineering Department, University of Kentucky, Lexington, KY 40506

M. Pinar Mengüç

Radiative Transfer Laboratory, Mechanical Engineering Department, University of Kentucky, Lexington, KY 40506menguc@engr.uky.edu

Gorden Videen

U.S. Army Research Laboratory AMSRL-CI-EE, 2800 Powder Mill Road, Adelphi, MD 20783

J. Heat Transfer 129(1), 60-70 (Jul 27, 2006) (11 pages) doi:10.1115/1.2401199 History: Received February 03, 2006; Revised July 27, 2006

## Abstract

There has long been an interest in nanosized metallic particles for numerous novel applications, from the productions of colored glass in medieval times to the molecular-level sensors of today. These particles are known to display considerably different, and size-dependent, optical properties than those of their bulk counterparts. Yet it is very difficult to determine the size and structure of these particles in situ, such as monitoring the actual self-assembly process, because of their small size. In this paper, we present a methodology to predict the patterns of nanosized particles and agglomerates subjected to surface plasmon waves. For this characterization, the scattering patterns of different types of particles and agglomerates on or near the surface are needed. A combination of the T-matrix method, image theory, and a double interaction model are considered. The incident and scattered fields are expanded by employing spherical harmonic functions. The surface effects are incorporated using the Fresnel equations, in the incident-field expansion coefficients, and by including particle-surface interaction fields. The premise of the method is that the T-matrix is independent of incident and scattered fields and hence can be used effectively for cases involving incident surface waves. By obtaining the T-matrix for clusters or agglomerates of metallic particles, the scattering matrix elements ($M11$, $M12$, $M33$, and $M34$) of agglomerated structures on the surface are calculated using an additional T-matrix operation. The effect of size, shape, and orientation of gold nanosized particles on their scattering patterns are explored both in the visible spectrum and at resonance wavelengths. The results show that the normalized scattering matrix elements at certain observation angles and incident wavelengths provide significant information to monitor the structural change of gold nanosized particles on a gold substrate.

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## Figures

Figure 1

The schematic of the scattering from a group of particles on (h=0) or near (h>0) a thin film. d is the distance between the surface of the film and the center point of the agglomerated structure.

Figure 2

Schematic for the hybrid method used

Figure 3

Spectral variation of gold refractive index

Figure 4

Spectral variation of critical angle at quartz-gold interface (n-quart=1.75)

Figure 5

Particle shape configurations and orientations considered

Figure 6

10nm diameter particle configurations (shown in Model I-a) on a gold substrate (top) and on a quartz substrate (bottom)

Figure 7

Scattering profiles for particle configurations shown in Models I-b, II, and III-a, for a particle diameter of 10nm

Figure 8

M11 profile for particle configurations shown in Models I-b, II, and III-a, for a particle diameter of 20nm

Figure 9

Scattering profiles for particle configuration shown in Model II, for a particle diameter of 20nm

Figure 10

Scattering profiles for particle configurations shown in Models IV-a and IV-b, for a particle diameter of 20nm

Figure 11

Scattering profiles for particle configurations shown in Model V, for a particle diameter of 20nm

Figure 12

M11 profiles for 20-nm-diameter particles placed on the surface for arrangements shown in Model III-a (a) and III-b (b)

Figure 13

M12 profiles for 20-nm-diameter particles on the surface for arrangements shown in Model III-a (a) and III-b (b)

Figure 14

M33 profiles for 20-nm-diameter particles on the surface for arrangements shown in Model III-a (a) and III-b (b)

Figure 15

M34 profiles for 20-nm-diameter particles on the surface for arrangements shown in Model III-a (a) and III-b (b)

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