Linear refractive index and absorption
measurements of nonlinear optical
liquids in the visible and near-infrared
spectral region
S. Kedenburg, M. Vieweg, T. Gissibl, and H. Giessen*
4th Physics Institute and Research Center SCOPE, University of Stuttgart,
70550 Stuttgart, Germany
*h.giessen@pi4.uni-stuttgart.de
Abstract: Liquid-filled photonic crystal fibers and optofluidic devices
require infiltration with a variety of liquids whose linear optical properties
are still not well known over a broad spectral range, particularly in the near
infrared. Hence, dispersion and absorption properties in the visible and
near-infrared wavelength region have been determined for distilled water,
heavy water, chloroform, carbon tetrachloride, toluene, ethanol, carbon
disulfide, and nitrobenzene at a temperature of 20 °C. For the refractive
index measurement a standard Abbe refractometer in combination with a
white light laser and a technique to calculate correction terms to compensate
for the dispersion of the glass prism has been used. New refractive index
data and derived dispersion formulas between a wavelength of 500 nm and
1600 nm are presented in good agreement with sparsely existing reference
data in this wavelength range. The absorption coefficient has been deduced
from the difference of the losses of several identically prepared liquid filled
glass cells or tubes of different lengths. We present absorption data in the
wavelength region between 500 nm and 1750 nm.
© 2012 Optical Society of America
OCIS codes: (160.4330) Nonlinear optical materials; (260.2030) Dispersion; (300.1030) Ab-
sorption.
References and links
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optics,” Nature (London) 442, 381–386 (2006).
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106–114 (2007).
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uum generation,” Opt. Express 14, 6800–6812 (2006).
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1. Introduction
Liquids offer striking possibilities for the field of optics. New optical devices have been devel-
oped which opened a new field: optofluidics, which combines liquids and photonics [1,2]. This
field has encountered an increased amount of interest in the recent past due to novel flexible
concepts.
Liquids are especially suited for generating supercontinua due to their relatively high nonlin-
ear refractive index n2 with respect to solids. Examples for applications are include selectively
liquid-filled photonic crystal fibers [3–6], and liquid-core optical fibers [7] whose dispersion
properties can be tailored accordingly for the formation of a supercontinuum. Liquid-filled
patterns in such fibers allow for the realization of directional couplers [8,9], all-optical switch-
ing [10] as well as discrete optofluidic spatial solitons in waveguide arrays [11]. Furthermore,
characteristics of stimulated Brillouin scattering [12] and self-phase modulation [13] can be
studied. Also pulse propagation in tapered fibers immersed in liquids can be tailored [14].
Moreover, the transparency in the visible and near-infrared range plays an important role for
unobstructed propagation of light in these structures.
There is an increasing need for rapid and easy measurements of linear optical properties of
nonlinear liquids over a broad wavelength range. The knowledge of the linear refractive index n
and the absorption coefficient α are important to control the optical properties and to determine
n2 [15].
Due to the fact that published papers [15–20] and reference books [21, 22] currently cannot
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cover a broad wavelength range in the visible and near-infrared and some data even seem to
not exist in published form, we take measurements in regions which have previously not been
investigated to our knowledge.
In this paper precise constants for Cauchy and Sellmeier dispersion equations of linear re-
fractive indices at a temperature of 20 °C are derived from measurement data between a wave-
length of 500 nm and 1600 nm for the following eight liquids: distilled water (H2O), heavy wa-
ter (D2O), chloroform (CHCl3), carbon tetrachloride (CCl4), toluene (C7H8), ethanol (C2H6O),
carbon disulfide (CS2), and nitrobenzene (C6H5NO2). A measurement method which is based
on an extension of a standard Abbe refractometer is used to determine n(λ ) [16]. The required
correction terms for the application in the near-infrared and the experimental realization are
described in detail.
Furthermore, the absorption coefficient α as a function of wavelength is given between
500 nm and 1750 nm for distilled water, heavy water, chloroform, toluene, ethanol, and car-
bon tetrachloride (up to a wavelength of 1500 nm). For the measurement of α thin glass cells
or long tubes filled with the liquids have been used, depending on the magnitude of absorp-
tion. Accurate alignments of the samples were required because α has been calculated from
the difference of the losses of several equally prepared specimens of different lengths [17]. The
description of the utilized methods and the experimental setups are also presented in this paper.
The structure of the paper is as follows: First the measurement techniques and the experimen-
tal setups for the determination of the linear refractive index and the absorption coefficients are
described. Second, in Section 3, the measurement results are presented, starting with the refrac-
tive index values and dispersion curves, followed by the absorption spectra of the investigated
liquids. The absorption coefficient values are given in the supplement as comma-separated value
text files.
2. Measurement techniques
2.1. Refractive index
2.1.1. Abbe refractometer
An easy and precise method to measure the linear refractive index n in the visible spectral
range is provided by an Abbe refractometer. Commonly, such instruments are designed for the
use at the wavelength of the sodium D line (589.3 nm). Correction tables enable the use of the
refractometer in the complete spectral range covered by the listed values therein. A different
description is given in the paper of J. Rheims et al. [16] which allows determination of the
refractive index over a wider wavelength regime. However, since the refractometer is an optical
measurement device which is read out by naked eye, the wavelength region is still limited to
the visible. Only by using infrared-cameras as replacement for the human eye, the method can
be extended to the infrared-region.
Regardless of the wavelength, the general working principle is based on the dependence
of the angle of total reflection from the refractive index of the investigated liquid. The Abbe
refractometer is composed of two orthogonal prisms as shown in Fig. 1.
To apply the principle of total reflection the refractive index of the investigated liquid nliq
has to be smaller than the refractive index of the measuring prism npr. The specimen is placed
between the two prisms and the incoming light is transmitted only in an angular range below
the angle of total reflection αT , generating a sharp separation line between the bright and the
dark range. This image can be observed with the eyepiece of the refractometer. Matching the
separation line with the point of intersection of a reticle allows for readout of the measured
refractive index n′liq from a scale.
However, the measured refractive index n′liq only corresponds to the actual refractive index
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(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1590
b aT
f
illumination prism
measuring prism with
refractive index npr investigated liquid with
refractive index nliq
bright-dark
separation line
image
aT
Fig. 1. Beam path in the Abbe refractometer: in transmission mode (solid line) the incoming
light passes the illumination prism and is scattered in all directions at the rough surface.
However, the light is only transmitted into the measuring prism if the incident angle is
below the angle of total reflection αT . The image displays a sharp separation between the
bright and dark range. The image is observed with a telescope and the point of intersection
of the reticle has to be adjusted to this separation line. One can then read the measured
refractive index n′liq from a scale of the refractometer; in reflection mode (dotted line)
the measuring prism is directly illuminated and the incoming light is only reflected in the
angular range above the angle of total reflection. Hence, the bright and the dark range are
interchanged which does not affect the deflection angle β which has a fixed geometrical
relationship to the measured refractive index (see Eq. (5)). φ is the prism apex angle which
is 63 °in our case.
nliq of the liquid at the sodium D line at λD = 589.3 nm because of the used calibration from the
manufacturer Carl Zeiss. To deduce the refractive index nliq also at other wavelengths one has
to apply a correction term ∆nliq to n′liq to compensate for the dispersion of the glass prism. Cor-
rection tables are offered by the manufacturer of the refractometer where ∆nliq depends on the
illumination wavelength, the measured refractive index, and the used glass prism. However, the
correction data are only provided in the visible spectral range between 400 nm and 680 nm [23].
