Far-infrared laser measurement of the refractiveindex of polypropylene

Jesus Flores-Mijangos and Virgilio Beltran-Lopez

The refractive index of polypropylene in the far infrared �FIR� is measured by means of a suitablymodified laser of a FIR spectrometer. When thin polypropylene films of 12.7-�m nominal thickness areintroduced in the optical cavity of a laser at the Brewster angle, the radiation ceases because of the changein the optical path of the laser beam. This change is measured from the displacement of one of the lasermirrors, which is necessary to restore the laser resonance. The refractive index of polypropylene isdeduced from this measurement and from the film thickness, as obtained from an independent mea-surement based in pycnometry. The value obtained for the refractive index is 1.492�15� for the wave-lengths between 118.834 and 251.140 �m, for a polypropylene film of 12.71�2�-�m thickness and 0.9049�7�g�cm3 density. © 2003 Optical Society of America

OCIS codes: 120.3180, 140.3070, 310.6860.

1. Introduction

The determination of the optical constants of plasticmaterials in the far infrared �FIR� is important forthe design of windows, beam splitters, substrates,or lenses to be used in this part of the electromag-netic spectrum.1 Many of these materials areavailable and are used as thin films in applicationsfor which a good knowledge of the index of refrac-tion is necessary, such as Brewster windows in la-ser technology. Likewise, polypropylene films areused for beam splitters and polarizers in laser mag-netic resonance �LMR� spectrometers.2,3 This filmalso separates the active medium from the reactioncell in the optical cavity of the tunable FIR laser ofthe spectrometer.

In this paper, we use the tunable FIR laser of ourLMR spectrometer4 to measure the refraction indexof a polypropylene film of 12.7-�m nominal thicknessat several wavelengths in the range 118–252 �m.The method employed is based essentially on themeasurement of the optical path of the laser radia-tion incident on a stack of N films that have a total

J. Flores-Mijangos (flores@nuclecu.unam.mx) is with the Insti-tuto de Ciencias Nucleares, Universidad Nacional Autonoma deMexico, Cuidad Universitaria, A. Postal 70-453, C. P. 04510, Mex-ico. V. Beltran-Lopez is deceased.

Received 15 March 2002; revised manuscript received 11 Sep-tember 2002.

0003-6935�03�030592-05$15.00�0© 2003 Optical Society of America

592 APPLIED OPTICS � Vol. 42, No. 3 � 20 January 2003

thickness d and an index of refraction n�. The indi-vidual film thickness t � d�N is determined frompycnometry density measurements of polypropylenefilm samples of known area and mass. The opticalpath, on the other hand, is determined from an ex-periment in which, by adjusting the length of theoptical cavity, the laser resonance is reestablishedafter being destroyed by the insertion of polypro-pylene films in the laser beam path. The index ofrefraction n� is given in terms of these two measure-ments. The method may be classified as an inter-ferometric measurement,1 since it relies in areestablishing of the constructive interference of in-cident and reflected waves inside the laser opticalcavity.

We are aware of the use of ellipsometry to measurethe index of refraction in the FIR, but the techniqueis still under development. Therefore the work pre-sented here constitutes an effective alternative tech-nique for the measuring of the refractive index ofseveral materials in this region of the electromag-netic spectrum.

2. Theory

Our method to determine the refraction index ofpolypropylene consists essentially in a measuring ofthe change in the optical path of a laser beam whena set of N thin films, of total thickness d, is inter-posed in the path of the beam inside the opticalcavity.

Since the resonance condition for laser action in asymmetric cavity is given by

nL �12

m�, (1)

where nL is the optical path of the laser radiationbefore insertion of the films, m is an integer, and � isthe wavelength of the laser radiation, this conditionwill cease to be satisfied if the laser beam is inter-rupted by one or several refringement films owing tothe increase of the optical path that the beam coversinside the films. In this case, it will be necessary toreposition one of the mirrors of the optical cavity overa minimum distance �L equal to the change in theoptical path brought about by the inserted films.This distance depends on the refraction index n� ofthe refringent material, on its thickness d, and on theangle of incidence � of the laser beam on the film. Ifthe distance between the mirrors is decreased untillaser action is achieved again, the new resonancecondition is

nL � n�y � nx � n�L �12

m�, (2)

where y and x are the lengths of the path traversed bythe beam with and without the film and m is a largeinteger.

Using Eq. �1�, the geometrical relations �Fig. 1� andSnell’s law, we can write Eq. �2� in terms of the angleof incident ��� and the ratio a � �L�d,

�n�

n �2

� �a � cos ����n�

n �2

� sin2 ��1�2

� sin2 �. (3)

For the Brewster angle, n��n � tan �, and we can usethis relation to write Eq. �3� as a polynomial of thefourth grade in n��n,

�n�

n �4

� �2 � a2��n�

n �2

� 1 � a2 � 0. (4)

The solutions are:

�n�

n �2

� 1 �a2

a � �8 � a2�1�2. (5)

Given that n��n � 1, we take the solution with theplus sign.

