Calculated Absorption and Scattering Properties of Gold Nanoparticles of Different Size,
Shape, and Composition: Applications in Biological Imaging and Biomedicine
Prashant K. Jain,
†
Kyeong Seok Lee,
†
Ivan H. El-Sayed,*
,‡
and Mostafa A. El-Sayed*
,†
Laser Dynamics Laboratory, School of Chemistry and Biochemistry, Georgia, Institute of Technology,
Atlanta, Georgia 30332-0400, and Department of OtolaryngologysHead and Neck Surgery,
ComprehensiVe Cancer Center, UniVersity of California at San Francisco, San Francisco, California 94143
ReceiVed: December 8, 2005; In Final Form: February 22, 2006
The selection of nanoparticles for achieving efficient contrast for biological and cell imaging applications, as
well as for photothermal therapeutic applications, is based on the optical properties of the nanoparticles. We
use Mie theory and discrete dipole approximation method to calculate absorption and scattering efficiencies
and optical resonance wavelengths for three commonly used classes of nanoparticles: gold nanospheres,
silica-gold nanoshells, and gold nanorods. The calculated spectra clearly reflect the well-known dependence
of nanoparticle optical properties viz. the resonance wavelength, the extinction cross-section, and the ratio of
scattering to absorption, on the nanoparticle dimensions. A systematic quantitative study of the various trends
is presented. By increasing the size of gold nanospheres from 20 to 80 nm, the magnitude of extinction as
well as the relative contribution of scattering to the extinction rapidly increases. Gold nanospheres in the size
range commonly employed (∼40 nm) show an absorption cross-section 5 orders higher than conventional
absorbing dyes, while the magnitude of light scattering by 80-nm gold nanospheres is 5 orders higher than
the light emission from strongly fluorescing dyes. The variation in the plasmon wavelength maximum of
nanospheres, i.e., from ∼520 to 550 nm, is however too limited to be useful for in vivo applications. Gold
nanoshells are found to have optical cross-sections comparable to and even higher than the nanospheres.
Additionally, their optical resonances lie favorably in the near-infrared region. The resonance wavelength
can be rapidly increased by either increasing the total nanoshell size or increasing the ratio of the core-to-
shell radius. The total extinction of nanoshells shows a linear dependence on their total size, however, it is
independent of the core/shell radius ratio. The relative scattering contribution to the extinction can be rapidly
increased by increasing the nanoshell size or decreasing the ratio of the core/shell radius. Gold nanorods
show optical cross-sections comparable to nanospheres and nanoshells, however, at much smaller effective
size. Their optical resonance can be linearly tuned across the near-infrared region by changing either the
effective size or the aspect ratio of the nanorods. The total extinction as well as the relative scattering contri-
bution increases rapidly with the effective size, however, they are independent of the aspect ratio. To compare
the effectiveness of nanoparticles of different sizes for real biomedical applications, size-normalized optical
cross-sections or per micron coefficients are calculated. Gold nanorods show per micron absorption and
scattering coefficients that are an order of magnitude higher than those for nanoshells and nanospheres. While
nanorods with a higher aspect ratio along with a smaller effective radius are the best photoabsorbing
nanoparticles, the highest scattering contrast for imaging applications is obtained from nanorods of high aspect
ratio with a larger effective radius.
Introduction
The strongly enhanced surface plasmon resonance of noble
metal nanoparticles at optical frequencies makes them ex-
cellent scatterers and absorbers of visible light.
1-3
Superior
optical properties, coupled with recent advances in nano-
particle synthesis,
4
conjugation,
5
and assembly,
6
have stimu-
lated interest in the use of plasmon-resonant nanoparticles
and nanostructures for optical and photonic applications
7,8
and,
more recently, for biomedical applications.