To extend the application range of the refractometer one has to establish a relationship be-
tween the deflection angle β and the displayed refractive index n′liq from the scale of the refrac-
tometer. This geometrical relationship has to be determined only once because it is not affected
by changing the illumination wavelength [16].
2.1.2. Correction terms
The refractive index of a liquid is given by Snellius’ law as
nliq = npr sinαT . (1)
By geometrical thoughts and trigonometrical identities (see Fig. 1) and the fact that the change
in the refractive index with temperature is negligible for the glass prism [16] one obtains
nliq(λ ,T ) = sinφ
√
n2pr(λ )− sin2 β (λ ,T )− cosφ sinβ (λ ,T ). (2)
Thus, the refractive index of the liquid for a certain wavelength and temperature is a function
of the deflection angle β , the refractive index npr, and the apex angle φ of the glass prism.
In order to obtain the actual refractive index of the liquid nliq, the measured refractive index
n′liq has to be corrected by the term ∆nliq
nliq(λ ,T ) = n′liq(λ ,T )+∆nliq(λ ,n′liq). (3)
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(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1591
As the Abbe refractometer is calibrated with respect to the sodium D line, ∆nliq(λD,n′liq) be-
comes zero and nliq is equal to n′liq for this wavelength (see Eq. (3)). Replacing nliq by n′liq in
Eq. (2) one obtains the desired fixed relationship between n′liq and β
n′liq(λD,T ) = sinφ
√
n2pr(λD)− sin2 β (λD,T )− cosφ sinβ (λD,T ). (4)
Solving Eq. (4) for β yields
sinβ (λ ,T ) = sinφ
√
n2pr(λD)−n′2liq(λ ,T )−n′liq(λ ,T )cosφ . (5)
Hence, by inserting Eq. (5) into Eq. (2) the expression for the actual refractive index reads
nliq(λ ,T,n′liq) = sinφ [n2pr(λ )− (sinφ
√
n2pr(λD)−n′2liq(λ ,T )− (6)
n′liq(λ ,T )cosφ)2]1/2−
cosφ(sinφ
√
n2pr(λD)−n′2liq(λ ,T )−n′liq(λ ,T )cosφ).
This equation gives the actual refractive index at a certain wavelength in dependence of the
prism dispersion, the prism apex angle, and the measured index value n′liq.
In our experiment we use an Abbe refractometer Model A from Carl Zeiss with the serial
number 7 and device number 64305. The apex angle of the glass prism φ is given in the engi-
neering drawing as 63 ° in the present case [24]. The refractive index of the glass prism made
from Schott SF13 glass is given from the glass manufacturer at different wavelengths [25]. At
λD = 589.3 nm the refractive index of the prism is npr(λD) = 1.74054. For npr(λ ) the Cauchy
formula in Eq. (7) is used:
npr = 1.70708+
10943.47279
λ 2 +
2.54416×108
λ 4 +
3.46802×1013
λ 6 −2.93242×10
−9λ 2. (7)
The Cauchy formula together with the given refractive indices of SF13 are plotted in Fig. 2.
0.6 1.0 1.4 1.8 2.2
1.70
1.74
1.78
Wavelength ( m)μ
R
e
fr
a
c
ti
v
e
 i
n
d
e
x
 n
p
r
Data points [25]
Cauchy dispersion formula
Fig. 2. Dispersion of refractive index of the measuring prism made of SF13. The data
points (diamonds) are listed in the datasheet from the glass manufacturer Schott [25]. The
calculated Cauchy dispersion formula (blue line) is given in Eq. (7).
For verification the calculated correction term ∆nliq is compared with data from a correction
table provided by Zeiss at two wavelengths of λ = 500 nm and λ = 680 nm [23]. The results
are plotted in Fig. 3. ∆nliq matches very well with the original data given by Zeiss and the
maximum deviation is less than 1× 10−4 at 500 nm. At a wavelength of 680 nm the deviation
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1592
0.0141
0.0143
0.0145
0.0147
Calculated corrections
Original Zeiss corrections [23]
1.30 1.40 1.50 1.60 1.70
-0.0089
-0.0087
-0.0085
Measured refractive index n‘liq
(a)
(b)
C
o
rr
e
c
ti
o
n
 v
a
lu
e
n
liq
∆
C
o
rr
e
c
ti
o
n
 v
a
lu
e
n
liq
∆
Fig. 3. The calculated correction term ∆nliq (blue line) for our Abbe refractometer from Eq.
(6) as a function of the measured refractive index n′liq at a wavelength of (a) 500 nm and (b)
680 nm in comparison with original data (dashed line) from a correction table provided by
Carl Zeiss AG [23].
is slightly more pronounced but always below 2×10−4 which allows the use of the described
method for calculating the correction terms in the complete wavelength region of interest.
In Fig. 4 absolute values of the calculated correction terms ∆nliq are shown for several wave-
lengths in the visible and near-infrared range, as used in our experiment. Below the wavelength
of 589.3 nm the corrections are positive, above λD they are negative.
1.30 1.40 1.50 1.60 1.70
0
0.010
0.020
0.030
Measured refractive index n‘liq
λ = 500 nm
λ = 600 nm
λ = 700 nm
λ = 800 nm
λ = 900 nm
λ = 1000 nm
λ = 1100 nm
λ = 1200 nm
λ = 1300 nm
λ = 1400 nm
λ = 1500 nm
λ = 1600 nm
C
o
rr
e
c
ti
o
n
 v
a
lu
e
 |
n
|
liq
∆
Fig. 4. Absolute values of the calculated correction terms ∆nliq for our Abbe refractometer
from Eq. (6) as a function of the measured refractive index n′liq for different wavelengths.
2.1.3. Refractometer setup
The experimental setup is shown in Fig. 5a. The Abbe refractometer (Carl Zeiss, model A, se-
rial number 7, device number 64305, see Fig. 5b) is connected to a cooling system to ensure
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1593
a constant temperature of 20 °C which can be controlled by a thermometer at the illumination
prism. Due to the cooling mechanism the temperature varies in the range of ±0.5 °C. A super-
continuum generated by a tapered fiber with fiber diameters of 2.5 µm or 3.0 µm, respectively,
are used as light sources [26]. A modelocked Ti:Sapphire femtosecond laser at a central wave-
length of 800 nm for the 2.5 µm fiber and a modelocked PolarOnyx Uranus fiber laser with fs
pulse compressor at a central wavelength of 1035 nm for the 3.0 µm fiber serve as pump sources
to ensure a broad spectral range. White light spectra are shown in Fig. 6. Bandpass filters with
a bandwidth of ∆λ = 10 nm and a tolerance of the central filter wavelength of ±2nm [27] are
placed into the laser beam path to select certain wavelengths between 500 nm and 1600 nm.
bandpass filter
Abbe refractometer
infrared viewer or
infrared camera
white light laser
illumination prism
measuring prism
telescope
(b)(a)
Fig. 5. (a) Experimental setup for refractive index measurements with the Abbe refractome-
ter in the visible and near-infrared in transmission mode. In reflection mode one directly
illuminates the measuring prism. (b) Abbe refractometer model A from Carl Zeiss.
