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Interferometric Measurements of Refractive
Index Dispersion in Polymers over the Visible
and Near-Infrared Spectral Range
Sarah Caudill and W. Tandy Grubbs, Department of Chemistry, Stetson University
Unit 6035, DeLand, FL 32720, 386-409-8293, [email protected]
Experimental Setup (cont.)
The index of refraction of a material can be used to determine how
light bends as the rays travel through a substance. Therefore, this property is
key to optical research. Currently, refractive index measurements are
performed primarily with refractrometric instruments. These instruments
measure the angle of refraction of light through a material. The refractive
index is then determined using Snell’s law. However, the instruments require
careful calibration if the researcher seeks to measure refractive index over a
wide spectral range with high accuracy and precision. Furthermore,
refractometers can only be used for measurements of liquid, gel, and thin
solid samples. Analysis of bulk polymer samples is not possible. To
confront these restrictions, a low-coherence Michelson interferometric
method has been developed to measure the refractive index of bulk samples
over the 400nm to 1600 nm spectral range. The accuracy and precision of
this new method has been demonstrated by carrying out measurements for
the following glass and polymer samples: fused silica, BK7 glass, Borofloat
glass, magnesium fluoride, polycarbonate, poly(methyl methacrylate), and
polystyrene bulk samples1.
Data for the interference intensities of the arc-lamp and the HeNe
laser are collected while the movable mirror is translated over the
appropriate range. Three interference wave packets are observed for arclamp interference versus mirror displacement as shown in Figure 2 below.
The first packet corresponds to light that passed through the sample,
reflected off the fixed mirror in the interferometer, and then passed through
the sample again. The middle packet corresponds to light that passed
through the sample only once on its round trip. The last packet corresponds
to light that never passed through the sample but was still reflected off the
fixed mirror. Only the first and last packets are required to calculate the
refractive index of a material.
Interferometric determinations of refractive index, n, are based on the
expression n = p/l where l is the thickness of the optical sample, and p is the
distance the monochromatic light would have to travel in a vacuum in order
to simulate the passage of the light through the sample. Interferometry
determines the distance, Δp, between the two interference wave packets. The
expression Δp /l determines the refractive index of the sample relative to air.
The refractive index of air can be assumed to be one for most practical
applications. Therefore, if one is added to Δp /l, then the refractive index of
the sample is obtained1.
Data was collected for the inorganic and polymer optics over the
wavelength range 400nm - 900nm and in some cases 400nm – 1600nm.
Normal dispersion for a given material can be written in terms of the
empirical Cauchy formula1:
For this project, a variation on the above idea was used. For each
interference trace, the refractive index was found using the expression:
Helium-Neon Laser
Frequency-Stabilized
Translation
Stage Controller
Monochromator
The analysis of bulk polymer samples is important to those interested
in “all-optical” networking for high-bandwidth transmission media. While
the presently used single-mode silica fibers do possess high transmission
windows centered at the near-infrared communication wavelengths (850nm,
1300nm, and 1550 nm), the use of silica in local area networks (LAN) is
unrealistic due to the numerous couplings that exist between the backbone
wide area network and the desktop user. The use of polymer-based
multimode fibers in place of silica would be advantageous for several
reasons. Primarily, polymers are more flexible, and larger diameter fibers
could be manufactured for easier coupling in LAN environments.
Furthermore, polymers can be fabricated at low costs. However, research
and development of optical polymers is currently hindered due to the
restrictions of refractometer instruments. The bandwidth capacity of bulk
polymers in the visible and near-infrared spectral range is difficult to
characterize with presently available methods2-4. However, an apparatus for
interferometric measurements of refractive index dispersion in polymers can
achieve what the refractometers cannot.
n  c0  c1
1

2
 c2
1
4
The coefficients of this equation were found for each material using
the experimentally determined interferometric refractive index data at each
corresponding wavelength. A plot of n versus λ can be constructed for each
material, and the Cauchy equation can be used to generate an empirical fit to
the data as shown in Figure 4.