9-26
Nanopar-
ticles composed of gold offer, in addition to their enhanced
absorption and scattering, good biocompatibility, facile synthe-
sis,
4
and conjugation to a variety of biomolecular ligands,
antibodies, and other targeting moieties,
5
making them suitable
for use in biochemical sensing and detection,
9-11
medical
diagnostics, and therapeutic applications.
12,13
There have been
several demonstrations of bioaffinity sensors based on the
plasmon absorption and scattering of nanoparticles
9,10
and their
assemblies.
11
Another notable use of gold nanoparticles has been as con-
trast agents in cellular and biological imaging.
14-17
Contrast
* Corresponding authors. E-mail: Mostafa A. El-Sayed: mostafa.
el-sayed@chemistry.gatech.edu (M.A.E.); ielsayed@ohns.ucsf.edu (I.H.E.).
Telephone: 404-894-0292 (M.A.E.); 415-353-2401 (I.H.E.). Fax: 404-894-
0294 (M.A.E.); Fax: 415-353-2603 (I.H.E.).
†
Georgia Institute of Technology.
‡
University of California at San Francisco.
7238 J. Phys. Chem. B 2006, 110, 7238-7248
10.1021/jp057170o CCC: $33.50 © 2006 American Chemical Society
Published on Web 03/18/2006
agents in medical and biological imaging
18
improve the sensitiv-
ity and diagnostic ability of the imaging modality by site-
specifically labeling tissues or cells of interest. Cellular imaging
utilizing microscopy techniques and immunotargeted optical
contrast agents provides anatomic details of cells and tissue
architecture important for diagnosis of cancer as well as other
disorders. Biomedical imaging contrast agents have been
traditionally based on photoabsorbing and fluorescent dyes such
as malachite green and rhodamine-6G.
19
More recently, quantum
dots have been used and studied for biological and cell imaging
due to their unique size-dependent fluorescence properties.
20,21
However, the potential human toxicity and cytotoxicity of the
semiconductor material are two major problems for its in vitro
and in vivo application. Colloidal gold nanoparticles have
become an important alternative as imaging agents due to their
potential noncytotoxic, facile immunotargeting
5
as well as due
to their nonsusceptibility to photobleaching or chemical/thermal
denaturation, a problem commonly associated with dyes.
22
Immunogold nanoparticles conjugated to antibodies have been
widely used for biological labeling and staining for electron
microscopy.
23
Recently, strongly absorbing nanoparticles com-
posed of gold have been shown to offer excellent promise for
cell and tissue imaging by using techniques such as multi-
photon plasmon resonance microscopy
14
and photoacoustic
tomography.
15
Similarly, the strong light scattering of gold
nanoparticles has been exploited for real-time optical imaging
of precancer by using confocal reflectance microscopy.
16
El-Sayed et al. have demonstrated differentiation of cancerous
cells from noncancerous cells by dark field light-scattering
imaging and absorption spectroscopy of solid ∼40 nm gold
nanospheres immunotargeted to EGFR overexpressed on cancer
cells.
17
Along with cancer imaging and diagnostic applications,
the ability of gold nanoparticles to efficiently convert absorbed
light into localized heat can be readily employed for therapy
based on photothermal destruction of cancerous cells.
24-28
For
example, Hirsch et al.
24
employed NIR absorbing silica-gold
core-shell particles for photothermal destruction of human
breast carcinoma cells in vitro as well as solid tumors in vivo.
Recently, Loo et al.
25
reported simultaneous imaging and therapy
of breast cancers in vitro using silica-gold nanoshells that were
conjugated with anti-Her2 antibodies. El-Sayed et al. and Huang
et al. used immunotargeted nanospheres of solid gold for
imaging and selective photothermal destruction of cancer cells
by Ar laser irradiation.
26,27
More recently, Huang et al. provided
an in vitro demonstration of gold nanorods conjugated to anti-
EGFR antibodies as novel contrast agents for both NIR cell
imaging and photothermal cancer therapy.
