Abstract

The calculations of the monolayer coherent transmittance of isotropic, homogeneous, spherical scatterers is compared in the single-scattering and quasi-crystalline approximations for values of size parameters smaller than 10.0 and monolayer filling coefficients smaller than 0.6. The radial particle distribution function is described in the approximation of absolutely hard disks. The difference in calculation in the single-scattering and quasi-crystalline approximations is shown to be less than a few tenths of 1% for refractive index m=1.1-i0.0 and less than 1% for m=1.2-i0.0. A difference of 5% occurs for filling coefficients smaller than 0.4 for m=1.4-i0.0.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. P. Ivanov, V. A. Loiko, V. P. Dick, Propagation of Light in Densely Packed Disperse Media (Nauka i Tekhnika, Minsk, 1988), Chap. 2 (in Russian).
  2. K. M. Hong, “Multiple scattering of electromagnetic waves by a crowded monolayer of spheres: application to migration imaging films,” J. Opt. Soc. Am. 70, 821–826 (1980).
    [CrossRef]
  3. J. R. Kelly, Wei Wu, “Multiple scattering effects in polymer dispersed liquid crystals,” Liq. Cryst. 14, 1683–1694 (1993).
    [CrossRef]
  4. R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, T. J. Bunning, W. W. Adams, “Electrically switchable volume grating in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
    [CrossRef]
  5. T. J. Bunning, L. V. Natarajan, V. Tondiglia, Sutherland, D. L. Vezie, W. W. Adams, “The morphology and performance of holographic transmission gratings recorded in polymer dispersed liquid crytals,” Polymer 36, 2699–2707 (1995).
    [CrossRef]
  6. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983), Chap. 3.
  7. H. C. van de Hulst, Light Scattering by Small Particles (Wiley-Interscience, New York, 1957), Chap. 4.
  8. L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985), Chap. 6.
  9. R. West, J. Gibbs, L. Tsang, A. H. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11, 1854–1858 (1994).
    [CrossRef]
  10. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 6.
  11. V. Twersky, “Transparency of pair correlated, random distributions of small scatterers with applications to cornea,” J. Opt. Soc. Am. 65, 524–530 (1975).
    [CrossRef] [PubMed]
  12. V. Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
    [CrossRef]
  13. V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection of a monolayer of discrete scatterers at oblique incidence of light waves,” Opt. Spectrosc. 79, 304–310 (1995) [translated from Opt. Spektrosk. (Russia) 79, 329–336 (1995)].
  14. V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection by a monolayer of disperse scatterers,” Part. Part. Syst. Charact. 13, 227–233 (1996).
    [CrossRef]
  15. V. P. Dick, V. A. Loiko, A. P. Ivanov, “Light transmission by a monolayer of particles: comparison of experimental data with calculation as a single-scattering approximation,” Appl. Opt. 36, 6119–6122 (1997).
    [CrossRef] [PubMed]
  16. L. S. Ornstein, F. Zernike, “Accidental deviations of density and opalescence at the critical point of a single substance,” Proc. Acad. Sci. Amsterdam 17, 793–806 (1914).
  17. J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
    [CrossRef]
  18. A. P. Ivanov, V. A. Loiko, V. P. Dick, “Particularities in the extinction of light by the monolayer of particles,” J. Appl. Spectrosc. 47, 966–971 (1987) [translated from Zh. Priklad. Spektrosk. (Russia) 47, 494–500 (1987)].
  19. V. A. Loiko, A. P. Ivanov, V. P. Dick, “Some peculiarities of passage of light through dispersion layers with a high concentration of dispersion material,” in Optics for Science and Technology, Proc. SPIE2778, 321–322 (1996).
  20. J. M. Ziman, Models of Disorder (Cambridge U. Press, Cambridge, UK, 1979), Chap. 2.

1997 (1)

1996 (1)

V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection by a monolayer of disperse scatterers,” Part. Part. Syst. Charact. 13, 227–233 (1996).
[CrossRef]

1995 (2)

V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection of a monolayer of discrete scatterers at oblique incidence of light waves,” Opt. Spectrosc. 79, 304–310 (1995) [translated from Opt. Spektrosk. (Russia) 79, 329–336 (1995)].

