Optical properties of morphology-controlled gold nanoparticles Qiguang Yang,1* Jaetae Seo,1* Wan-Joong Kim,2 SungSoo Jung,3 Bagher Tabibi,1 Justin Vazquez,1 Jasmine Austin,1 and Doyle Temple1 1
Department of Physics, Hampton University, Hampton, VA 23668, USA *E-mail:
[email protected];
[email protected] 2 Electronics and Telecommunications Research Institute, Daejeon, 305-700, South Korea 3 Korea Research Institute of Standards and Science, Daejeon, 305-600, South Korea ABSTRACT Both linear and nonlinear optical properties of metal nanoparticles strongly depend on their particle sizes. Sizedependent surface plasmon resonant absorption of gold nanoparticles was theoretically accessed using Mie scattering theory based on empirical optical absorption and TEM measurements, which allows to estimate the average size of gold nanoparticles with simple absorption measurement. The nonlinear optical properties of the gold nanoparticles were studied with Z-scan and forward degenerate four-wave mixing techniques.
Keywords: surface plasmon resonant, third-order nonlinear susceptibility, gold nanoparticles 1. INTRODUCTION Metals, which have completely filled valence bands and partially filled conduction bands, have been widely utilized for electronic and optical applications. Their dielectric functions are governed by both intraband and interband transitions. The intraband contribution is due to the response of free electrons to the applied field while the interband contribution is caused by the transition from the filled d-band to the empty conduction band above Fermi level1. The former transition is well described by Drude-Lorentz-Sommerfeld model 2 and the latter transition is usually described by Bassani and Parravicini model 3, 4 . As the size of the metals is reduced to few nanometers, evidence of an enhanced interband absorption in Au nanoparticles has been observed in UV wavelength range 5 . In visible wavelength range, surface plasmon resonance (SPR) absorption arises from the collective oscillations of free electrons in the conduction band of metal nanoparticles6. The excited electrons thermalize and generate a hot Fermi distribution via electron-electron scattering on femtosecond time scale and then thermally equilibrate with lattice through electron-phonon coupling in several picoseconds for gold nanoparticles6. Finally the heat released to the surrounding medium increases the overall temperature of the system by phonon-phonon scattering within few hundred picoseconds5. For thermalization in nanoshells for medical applications, The temperature increase of the gold nanoshell hydrosol with 1% volume concentration as high as 30 0C under exposure of an 808 nm coherent diode laser with a power density of 5 W/cm2 was reported7.
2. SIZE AND SHAPE MEASUREMENTS USING TEM METHOD The Au nanoparticles were synthesized using a sodium citrate reduction method. The nanoparticles with polyvinylpyrrolidone (PVP) surfactant were distributed in water. The average size and shape of the used Au NPs were obtained using transmission electron microscope (TEM) (JEOL JEM-2010) operating at 200 kV. Figures 1 and 2 show a typical TEM picture of Au NPs with a 100-nm scale bar and their size distribution, respectively. The distribution bars in figure 2 has been fitted using a Gaussian function. The best fitting gave the average size of about 15 nm of the Au NPs and its distribution width was about 2.2 nm.
Photonics and Optoelectronics Meetings (POEM) 2008: Laser Technology and Applications edited by Peixiang Lu, Katsumi Midorikawa, Bernd Wilhelmi, Proc. of SPIE Vol. 7276, 727617 © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.822839 Proc. of SPIE Vol. 7276 727617-1
40 Sample Au: 4_1 Gaussian fit Ave. diameter:15.11 nm Width:2.24 nm
Number
30 20 10 --
-S
0 10
::..?.! - - i!.!. .S.S
15
S ......:.:.
20
Diameter (nm)
Fig. 1 Typical TEM picture of Au nanoparticles
Fig. 2 Typical size distribution of the Au nanoparticles in water
3. LINEAR OPTICAL PROPERTIES OF GOLD NANOPARTICLES The linear optical property of bulk gold metal is determined by both conduction and bound electron responses. Its dielectric function is given by
H bulk
H f H bound
H 1 iH 2
(1)
where the main contribution to the bound electron term is the interband transitions from filled 5d10 band to 6sp conduction band above Fermi level for gold. The behavior of the conduction electron in gold may be considered as a simple harmonic oscillator driven by the applied electric field. The displacement of the electron thus may be easily obtained and the corresponding dielectric functions is given by8
H f (Z ) 1 here
Zp
Z p2
(2)
Z 2 i*0Z
ne 2 is the Drude plasma frequency, n is the electron density, me is the effective mass, e is the electric H 0 me
charge of the electron,
H0
is the electric permittivity of free space, and *0 is the damping constant. The damping
constant is determined by electron scattering processes and is related to the electron mean free path l as *0
VF , l
where V F is Fermi velocity. Using the dielectric function given in reference 8, one may obtain the linear absorption coefficient by
D bulk
2Z c
H H 2
2
1
2
2
Proc. of SPIE Vol. 7276 727617-2
H1
(3)
Absorption Coefficent (1/m)
7
8.5x10
7
8.0x10
7
7.5x10
7
7.0x10
7
6.5x10
Bulk Au
7
6.0x10
7
5.5x10
7
5.0x10
7
4.5x10
200
400
600
800
1000
1200
1400
Wavelength (nm) Fig. 3 Absorption coefficient of bulk gold metal
Fig. 3 shows the calculated absorption coefficient obtained through equation (3). The absorption is very strong in the whole UV-near IR wavelength range. When the size of Au metal is reduced to nanometer scale, its optical properties will be changed significantly due to both quantum confinement and dielectric confinement effects. In visible wavelength range, the main contribution to the change in optical absorption is the dielectric confinement effect which directly leads to surface plasmon resonance. In 1908, Mie explained the color of colloidal gold by solving Maxwell’s equation. According to Mie theory, the optical extinction coefficient of homogenous spherical particles with size 2r