28
The effectiveness of nanoparticles as biomedical imaging
contrast and therapeutic agents depends on their optical
properties. For instance, a high-scattering cross-section is
essential for cell imaging applications based on light-scat-
tering microscopy. On the other hand, effective photothermal
therapy with minimal laser dosage requires a high nano-
particle absorption cross-section with low scattering losses.
Biosensing applications based on surface plasmon resonance
shifts necessitate strong resonance in the wavelength sen-
sitivity range of the instrument as well as narrow optical
resonance line widths.
29
For actual in vivo imaging and thera-
peutic applications, the optical resonance of the nanoparticles
is strongly desired to be in the near-infrared (NIR) region of
the biological water window, where the tissue transmissivity is
the highest.
30
In addition, the nanoparticle size is also an
important consideration for nanoparticle uptake and retention
by cells and tissue.
31
It is well-known that the plasmon resonance of metal
nanoparticles is strongly sensitive to the nanoparticle size, shape,
and the dielectric properties of the surrounding medium. Op-
tical properties of gold nanoparticles can thus be readily
tuned by varying their size and shape.
1,2,32-34
In addition, Halas
and co-workers have shown that the use of composite nano-
particles based on a core-shell morphology (e.g., silica-gold
nanoshells) allows optical tunability by variation in the com-
position.
35
There have been several experimental reports
2,36
on the optical
properties of metal nanoparticles, including gold nano-
spheres,
33,34,36-42
nanorods,
33,34,36,43
and nanoprisms,
44
silver
nanospheres,
36,37,39,45-47
nanowires,
48
and nanoprisms,
49-52
cop-
per nanospheres,
37,45,53
aluminum nanospheres,
36
bimetallic
nanoparticles,
54,55
composite nanoparticles with a core-shell
structure,
35,56-60
and nanoparticle chains and assemblies.
61-63
At the same time, well-established theoretical tools based on
the Mie theory
64
and the discrete dipole approximation (DDA)
65
method have been readily exploited for a quantitative study of
the nanoparticle optical properties of different size, shape,
composition, and aggregation state, etc.
2,36,66-73
In this paper,
we use Mie theory and the DDA method to calculate the ab-
sorption and scattering efficiencies and optical resonance wave-
lengths of gold nanospheres, silica-gold nanoshells, and gold
nanorods, for various nanoparticle dimensions, so as to aid the
selection of nanoparticles for specific biomedical applica-
tions. The calculated optical cross-sections of all three nano-
particle classes are found to be a few orders of magnitude higher
than those for conventionally used absorbing and fluorescent
dyes. Besides, the optical properties of nanoparticles, i.e., the
optical resonance wavelength, the extinction cross-section, and
the relative contribution of scattering to the extinction, are
strongly dependent on the nanoparticle dimensions, allowing
tunability for specific applications. For all three nanoparticle
types, the increase in the size results in an increase in the
extinction as well as the relative contribution of scattering.
Nanospheres offer resonance wavelengths in the visible region,
however, the tunability of the wavelength with size is too limited
to be useful for in vivo biomedical applications. In the case of
nanoshells, the resonance wavelength can be rapidly tuned in
the NIR region by either changing the total nanoshell size or
the ratio of the core/shell radius. Similarly, the optical reso-
nance of nanorods can be linearly tuned across the near-infrared
region by changing either the effective size or the aspect ratio
of the nanorods. To compare the effectiveness of nanoparticles
of different size for real-life biomedical applications, size-
normalized optical cross-sections or per micron coefficients have
been calculated. Gold nanorods on account of an order of
magnitude higher per micron absorption and scattering coef-
ficients, combined with easy resonance tunability and lack of
cytotoxicity, are concluded to offer the best imaging contrast
as well as the highest effectiveness for photothermal therapy
applications.
Calculation Method
The optical properties of gold nanospheres, nanorods, and
silica-gold nanoshells were quantified in terms of their
calculated absorption and scattering efficiency (Q
abs
and Q
sca
)
and their optical resonance wavelength (λ
max
).
