Refractive index change by photothermal effect with a constant density
detected as temperature grating in various fluids
Masahide Terazima
Department of Chemistry, Faculty of Science, Kyoto University, Kyoto 606 Japan
͑Received 10 July 1995; accepted 18 December 1995͒
Two origins of the refractive index variation after depositing heat energy to a fluid are separately
investigated by using the transient grating ͑TG͒ method; the variations are caused by a density
fluctuation and a temperature fluctuation with a constant density. Although the relative contribution
of the temperature rise ͑constant density͒ component is small in the total refractive index change, a
precise measurement of the TG signal enables us to determine the magnitude and it is found that
they are as large as 3%–6% in magnitude of dn/dT except water, in which the relative contribution
strongly depends on temperature. The origin of the temperature rise component is interpreted in
terms of the interaction induced polarizability change of the fluid molecules. An application of this
component to the ultrafast detection of the photothermal techniques is discussed. © 1996
American Institute of Physics. ͓S0021-9606͑96͒00412-1͔
I. INTRODUCTION
Local inhomogeneity of the refractive index ͑or dielec-
tric constant͒ and its fluctuation in time are the main causes
of the light scattering in condensed phase. When the fluctua-
tion is induced by the photoexcitation of light-absorbing dye
molecules, the stimulated ͑forced͒ light scattering is ob-
served. This light scattering method, as well as other related
versions as the photothermal techniques, have been used for
studying the energy dynamics of photoexcited states.
1–23
The
temperature dependence of the refractive index is the key
step in these various measurements and has been extensively
studied. For instance, chosen the density
and temperature T
as the independent state variables ͑other choice will be dis-
cussed in a later section͒, the variation of the refractive index
(⌬n) after depositing heat in solution will be expressed by
⌬n ϭn Ϫn
0
ϭ
ͩ
ץ
n
ץ
ͪ
T
d
ϩ
ͩ
ץ
n
ץ
T
ͪ
dT, ͑1͒
where n
0
is the unperturbed refractive index. In many fluids,
the first term dominates over the second term significantly.
Indeed, this contribution is so large that the second term has
been frequently neglected for the cause of the light scattering
or photothermal signals explicitly or implicitly.
4,7,9,12
This
paper presents the contribution of the refractive index varia-
tion without accompanying density change after heating up
various fluids by using one of the photothermal techniques,
the transient grating ͓stimulated Brillouin ͑Rayleigh͒ scatter-
ing͔ technique.
Historically several groups have tried to detect the sec-
ond component in light scattering signals.
4,7,24–29
Some of
them have failed because of the so small contribution in the
total refractive index change.
7,24–27
One exceptional sub-
stance is water.
28,29
For example, Eisenberg found an empiri-
cal formula for the refractive index of water as
28
f
͑
n
͒
ϵ
͑
n
2
Ϫ1
͒
/
͑
n
2
ϩ2
͒
ϭA
B
exp
͑
ϪCT
͒
, ͑2͒
where A, B, and C are constants. The constant C is related to
(
ץ
n/
ץ
T)
, which is the quantity we are interested in here as
CϭϪ
ͫ
ln
ץ
f
͑
n
͒
ץ
T
ͬ
. ͑3͒
He discussed the nonzero quantity C with respect to the in-
termolecular structure of water relating with the hydrogen
bonding network.
28
In 1986, Maison et al. have shown the
non-negligible second term in Eq. ͑1͒ of water from the mea-
surement of the Landau–Placzek ratio of the light scattering
spectrum.
29
Recently Terazima and Hirota have reported the
first observation of the contribution of the second term in the
thermal lens ͑TL͒ signal.
17
Successively, a similar compo-
nent in the transient grating ͑TG͒ signal has been observed
and the component is clearly manifested itself at a tempera-
ture near 4 °C.
30
These photothermal techniques, TL and TG,
are well known to be sensitive optical detection methods of
heat ͑which is released by the radiationless transition͒ with
fairly fast time responses and have been important tech-
niques in various fields such as the molecular
spectroscopy.
2,3,7–23
Theoretically the same type of temperature contribution
with constant density should exist also in all fluids beside
water. However, the data on the quantity (
ץ
n/
ץ
T)
except
water are very limited
8,10,26
and some of the estimated values
are incorrect ͑vide infra͒. This quantity of various liquids has
been investigated by the TG method, and it was found that
the quantity (
ץ
n/
ץ
T)
possesses a positive correlation with
the average polarizability per unit volume of the fluids. The
quantity is discussed in terms of the interaction induced po-
larizability of the fluids.
For the sake of convenience and clearness in this paper,
the contribution of the second term of Eq. ͑1͒ in the TG and
TL signals are referred as the temperature grating ͑Temp.G͒
and temperature lens ͑Temp.L͒, respectively, following the
previous papers.
17,30
The conventional signals of the TG and
TL due to the refractive index variation by the density
change are explicitly named the density grating ͑Dens.G͒ and
density lens ͑Dens.L͒ signals. The notations of the ‘‘TG’’ and
‘‘TL’’ signals are reserved to indicate the experimentally ob-
4988 J. Chem. Phys. 104 (13), 1 April 1996 0021-9606/96/104(13)/4988/11/$10.00 © 1996 American Institute of Physics