Depending on the absorption strength of the investigated liquid, the refractometer can also be
used in reflection mode to enhance the visibility of the dark-bright separation line. Therefore a
second illumination window is mounted at the front of the measuring prism. Thus the beam path
shown in Fig. 1 is somewhat modified which does not affect the formula of the correction term.
The compensator of the refractometer, which filters out the sodium D line and deflects other
wavelengths, is set during the whole measurement to the position 30 in which no wavelength
dependent beam deviation occurs. To match the reticle with the separation line an infrared
viewer of FJW Optical Systems (Find-R-Scope Model 84499A) is used in the wavelength range
between 500 nm and 1200 nm. Due to the reduced sensitivity of the infrared viewer above a
wavelength of 1200 nm, an infrared camera NIR-300FGE from Allied Vision Technologies is
used in the wavelength region between 900 nm and 1600 nm.
2.2. Absorption coefficient
2.2.1. Loss spectroscopy
According to the Lambert-Beer law the transmitted intensity through a sample declines expo-
nentially with increasing length L
I(L) = I(0)exp(−αL). (8)
I(0) is the intensity of the incident light and α the absorption coefficient of the investigated
liquid per unit length. To measure the absorption coefficient as a function of the wavelength,
the difference in the losses of two identically prepared samples of different lengths has to be
determined [17]. For the ratio of the transmitted intensities for two liquid filled tubes of lengths
L1 and L2 at the wavelength λ one obtains [17]
Iliq(L1,λ )
Iempty(L1,λ )
Iempty(L2,λ )
Iliq(L2,λ )
= exp(α(L2−L1)). (9)
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1594
0.6 0.8 1.0 1.2
10
-9
10
-7
In
te
n
s
it
y
 (
a
rb
. 
u
n
it
s
)
Ti:Sapphire laser
10
-5
Wavelength (µm)
(a)
0.9 1.1 1.3 1.5 1.7
10
-4
10
-3
10
-2
Wavelength (µm)
In
te
n
s
it
y
 (
a
rb
. 
u
n
it
s
)
PolarOnyx laser
(b)
Fig. 6. White light spectra of (a) a Ti:Sapphire laser with a 2.5 µm thick tapered fiber and
(b) a PolarOnyx laser with a 3.0 µm thick tapered fiber with 80 mm waist length.
As a reference signal the corresponding transmitted intensity through the empty tube Iempty is
used. Rewriting the Eq. (9) one can calculate the absorption coefficient
α(λ ) =
ln
(
Iliq(L1,λ )
Iliq(L2,λ )
Iempty(L2,λ )
Iempty(L1,λ )
)
L2−L1
. (10)
The effect of reflections at the end faces of the sample which also diminish the transmitted
intensity cancels out by division of the measured intensities since for identically prepared sam-
ples these losses are the same and do not depend on the length of the tube. Furthermore, one
can neglect multiple interferences according to the paper of K. C. Kao et al. [17].
2.2.2. Absorption setup
The experimental setup is shown in Fig. 7a. A Yokogawa AQ4305 white light source is used
as light source. Because of its broad wavelength range spanning from 400 nm to 1800 nm and
its very stable intensity spectrum, the light source is particularly suitable for the application of
wavelength dependent loss spectroscopy.
A 4x objective with a numerical aperture of 0.10 provides a suitable collimation of the beam.
The liquids are either filled into glass cells of Hellma Analytics or into quadratic stainless steel
tubes with 1 mm thick microscope slides from Menzel Gla¨ser at their end faces, depending on
the absorption magnitude (see Fig. 7b). The glass cells provide shorter, the tubes longer sample
lengths. The glass cell lengths vary between 1 mm and 40 mm and the tube lengths between
25 mm and 1000 mm. The collimated beam of about 7 mm diameter travels through the tubes or
glass cells whose parallel end faces have to be precisely aligned perpendicular to the incoming
light to avoid beam displacement. Furthermore, it has to be considered that the samples with and
without the liquid are placed identically so that the reflection coefficients, which are dependent
on the incident angle, remain unchanged. A system of mirrors and a lens focus the beam directly
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1595
spectrometer
lens
objectivewhite light source
stainless steel tube with glass end faces
or glass cells
sample holder
deflecting mirror
multimode
glass fiber
(b)(a)
Fig. 7. (a) Experimental setup for absorption measurements in the visible and near-infrared.
(b) Glass cells and stainless steel tubes enclosed with glass plates.
into the Ando AQ-6315E spectrometer with a spectral measuring range from 350 nm up to
1750 nm. With the last two mirrors one can compensate slight beam displacements to obtain a
maximum detection signal.
3. Experimental data and numerical dispersion results
3.1. Refractive indices
At each wavelength several measurements at a temperature of 20 °C are taken to calculate
the arithmetic average of n′liq(λ ). With this averaged value the actual refractive index of the
liquid nliq is then obtained by using Eq. (6) and Eq. (7) with npr(λD) = 1.74054 and φ = 63 °.
To calculate the uncertainties associated with the measurement, error propagation is used to
account for the uncertainties in the dispersion of the prism ∆npr and in the measured refractive
index ∆n′liq. The error for the dispersion of the prism can be obtained from the standard error of
the Cauchy formula (Eq. (7)) and is 1× 10−4. The uncertainty in n′liq is given by the standard
error of the single measurements. Hence, the absolute maximum error at each wavelength can
be calculated by
∆nliq =
∣∣∣∣
∂nliq
∂npr
∣∣∣∣∆npr +
∣∣∣∣∣
∂nliq
∂n′liq
∣∣∣∣∣∆n
′
liq. (11)
The corrected refractive indices with their uncertainties are listed in Table 1 and Table 2 for
the eight investigated liquids. The absolute maximum error ∆nliq(λ ) ranges between 1×10−4
and 6× 10−4 and arise from temperature variations, reading and adjustment errors of the re-
fractometer, the bandwidth of the filters, and errors in the dispersion of the prism. During
the measuring procedure filters in 50 nm steps in the wavelength region between 500 nm and
900 nm and in 100 nm steps from 900 nm up to 1600 nm are used. Furthermore, the measure-
ment series from the different white light sources match very well so that they can be combined
and used for a single dispersion formula that covers the whole spectral range in the visible and
near-infrared.