The uncertainty ��n��n� in the value of n��n asso-ciated to the uncertainty �a in the basic measuredquantity a � �L�d, as obtained from Eq. �5�, is:

��n�

n � ��n��n�2 � 12

�n��n��8 � a2�1�2

�aa2 . (6)

The method followed for a measurement of n��nconsists of the following simple three steps: Quenchthe laser by inserting a stack of N parallel polypro-pylene films of total thickness d at the Brewster an-gle; restore the laser to operation on satisfying againthe resonance condition by displacing one of the lasermirrors a distance �L parallel to itself while simul-taneously optimizing the orientation of the stack offilms for maximum transmission; and calculate a ��L�d and substitute this value in Eqs. �5� and �6�.

The total film thickness d is obtained from a sep-arate measurement of the thickness t � d�N of eachfilm by pycnometry methods.

3. Experimental Setup

The experiments were conducted in the FIR laser ofour LMR spectrometer with the modified reaction cellshown in Fig. 2. In this setup, the N polypropylenefilms are placed in two sets of concentric, brassstretcher rings. Each set can accommodate up tofive unwrinkled parallel polypropylene films, whichcan be displaced up or down or rotated around avertical axis by an attached brass rod that crossesperforated rubber stoppers, and intercepts the diam-eter of the laser beam. We use commercial polypro-pylene �CAS No. 9003-07-0�; this polypropylene ishighly isotactic.5 The angle of incidence on theplane of the ring is set for maximum transmission,ensuring that it is placed at the Brewster angle.The beam must clear the aperture presented to it bythe ring rotated at this angle so that the laser is notturned off by losses if it touches the periphery of thering. Each set has six rings. The outside ring issupported by a rod of approximately 0.32 cm of diam-eter and 15 cm in length. Each ring is 0.32 cm thickand has a difference between outside and inside di-

Table 1. Index of Refraction of Polypropylene Film in the Far Infrared

Wavelength, �a �La RatioIndex of

Refraction, n

118.834 52.4 �9� 0.687 �13� 1.495 �10�163.034 52.3 �9� 0.686 �13� 1.494 �10�164.600 8.77 �36� 0.690 �29� 1.497 �21�170.576 8.65 �40� 0.680 �32� 1.490 �24�251.140 25.8 �5� 0.676 �14� 1.487 �10�

aIn �m.ba � �L�d.

Fig. 1. A stack of polypropylene films of total thickness d � ODinterposed in the path of a laser beam brings it off resonance whenthe optical path is increased. Laser resonance is restored by aparallel displacement of one mirror of the optical cavity over adistance �L, which compensates the increase in the optical path.The change in the optical path is given in terms of y � OY and x �OX.

20 January 2003 � Vol. 42, No. 3 � APPLIED OPTICS 593

ameters of 0.32 cm. The outer diameter of the big-ger ring is 5.4 cm. The radiation source is a FIRlaser. The FIR laser active medium was methanol�CH3OH�.

The experimental setup is similar to the one de-scribed in Ref. 4 �Fig. 3�. Briefly, the pumping radi-ation passes through a mechanical chopper beforeentering the lasing medium cavity. A small fractionof the FIR radiation is reflected by a coupling copperrod, passes through a polyethylene window of0.16-cm thickness, and then falls onto a silicon bo-lometer �Infrared Laboratories, Inc.�, which is usedas a detector. The bolometer output is sent to aoscilloscope that is synchronized with the signal gen-erated by the chopper control. To measure thechange in the optical path of the beam, we firstturned on the FIR laser without any film along thebeam. A set of stretcher rings was then introducedin this path and oriented closely to an angle of 30°with respect to the axis of the optical cavity; the laserthen ceased to oscillate. The micrometer head wasthen moved inwards �i.e., in the sense of decreasingthe length of the optical cavity� until the laser cameback on again, and the orientation of the film stackwas adjusted to reach the maximum intensity. The

second set of films was then introduced and the aboveoperations repeated until the laser was again in op-eration at maximum intensity. The total change �Lin the optical path was taken to be equal to the dif-ference between the initial and final readings in themicrometer head. If the maximum intensity is lo-cated with an error of 5% in �L, then the error in a isapproximately 5% for �d 1%. In this case thefilm orientation has an associated error of less than1%, given the Brewster condition. Several indepen-dent measurements of �L were made in each exper-iment with FIR laser resonances located at differentinitial readings of the micrometer head. The aver-age value of these were taken for �L and their meansquare value for their experimental uncertainty. InFig. 4 we present a histogram for each wavelengthand the corresponding distribution function ��l �.This function ��l � is constructed from the statisticaldata subject to the condition

���

�

��l �dl � C, (7)

where C is the total number of measurements forwavelength �.

Given that the absorption in polypropylene de-pends strongly on the wavelength, it was not possibleto use the same numbers of films for each wave-length. For 118.843 and 163.034 �m we used sixfilms; for 164.600 and 170.576 �m, one film; and for251.140 �m, three films.

