Holographic gratings are recorded in colloidal suspensions of silver nanoparticles by utilizing interfering nanosecond pulses. The diffraction efficiency is measured with continuous-wave light. An instantaneous response together with a transient grating are observed: the nanoparticles absorb the pump light and heat up. Heat is transferred to the solvent, and a delayed thermal grating appears. The final decay time constant of this grating depends quadratically on the period length and has a typical value of 1 µs for grating spacings of several micrometers

Adleman, James R.

Buse, Karsten

Eggert, Helge A.

Psaltis, Demetri

Caltech Authors - Main

February 15, 2006 / Vol. 31, No. 4 / OPTICS LETTERS 447Holographic grating formation in a colloidal
suspension of silver nanoparticles
James R. Adleman
Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125
Helge A. Eggert and Karsten Buse
Institute of Physics, University of Bonn, Wegelerstrasse 8, D-53115 Bonn, Germany
Demetri Psaltis
Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125
Received October 7, 2005; revised November 9, 2005; accepted November 9, 2005; posted November 14, 2005 (Doc. ID 65235)
Holographic gratings are recorded in colloidal suspensions of silver nanoparticles by utilizing interfering
nanosecond pulses. The diffraction efficiency is measured with continuous-wave light. An instantaneous re-
sponse together with a transient grating are observed: the nanoparticles absorb the pump light and heat up.
Heat is transferred to the solvent, and a delayed thermal grating appears. The final decay time constant of
this grating depends quadratically on the period length and has a typical value of 1 s for grating spacings
of several micrometers. © 2006 Optical Society of America
OCIS codes: 090.7330, 160.4330, 190.3970.Colloidal suspensions of metal nanoparticles have in-
teresting optical properties. The high third-order
nonlinear response of the nanoparticles for wave-
lengths close to the surface plasmon resonance has
been the subject of intense studies.1–3 Since the ab-
sorption due to the nanoparticles also causes heating
of the surrounding solvent, a temperature pattern
can be created by means of structured illumination.
This leads to a thermal change of the refractive index
as well as to a particle redistribution caused by the
so-called Soret effect.4 These thermal forces or the
use of optical tweezers can allow on-demand configu-
ration of, e.g., microfluidic devices or holographic
Bragg filters.5 An advantage of colloidal suspensions
compared with fabrication of structures in doped
glasses is that the nanoparticles in suspension are
easily reconfigurable.6 By choosing the right illumi-
nation conditions it is possible not only to transport
and structure the nanoparticle distribution but also
to get a patterned nonlinear optical response.
In this Letter we study the optical and thermal re-
sponse as well as the transport properties of colloidal
suspensions of silver nanoparticles. In these materi-
als the light–matter interaction is still not completely
understood, especially on the nanosecond time scale.7
We probe the material response by means of a simple
holographic experiment. Elementary holographic
gratings are recorded with nanosecond pulses in
samples of different volume fractions of nanopar-
ticles. The diffraction efficiency of these gratings is
monitored with continuous-wave light. Maximum dif-
fraction efficiencies of around 3% were measured,
corresponding to phase gratings with refractive index
contrasts of approximately 110−5.
Experiments are performed with chemically syn-
thesized silver spheres with a mean diameter of
3.8 nm suspended in toluene. The surface plasmon
0146-9592/06/040447-3/$15.00 ©resonance has its maximum around 435 nm. Various
concentrations between 3.51014 cm−3 and 0.7
1014 cm−3 (optical density, OD, at 532 nm of 1.1–
0.22) were produced by dilution. The particle size is
determined from the measured spectra by Mie theory
calculations with a semiclassical correction, following
Collier.8 To record a holographic grating, interference
of two plane waves is used. Frequency-doubled pulses
from a Nd:YAG laser (wavelength =532 nm, inten-
sity I=10 GW/m2, pulse duration =6 ns, FWHM
beam diameter 6 mm) are split into two parts of
