Abstract

Polymer-dispersed liquid crystal (PDLC) films are potentially useful for electronic displays, windows with electrically controllable light transmission, and other applications. PDLC film performance may depend strongly on the angular distribution of the light scattered by the films. We have measured the angular distributions of light scattered by both chemically cured and UV-cured PDLC films as a function of incident and scattered optical polarization. The measured angular dependences differ significantly from those produced by a collection of optically isotropic scatterers: off-diagonal elements of the amplitude scattering matrix are nonzero and comparable in magnitude to the diagonal elements. Furthermore, the scattered intensity for incident light polarized parallel to the scattering plane is not simply related to the scattered intensity for incident light polarized perpendicular to the scattering plane. Comparison of these results with a recent theory of light scattering from a nematic liquid-crystal droplet indicates that multiple scattering is important in PDLC films even in their on state. This multiple scattering is, at least in part, produced by total internal reflection at air-sample interfaces for certain scattering angles. From our polarization-dependent intensity measurements, we have computed the fractions of incident light scattered into the forward and backward hemispheres. The forward-scattered intensity is 2.5–4 times as large as the backscattered intensity for our samples.

© 1988 Optical Society of America

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References

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  1. J. W. Doane, N. A. Vaz, B.-G. Wu, S. Žumer, Appl. Phys. Lett. 48, 269 (1986).
    [CrossRef]
  2. N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 1 (1987).
    [CrossRef]
  3. N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 17 (1987).
    [CrossRef]
  4. J. W. Doane, A. Golemme, J. West, B.-G. Wu, S. Žumer, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.
  5. B.-G. Wu, S. Žumer, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.
  6. S. Žumer, A. Golemme, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.
  7. J. L. West, N. A. Vaz, H. Vithana, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.
  8. We use the double subscripts pp, pn, np, and nn in the scattering matrix rather than the usual single subscripts 2, 3, 4, and 1 of van de Hulst9 because their physical significance is easier to remember; for example, SnpE0p gives the contribution to the n component Esn of the scattered field that is due to the p component E0p of the incident field. We use subscripts n and p to avoid the confusion associated with the use of H or V subscripts for horizontal (parallel) and vertical (normal) polarization10 since the H and V notation is also used in a different context by other authors.11,12 This notation should also avoid confusion with the use of p and s or π and σ subscripts, which are conventionally used to define polarization components parallel and perpendicular to the plane of incidence; this plane is sometimes, but not always, coincident with the scattering plane. We hope that this notation will be less confusing than the notation of van de Hulst9 in which l and r, the last letters in the words parallel and perpendicular, are used to specify the field components parallel and normal to the scattering plane.
  9. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  10. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  11. S. Žurner, J. W. Doane, Phys. Rev. A 34, 3373 (1986).
    [CrossRef]
  12. J. V. Champion, A. Killey, G. H. Meeten, J. Polym. Sci. Polym. Phys. Ed. 23, 1467 (1985).
    [CrossRef]
  13. We use the term intensity in this paper to denote either the absolute square of an electric field or the signal measured by a photodetector, as appropriate. In presenting numerical results we avoid problems associated with units and proportionality constants by always normalizing measured signals from our samples to signals produced by the incident beam when no sample is present.
  14. In fact, polarized light can be described completely in terms of four Stokes parameters, which can be measured using suitable polarizer–analyzer combinations. See, for example, C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  15. No confusion should result from using u for both unpolarized and unanalyzed light. As the first of two subscripts, u refers to the scattered light, for which the designation unanalyzed is appropriate. As the second subscript, u refers to the incident light, for which unpolarized is the proper description.
  16. E7 is a commercial mixture of biphenyl and terphenyl compounds available from EM Chemicals, Hawthorne, N.Y.
  17. ROTN-403 is a commercial mixture of biphenyl, terphenyl, and pyrimidine compounds available from Roche Chemical Division, F. Hoffmann-LaRoche, Inc., Nutley, N.J.
  18. H. Tarry, Royal Signals and Radar Establishment, Great Malvern, Worcs., UK (personal communication to M. Schadt cited in Ref. 19).
  19. M. Schadt, F. Müller, IEEE Trans. Electron Devices ED-25, 1125 (1978).
    [CrossRef]
  20. N. A. Vaz, G. P. Montgomery, J. Appl. Phys. 62, 3161 (1987).
    [CrossRef]
  21. M. V. Klein, Optics (Wiley, New York, 1970), Chap. 4.
  22. B. Chu, Laser Light Scattering (Academic, New York, 1974).
  23. The laser in our system is sufficiently stable that no major effects of laser drift or fluctuation are observed in our measurements. We have measured the angular distributions for sample 3211 at various times over a one-year period with results reproducible to within a few percent.
  24. It is well known that the scattered intensity is not azimuthally symmetric when the incident light is polarized, even when the scattering system is optically isotropic. See Ref. 9 or 10 for further discussion.

