Abstract

Coherent and incoherent transmittance values of a monolayer of particles are considered. Such a monolayer is a set of particles whose centers are located in the same plane. We set forth the conditions for the effect of coherent-transmittance quenching, which takes place as a result of the interference between incident and forward-scattered waves. Using the single-scattering approximation we determined size parameters and particle refractive indexes for this interference effect in the case of identical isotropic spherical particles. The influence of polydispersity and the fine structure of light-scattering characteristics on the quenching effect has been estimated. It is shown that the polydispersity destroys this interference effect only at large widths of particle-size distribution functions. The influence of multiple scattering on this effect is considered in the quasi-crystalline approximation. Multiple scattering results in increasing size parameters and decreasing particle concentration at which coherent transmittance quenching takes place in comparison with the case of single scattering. Our theoretical results for suspensions of latex particles in water are in fairly good agreement with the experimental results.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983), Chap. 3.
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    [CrossRef]
  20. A. F. Sarofim, H. C. Hottel, E. J. Fahimian, “Scattering of radiation by particle layers,” AIAA J. 6, 2262–2266 (1968).
    [CrossRef]
  21. V. A. Loiko, A. V. Konkolovich, V. V. Presnyakov, V. Ya. Zyryanov, A. V. Shabanov, “Electrooptical response of nematic polymer dispersed liquid crystal monolayer,” in Advanced Display Technologies, Proceedings of the Society for Information Display’s 8th International Symposium (Society for Information Display, Kiev, Ukraine, 1999), pp. 21–23.

1999

1998

1997

1996

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

1992

1983

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

1982

A. Ya. Khairullina, “Regularities of regular and diffuse transmission of particle monolayers with different packing densities and optical properties,” Opt. Spectrosc. 53, 1043–1048 (1982) (translated from Russian).

1981

A. Killey, G. H. Meeten, “Optical extinction and refraction of concentrated latex dispersions,” J. Chem. Soc., Faraday Trans. 77, 587–599 (1981).
[CrossRef]

1980

1975

1973

C. R. Berry, “On the need to apply electromagnetic theory to optical behavior of photographic emulsions,” Photograph. Sci. Eng. 17, 394–399 (1973).

L. F. Gate, “Light-scattering cross sections in dense colloidal suspensions of spherical particles,” J. Opt. Soc. Am. 63, 312–317 (1973).
[CrossRef]

1968

A. F. Sarofim, H. C. Hottel, E. J. Fahimian, “Scattering of radiation by particle layers,” AIAA J. 6, 2262–2266 (1968).
[CrossRef]

1967

S. W. Hawley, T. H. Kays, V. Tversky, “Comparison of distribution functions from scattering data on different sets of spheres,” IEEE Trans. Antennas Propag. 15, 118–138 (1967).
[CrossRef]

1962

Balgi, G.

Banerjee, S.

Berry, C. R.

C. R. Berry, “On the need to apply electromagnetic theory to optical behavior of photographic emulsions,” Photograph. Sci. Eng. 17, 394–399 (1973).

C. R. Berry, “Turbidity of monodisperse suspensions of AgBr,” J. Opt. Soc. Am. 52, 888–895 (1962).
[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.

Bringi, V. N.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

Dick, V. P.

Ding, K. H.

Fahimian, E. J.

A. F. Sarofim, H. C. Hottel, E. J. Fahimian, “Scattering of radiation by particle layers,” AIAA J. 6, 2262–2266 (1968).
[CrossRef]

Gate, L. F.

Hawley, S. W.

S. W. Hawley, T. H. Kays, V. Tversky, “Comparison of distribution functions from scattering data on different sets of spheres,” IEEE Trans. Antennas Propag. 15, 118–138 (1967).
[CrossRef]

Hong, K. M.

Hottel, H. C.

A. F. Sarofim, H. C. Hottel, E. J. Fahimian, “Scattering of radiation by particle layers,” AIAA J. 6, 2262–2266 (1968).
[CrossRef]

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.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

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, Propagation of Light in Closely-Packed Disperse Media (Naukai Tekhnika, Minsk, Belarus, 1988), Chap. 2 (in Russian).

Kays, T. H.

S. W. Hawley, T. H. Kays, V. Tversky, “Comparison of distribution functions from scattering data on different sets of spheres,” IEEE Trans. Antennas Propag. 15, 118–138 (1967).
[CrossRef]

Khairullina, A. Ya.

A. Ya. Khairullina, “Regularities of regular and diffuse transmission of particle monolayers with different packing densities and optical properties,” Opt. Spectrosc. 53, 1043–1048 (1982) (translated from Russian).

Killey, A.

