Abstract

The refractive index of polypropylene in the far infrared (FIR) is measured by means of a suitably modified laser of a FIR spectrometer. When thin polypropylene films of 12.7-μm nominal thickness are introduced in the optical cavity of a laser at the Brewster angle, the radiation ceases because of the change in the optical path of the laser beam. This change is measured from the displacement of one of the laser mirrors, which is necessary to restore the laser resonance. The refractive index of polypropylene is deduced from this measurement and from the film thickness, as obtained from an independent measurement based in pycnometry. The value obtained for the refractive index is 1.492(15) for the wavelengths between 118.834 and 251.140 μm, for a polypropylene film of 12.71(2)-μm thickness and 0.9049(7) g/cm3 density.

© 2003 Optical Society of America

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References

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  1. D. R. Smith, E. V. Lowenstein, “Optical constants of far infrared materials. 3. plastics,” Appl. Opt. 14, 1335–1341 (1975).
    [CrossRef] [PubMed]
  2. J. S. Wells, K. M. Evenson, “A new LEPR spectrometer,” Rev. Sci. Inst. 41, 226–227 (1970).
    [CrossRef]
  3. V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Laser magnetic resonance (LMR) spectrometer,” Instrumentation and Development 3, 40–43 (1998).
  4. V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Continuous-wave far-infrared laser,” Instrum. Dev. 3, 31–38 (1997).
  5. E. P. Moore, “Polypropylene (commercial),” in Polymeric Materials Encyclopedia, J. C. Salamone, ed. (CRC Press, Inc., Boca Raton, Fla., 1996), pp. 6578–6588.
  6. R. P. Quirk, M. A. A. Alsamarraie, “Physical constant of poly(propylene),” in Polymer Handbook, J. Brandrup, E. H. Immergut, eds. (Wiley, New York, 1989), pp. V, 27–34.
  7. J. C. Seferis, “Refractive indices of polymers,” in Polymer Handbook, J. Brandrup, E. H. Immergut, eds. (Wiley, New York, 1989), pp. VI, 451–462.

1998 (1)

V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Laser magnetic resonance (LMR) spectrometer,” Instrumentation and Development 3, 40–43 (1998).

1997 (1)

V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Continuous-wave far-infrared laser,” Instrum. Dev. 3, 31–38 (1997).

1975 (1)

1970 (1)

J. S. Wells, K. M. Evenson, “A new LEPR spectrometer,” Rev. Sci. Inst. 41, 226–227 (1970).
[CrossRef]

Alsamarraie, M. A. A.

R. P. Quirk, M. A. A. Alsamarraie, “Physical constant of poly(propylene),” in Polymer Handbook, J. Brandrup, E. H. Immergut, eds. (Wiley, New York, 1989), pp. V, 27–34.

Beltrán-López, V.

V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Laser magnetic resonance (LMR) spectrometer,” Instrumentation and Development 3, 40–43 (1998).

V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Continuous-wave far-infrared laser,” Instrum. Dev. 3, 31–38 (1997).

Brandrup, J.

J. C. Seferis, “Refractive indices of polymers,” in Polymer Handbook, J. Brandrup, E. H. Immergut, eds. (Wiley, New York, 1989), pp. VI, 451–462.

Evenson, K. M.

J. S. Wells, K. M. Evenson, “A new LEPR spectrometer,” Rev. Sci. Inst. 41, 226–227 (1970).
[CrossRef]

Flores-Mijangos, J.

V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Laser magnetic resonance (LMR) spectrometer,” Instrumentation and Development 3, 40–43 (1998).

V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Continuous-wave far-infrared laser,” Instrum. Dev. 3, 31–38 (1997).

Immergut, E. H.

J. C. Seferis, “Refractive indices of polymers,” in Polymer Handbook, J. Brandrup, E. H. Immergut, eds. (Wiley, New York, 1989), pp. VI, 451–462.

Jiménez-Mier, J.

V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Laser magnetic resonance (LMR) spectrometer,” Instrumentation and Development 3, 40–43 (1998).

V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Continuous-wave far-infrared laser,” Instrum. Dev. 3, 31–38 (1997).

Lowenstein, E. V.

Moore, E. P.

E. P. Moore, “Polypropylene (commercial),” in Polymeric Materials Encyclopedia, J. C. Salamone, ed. (CRC Press, Inc., Boca Raton, Fla., 1996), pp. 6578–6588.

Quirk, R. P.

R. P. Quirk, M. A. A. Alsamarraie, “Physical constant of poly(propylene),” in Polymer Handbook, J. Brandrup, E. H. Immergut, eds. (Wiley, New York, 1989), pp. V, 27–34.

Seferis, J. C.

J. C. Seferis, “Refractive indices of polymers,” in Polymer Handbook, J. Brandrup, E. H. Immergut, eds. (Wiley, New York, 1989), pp. VI, 451–462.

Smith, D. R.

Wells, J. S.

J. S. Wells, K. M. Evenson, “A new LEPR spectrometer,” Rev. Sci. Inst. 41, 226–227 (1970).
[CrossRef]

Appl. Opt. (1)

Instrum. Dev. (1)

V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Continuous-wave far-infrared laser,” Instrum. Dev. 3, 31–38 (1997).

Instrumentation and Development (1)

V. Beltrán-López, J. Flores-Mijangos, J. Jiménez-Mier, “Laser magnetic resonance (LMR) spectrometer,” Instrumentation and Development 3, 40–43 (1998).

Rev. Sci. Inst. (1)

J. S. Wells, K. M. Evenson, “A new LEPR spectrometer,” Rev. Sci. Inst. 41, 226–227 (1970).
[CrossRef]

Other (3)

E. P. Moore, “Polypropylene (commercial),” in Polymeric Materials Encyclopedia, J. C. Salamone, ed. (CRC Press, Inc., Boca Raton, Fla., 1996), pp. 6578–6588.

R. P. Quirk, M. A. A. Alsamarraie, “Physical constant of poly(propylene),” in Polymer Handbook, J. Brandrup, E. H. Immergut, eds. (Wiley, New York, 1989), pp. V, 27–34.

J. C. Seferis, “Refractive indices of polymers,” in Polymer Handbook, J. Brandrup, E. H. Immergut, eds. (Wiley, New York, 1989), pp. VI, 451–462.

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Figures (4)

Fig. 1
Fig. 1

A stack of polypropylene films of total thickness d = OD¯ interposed in the path of a laser beam brings it off resonance when the optical path is increased. Laser resonance is restored by a parallel displacement of one mirror of the optical cavity over a distance ΔL, which compensates the increase in the optical path. The change in the optical path is given in terms of y = OY¯ and x = OX¯.

Fig. 2
Fig. 2

Sample cell of the FIR laser modified for the measurement of the index of refraction of polypropylene. Two stacks of films oriented at the Brewster’s angle to the laser beam are shown.

Fig. 3
Fig. 3

Block diagram of the experimental setup used to measure the change in the optical path of the laser beam by introduced polypropylene films. The films are oriented at the Brewster’s angle.

Fig. 4
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 μm. Combined with the data frequencies the distribution function Ψ(l) is shown. In each histogram the base of the rectangles is 0.5 μm and the height is twice the frequency, so that the total area is equal to the total number of measurements for wavelength.

Tables (1)

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

Equations (7)

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nL=12 mλ,
nL+ny-nx-nΔL= 12 mλ,
nn2=a+cos θnn2-sin2 θ1/2+sin2 θ.
nn4-2+a2nn2+1-a2=0.
nn2=1+ a2a±8+a21/2.
δnn= n/n2-12n/n8+a21/2δaa2.
- Ψldl=C,

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