Gold Nanospheres and Silica-Gold Nanoshells. For nano-
spheres of gold, Q
abs
and Q
sca
were calculated on the basis of
Mie theory for homogeneous spheres.
64
The Mie total extinction
and scattering efficiency Q
ext
and Q
sca
for a homogeneous sphere
are expressed as infinite series:
Absorption and Scattering Properties of Gold Nanoparticles J. Phys. Chem. B, Vol. 110, No. 14, 2006 7239
where m is the ratio of refractive index of the sphere n to that
of the surrounding medium n
m
, x is the size parameter given as
2πn
m
R/λ, ψ
n
and ξ
n
are the Riccati-Bessel functions, and the
prime represents first differentiation with respect to the argument
in parentheses. Numerical calculations of the Mie series were
performed at discrete points in the wavelength range from 300
to 800 nm.
Calculations of the optical absorption and scattering efficiency
of silica-gold nanoshells were performed by using a computer
code employing Mie scattering for concentric sphere geometry
developed by Ivan Charamisinau.
74
The required parameters for
the code were the value of the core and shell radii, R
1
and R
2
,
and the complex refractive indices for the core, shell, and the
surrounding medium, n
c
, n
s
, and n
m
, respectively. n
c
was taken
to be 1.44 + 0i for the silica core at all wavelengths.
For gold, values of the complex dielectric function at dif-
ferent wavelengths were obtained from Johnson and Christy
75
and corrected for nanoparticle size.
76,77
Cubic interpolation
was used to calculate the complex refractive indices at inter-
mediate wavelengths, where data was not available directly from
Johnson and Christy. The embedding medium for both nano-
spheres and nanoshells was considered to be water with a
refractive index n
m
of 1.33 + 0i. The results of the Mie code
for core-shell particles were checked against the Mie theory
results for homogeneous spheres for three cases: vanishing
shell, vanishing core, and vanishing refractive index dif-
ference between core and shell materials. There was excel-
lent agreement in the calculated Q
abs
and Q
sca
by the two
methods, verifying the accuracy of the Mie code for core-shell
particles.
In the case of nanospheres, the diameter D of the particles is
the only size variable. Mie theory calculations were performed
for three different sizes, i.e., D ) 20, 40, and 80 nm,
corresponding to the size range of gold nanospheres used in
earlier demonstrations of light-scattering imaging
16,17
and selec-
tive photothermal destruction of cancer cells.
26,27
Mie parameters
were also evaluated for 300-nm diameter polystyrene nano-
spheres, so as to serve as a basis for comparison of the optical
properties of the metal nanoparticles. A refractive index value
of 1.56 + 0i was used for polystyrene at all wavelengths.
Nanoshells, on the other hand, can be defined by two distinct
variables: the total particle radius R
2
and the ratio of the core
radius to the shell radius R
1
/R
2
. Calculations for nanoshells were
performed for two different cases: first, at a fixed R
2
of 70 nm
and R
1
varying as 40, 50, and 60 nm, and second, for a fixed
R
1
/R
2
∼ 0.857 and R
2
) 70, 105, and 140 nm.
Gold Nanorods. The calculation of the optical extinction,
absorption, and scattering efficiency of gold nanorods was
performed by using the discrete dipole approximation (DDA)
method,
65
which has been regarded as one of the most powerful
and flexible electrodynamic methods for computing the optical
properties of particles with an arbitrary geometry. For this
calculation, we adopted the DDA code developed by Draine
and Flatau
65
and characterized the gold nanorod case with fixed
target orientation, where the propagation direction of the incident
light was assumed to be perpendicular to the optic axis of the
nanorod. Only two orthogonal polarizations of incident light
were considered in the calculation, one with an electric field
parallel to the optic axis and another that is perpendicular to it.