1987 (3)

N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 1 (1987).
[CrossRef]

N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 17 (1987).
[CrossRef]

N. A. Vaz, G. P. Montgomery, J. Appl. Phys. 62, 3161 (1987).
[CrossRef]

1986 (2)

J. W. Doane, N. A. Vaz, B.-G. Wu, S. Žumer, Appl. Phys. Lett. 48, 269 (1986).
[CrossRef]

S. Žurner, J. W. Doane, Phys. Rev. A 34, 3373 (1986).
[CrossRef]

1985 (1)

J. V. Champion, A. Killey, G. H. Meeten, J. Polym. Sci. Polym. Phys. Ed. 23, 1467 (1985).
[CrossRef]

1978 (1)

M. Schadt, F. Müller, IEEE Trans. Electron Devices ED-25, 1125 (1978).
[CrossRef]

Bohren, C. F.

In fact, polarized light can be described completely in terms of four Stokes parameters, which can be measured using suitable polarizer–analyzer combinations. See, for example, C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Champion, J. V.

J. V. Champion, A. Killey, G. H. Meeten, J. Polym. Sci. Polym. Phys. Ed. 23, 1467 (1985).
[CrossRef]

Chu, B.

B. Chu, Laser Light Scattering (Academic, New York, 1974).

Doane, J. W.

S. Žurner, J. W. Doane, Phys. Rev. A 34, 3373 (1986).
[CrossRef]

J. W. Doane, N. A. Vaz, B.-G. Wu, S. Žumer, Appl. Phys. Lett. 48, 269 (1986).
[CrossRef]

B.-G. Wu, S. Žumer, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

S. Žumer, A. Golemme, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

J. W. Doane, A. Golemme, J. West, B.-G. Wu, S. Žumer, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

J. L. West, N. A. Vaz, H. Vithana, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

Golemme, A.

J. W. Doane, A. Golemme, J. West, B.-G. Wu, S. Žumer, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

S. Žumer, A. Golemme, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

Huffman, D. R.

In fact, polarized light can be described completely in terms of four Stokes parameters, which can be measured using suitable polarizer–analyzer combinations. See, for example, C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Killey, A.

J. V. Champion, A. Killey, G. H. Meeten, J. Polym. Sci. Polym. Phys. Ed. 23, 1467 (1985).
[CrossRef]

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970), Chap. 4.

Meeten, G. H.

J. V. Champion, A. Killey, G. H. Meeten, J. Polym. Sci. Polym. Phys. Ed. 23, 1467 (1985).
[CrossRef]

Montgomery, G. P.

N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 1 (1987).
[CrossRef]

N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 17 (1987).
[CrossRef]

N. A. Vaz, G. P. Montgomery, J. Appl. Phys. 62, 3161 (1987).
[CrossRef]

Müller, F.

M. Schadt, F. Müller, IEEE Trans. Electron Devices ED-25, 1125 (1978).
[CrossRef]

Schadt, M.

M. Schadt, F. Müller, IEEE Trans. Electron Devices ED-25, 1125 (1978).
[CrossRef]

Smith, G. W.

N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 1 (1987).
[CrossRef]

N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 17 (1987).
[CrossRef]

Tarry, H.

H. Tarry, Royal Signals and Radar Establishment, Great Malvern, Worcs., UK (personal communication to M. Schadt cited in Ref. 19).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Vaz, N. A.

N. A. Vaz, G. P. Montgomery, J. Appl. Phys. 62, 3161 (1987).
[CrossRef]

N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 17 (1987).
[CrossRef]

N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 1 (1987).
[CrossRef]

J. W. Doane, N. A. Vaz, B.-G. Wu, S. Žumer, Appl. Phys. Lett. 48, 269 (1986).
[CrossRef]

J. L. West, N. A. Vaz, H. Vithana, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

Vithana, H.

J. L. West, N. A. Vaz, H. Vithana, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

West, J.