From the various refractive indices at different wavelengths one can calculate a dispersion
equation by nonlinear curve fitting using the least square method. Among the various dispersion
equations the Sellmeier and the Cauchy formula are the most common. The ansatz of Sellmeier
can be used in the whole spectral region and is up to the second order given by
n2(λ ) = 1+ A1λ
2
λ 2−B1
+
A2λ 2
λ 2−B2
, (12)
with A1/2 being material parameters and
√
B1/2 the wavelengths of corresponding absorption
bands.
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1596
Table 1. Experimental values of the refractive index of distilled water, heavy water, ethanol,
and toluene at a temperature of 20 °C.
λ (µm) nwater nheavy water nethanol ntoluene
0.50 1.3372±0.0002 1.3315±0.0002 1.3653±0.0004 1.5059±0.0002
0.55 1.3345±0.0002 1.3294±0.0002 1.3625±0.0002 1.4998±0.0003
0.60 1.3328±0.0002 1.3278±0.0002 1.3612±0.0003 1.4958±0.0003
0.65 1.3314±0.0003 1.3264±0.0002 1.3596±0.0002 1.4926±0.0003
0.70 1.3301±0.0002 1.3258±0.0002 1.3589±0.0003 1.4901±0.0003
0.75 1.3291±0.0003 1.3248±0.0002 1.3579±0.0003 1.4879±0.0003
0.80 1.3282±0.0001 1.3240±0.0002 1.3573±0.0003 1.4865±0.0002
0.85 1.3273±0.0002 1.3235±0.0002 1.3569±0.0003 -
0.90 1.3263±0.0003 1.3228±0.0002 1.3565±0.0003 1.4837±0.0003
1.00 1.3249±0.0002 1.3217±0.0004 1.3551±0.0004 1.4823±0.0003
1.10 1.3235±0.0003 1.3209±0.0004 1.3542±0.0003 1.4809±0.0003
1.20 1.3218±0.0004 1.3198±0.0003 1.3539±0.0003 1.4800±0.0003
1.30 1.3201±0.0002 1.3191±0.0002 1.3532±0.0003 1.4792±0.0003
1.40 1.3183±0.0003 1.3183±0.0003 1.3528±0.0003 1.4783±0.0003
1.50 1.3167±0.0004 1.3173±0.0004 1.3522±0.0003 1.4779±0.0003
1.60 1.3141±0.0004 1.3167±0.0005 1.3518±0.0004 1.4773±0.0004
Table 2. Experimental values of the refractive index of carbon disulfide, carbon tetrachlo-
ride, chloroform, and nitrobenzene at a temperature of 20 °C.
λ (µm) ncarbon disulfide ncarbon tetrachloride nchloroform nnitrobenzene
0.50 1.6473±0.0003 1.4652±0.0002 1.4495±0.0003 1.5671±0.0002
0.55 1.6348±0.0006 1.4616±0.0002 1.4461±0.0002 1.5574±0.0003
0.60 1.6266±0.0004 1.4595±0.0002 1.4434±0.0002 1.5505±0.0005
0.65 1.6186±0.0005 1.4570±0.0003 1.4418±0.0002 1.5456±0.0003
0.70 1.6136±0.0005 1.4558±0.0002 1.4402±0.0004 1.5420±0.0003
0.75 1.6091±0.0003 1.4547±0.0002 1.4391±0.0002 1.5390±0.0002
0.80 1.6058±0.0004 1.4536±0.0002 1.4383±0.0003 1.5367±0.0004
0.85 1.6032±0.0005 1.4523±0.0002 1.4374±0.0003 1.5346±0.0004
0.90 1.6008±0.0005 1.4519±0.0002 1.4369±0.0005 1.5333±0.0002
1.00 1.5976±0.0004 1.4512±0.0003 1.4357±0.0004 1.5307±0.0003
1.10 1.5947±0.0004 1.4504±0.0003 1.4351±0.0004 1.5290±0.0003
1.20 1.5929±0.0003 1.4497±0.0004 1.4346±0.0003 1.5273±0.0002
1.30 1.5909±0.0005 1.4491±0.0004 1.4342±0.0003 1.5264±0.0003
1.40 1.5900±0.0004 1.4488±0.0004 1.4340±0.0003 1.5256±0.0003
1.50 1.5888±0.0003 1.4484±0.0003 1.4335±0.0003 1.5247±0.0003
1.60 1.5880±0.0004 1.4479±0.0003 1.4332±0.0003 1.5240±0.0003
Far away from any resonance one can use the simpler Cauchy equation. Therefore the first
order Sellmeier equation can be expanded into a power series. Up to the second order one
obtains
n2(λ ) = 1+ A1λ
2
λ 2−B1
≈ 1+A1(1+
B1
λ 2 +
B21
λ 4 ) = C0 +
C1
λ 2 +
C2
λ 4 . (13)
An improvement in fitting the refractive index of liquids in the visible to near-infrared region
can be expected if a term C3λ 2 in Eq. (13) is added due to infrared vibrational absorption
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1597
bands [15] which leads to
n2(λ ) = C0 +
C1
λ 2 +
C2
λ 4 +C3λ
2. (14)
For each liquid the constants of the Sellmeier and the Cauchy formulas are calculated. To
choose the number of terms, the standard error of the constants, the summed squares of residuals
(SSE), the adjusted R-square, and the fit standard error (Root Mean Squared Error, RMSE) are
taken into account.
By careful comparison of the fitting results it turns out that one or two terms in the Sellmeier
formula (Eq. (12)) deliver satisfying results. However, the additional term in Eq. (14) offers
indeed better fitting results than Eq. (13) for the Cauchy formula.
In Table 3 and Table 4 the constants of Sellmeier and Cauchy formula and their statistics are
given for each liquid. The values of the standard deviation indicate good quality of the fits. The
error for n2liq is in the best case about 3.0×10−4 for chloroform and still below 6.2×10−4 for
carbon tetrachloride in the worst case.
Sellmeier and Cauchy formulas shown in the following Figs. 8, 9, 10, 11, 12, 13, 14, 15 are
based on data between wavelengths of 500 nm and 1600 nm. For reasons of clarity no absolute
error bars associated with each measured refractive index value are plotted. In general, the re-
fractive index in the wavelength range of the visible to the near-infrared is caused by electronic
absorption in the ultraviolet and the vibrational absorption in the infrared. In the following
previously published data are shown in comparison, being in very good agreement with our
measurements.
3.1.1. Refractive index of distilled water
In Fig. 8 the measured values for the refractive index of distilled water are shown which are
listed in Table 1. We plotted there as well the Sellmeier formula given in Table 3 together with
reference values from Refs. [16, 18, 21]. For distilled water many reference data have been
published; only three are shown in Fig. 8. The dispersion curve from Ref. [18] is plotted in the
wavelength range between 405 nm and 1129 nm. From a wavelength of 800 nm upwards the
0.6 0.8 1.0 1.2 1.4 1.6
1.31
1.32
1.33
Wavelength (µm)
R
e
fr
a
c
ti
v
e
 i
n
d
e
x
Measured values
Sellmeier formula of measurement
Reference values [18]
Sellmeier formula of reference [18]
Reference values [16,21]
WATER (H O)2
Fig. 8. Dispersion of the linear refractive index of liquid water at a temperature of 20 °C.