A. Killey, G. H. Meeten, “Optical extinction and refraction of concentrated latex dispersions,” J. Chem. Soc., Faraday Trans. 77, 587–599 (1981).
[CrossRef]

Koh, G.

G. Koh, “Experimental study of electromagnetic wave propagation in dense random media,” Waves Random Media 2, 39–48 (1992).
[CrossRef]

Konkolovich, A. V.

V. A. Loiko, A. V. Konkolovich, V. V. Presnyakov, V. Ya. Zyryanov, A. V. Shabanov, “Electrooptical response of nematic polymer dispersed liquid crystal monolayer,” in Advanced Display Technologies, Proceedings of the Society for Information Display’s 8th International Symposium (Society for Information Display, Kiev, Ukraine, 1999), pp. 21–23.

Loiko, V. A.

V. A. Loiko, V. P. Dick, V. I. Molochko, “Monolayers of discrete scatterers: comparison of the single-scattering and quasi-crystalline approximation,” J. Opt. Soc. Am. A 15, 2351–2354 (1998).
[CrossRef]

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 discrete scatterers,” Part. Part. Syst. Charact. 13, 227–233 (1996).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, V. V. Presnyakov, V. Ya. Zyryanov, A. V. Shabanov, “Electrooptical response of nematic polymer dispersed liquid crystal monolayer,” in Advanced Display Technologies, Proceedings of the Society for Information Display’s 8th International Symposium (Society for Information Display, Kiev, Ukraine, 1999), pp. 21–23.

A. P. Ivanov, V. A. Loiko, V. P. Dick, Propagation of Light in Closely-Packed Disperse Media (Naukai Tekhnika, Minsk, Belarus, 1988), Chap. 2 (in Russian).

Mandt, C. E.

Meeten, G. H.

A. Killey, G. H. Meeten, “Optical extinction and refraction of concentrated latex dispersions,” J. Chem. Soc., Faraday Trans. 77, 587–599 (1981).
[CrossRef]

Molochko, V. I.

V. A. Loiko, V. P. Dick, V. I. Molochko, “Monolayers of discrete scatterers: comparison of the single-scattering and quasi-crystalline approximation,” J. Opt. Soc. Am. A 15, 2351–2354 (1998).
[CrossRef]

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

Pierce, J.

Presnyakov, V. V.

V. A. Loiko, A. V. Konkolovich, V. V. Presnyakov, V. Ya. Zyryanov, A. V. Shabanov, “Electrooptical response of nematic polymer dispersed liquid crystal monolayer,” in Advanced Display Technologies, Proceedings of the Society for Information Display’s 8th International Symposium (Society for Information Display, Kiev, Ukraine, 1999), pp. 21–23.

Reynolds, J.

Richter, S.

Sarofim, A. F.

A. F. Sarofim, H. C. Hottel, E. J. Fahimian, “Scattering of radiation by particle layers,” AIAA J. 6, 2262–2266 (1968).
[CrossRef]

Sevick-Muraca, E.

Shabanov, A. V.

V. A. Loiko, A. V. Konkolovich, V. V. Presnyakov, V. Ya. Zyryanov, A. V. Shabanov, “Electrooptical response of nematic polymer dispersed liquid crystal monolayer,” in Advanced Display Technologies, Proceedings of the Society for Information Display’s 8th International Symposium (Society for Information Display, Kiev, Ukraine, 1999), pp. 21–23.

Shinde, R.

Tsang, L.

Tversky, V.

S. W. Hawley, T. H. Kays, V. Tversky, “Comparison of distribution functions from scattering data on different sets of spheres,” IEEE Trans. Antennas Propag. 15, 118–138 (1967).
[CrossRef]

V. Tversky, “Multiple scattering of waves and optical phenomena,” J. Opt. Soc. Am. 52, 145–171 (1962).
[CrossRef]

Twersky, V.

van de Hulst, H. C.

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

Varadan, V. K.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

Varadan, V. V.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

Zyryanov, V. Ya.

V. A. Loiko, A. V. Konkolovich, V. V. Presnyakov, V. Ya. Zyryanov, A. V. Shabanov, “Electrooptical response of nematic polymer dispersed liquid crystal monolayer,” in Advanced Display Technologies, Proceedings of the Society for Information Display’s 8th International Symposium (Society for Information Display, Kiev, Ukraine, 1999), pp. 21–23.

AIAA J.

A. F. Sarofim, H. C. Hottel, E. J. Fahimian, “Scattering of radiation by particle layers,” AIAA J. 6, 2262–2266 (1968).
[CrossRef]

Appl. Opt.

IEEE Trans. Antennas Propag.