T. J. Bunning, L. V. Natarajan, V. Tondiglia, Sutherland, D. L. Vezie, W. W. Adams, “The morphology and performance of holographic transmission gratings recorded in polymer dispersed liquid crytals,” Polymer 36, 2699–2707 (1995).
[CrossRef]

1994 (2)

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, T. J. Bunning, W. W. Adams, “Electrically switchable volume grating in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

R. West, J. Gibbs, L. Tsang, A. H. Fung, “Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media,” J. Opt. Soc. Am. A 11, 1854–1858 (1994).
[CrossRef]

1993 (1)

J. R. Kelly, Wei Wu, “Multiple scattering effects in polymer dispersed liquid crystals,” Liq. Cryst. 14, 1683–1694 (1993).
[CrossRef]

1987 (1)

A. P. Ivanov, V. A. Loiko, V. P. Dick, “Particularities in the extinction of light by the monolayer of particles,” J. Appl. Spectrosc. 47, 966–971 (1987) [translated from Zh. Priklad. Spektrosk. (Russia) 47, 494–500 (1987)].

1980 (1)

1978 (1)

V. Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
[CrossRef]

1975 (1)

1958 (1)

J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[CrossRef]

1914 (1)

L. S. Ornstein, F. Zernike, “Accidental deviations of density and opalescence at the critical point of a single substance,” Proc. Acad. Sci. Amsterdam 17, 793–806 (1914).

Adams, W. W.

T. J. Bunning, L. V. Natarajan, V. Tondiglia, Sutherland, D. L. Vezie, W. W. Adams, “The morphology and performance of holographic transmission gratings recorded in polymer dispersed liquid crytals,” Polymer 36, 2699–2707 (1995).
[CrossRef]

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, T. J. Bunning, W. W. Adams, “Electrically switchable volume grating in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983), Chap. 3.

Bunning, T. J.

T. J. Bunning, L. V. Natarajan, V. Tondiglia, Sutherland, D. L. Vezie, W. W. Adams, “The morphology and performance of holographic transmission gratings recorded in polymer dispersed liquid crytals,” Polymer 36, 2699–2707 (1995).
[CrossRef]

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, T. J. Bunning, W. W. Adams, “Electrically switchable volume grating in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

Dick, V. P.

V. P. Dick, V. A. Loiko, A. P. Ivanov, “Light transmission by a monolayer of particles: comparison of experimental data with calculation as a single-scattering approximation,” Appl. Opt. 36, 6119–6122 (1997).
[CrossRef] [PubMed]

A. P. Ivanov, V. A. Loiko, V. P. Dick, “Particularities in the extinction of light by the monolayer of particles,” J. Appl. Spectrosc. 47, 966–971 (1987) [translated from Zh. Priklad. Spektrosk. (Russia) 47, 494–500 (1987)].

A. P. Ivanov, V. A. Loiko, V. P. Dick, Propagation of Light in Densely Packed Disperse Media (Nauka i Tekhnika, Minsk, 1988), Chap. 2 (in Russian).

V. A. Loiko, A. P. Ivanov, V. P. Dick, “Some peculiarities of passage of light through dispersion layers with a high concentration of dispersion material,” in Optics for Science and Technology, Proc. SPIE2778, 321–322 (1996).

Fung, A. H.

Gibbs, J.

Hong, K. M.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983), Chap. 3.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 6.

Ivanov, A. P.

V. P. Dick, V. A. Loiko, A. P. Ivanov, “Light transmission by a monolayer of particles: comparison of experimental data with calculation as a single-scattering approximation,” Appl. Opt. 36, 6119–6122 (1997).
[CrossRef] [PubMed]

A. P. Ivanov, V. A. Loiko, V. P. Dick, “Particularities in the extinction of light by the monolayer of particles,” J. Appl. Spectrosc. 47, 966–971 (1987) [translated from Zh. Priklad. Spektrosk. (Russia) 47, 494–500 (1987)].

A. P. Ivanov, V. A. Loiko, V. P. Dick, Propagation of Light in Densely Packed Disperse Media (Nauka i Tekhnika, Minsk, 1988), Chap. 2 (in Russian).

V. A. Loiko, A. P. Ivanov, V. P. Dick, “Some peculiarities of passage of light through dispersion layers with a high concentration of dispersion material,” in Optics for Science and Technology, Proc. SPIE2778, 321–322 (1996).

Kelly, J. R.

J. R. Kelly, Wei Wu, “Multiple scattering effects in polymer dispersed liquid crystals,” Liq. Cryst. 14, 1683–1694 (1993).
[CrossRef]

Kong, J.

L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985), Chap. 6.

Loiko, V. A.