Diamonds represent the experimental data listed in Table 1; the solid red curve is the cal-
culated Sellmeier dispersion formula given in Table 3; for comparison we also plotted the
reference data as squares and the corresponding dispersion curve (dashed black line) from
Ref. [18]. Circles are published data extracted from Refs. [16, 21].
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1598
Table 3. Constants of Sellmeier and Cauchy formula of distilled water, heavy water, chlo-
roform, and carbon tetrachloride at a temperature of 20 °C.
Sellmeier formula Cauchy formula
Parameter y = n2(A1,B1,A2,B2) Parameter y = n2(C0,C1,C2,C3)
WATER
A1 0.75831±0.00082 C0 1.76880±0.00134
B1 (µm−2) 0.01007±0.00027 C1 (µm2) 0.00237±0.00093
A2 0.08495±0.01912 C2 (µm4) 0.00087±0.00017
B2 (µm−2) 8.91377±1.35076 C3 (µm−2) −0.01651±0.00048
SSE (10−6) 1.57 SSE (10−6) 1.92
Adj. R-Square 0.99957 Adj. R-Square 0.99948
RMSE (10−4) 3.62 RMSE (10−4) 4.00
HEAVY WATER
A1 −0.30637±0.76766 C0 1.74679±0.00108
B1 (µm−2) −47.26686±126.47658 C1 (µm2) 0.00633±0.00075
A2 0.74659±0.00104 C2 (µm4) 0.00014±0.00014
B2 (µm−2) 0.00893±0.00031 C3 (µm−2) −0.00623±0.00038
SSE (10−6) 1.26 SSE (10−6) 1.24
Adj. R-Square 0.99922 Adj. R-Square 0.99922
RMSE (10−4) 3.24 RMSE (10−4) 3.22
CHLOROFORM
A1 1.04647±0.00921 C0 2.05159±0.00100
B1 (µm−2) 0.01048±0.00130 C1 (µm2) 0.01005±0.00069
A2 0.00345±0.00941 C2 (µm4) 0.00059±0.00013
B2 (µm−2) 0.15207±0.09540 C3 (µm−2) −0.00052±0.00035
SSE (10−6) 1.13 SSE (10−6) 1.06
Adj. R-Square 0.99951 Adj. R-Square 0.99954
RMSE (10−4) 3.07 RMSE (10−4) 2.98
CARBON TETRACHLORIDE
A1 1.09215±0.00027 C0 2.09503±0.00208
B1 (µm−2) 0.01187±0.00012 C1 (µm2) 0.01102±0.00144
C2 (µm4) 0.00050±0.00026
C3 (µm−2) −0.00102±0.00074
SSE (10−6) 5.35 SSE (10−6) 4.61
Adj. R-Square 0.99826 Adj. R-Square 0.99826
RMSE (10−4) 6.18 RMSE (10−4) 6.20
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1599
Table 4. Constants of Sellmeier and Cauchy formula of toluene, ethanol, carbon disulfide,
and nitrobenzene at a temperature of 20 °C.
Sellmeier formula Cauchy formula
Parameter y = n2(A1,B1,A2,B2) Parameter y = n2(C0,C1,C2,C3)
TOLUENE
A1 1.17477±0.00022 C0 2.17873±0.00138
B1 (µm−2) 0.01825±0.00009 C1 (µm2) 0.01886±0.00095
C2 (µm4) 0.00086±0.00017
C3 (µm−2) −0.00145±0.00049
SSE (10−6) 3.20 SSE (10−6) 1.82
Adj. R-Square 0.99964 Adj. R-Square 0.99976
RMSE (10−4) 4.96 RMSE (10−4) 4.07
ETHANOL
A1 0.83189±0.00196 C0 1.83347±0.00199
B1 (µm−2) 0.00930±0.00052 C1 (µm2) 0.00648±0.00138
A2 −0.15582±1.59085 C2 (µm4) 0.00031±0.00025
B2 (µm−2) −49.45200±537.47222 C3 (µm−2) −0.00352±0.00071
SSE (10−6) 4.53 SSE (10−6) 4.23
Adj. R-Square 0.99667 Adj. R-Square 0.99689
RMSE (10−4) 6.15 RMSE (10−4) 5.94
CARBON DISULFIDE
A1 1.50387±0.00027 C0 2.50984±0.00161
B1 (µm−2) 0.03049±0.00008 C1 (µm2) 0.04101±0.00112
C2 (µm4) 0.00252±0.00021
C3 (µm−2) −0.00183±0.00057
SSE (10−6) 5.84 SSE (10−6) 2.77
Adj. R-Square 0.99987 Adj. R-Square 0.99993
RMSE (10−4) 6.46 RMSE (10−4) 4.81
NITROBENZENE
A1 1.30628±0.00449 C0 2.31952±0.00125
B1 (µm−2) 0.02268±0.00079 C1 (µm2) 0.02355±0.00087
A2 0.00502±0.00474 C2 (µm4) 0.00266±0.00016
B2 (µm−2) 0.18487±0.02830 C3 (µm−2) −0.00259±0.00044
SSE (10−6) 2.57 SSE (10−6) 1.67
Adj. R-Square 0.99986 Adj. R-Square 0.99991
RMSE (10−4) 4.63 RMSE (10−4) 3.73
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1600
red solid and dashed black lines run nearly parallel to each other with a maximum deviation
of 6× 10−4. Also, the values given in the Refs. [16] and [21] match very well with our data.
Moreover, a Cauchy formula from Ref. [16] in the range between 486 nm and 943 nm and the
values of Ref. [22] fit quite well our own measured values but are not shown in Fig. 8 for
reasons of clarity.
In general, the trend of dispersion of water differs from that of the other investigated liquids
due to the huge vibrational overtone absorption band at a wavelength of around 1400 nm (see
Fig. 16).
3.1.2. Refractive index of heavy water
In Fig. 9 the measured values for the refractive index of heavy water are shown which are
also listed in Table 1. Presented there as well are the Sellmeier data given in Table 3 together
with reference values from Ref. [21]. The corresponding dispersion curve is plotted in the wave-
length range between 405 nm and 768 nm. In this regime the solid red and the dashed black lines
show good agreement and deviate between 1.5× 10−4 and 4.5× 10−4. The deviations of the
extended Cauchy formula derived in Ref. [21] from our own Sellmeier formula increase with
increasing wavelength which indicates the limited usability of dispersion curves beyond their
measuring range. Furthermore, we observe a weaker influence of the first overtone vibration
on the dispersion curve compared to H2O since the absorption band is shifted to higher wave-
lengths (around 2.1 µm). This effect results from the heavier deuterium nucleus (see Fig. 17).