The gold nanorod was considered to have the geometry of a
cylinder capped with two hemispheres. It is common to specify
the size of a particle of an arbitrary shape and volume V in
terms of an effective radius given by:
which represents the radius of a sphere having a volume equal
to that of the particle. Thus r
eff
defines the volume of the
nanorod. An additional defining size variable in case of nanorods
is the aspect ratio (R), i.e., the ratio of the nanorod dimension
along the long axis to that along the short axis. The calculations
were therefore carried out for two different cases, one for
nanorods with a fixed effective radius (and hence volume) r
eff
) 11.43 nm but different aspect ratios of 3.1, 3.9, and 4.6 and
the other for nanorods with a fixed R of 3.9 but different r
eff
of
8.74, 11.43, 17.9, and 21.86 nm. Dielectric constants for gold
at different wavelengths were assumed to be the same as that
of the bulk metal.
75
The refractive index of the surrounding
medium was considered to be 1.34 + 0i at all wavelengths,
close to that of water. Details of the DDA calculations for
nanorods have been described elsewhere.
68
Results and Discussion
Gold Nanospheres. Figure 1 shows the calculated spectra
of the efficiency of absorption Q
abs
, scattering Q
sca
, and
extinction Q
ext
for gold nanospheres (D ) 20, 40, and 80 nm)
and polystyrene nanospheres (D ) 300 nm). The dimensionless
efficiencies Q
abs
, Q
sca
, and Q
ext
can be converted to the
corresponding cross-sections C
abs
, C
sca
, and C
ext
by multiplica-
tion with the cross-sectional area of the nanoparticle. C
abs
, C
sca
,
and C
ext
have units of m
2
because they represent an equivalent
cross-sectional area of the particle that contributes to the
absorption, scattering, and extinction of the incident light. The
cross-sections can also be directly related to the molar coef-
ficients measured by spectrophotometry.
It is seen that the optical cross-sections of the gold nano-
spheres are typically 4-5 orders of magnitude higher compared
to those of conventionally used dyes. For instance, gold
nanospheres with a diameter of 40 nm, which have been
successfully used by El-Sayed et al.
26
and Huang et al.
27
for
laser photothermal destruction of cancer cells, have a calculated
absorption cross-section of 2.93 × 10
-15
m
2
(thus corresponding
to a molar absorption coefficient of 7.66 × 10
9
M
-1
cm
-1
)
78
at a plasmon resonance wavelength maximum λ
max
of 528 nm.
This value is 5 orders larger than the molar extinction coefficient
for indocyanine green ( ) 1.08 × 10
4
M
-1
cm
-1
at 778 nm
79
),
a NIR dye commonly used in laser photothermal tumor
therapy.
80,81
Similarly other strongly absorbing dyes such as
rhodamine-6G ( ) 1.16 × 10
5
M
-1
cm
-1
at 530 nm)
82
and
malachite green ( ) 1.49 × 10
5
M
-1
cm
-1
at 617 nm)
82
have
4 orders much lower absorption as compared to the nanopar-
ticles.
In addition, the magnitude of visible light scattering by the
metal nanoparticles (C
sca
) 1.23 × 10
-14
m
2
at 560 nm for
Q
ext
)
2
x
2
∑
n)1
∞
(2n + 1)Re[a
n
+ b
n
] (1)
Q
sca
)
2
x
2
∑
n)1
∞
(2n + 1)[a
n
2
+ b
n
2
] (2)
Q
abs
) Q
ext
- Q
sca
(3)
a
n
)
mψ
n
(mx)ψ′
n
(x) - ψ
n
(x)y′
n
(mx)
mψ
n
(mx)ξ′
n
(x) - mξ
n
(x)ψ′
n
(mx)
(4)
b
n
)
ψ
n
(mx)ψ′
n
(x) - mψ
n
(x)ψ′
n
(mx)
ψ
n
(mx)ξ′
n
(x) - mξ
n
(x)ψ′
n
(mx)
(5)
r
eff
) (3V/4π)
1/3
(6)
7240 J. Phys. Chem. B, Vol. 110, No. 14, 2006 Jain et al.
80-nm gold nanospheres) is comparable to the scattering from
the much larger 300-nm polystyrene nanospheres (C
sca
) 1.77
× 10
-14
at 560 nm), which are commonly used in confocal
imaging of cells.
