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@example.com. Abstract.
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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, firstname.lastname@example.org
Experimental Setup (cont.)
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:
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.
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.
For this project, a variation on the above idea was used. For each interference trace, the refractive index was found using the expression:
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 arc-lamp 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.
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.
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.
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.
Figure 4: Variation in n over the wavelength range 400-900nm for a bulk
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.
Figure 1: Schematic of the Michelson Interferometric Apparatus.
This research was funded by the National Science Foundation (DMR-0215407). Thanks to Dr. W. Tandy Grubbs and the chemistry department at Stetson University for the opportunity to participate in this project.
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 Helium-Neon (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.
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 Optoelectronics1997, 144, 397.
4. Garito, A. F.; Wang, J.; Gao, R. Science1998, 281, 962.
Figure 2: Interference Trace for Magnesium Fluoride at λ = 790 nm
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.