V. P. Dick, V. A. Loiko, A. P. Ivanov, “Light transmission by a monolayer of particles: comparison of experimental data with calculation as a single-scattering approximation,” Appl. Opt. 36, 6119–6122 (1997).
[CrossRef] [PubMed]

V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection by a monolayer of disperse scatterers,” Part. Part. Syst. Charact. 13, 227–233 (1996).
[CrossRef]

V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection of a monolayer of discrete scatterers at oblique incidence of light waves,” Opt. Spectrosc. 79, 304–310 (1995) [translated from Opt. Spektrosk. (Russia) 79, 329–336 (1995)].

A. P. Ivanov, V. A. Loiko, V. P. Dick, “Particularities in the extinction of light by the monolayer of particles,” J. Appl. Spectrosc. 47, 966–971 (1987) [translated from Zh. Priklad. Spektrosk. (Russia) 47, 494–500 (1987)].

A. P. Ivanov, V. A. Loiko, V. P. Dick, Propagation of Light in Densely Packed Disperse Media (Nauka i Tekhnika, Minsk, 1988), Chap. 2 (in Russian).

V. A. Loiko, A. P. Ivanov, V. P. Dick, “Some peculiarities of passage of light through dispersion layers with a high concentration of dispersion material,” in Optics for Science and Technology, Proc. SPIE2778, 321–322 (1996).

Molochko, V. I.

V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection by a monolayer of disperse scatterers,” Part. Part. Syst. Charact. 13, 227–233 (1996).
[CrossRef]

V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection of a monolayer of discrete scatterers at oblique incidence of light waves,” Opt. Spectrosc. 79, 304–310 (1995) [translated from Opt. Spektrosk. (Russia) 79, 329–336 (1995)].

Natarajan, L. V.

T. J. Bunning, L. V. Natarajan, V. Tondiglia, Sutherland, D. L. Vezie, W. W. Adams, “The morphology and performance of holographic transmission gratings recorded in polymer dispersed liquid crytals,” Polymer 36, 2699–2707 (1995).
[CrossRef]

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, T. J. Bunning, W. W. Adams, “Electrically switchable volume grating in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

Ornstein, L. S.

L. S. Ornstein, F. Zernike, “Accidental deviations of density and opalescence at the critical point of a single substance,” Proc. Acad. Sci. Amsterdam 17, 793–806 (1914).

Percus, J. K.

J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[CrossRef]

Shin, R.

L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985), Chap. 6.

Sutherland,

T. J. Bunning, L. V. Natarajan, V. Tondiglia, Sutherland, D. L. Vezie, W. W. Adams, “The morphology and performance of holographic transmission gratings recorded in polymer dispersed liquid crytals,” Polymer 36, 2699–2707 (1995).
[CrossRef]

Sutherland, R. L.

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, T. J. Bunning, W. W. Adams, “Electrically switchable volume grating in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

Tondiglia, V.

T. J. Bunning, L. V. Natarajan, V. Tondiglia, Sutherland, D. L. Vezie, W. W. Adams, “The morphology and performance of holographic transmission gratings recorded in polymer dispersed liquid crytals,” Polymer 36, 2699–2707 (1995).
[CrossRef]

Tondiglia, V. P.

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, T. J. Bunning, W. W. Adams, “Electrically switchable volume grating in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

Tsang, L.

Twersky, V.

V. Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
[CrossRef]

V. Twersky, “Transparency of pair correlated, random distributions of small scatterers with applications to cornea,” J. Opt. Soc. Am. 65, 524–530 (1975).
[CrossRef] [PubMed]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley-Interscience, New York, 1957), Chap. 4.

Vezie, D. L.

T. J. Bunning, L. V. Natarajan, V. Tondiglia, Sutherland, D. L. Vezie, W. W. Adams, “The morphology and performance of holographic transmission gratings recorded in polymer dispersed liquid crytals,” Polymer 36, 2699–2707 (1995).
[CrossRef]

West, R.

Wu, Wei

J. R. Kelly, Wei Wu, “Multiple scattering effects in polymer dispersed liquid crystals,” Liq. Cryst. 14, 1683–1694 (1993).
[CrossRef]

Yevick, G. J.

J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[CrossRef]

Zernike, F.

L. S. Ornstein, F. Zernike, “Accidental deviations of density and opalescence at the critical point of a single substance,” Proc. Acad. Sci. Amsterdam 17, 793–806 (1914).

Ziman, J. M.

J. M. Ziman, Models of Disorder (Cambridge U. Press, Cambridge, UK, 1979), Chap. 2.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, T. J. Bunning, W. W. Adams, “Electrically switchable volume grating in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

J. Appl. Spectrosc. (1)

A. P. Ivanov, V. A. Loiko, V. P. Dick, “Particularities in the extinction of light by the monolayer of particles,” J. Appl. Spectrosc. 47, 966–971 (1987) [translated from Zh. Priklad. Spektrosk. (Russia) 47, 494–500 (1987)].