0.6 0.8 1.0 1.2 1.4 1.6
1.315
1.321
1.327
R
e
fr
a
c
ti
v
e
 i
n
d
e
x
Measured values
Sellmeier formula of measurement
Reference values [21]
Cauchy formula of reference [21]
HEAVY WATER (D O)2
Wavelength ( m)μ
Fig. 9. Dispersion of the linear refractive index of liquid heavy water at a temperature
of 20 °C. Diamonds represent the experimental data listed in Table 1; the solid red curve
represents the calculated Sellmeier dispersion formula given in Table 3; for comparison we
also plotted the reference data as squares and the corresponding dispersion curve (dashed
black line) from Ref. [21].
3.1.3. Refractive index of chloroform
In Fig. 10 the measured values for the refractive index of chloroform are shown which are
listed in Table 2. Presented there as well are the Sellmeier data from Table 3 together with
reference values from Ref. [22]. The single data points from Ref. [22] match very good with
the solid red curve and the deviations lie always below 4×10−4. We observe a deviation of at
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1601
maximum 20×10−4 in comparison to Ref. [15]. In this reference the data points are located in
the wavelength range between 265 nm and 2480 nm, however, with a lack of measured values
between 656 nm and 2130 nm which is the reason for this huge deviation. Dispersion effects
due to the absorption bands displayed in Fig. 18 have not been found since the vibrational
overtones are too weak in the infrared range.
CHLOROFORM (CHCl )3
0.6 0.8 1.0 1.2 1.4 1.6
1.432
1.440
1.448
R
e
fr
a
c
ti
v
e
 i
n
d
e
x
Measured values
Sellmeier formula of measurement
Reference values [22]
Wavelength ( m)μ
Fig. 10. Dispersion of the linear refractive index of liquid chloroform at a temperature of
20 °C. Diamonds represent the experimental data listed in Table 2; the solid red curve is the
calculated Sellmeier dispersion formula given in Table 3; also shown is for comparison the
reference data from Ref. [22] as squares.
3.1.4. Refractive index of carbon tetrachloride
In Fig. 11 the measured values for the refractive index of carbon tetrachloride are plotted as
listed in Table 2. Presented as well is our Cauchy fit from Table 3 together with reference
0.6 0.8 1.0 1.2 1.4 1.6
1.447
1.453
1.459
1.465
R
e
fr
a
c
ti
v
e
 i
n
d
e
x
Measured values
Cauchy formula of measurement
Reference values [16,21,22]
CARBON TETRACHLORIDE (CCl )4
Wavelength ( m)μ
Fig. 11. Dispersion of the linear refractive index of liquid carbon tetrachloride at a tem-
perature of 20 °C. Diamonds represent the experimental data listed in Table 2; the solid
red curve is the calculated Cauchy dispersion formula given in Table 3; for comparison we
show the reference data from Refs. [16, 21, 22] as squares.
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1602
values from Refs. [16, 21, 22]. The three single reference data points lie slightly above the
red solid curve, but differ not more than 4× 10−4. Due to the consistently small absorption
coefficient (see Fig. 19) no influences on the dispersion trend are noticeable.
3.1.5. Refractive index of toluene
In Fig. 12 we plot the measured values for the refractive index of toluene which are listed in
Table 1. Presented there as well are the Cauchy data given in Table 4 together with reference
values from Refs. [16, 22]. The dispersion curve from Ref. [15] is plotted in the wavelength
range between 405 nm and 830 nm. The solid red and dashed black curve match very well, and
the largest deviation above a wavelength of 600 nm is less than 2× 10−4. Also the measured
reference value of Ref. [16] derived with the Abbe refractometer at a wavelength of λ = 830 nm
differs less than 1×10−4. The steep decline of the refractive index of toluene is not affected by
the observed resonances shown in Fig. 20.
0.6 0.8 1.0 1.2 1.4 1.6
1.48
1.49
1.50
R
e
fr
a
c
ti
v
e
 i
n
d
e
x
Measured values
Cauchy formula of measurement
Reference values [16,22]
Cauchy formula of reference [15]
TOLUENE (C H )7 8
Wavelength ( m)μ
Fig. 12. Dispersion of the linear refractive index of liquid toluene at a temperature of 20 °C.
Diamonds represent the experimental data listed in Table 1; the solid red curve is the cal-
culated Cauchy dispersion formula given in Table 4; for comparison we also plotted the
reference data from Refs. [16, 22] as squares as well as the dispersion curve (dashed black
line) from Ref. [15].
3.1.6. Refractive index of ethanol
In Fig. 13 the measured values for the refractive index of ethanol are shown as given in Table 1.
Presented there are also the Sellmeier data given in Table 4 together with reference values
from Refs. [16, 21, 22]. The dispersion curve from Ref. [16] is plotted in the wavelength range
between 476 nm and 633 nm. The solid red and dashed black curve agree very well and do
not differ more than 2× 10−4. The reference data point from Ref. [16] at a wavelength of
λ = 830 nm varies not more than 1×10−4 from our own Sellmeier equation, whereas the other
points from Refs. [21,22] a more scattered. The bend of the solid red curve is slightly influenced
by the strong absorption bands at a wavelength of around 1500 nm shown in Fig. 21.
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1603
0.6 0.8 1.0 1.2 1.4 1.6
1.350
1.354
1.358
1.362
1.366
R
e
fr
a
c
ti
v
e
 i
n
d
e
x
Measured values
Sellmeier formula of measurement
Reference values [16,21,22]
Cauchy formula of reference [16]
ETHANOL (C H O)2 6
Wavelength ( m)μ
Fig. 13. Dispersion of the linear refractive index of liquid ethanol at a temperature of 20 °C.
Diamonds represent the experimental data listed in Table 1; the solid red curve is the cal-
culated Sellmeier dispersion formula given in Table 4; for comparison we also plotted the
reference data as squares from Refs. [16, 21, 22] and the dispersion curve (dashed black
line) from Ref. [16].
3.1.7. Refractive index of carbon disulfide
In Fig. 14 the measured values for the refractive index of carbon disulfide are displayed as listed
in Table 2. We also plot the Cauchy fit as given in Table 4 together with the dispersion curve
from Ref. [15] plotted in the wavelength range between 340 nm and 2430 nm. The trend of the
solid red and dashed black curve match very well. Due to the very steep decline of the refractive
index the maximal deviation is around 8×10−4.
0.6 0.8 1.0 1.2 1.4 1.6
1.59
1.61
1.63
1.65
R
e
fr
a
c
ti
v
e
 i
n
d
e
x
Measured values
Cauchy formula of measurement
Cauchy formula of reference [15]
CARBON DISULFIDE (CS )2
Wavelength ( m)μ
Fig. 14. Dispersion of the linear refractive index of liquid carbon disulfide at a temperature
of 20 °C. Diamonds represent the experimental data listed in Table 2; the solid red curve is
the calculated Cauchy dispersion formula given in Table 4; for comparison we also plotted
the dispersion curve (dashed black line) from Ref. [15].