equal intensity that overlap and interfere inside a
4 mm thick and 10 mm broad cuvette filled with the
nanoparticle suspension. The angle between the
pulses can be adjusted such that grating periods 
between 1 and 2.5 m are possible. The induced grat-
ing is observed by diffracting a Bragg-matched,
continuous-wave beam of a laser diode at =785 nm
with a beam diameter of 2 mm. All three beams are s
polarized. A fast photodiode with a rise time of 1 ns
and a digital oscilloscope (bandwidth 1 GHz) are
used to capture the time evolution of the diffracted
signal. A bandpass filter (800 nm, 40 nm FWHM) at
the read-out wavelength blocks the pump light at the
detector. Between each recording experiment the
sample is allowed to cool for at least 1 min to avoid
boiling of the solvent. This time is also sufficient to
flatten out a possible concentration distribution of
the nanoparticles.4 The absorption spectra of all
samples were measured before and after each experi-
ment, and no change was observed. This indicates
that the pulsed illumination does not lead to agglom-
eration or shape changes of the nanoparticles.
The diffraction efficiency of the grating depends
strongly on the concentration of the nanoparticles
and on the light intensity. At lower intensities the dif-
fracted signal shows an abrupt rise time of around
2006 Optical Society of America
448 OPTICS LETTERS / Vol. 31, No. 4 / February 15, 20066 ns, and then a monoexponential decay with a time
constant of =220 ns. This decay time constant does
not vary with concentration [Figs. 1(a)–1(c)].
At the highest intensities measured, the time evo-
lution of the diffracted signal is qualitatively differ-
ent for different concentrations [Figs. 1(d)–1(f)]. At
the two lowest concentrations (OD 0.32, 0.22) the ini-
tial rise still occurs in 6 ns, followed by a dip and a
slower second rise that peaks at around 150 ns. This
is followed by the decay of the grating, with the same
time constant as before [Fig. 1(f)].
At the intermediate concentration (OD 0.55) the
first minimum is not present. However there is still a
slow rise and decay of the signal [Fig. 1(e)]. Finally,
at the highest concentrations and intensities, an ini-
tial peak is again present in the diffracted efficiency
curve. The magnitude of the first maximum is now
smaller than the second. The rise and fall times of
the first peak are faster, at around 3 ns [Fig. 1(d)].
Comparing measurements at different intensities
in single samples, we see a smooth evolution in the
behavior of the diffracted signal. At low intensities a
monoexponential decay is seen; as the intensity in-
creases, the faster transient effects grow in magni-
tude. The position of the second maximum shifts to
later times with increasing intensity (Fig. 2).
Variation of the grating period length  between 1
and 2.4 m has no influence on the first peak or on
the buildup of the second one. However, the ampli-
tude of the grating decays slower with increasing
grating spacings, clearly pointing to thermal effects
(Fig. 3). Thus the final time evolution of the diffrac-
tion efficiency can be explained by the presence of a
Fig. 1. Intensity of the diffracted beam versus time t for
different particle concentrations. Pump intensities (a)–(c)
I=4.6 GW/m2 and (d)–(f) I=10 GW/m2. Particle concentra-
tions (a), (d) 3.471014 cm3 OD 1.1, (b), (e) 1.74
1014 cm3 OD 0.55, and (c), (f) 0.71014 cm3 OD 0.22.thermal grating in the solvent: energy absorbed bythe nanoparticles heats the solvent. Since each nano-
particle heats a spherical volume of solution with a
diameter equal to the mean interparticle spacing
(150–250 nm), there can be some delay in building up
a smooth sinusoidal temperature distribution. In our
experiments a strong thermal grating has been es-
tablished by 200 ns after the recording pulses. The
decay afterward is governed solely by thermal con-
ductivity and can be used to determine the thermal
diffusivity of the sample.9,10 The temperature ampli-
tude T of the thermal grating decays exponentially,
T = T0 exp− t/th, 1
with the time constant
th = 2/42. 2
Here  is the thermal diffusivity of the solvent. The
refractive index change of the solvent is proportional
to T, and hence, according to the coupled-wave
theory,11 the diffraction efficiency is proportional to
the square of the temperature change for small dif-