J. W. Doane, A. Golemme, J. West, B.-G. Wu, S. Žumer, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

West, J. L.

J. L. West, N. A. Vaz, H. Vithana, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

Wu, B.-G.

J. W. Doane, N. A. Vaz, B.-G. Wu, S. Žumer, Appl. Phys. Lett. 48, 269 (1986).
[CrossRef]

B.-G. Wu, S. Žumer, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

J. W. Doane, A. Golemme, J. West, B.-G. Wu, S. Žumer, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

Žumer, S.

J. W. Doane, N. A. Vaz, B.-G. Wu, S. Žumer, Appl. Phys. Lett. 48, 269 (1986).
[CrossRef]

B.-G. Wu, S. Žumer, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

J. W. Doane, A. Golemme, J. West, B.-G. Wu, S. Žumer, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

S. Žumer, A. Golemme, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

Žurner, S.

S. Žurner, J. W. Doane, Phys. Rev. A 34, 3373 (1986).
[CrossRef]

Appl. Phys. Lett. (1)

J. W. Doane, N. A. Vaz, B.-G. Wu, S. Žumer, Appl. Phys. Lett. 48, 269 (1986).
[CrossRef]

IEEE Trans. Electron Devices (1)

M. Schadt, F. Müller, IEEE Trans. Electron Devices ED-25, 1125 (1978).
[CrossRef]

J. Appl. Phys. (1)

N. A. Vaz, G. P. Montgomery, J. Appl. Phys. 62, 3161 (1987).
[CrossRef]

J. Polym. Sci. Polym. Phys. Ed. (1)

J. V. Champion, A. Killey, G. H. Meeten, J. Polym. Sci. Polym. Phys. Ed. 23, 1467 (1985).
[CrossRef]

Mol. Cryst. Liq. Cryst. (2)

N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 1 (1987).
[CrossRef]

N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 146, 17 (1987).
[CrossRef]

Phys. Rev. A (1)

S. Žurner, J. W. Doane, Phys. Rev. A 34, 3373 (1986).
[CrossRef]

Other (17)

J. W. Doane, A. Golemme, J. West, B.-G. Wu, S. Žumer, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

B.-G. Wu, S. Žumer, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

S. Žumer, A. Golemme, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

J. L. West, N. A. Vaz, H. Vithana, J. W. Doane, presented at Eleventh International Liquid Crystal Conference, Berkeley, Calif., June 1986.

We use the double subscripts pp, pn, np, and nn in the scattering matrix rather than the usual single subscripts 2, 3, 4, and 1 of van de Hulst9 because their physical significance is easier to remember; for example, SnpE0p gives the contribution to the n component Esn of the scattered field that is due to the p component E0p of the incident field. We use subscripts n and p to avoid the confusion associated with the use of H or V subscripts for horizontal (parallel) and vertical (normal) polarization10 since the H and V notation is also used in a different context by other authors.11,12 This notation should also avoid confusion with the use of p and s or π and σ subscripts, which are conventionally used to define polarization components parallel and perpendicular to the plane of incidence; this plane is sometimes, but not always, coincident with the scattering plane. We hope that this notation will be less confusing than the notation of van de Hulst9 in which l and r, the last letters in the words parallel and perpendicular, are used to specify the field components parallel and normal to the scattering plane.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

We use the term intensity in this paper to denote either the absolute square of an electric field or the signal measured by a photodetector, as appropriate. In presenting numerical results we avoid problems associated with units and proportionality constants by always normalizing measured signals from our samples to signals produced by the incident beam when no sample is present.

In fact, polarized light can be described completely in terms of four Stokes parameters, which can be measured using suitable polarizer–analyzer combinations. See, for example, C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

No confusion should result from using u for both unpolarized and unanalyzed light. As the first of two subscripts, u refers to the scattered light, for which the designation unanalyzed is appropriate. As the second subscript, u refers to the incident light, for which unpolarized is the proper description.

E7 is a commercial mixture of biphenyl and terphenyl compounds available from EM Chemicals, Hawthorne, N.Y.

ROTN-403 is a commercial mixture of biphenyl, terphenyl, and pyrimidine compounds available from Roche Chemical Division, F. Hoffmann-LaRoche, Inc., Nutley, N.J.

H. Tarry, Royal Signals and Radar Establishment, Great Malvern, Worcs., UK (personal communication to M. Schadt cited in Ref. 19).