S. W. Hawley, T. H. Kays, V. Tversky, “Comparison of distribution functions from scattering data on different sets of spheres,” IEEE Trans. Antennas Propag. 15, 118–138 (1967).
[CrossRef]

J. Chem. Soc., Faraday Trans.

A. Killey, G. H. Meeten, “Optical extinction and refraction of concentrated latex dispersions,” J. Chem. Soc., Faraday Trans. 77, 587–599 (1981).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Opt. Spectrosc.

A. Ya. Khairullina, “Regularities of regular and diffuse transmission of particle monolayers with different packing densities and optical properties,” Opt. Spectrosc. 53, 1043–1048 (1982) (translated from Russian).

Part. Part. Syst. Charact.

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

Photograph. Sci. Eng.

C. R. Berry, “On the need to apply electromagnetic theory to optical behavior of photographic emulsions,” Photograph. Sci. Eng. 17, 394–399 (1973).

Radio Sci.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

Waves Random Media

G. Koh, “Experimental study of electromagnetic wave propagation in dense random media,” Waves Random Media 2, 39–48 (1992).
[CrossRef]

Other

A. P. Ivanov, V. A. Loiko, V. P. Dick, Propagation of Light in Closely-Packed Disperse Media (Naukai Tekhnika, Minsk, Belarus, 1988), Chap. 2 (in Russian).

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, New York, 1957), Chap. 4.

V. A. Loiko, A. V. Konkolovich, V. V. Presnyakov, V. Ya. Zyryanov, A. V. Shabanov, “Electrooptical response of nematic polymer dispersed liquid crystal monolayer,” in Advanced Display Technologies, Proceedings of the Society for Information Display’s 8th International Symposium (Society for Information Display, Kiev, Ukraine, 1999), pp. 21–23.

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Figures (7)

Fig. 1
Fig. 1

Isolines for L=0.5 (vertical) and η=2/Q (nonvertical) in the SSA (dashed lines). The intersection point of the dashed lines shows the values of x0 and η0 at which quenching of the coherent component of transmitted light in the SSA takes place; the intersection point of the solid lines shows this for the QCA.

Fig. 2
Fig. 2

Values of n, x0, and η0 at which Tc=0.

Fig. 3
Fig. 3

(a) Im S(0) and (b) Q as a function of particle size x. The lines (a) Im S(0)=0 and (b) Q=2/ηmax are auxiliary. The digits 1, 2, and 3 above the line Im S(0)=0 show three orientational positions of x0 values. n=1.2.

Fig. 4
Fig. 4

(a) Im S(0) as a function of x at n=1.2 in the region of x labeled 3 in Fig. 3.

Fig. 5
Fig. 5

Isolines for L=0.5 (vertical lines) and η=2/Q (nonvertical curves) for various half-widths of the size-distribution function: 1, Θ=0 (solid curves); 2, Θ=0.25 (long-dashed curves); 3, Θ=0.5 (dotted–dashed curves); 4, Θ=0.8 (short-dashed curves). n=1.07.

Fig. 6
Fig. 6

Coherent transmittance Tc as a function of filling coefficient η and size parameter x calculated in the QCA for n=1.4.

Fig. 7
Fig. 7

Transmittance T=Tc+Tinc of monodisperse latex particles (d=3.75 μm) as a function of λ for various filling coefficients η. The thick curve represents η=0.78 at which the minimum transmission is achieved. Points are experimental results and are connected by thin curves.

Equations (18)

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

U(R)=Up(R)+Ui(R).
I=|U(R)|2=|Up(R)|2+|Ui(R)|2+2 Re[Up*(R)Ui(R)].
|Up(r)|2=jNkNUj(Rs)Uk*(Rs)×exp[ik(rj-rk)(si-s)],
|Up(R)|2=|U(Rs)|2N+|U(Rs)|2N(N-1)×[W(r)-1]exp(ikr(si-s)) dsjAdskA+|U(R)|2.
|U(R)|2=|U(R)|2+|U(Rs)|2N+|U(Rs)|2N(N-1)×[W(r)-1]×exp[ikr(si-s)] dsjAdskA.
Ic=|U(R)|2,
Iin=|U(Rs)|2N+|U(Rs)|2N(N-1)
×[W(r)-1]exp[ikr(si-s)] dsjAdskA.
Iin(Rs)=|U(Rs)|2NS(s, si)=PΛΩηp(γs)S(s, si),
S(s, si)=1+(N-1)[W(r)-1]×exp[ikr(si-s)] dsjAdskA
S(s, si)=S(α, αi)=1+8η0[W(y)-1]×J0[2x(sin αi-sin α)y]dy.
Tc=1-2ηx2cos αi S(0)2,
Tc=1-Q ηcos αi+L2Q ηcos αi2,
zL=4πp(0)ΛQx2.
L=0.5,
η=2/Q.
T=Tc+Tin.
Tin=π Qη (1-η)3(1+η) p(0)γ2.

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