J. Math. Phys. (1)

V. Twersky, “Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers,” J. Math. Phys. 19, 215–230 (1978).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Liq. Cryst. (1)

J. R. Kelly, Wei Wu, “Multiple scattering effects in polymer dispersed liquid crystals,” Liq. Cryst. 14, 1683–1694 (1993).
[CrossRef]

Opt. Spectrosc. (1)

V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection of a monolayer of discrete scatterers at oblique incidence of light waves,” Opt. Spectrosc. 79, 304–310 (1995) [translated from Opt. Spektrosk. (Russia) 79, 329–336 (1995)].

Part. Part. Syst. Charact. (1)

V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection by a monolayer of disperse scatterers,” Part. Part. Syst. Charact. 13, 227–233 (1996).
[CrossRef]

Phys. Rev. (1)

J. K. Percus, G. J. Yevick, “Analysis of classical statistical mechanics by means of collective coordinates,” Phys. Rev. 110, 1–13 (1958).
[CrossRef]

Polymer (1)

T. J. Bunning, L. V. Natarajan, V. Tondiglia, Sutherland, D. L. Vezie, W. W. Adams, “The morphology and performance of holographic transmission gratings recorded in polymer dispersed liquid crytals,” Polymer 36, 2699–2707 (1995).
[CrossRef]

Proc. Acad. Sci. Amsterdam (1)

L. S. Ornstein, F. Zernike, “Accidental deviations of density and opalescence at the critical point of a single substance,” Proc. Acad. Sci. Amsterdam 17, 793–806 (1914).

Other (7)

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983), Chap. 3.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley-Interscience, New York, 1957), Chap. 4.

L. Tsang, J. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985), Chap. 6.

A. P. Ivanov, V. A. Loiko, V. P. Dick, Propagation of Light in Densely Packed Disperse Media (Nauka i Tekhnika, Minsk, 1988), Chap. 2 (in Russian).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1, Chap. 6.

V. A. Loiko, A. P. Ivanov, V. P. Dick, “Some peculiarities of passage of light through dispersion layers with a high concentration of dispersion material,” in Optics for Science and Technology, Proc. SPIE2778, 321–322 (1996).

J. M. Ziman, Models of Disorder (Cambridge U. Press, Cambridge, UK, 1979), Chap. 2.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Values of the function F found in the SSA (dashed curves) and in the QCA (solid curves) at x=2 and x=4 for overlap coefficients η given at each pair of curves. Points with equal η are linked by short solid lines. The refractive index of the particles is m=1.4+i0.0.

Fig. 2
Fig. 2

Isolines of the relative error for coherent transmittance ΔT/T1 (solid curves) 1, ΔT/T1=0.0003; 2, 0.001; and 3, 0.003 and for coherent transmittance T1 (dashed curves) I, -T1=1; II, 0.98; III, 0.8; IV, 0.6; and V -0.4. In the shaded region in this and the following figures, T1>1. m=1.1+i0.0.

Fig. 3
Fig. 3

Isolines of the relative error for coherent transmittance ΔT/T1 (solid curves) 1, ΔT/T1=0.0001; 2, 0.003; 3, 0.01 and for coherent transmittance T1 (dashed curves) I, T1=1; II, 0.9; III, 0.8; IV, 0.5; and V, 0.3. m=1.2+i0.0.

Fig. 4
Fig. 4

Isolines of the relative error for coherent transmittance ΔT/T1 (solid curves) 1, ΔT/T1=0.01; 2, 0.05; and 3, 0.3 and coherent tansmittance T1 (dashed curves) I, T1=1; II, 0.9; III, 0.7; and IV, 0.5. m=1.4+i0.0.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

T1=|t1|2=1-2ηx2 cos αS1(0)2,
T=|t|2=1-2ηx2 cos αS(0)2.
T1=1-QηMT,
R1=QηMR.
MT=1-l(0),
MR=l(π),
l(0)=4ηQS1(0)x22,
l(π)=4ηQS1(π)x22,
l(θ)=Qη41+Im S1(θ)Re S1(θ)2.
ΔTT1=|tQCA|2-|t1|2|t1|22 Δ|t||t1|2 2ηx2ΔST1,
Δ|t|=|tQCA|-|t1|2ηx2(SQCA-S1)=2ηx2ΔS,
F=-2ηx2SQCA-2ηx2S1,
4πX(0)Λ/Qx2=0.5,
η=2/Q.

Metrics