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1604
3.1.8. Refractive index of nitrobenzene
In Fig. 15 the measured values for the refractive index of nitrobenzene are shown which are
listed in Table 2. Presented there as well is the Cauchy formula given in Table 4 together with
reference values from Ref. [22]. The difference between the solid red curve and the reference
data points lies between 7× 10−4 and 9× 10−4. There also exist published data in Ref. [21]
which differ between 4×10−4 and 26×10−4 from our own Cauchy equation. The considerable
variations in the deviations result from the multitude of different reference sources mentioned
in the Handbook of Nikogosyan [21].
0.6 0.8 1.0 1.2 1.4 1.6
1.522
1.538
1.554
1.570
R
e
fr
a
c
ti
v
e
 i
n
d
e
x
Measured values
Cauchy formula of measurement
Reference values [22]
NITROBENZENE (C H NO )6 5 2
Wavelength ( m)μ
Fig. 15. Dispersion of the linear refractive index of liquid nitrobenzene at a temperature of
20 °C. Diamonds represent the experimental data listed in Table 2; the solid red curve is the
calculated Cauchy dispersion formula given in Table 4; for comparison we also plotted the
reference data from Ref. [22] as squares.
3.2. Absorption coefficients
At each tube length several measurements at a room temperature of 20 °C are taken to mini-
mize the effect of unequal coupling into the spectrometer. From the transmission spectra for
each tube length with and without liquid filling one can calculate the wavelength dependent
absorption coefficient by Eq. (10). An average absorption coefficient can be calculated from
several possible combinations of the different sample lengths. On the one hand, at wavelengths
with strong absorption, only the short glass cells provide meaningful results because they can
best follow the steep rise and decline at the resonance positions. More light can be collected
by the spectrometer with the short cells. On the other hand at weak absorption regimes the
long tube lengths deliver more precise results since they can resolve the reduced effect of the
absorption by an increased propagation length (see Eq. (8)). All values of the absorption co-
efficient of the six investigated liquids and their standard error are given in the appendix as
comma-separated value text files. The uncertainty at each wavelength is calculated by the stan-
dard deviation of the average value. Generally, the absolute standard error is quite small, but
for low values of the absorption coefficient the relative deviation can become large as can also
be seen in the comparison with reference values in the water measurement in Section 3.2.1.
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1605
3.2.1. Absorption of distilled water
In Fig. 16 the measured absorption coefficient of distilled water together with the reference
values of Ref. [22] are shown. The trend of the solid red and dashed black curve match well
apart from the height of the resonance peak at a wavelength of around 1450 nm. In Ref. [19] an
absorption coefficient of about 24cm−1 at the 1450 nm resonance peak is given. The deviation
of the peak heights at resonance positions can be related to the limited response and sensitivity
of the spectrometer. In our measurements cells not thinner than 1 mm and 2 mm are available
to increase the transmitted intensities.
WATER (H O)2
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
0
10
20
30
Wavelength (nm)
A
b
s
o
rp
ti
o
n
 c
o
e
ff
ic
ie
n
t 
(1
/c
m
)
Measurement
Reference [22]
Linear scale
0.6 0.8 1.0 1.2 1.4 1.6
0.001
0.01
0.1
1
10
Wavelength ( m)μ
A
b
s
o
rp
ti
o
n
 c
o
e
ff
ic
ie
n
t 
(1
/c
m
)
Measurement
Reference [22]
Logarithmic scale
Fig. 16. Measured absorption coefficient of liquid distilled water at a temperature of 20 °C
on (a) linear and (b) logarithmic scale as a function of wavelength. For comparison to our
measured values (solid red line) we also plotted linearised reference data (dashed black
line) from Ref. [22] (Media 1).
A first larger absorption band occurs at a wavelength of 980 nm followed by another band at
around 1200 nm. The huge absorption band at a wavelength of around 1450 nm results from the
first overtone stretch vibration of the water molecule. The other two bands result from higher
overtones or combination vibrations. Our own measured resonance positions fit excellent to the
resonances mentioned in Ref. [19].
Upon comparison with the values of Refs. [19, 22], the used measurement method can be
successfully verified. Above a wavelength of 600 nm the relative deviation between the solid
red and dashed black curve is at its maximum 17 % but mostly clearly below except at the
steep rise at the wavelength of around 1365 nm where the difference is around 26 %. In the
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1606
range between 500 nm to 600 nm in which the absorption coefficient falls below 1×10−3 cm−1,
the relative deviation can become large. However, the average relative deviation over the full
measurement range is only 8.5 %.
Possible error sources arise from the different incoupling into the spectrometer entrance, the
temporal instability of the white light source, dust on the end faces or in the liquid, temperature
variations, the measurement inaccuracy of the spectrometer, and slightly different reflection
coefficients at the interfaces. The main error from the slight difference in beam incoupling can
be minimized by several measurements searching each time for the highest detection signal
by fine adjustments of the mirrors. All together, these errors can serve as explanation for the
standard deviation as well as for the differences between our measurements and the references
for distilled water. However, these effects will cause uncertainties in further measurements and
have to be minimized.
3.2.2. Absorption of heavy water
In Fig. 17 the measured absorption coefficient of heavy water is shown. In contrast to H2O the
absorption bands are considerably weaker and shifted to higher wavelengths due to the heavier
deuterium nucleus. Resonance positions occur at a wavelength of around 1000 nm, 1330 nm,
and 1600 nm. Because only the shorter glass cells are applied for measuring the absorption
coefficient below a wavelength of 1200 nm, the measurement is noisy. Some reference data
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
0.2
0.4
0.6
Wavelength (nm)
A
b
s
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rp
ti
o
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o
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ff
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t 
(1
/c
m
)
Measurement
Linear scale
0
0.6 0.8 1.0 1.2 1.4 1.6
0.01
0.1
0.5
Wavelength ( m)μ
A
b
s
o
rp
ti
o
n
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(1
/c
m
)
Measurement
Logarithmic scale
HEAVY WATER (D O)2
Fig. 17. Measured absorption coefficient of liquid heavy water at a temperature of 20 °C on
(a) linear and (b) logarithmic scale as a function of wavelength (Media 2).
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1607
have been published in Ref. [22] for the wavelength range between 400 nm and 790 nm. In this
reference the values for the absorption coefficient are clearly smaller and lie between 0.3×
10−3 cm−1 and 1.0×10−3 cm−1. The deviation results from the application of the shorter glass
cells instead of the longer tubes in this wavelength region with very low absorption. We did not
use the longer tubes for the absorption measurement in the visible due to the high cost of heavy
water.
3.2.3. Absorption of chloroform
In Fig. 18 the measured absorption coefficient of chloroform is shown. The absorption bands
of chloroform are relatively narrow when compared with water. They arise from overtones of
the CH-group stretch mode and from combination vibrations. Additionally to the sharp peaks
at a wavelength of around 1150 nm, 1420 nm, and 1680 nm, numerous smaller peaks below an
absorption coefficient of 0.2cm−1 can be observed. The large peak at a wavelength of 1680 nm
could only be measured exactly when using the thinnest glass cells of 1 mm and 2 mm length,
whereas the smaller peaks are only visible with the longest tubes.