83
The light emission from fluorescent mol-
ecules such as fluorescein ( ) 9.23 × 10
4
M
-1
cm
-1
with a
quantum yield ∼0.98 at 483 nm),
82
also commonly used in
imaging is 5 orders of magnitude lower than the light scattering
from the 80-nm gold nanospheres (C
sca
) 1.23 × 10
-14
m
2
corresponding to a molar scattering coefficient of 3.22 × 10
10
M
-1
cm
-1
). The superior scattering properties of gold nano-
spheres have already been exploited for the selective imaging
of cancer cells by using simple dark field microscopy
17
and
confocal microscopy.
16
The strongly enhanced absorption and
scattering of metal nanoparticles as compared to polystyrene
nanospheres or dyes is attributable to the well-known surface
plasmon oscillation of electrons of the metal nanoparticle.
2,36
Silica-Gold Nanoshells. Calculated spectra of Q
abs
, Q
sca
, and
Q
ext
for various dimensions of the silica-gold nanoshells (i.e.,
R
1
) 40 nm R
2
) 70 nm, R
1
) 50 nm R
2
) 70 nm, R
1
) 60
nm R
2
) 70 nm, R
1
) 90 nm R
2
) 105 nm, R
1
) 120 nm R
2
) 140 nm, and R
1
) 120 nm R
2
) 155 nm) are shown in Figure
2. The nanoshells show absorption and scattering cross-sections
(C
abs
) 5.09 × 10
-14
m
2
, C
sca
) 3.25 × 10
-14
for R
1
) 60 nm
R
2
) 70 nm nanoshell) that are comparable to and even higher
in magnitude than those of solid gold nanospheres. Additionally,
the nanoshell optical resonance lies in the NIR region (λ
max
)
892 nm for R
1
) 60 nm R
2
) 70 nm), where biological tissue
transmissivity is the highest
30
and away from the hemoglobin
visible absorption around 500-600 nm.
84
Thus the nanoshells
are much more suited to in vivo imaging and therapy applica-
tions as compared to the gold nanospheres. Silica-gold
nanoshells have been successfully employed in experimental
demonstrations by Hirsch et al.
24
and Loo et al.
25
However, there
have been concerns about the potential carcinogenicity of the
silica material of the nanoshell core.
85
It would thus be highly
desirable to have nanoparticles of solid gold with NIR absorp-
tion. However, as seen in Figure 4a, change in the nanosphere
size does not provide the desired tunability in the optical
resonance. In fact, it is known that pure gold nanospheres have
resonance around 528 nm for different sizes from tens to 100
nm.
33
Gold Nanorods. It is well-known that, by changing the shape
of nanoparticles to that of elongated rods, the optical charac-
teristics can be significantly changed.
2,33,34,36,43,73
Gold nanorods
possess, in addition to the surface plasmon band around 528
nm seen in gold nanospheres, a band at longer wavelengths due
to the plasmon oscillation of electrons along the long axis of
the nanorods.
2,33,34,36,43,73
The calculated absorption, scattering,
and extinction spectra of the surface plasmon band of gold
nanorods have been shown in Figure 3. Figure 3a shows
calculations for nanorods with a fixed aspect ratio R of 3.9 and
effective radius r
eff
) 8.74, 11.43, 17.90, and 21.86 nm.