The thickness t of the polypropylene film was de-termined with a pycnometry measurement of thedensity � of a film with a carefully predeterminedarea A and accurately measured mass M. A sheet ofthis film, 27.992�2� cm � 19.609�2� cm, was cut andthe length of its sides was carefully measured with acalibrated rule with Vernier accuracy of 0.002 cm.Its mass, obtained from the average of many mea-surements of its weight in a microbalance of 0.0001-gaccuracy, was determined to be M � 0.6314�3� g.Then another sheet of polypropylene was cut into 250smaller pieces of approximately 2.5 cm � 2.5 cm,which were introduced, one by one, into a 25-mLpycnometer, taking utmost care to free them from airbubbles that were occasionally carried in, by agita-tion in an ultrasonic clear tank. Temperature waskept stable within 0.1 °C during these measure-ments. The polypropylene density thus obtained forwas � � 0.9049�7� g�cm3; a value that falls very wellwithin the range established in the literature for iso-tactic polypropylene,6 0.90 � 0.91 g�cm3 and forpolypropylene film �0.900 � 0.905 g�cm3�. Thethickness was then calculated from the relation t �M��A��, with the measured values of M, A and �yielding the result t � 12.71�12� �m for our polypro-pylene film.

4. Discussion and Results

The values for n� in Ref. 7 are 1.4735 at 20 °C foratactic polypropylene with density of 0.8575 g�cm3 and

Fig. 2. Sample cell of the FIR laser modified for the measurementof the index of refraction of polypropylene. Two stacks of filmsoriented at the Brewster’s angle to the laser beam are shown.

Fig. 3. Block diagram of the experimental setup used to measurethe change in the optical path of the laser beam by introducedpolypropylene films. The films are oriented at the Brewster’sangle.

594 APPLIED OPTICS � Vol. 42, No. 3 � 20 January 2003

1.5030 at 20 °C of polypropylene with density of 0.9075g�cm3, both for the sodium lines �� � 0.5893 �m�.The results of our measurements are presented in Ta-ble 1. They cover a region that is a factor of 200 abovethe visible. In Ref. 6 the value of the density is be-tween 0.90 and 0.91 g�cm3 for isotactic polypropylene.The value for the index of refraction is 1.49 measuredat � � 0.5893 �m for polypropylene film, with densitybetween 0.900 and 0.905 g�cm3 �Ref. 6�.

With these values and our results, we extend toregion of the FIR �118–252 �m� the value of the indexof refraction, which stays fairly constant at 1.492�15�

for the polypropylene film of density 0.9049�7� g�cm3.With this result the Brewster angle is �B � 56.17�27�°0.9803�46� radian.

To the best of our knowledge, this is the first timethat index of refraction of a plastic film is reported inthis region of the spectrum. The precision achievedin this work is limited mainly by the mechanicalmeasurement of the change in the optical path insidethe laser cavity. If one used an interferometer tomeasurement this path, the precision would improvea factor of 1000. However, we think that it is im-portant to present the method here because it com-

Fig. 4. Histograms for the changes of the optical path: �a� 118.834, �b� 163.034, �c� 164.600, �d� 170.576, and �e� 251.140 �m. Combinedwith the data frequencies the distribution function ��l � is shown. In each histogram the base of the rectangles is 0.5 �m and the heightis twice the frequency, so that the total area is equal to the total number of measurements for wavelength.

20 January 2003 � Vol. 42, No. 3 � APPLIED OPTICS 595

bines the use of a laser source with intracavitydetection, making it particularly sensitive in the farinfrared region of the spectrum.

The authors thank G. Burillo for loan of the pycnom-eter. We thank S. Ham for making the glass cell andJ. Rangel for his machine work. We also thank E.Ley-Koo, J. Jimenez-Mier, and M. Villagran-Muniz forcomments during the preparation of the manuscript.This work was supported by Direccion General deAsuntos del Personal Academico �DGAPA-UNAM� un-der project No. IN-100399.

References1. D. R. Smith and E. V. Lowenstein, “Optical constants of far

infrared materials. 3. plastics,” Appl. Opt. 14, 1335–1341�1975�.

2. J. S. Wells and K. M. Evenson, “A new LEPR spectrometer,”Rev. Sci. Inst. 41, 226–227 �1970�.

3. V. Beltran-Lopez, J. Flores-Mijangos, and J. Jimenez-Mier, “La-ser magnetic resonance �LMR� spectrometer,” Instrumentationand Development 3, 40–43 �1998�.

4. V. Beltran-Lopez, J. Flores-Mijangos, J. Jimenez-Mier,“Continuous-wave far-infrared laser,” Instrum. Dev. 3, 31–38�1997�.

5. E. P. Moore, Jr., “Polypropylene �commercial�,” in PolymericMaterials Encyclopedia, J. C. Salamone, ed. �CRC Press, Inc.,Boca Raton, Fla., 1996�, pp. 6578–6588.

6. R. P. Quirk and M. A. A. Alsamarraie, “Physical constant ofpoly�propylene�,” in Polymer Handbook, J. Brandrup and E. H.Immergut, eds. �Wiley, New York, 1989�, pp. V, 27–34.

7. J. C. Seferis, “Refractive indices of polymers,” in Polymer Hand-book, J. Brandrup and E. H. Immergut, eds. �Wiley, New York,1989�, pp. VI, 451–462.

596 APPLIED OPTICS � Vol. 42, No. 3 � 20 January 2003