Wavelength ( m)μ
600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
0
5
10
15
20
Wavelength (nm)
A
b
s
o
rp
ti
o
n
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o
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ff
ic
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t 
(1
/c
m
)
Measurement
Linear scale
0.6 0.8 1.0 1.2 1.4 1.6
0.01
0.1
1
10
A
b
s
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ff
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(1
/c
m
)
Measurement
Logarithmic scale
CHLOROFORM (CHCl )3
Fig. 18. Measured absorption coefficient of liquid chloroform at a temperature of 20 °C on
(a) linear and (b) logarithmic scale as a function of wavelength (Media 3).
3.2.4. Absorption of carbon tetrachloride
In Fig. 19 the measured absorption coefficient of carbon tetrachloride is shown. Due to the con-
sistently small absorption coefficient α , which never exceeds 6× 10−3 cm−1, only the longest
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1608
tubes of 250 mm, 500 mm, 750 mm, and 1000 mm length are used to determine the value of α .
The wavelength range only spans from 500 nm up to 1500 nm as the glass cell measurements
above 1500 nm are dominated by noise.
500 600 700 800 900 1000 1100 1200 1300 1400 1500
0.002
0.004
0.006
Wavelength (nm)
A
b
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ff
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t 
(1
/c
m
)
Measurement
Linear scale
0
0.6 0.8 1.0 1.2 1.4
0.001
0.005
Wavelength ( m)μ
A
b
s
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t 
(1
/c
m
)
Measurement
Logarithmic scale
CARBON TETRACHLORIDE (CCl )4
Fig. 19. Measured absorption coefficient of liquid carbon tetrachloride at a temperature of
20 °C on (a) linear and (b) logarithmic scale as a function of wavelength (Media 4).
3.2.5. Absorption of toluene
In Fig. 20 the measured absorption coefficient of toluene is shown. The same shapes of the
three absorption bands at a wavelength of around 730 nm, 900 nm, and 1150 nm with decreas-
ing intensities indicate higher vibrational overtones. The pronounced peak at a wavelength of
around 1700 nm could not be fully resolved due to the decreasing intensity of the white light
source at this wavelength range. Toluene consists of a benzene ring with an additional CH3-
group. Amongst others, the absorption bands result from stretching overtones of the CH- and
CH3-group.
3.2.6. Absorption of ethanol
In Fig. 21 the measured absorption coefficient of ethanol is shown. The spectra are dominated
by vibrational overtones from the groups CH2, CH3 and CH2OH. The shapes of the absorption
bands at wavelengths of around 630 nm, 730 nm, 930 nm, and 1200 nm are very similar. Also
the peak at a wavelength of around 1700 nm could be not fully assessed.
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1609
TOLUENE (C H )7 8
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
4
8
12
Wavelength (nm)
A
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(1
/c
m
)
Measurement
Linear scale
0.6 0.8 1.0 1.2 1.4 1.6
0.01
0.1
1
10
Wavelength ( m)μ
A
b
s
o
rp
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(1
/c
m
)
Measurement
0
Logarithmic scale
Fig. 20. Measured absorption coefficient of liquid toluene at a temperature of 20 °C on (a)
linear and (b) logarithmic scale as a function of wavelength (Media 5).
4. Conclusion
The dispersion and absorption properties of several frequently used nonlinear liquids in the
visible and near-infrared have been measured at a temperature of 20 °C. The refractive index
measurement requires the calculation of correction terms in order to use a standard Abbe refrac-
tometer in a wider wavelength region beyond the visible. Comparisons with original corrections
from Zeiss confirm the used method. All modifications which are needed to extend the applica-
tion range are described and given in detail. Accurate measurement data between a wavelength
range from 500 nm up to 1600 nm together with their fitting constants of Cauchy and Sellmeier
equations are given for the first time over this broad wavelength region and were successfully
compared with sparsely existing published data.
The described technique can easily be applied and extended to longer wavelengths above
1600 nm with suitable cameras and more powerful and broadband white light sources. A lim-
iting factor due to the transmittance of lenses, prism, and their coatings according to Ref. [16]
could not be observed in our spectral range. Strongly absorbing liquids such as water or ethanol
have to be investigated in reflection mode and may cause problems at higher wavelengths due
to a reduction of the image contrast. Moreover, the refraction index measurement with the Abbe
refractometer can be easily transferred to further liquids. An improvement in accuracy could be
achieved by a more stable cooling system.
The absorption coefficient α can be determined from the transmitted intensity through cells
or tubes of different lengths. Due to the fact that each value α is calculated by using two
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1610
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
2
4
6
8
Wavelength (nm)
A
b
s
o
rp
ti
o
n
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o
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ff
ic
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t 
(1
/c
m
)
Measurement
Linear scale
0
0.6 0.8 1.0 1.2 1.4 1.6
0.001
0.01
0.1
1
10
Wavelength ( m)μ
A
b
s
o
rp
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n
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(1
/c
m
)
Measurement
Logarithmic scale
ETHANOL (C H O)2 6
Fig. 21. Measured absorption coefficient of liquid ethanol at a temperature of 20 °C on (a)
linear and (b) logarithmic scale as a function of wavelength (Media 6).
different length combinations, identical positioning and preparation of the samples have to be
taken into account. Also the suitable choice of cells or tubes depending on the magnitude of
absorption have to be considered. For small values of the absorption coefficient the longer tubes
are ideal, whereas at absorption resonances the thinner glass cells provide meaningful results.
The measurement technique could be successfully verified by comparison with reference data
for distilled water. Measurements in a wavelength region between 500 nm and 1750 nm (for
CCl4 only up to a wavelength of 1500 nm) were taken.
The used technique can also easily be extended to other liquids and different wavelengths.
However, for strongly absorbing liquids the application range is restricted because of the avail-
able thicknesses of the glass cells below 1 mm. The transmitted intensity could be increased
by a more powerful white light laser, however possibly at the expense of spectral stability and
therefore also leading to reduced accuracy.
In general, the presented methods provide an easy and accurate way to determine the refrac-
tive index and the absorption coefficient of liquids. If the desired liquid is not included in the
collection presented in this paper, all necessary information are provided here to transfer these
techniques and apply them to the liquid of interest.
Acknowledgments
This work was supported financially by DFG, BMBF, GIF, BW-Stiftung, and Alexander von
Humboldt Stiftung. We acknowledge support from the German Research Foundation (DFG)
within the funding program Open Access Publishing.
#170502 - $15.00 USD Received 12 Jun 2012; revised 26 Sep 2012; accepted 2 Oct 2012; published 15 Oct 2012
(C) 2012 OSA 1 November 2012 / Vol. 2,  No. 11 / OPTICAL MATERIALS EXPRESS  1611