M. V. Klein, Optics (Wiley, New York, 1970), Chap. 4.

B. Chu, Laser Light Scattering (Academic, New York, 1974).

The laser in our system is sufficiently stable that no major effects of laser drift or fluctuation are observed in our measurements. We have measured the angular distributions for sample 3211 at various times over a one-year period with results reproducible to within a few percent.

It is well known that the scattered intensity is not azimuthally symmetric when the incident light is polarized, even when the scattering system is optically isotropic. See Ref. 9 or 10 for further discussion.

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Figures (9)

Fig. 1
Fig. 1

Light-scattering geometry.

Fig. 2
Fig. 2

Schematic diagram of experimental system for angle-dependent light-scattering measurements.

Fig. 3
Fig. 3

Scattered power measured by detector normalized to incident laser power versus scattering angle θ measured in air for PDLC sample 3241. All curves are for normal incidence. On-state voltage in each figure is 70 Vrms: (a) Ipp, (b) Ipn, (c) Inp, (d) Inn.

Fig. 4
Fig. 4

Scattered power measured by detector normalized to incident laser power versus scattering angle θ measured in air for PDLC sample 3211. All curves are for normal incidence. On-state voltage in each figure is 70 Vrms: (a) Ipp, (b) Ipn, (c) Inp, (d) Inn.

Fig. 5
Fig. 5

Scattered power measured by detector normalized to incident laser power versus scattering angle θ measured in air for PDLC sample 3241. All curves are for a 40° angle of incidence. On-state voltage in each figure is 70 Vrms: (a) Ipp, (b) Ipn, (c) Inp, (d) Inn.

Fig. 6
Fig. 6

Scattered power measured by detector normalized to incident laser power versus scattering angle θ measured in air for PDLC sample 3211. All curves are for a 40° angle of incidence. On-state voltage in each figure is 70 Vrms: (a) Ipp, (b) Ipn, (c) Inp, (d) Inn.

Fig. 7
Fig. 7

Scattered power measured by detector normalized to incident laser power versus scattering angle θp measured inside the polymer matrix for PDLC samples in the on state (V = 70 Vrms) at different angles of incidence. Both incident and scattered light were polarized perpendicular to the scattering plane. The gaps in the curves are due to total internal reflection of the scattered light: (a) sample 3241, (b) sample 3211.

Fig. 8
Fig. 8

Intensity of unanalyzed scattered light for incident light polarized perpendicular to the scattering plane. In each figure one curve shows the experimentally measured intensity Iunmeas; the other curve shows the intensity Iunsum obtained by summing the measured intensities Ipn and Inn after correcting for analyzer transmittance. All curves are for sample 3241 at normal incidence: (a) off state, (b) on state (V = 70 Vrms).

Fig. 9
Fig. 9

Intensity of unanalyzed scattered light for incident light polarized parallel to the scattering plane. In each figure one curve shows the experimentally measured intensity Iupmeas; the other curve shows the intensity Iupsum obtained by summing the measured intensities Ipp and Inp after correcting for analyzer transmittance. All curves are for sample 3241 at normal incidence: (a) off state, (b) on state (V = 70 Vrms).

Tables (3)

Tables Icon

Table 1 Scattered Intensities for Various Polarizer–Analyzer Combinations

Tables Icon

Table 2 Refractive Indices of PDLC Films Used in Light-Scattering Experiments

Tables Icon

Table 3 Total Power Scattered by PDLC Samples

Equations (9)

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[ E s p E s n ] = [ S p p S p n S n p S n n ] [ E 0 p E 0 n ] .
I s = | E s p | 2 + | E s n | 2 = | S p p E 0 p + S p n E 0 n | 2 + | S n p E 0 p + S n n E 0 n | 2 .
I u p = | S p p E 0 p | 2 + | S n p E 0 p | 2 = I p p + I n p .
I u n = | S p n E 0 n | 2 + | S n n E 0 n | 2 = I p n + I n n .
I j u = I j p + I j n 2 ,
P s ( k ̂ ) = Δ A det | E s | 2 d A det ,
| E s | 2 = 1 r 2 d σ d Ω ( θ , ϕ ) | E 0 | 2 .
P s ( k ̂ ) = P L A L Δ Ω det d σ d Ω ( θ , ϕ ) d Ω .
P s ( k ̂ ) P L = A L 1 d σ d Ω ( θ , ϕ ) Δ Ω det .

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