fraction efficiencies.
From the fit in Fig. 3 and taking into account the
factor of 2 between the time constants for the diffrac-
tion efficiency and the refractive index change for
small diffraction efficiencies, we can then calculate
the thermal diffusivity of the solvent as 7.27
10−8 m2/s. This is in good agreement with the lit-
erature value of 8.8510−8 m2/s.12
The temporal evolution for times less than 200 ns
is more complex. At low concentrations and intensi-
ties the diffraction efficiencies are consistent with a
simple thermal grating. However, as the intensity in-
creases, another transient signal appears. Also, the
maximum diffraction efficiency scales linearly with
intensity, instead of quadratically. The disappearance
of the dip between the first and the second maximum
for intermediate concentrations, as well as the
change in position and magnitude of the second
Fig. 2. Diffracted intensity versus time t for three differ-
ent pump intensities in samples with particle concentra-
tions of (a) 2.41014 cm3 OD=0.76 and (b) 1.07
14 310 cm OD=0.34.
February 15, 2006 / Vol. 31, No. 4 / OPTICS LETTERS 449maximum relative to the first, suggests that there is
more than one physical effect operating on the short
time scale (Fig. 1).
Different mechanisms for optical nonlinear effects
in solutions of metal nanoparticles are known.13
Changes of the polarizability of the particles due to
hot electrons and electron-dipole transitions are in-
stantaneous in the nanosecond regime. Also, the field
enhancement in the vicinity of the particles due to
the surface plasmon resonance may lead to a high in-
stantaneous Kerr nonlinearity in the solvent. Mea-
surements with femtosecond and picosecond pulses
show positive nonlinear refractive index changes of
either the nanoparticles or the solvent. Heating the
solvent leads to thermal and thus negative changes
of the refractive index.
Despite the fast thermalization of absorbed energy
by the metal nanoparticles, it has been shown that
the heat transfer from nanoparticles excited by nano-
second pulses to the solvent can last for several tens
of nanoseconds. This behavior is strongly influenced
by both particle size and concentration.7 This diffu-
sion of thermal energy into the solvent could be the
mechanism responsible for the discrepancies in the
temporal evolution of the first peak and valley. A
thermally induced modification of the optical proper-
ties of the particles can perhaps lead to a change of
the fast nonlinear response. But another explanation
may be possible: the absorbed energy may be suffi-
cient to boil a small shell of the solvent around each
Fig. 3. Time constant  of the decay of the diffraction effi-
ciency versus grating period  of the thermal grating. The
solid curve is a quadratic fit according to the equation 
=a2.nanoparticle, thus leading to strong refractive indexchanges, resulting in a change of the surface plasmon
resonance and in light scattering at the phase bound-
ary in the solvent.14 In either case, the refractive in-
dex grating shortly after the pump pulse could be de-
scribed as the sum of an instantaneous Kerr effect, a
fast-forming simple thermal grating accounting for
the monoexponential trend, and a longer-lived de-
layed grating due to the thermal changes in the par-
ticles and the solvent. Further investigation is neces-
sary to determine the exact parameters of these
gratings.
In conclusion, we have shown that different nonlin-
ear effects compete when a colloidal suspension of sil-
ver nanoparticles is illuminated with 6 ns laser
pulses. The shorter-time-scale behavior of these sys-
tems is the sum of thermal and electronic nonlineari-
ties, which cause dramatic differences in properties
of holographic gratings written at different particle
concentrations and pump powers.
Financial support of the Deutsche Telekom AG, the
Deutsche Forschungsgemeinschaft, and the DARPA
center for optofluidic integration is gratefully ac-
knowledged.
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Holographic grating formation in a colloidal suspension of silver nanoparticles

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Holographic grating formation in a colloidal suspension of silver nanoparticles

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