Calculations for a fixed r
eff
(and hence volume) of 11.43 nm
but with different aspect ratios R ) 3.1, 3.9 and 4.6 are shown
in Figure 3b. Thus the figure shows that the plasmon maximum
of the nanorods (corresponding to the mode with the electric
field parallel to the long axis of the nanorod) lie in the desirable
NIR region, thus making gold nanorods potentially useful for
in vivo applications. The magnitude of their NIR absorption
and scattering (C
abs
) 1.97 × 10
-14
m
2
and C
sca
) 1.07 × 10
-14
at λ
max
) 842 nm for nanorods with r
eff
) 21.86 nm, R ) 3.9)
is comparable to that of the nanospheres and nanoshells, at a
much smaller size or volume.
Optical Tunability in Nanoparticles. The calculated spectra
for different nanoparticle types clearly reflect the well-known
fact
2,33,34,36
that the surface plasmon resonance wavelength as
Figure 1. Calculated spectra of the efficiency of absorption Q
abs
(red dashed), scattering Q
sca
(black dotted), and extinction Q
ext
(green solid) for
gold nanospheres (a) D ) 20 nm, (b) D ) 40 nm, (c) D ) 80 nm, and polystyrene nanospheres (d) D ) 300 nm.
Absorption and Scattering Properties of Gold Nanoparticles J. Phys. Chem. B, Vol. 110, No. 14, 2006 7241
well as the extent of the plasmon enhancement is highly
dependent on the size, shape, and core-shell composition of
the nanoparticles, thus allowing easy optical tunability, which
is lacking in the case of dyes. To aid the selection of an
appropriate nanoparticle for a suitable biomedical application,
a systematic quantitative discussion of the trends in the optical
tunability of nanoparticles follows.
Dependence of the Plasmon Resonance Maximum on
Nanoparticle Dimensions. Figure 4 summarizes the dependence
of the nanoparticle plasmon resonance wavelength maximum
λ
max
on the nanoparticle dimensions. Figure 4a shows the plot
of λ
max
versus the nanosphere diameter D. With increase in the
nanosphere diameter from 20 to 80 nm, there is a small red-
shift in the λ
max
from ∼520 to 550 nm. Similar red-shift has
been observed in the measured optical spectra of gold nano-
particles and is attributed to the effect of electromagnetic
retardation in larger nanoparticles.
2,34,36,38,39,66,86
Nevertheless,
changing the diameter D of the nanospheres does not offer
sufficient change in the surface plasmon resonance maximum
to be useful in the present applications.
On the other hand, the optical resonance wavelength of
nanoshells can be easily tuned by variation in their dimensions.
As shown in Figure 4b, the nanoshell λ
max
can be increased by
increasing the total nanoshell radius R
2
while keeping R
1
/R
2
fixed. Alternatively, Figure 4c shows that the λ
max
can be tuned
by changing the relative core-shell dimensions R
1
/R
2
at a fixed
total nanoshell size R
2
. In other words, reducing the shell
thickness shifts λ
max
to longer wavelengths. In the case of larger
nanoshells, the spectra show additional resonance peaks having
strong intensity at shorter wavelengths as compared to the
dipolar plasmon resonance. For example, for the nanoshell
configuration with R
1
) 120 nm R
2
) 140 nm, a resonance
peak can be seen around 756 nm in addition to the dipolar band
at 1120 nm (Figure 2e). An additional resonance can also be
seen in the case of R
1
) 120 nm R
2
) 155 (Figure 2f). These
additional resonances arise from quadrupolar oscillations in the
Figure 2. Calculated spectra of the efficiency of absorption Q
abs
(red dashed), scattering Q
sca
(black dotted), and extinction Q
ext
(green solid) for
silica-gold nanoshells with dimensions (a) R
1
) 40 nm, R
2
) 70 nm, (b) R
1
) 50 nm, R
2
) 70 nm, (c) R
1
) 60 nm, R
2
) 70 nm, (d) R
1
) 90 nm,
R
2
) 105 nm, (e) R
1
) 120 nm, R
2
) 140 nm, and (f) R
1
) 120 nm, R
2
) 155 nm.
7242 J. Phys. Chem. B, Vol. 110, No. 14, 2006 Jain et al.