1.78
1.76
1.74
1.72
Introduction
Arc
Lamp
Detector
BS
Motorized precision
translation stage
Polymer
Sample
HeNe
Detector
Fixed Mirror
Figure 1: Schematic of the Michelson Interferometric Apparatus.
where l is the thickness of the sample in µm, N is the number of light-to-dark
fringe cycles that are measured in the HeNe interference scan between the
maxima of the two wave packets in the arc-lamp interference scan, and the
factor of 0.632816 corresponds to the wavelength of the HeNe laser in µm1.
Two sources of error must be minimized during this analysis. The
thickness of the sample is measured with a caliper, yielding an accuracy out to
four decimal places. The other source of error involves the precision in
measuring Δp, the displacement between the two interference packets. The
precision in this measurement is limited by two factors: the error in locating
the maximum interference fringe on each packet (see Figure 3) and the error in
measuring the mirror displacement between the two limits. A computer
program is used to accurately find the maximum in each interference packet.
The packets are Gaussian in shape, so a Gaussian curve is fit to each packet in
order to more accurately locate the maximum. The error in the mirror
displacement is minimized by defining the displacement relative to the number
of fringes that are collected in the computer from the HeNe laser interference
signal1.
0.45
Magnesium Fluoride Sample
3.922
0.35
1.7
1.68
1.66
1.64
1.62
1.6
1.58
400
450
500
550
600
650
700
750
800
850
900
Wavelength (nm)
Figure 4: Variation in n over the wavelength range 400-900nm for a bulk
polycarbonate sample.
Conclusion
A new method for measuring the refractive index and refractive index
dispersion of bulk samples has been demonstrated. Calibration is not needed
each time a measurement is taken at a new wavelength. This method may
soon facilitate the creation of polymer-based optics for use in LAN
environments.
Arbitrary Intensity
0.25
Arbitrary Intensity
The schematic of the Michelson interferometric apparatus for measuring
refractive index is shown in Figure 1 below. Light from a Xenon arc-lamp is
directed through a monochromator in order to achieve the desired wavelengths in
the visible and near-infrared spectral region. From this point, the light travels
through a Michelson interferometer where one mirror is fixed, and the other
mirror is translated with the help of a precision motorized translation stage.
Alongside the monochromatic light, light from a frequency-stabilized HeliumNeon (HeNe) laser is also directed through the interferometer to act as a length
standard for defining the mirror displacement. The optical sample is placed in
one arm of the interferometer so that it eclipses approximately one-half of the
monochromatic light beam1.
Results (cont.)
N  (0.632816)
n
1
2l
Xe Arc
Lamp
Experimental Setup
Results
n
Abstract
Intensity
Acknowledgements
0.15
0.05
This research was funded by the National Science Foundation (DMR0215407). Thanks to Dr. W. Tandy Grubbs and the chemistry department at
Stetson University for the opportunity to participate in this project.
-0.05
-0.15
-0.25
References
-0.35
-0.45
3.102
0
0
20
40
60
80
100
120
Time
Time (pathlength)
Figure 2: Interference Trace for Magnesium Fluoride at λ = 790 nm
140
140
9
10
11
12
13
14
15
Time (seconds)
Figure 3: Expanded view of the first packet in Figure 2. A Gaussian curve
is fit to this shape to minimize error in finding the maximum.
1. Caudill, Sarah E., Jen-Chou Wang, and W. Tandy Grubbs. “Interferometric
Measurementsof Refractive Index Dispersion in Polymers over the Visible
and Near-Infrared Spectral Range,” to be submitted to the Journal of
Applied Polymer Science, 2005.
2. Chowdhury, J. Chem. Eng. 1987, 94, 14.
3. Zubia, J.; Arrue, J. IEEE Proceedings in Optoelectronics 1997, 144, 397.
4. Garito, A. F.; Wang, J.; Gao, R. Science 1998, 281, 962.