Abstract

An investigation of the coherent transmission and reflection coefficients of a monolayer of spherical scatterers as a function of their size, optical constants, and concentration is carried out. An analysis is performed of the quasi-crystalline approximation of the multiple-wave scattering theory and on the single-scattering approximation (SSA). The results permit determining the limits of applicability of the SSA to the layers with the partial ordering of spherical scatterers in analyzing the phases of the transmitted and the reflected waves. The phase of the transmitted and the reflected waves is investigated in the conditions of the quenching effect. It is shown that in such a case small changes in the refractive index of particles can cause dramatic phase changes. This effect can be used to modulate the light-wave phase, e.g., by electrically controlled composite liquid-crystals films.

© 2005 Optical Society of America

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    [CrossRef]
  7. V. A. Loiko, A. V. Konkolovich, “Interference effect of coherent transmittance quenching: theoretical study of optical modulation by surface ferroelectric liquid crystal droplets,” J. Phys. D. 33, 2201–2210 (2000).
    [CrossRef]
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    [CrossRef]
  13. A. P. Ivanov, V. A. Loiko, V. P. Dick, Propagation of Light in Closely Packed Disperse Media (Nauka i Tekhnika, 1988) (in Russian).
  14. P. C. Waterman, R. Truell, “Multiple scattering of waves,” J. Math. Phys. 2, 512–537 (1961).
    [CrossRef]
  15. M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
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  18. V. A. Loiko, V. I. Molochko, “Coherent transmission and reflection by a monolayer of discrete scatterers,” Part. Part. Syst. Charact. 13, 227–233 (1996).
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  19. J. A. Lock, Ch.-L. Chiu, “Correlated light scattering by a dense distribution of condensation droplets on a window pane,” Appl. Opt. 33, 4663–4671 (1994).
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    [CrossRef]
  21. J. M. Ziman, Models of Disorder (Cambridge University, 1979).
  22. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).
  23. V. A. Babenko, L. A. Astafyeva, V. N. Kuzmin, Electromagnetic Scattering in Disperse Media (Springer, 2003).
  24. D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum (Nauka, 1975;World Scientific, 1988).
  25. G. V. Arfken, H. J. Weber, Mathematical Methods for Physicists (Academic, 1995).
  26. L. Tsang, J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics (Wiley, 2001).
  27. A. Ishimaru, Y. Kuga, “Attenuation constant of a coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
    [CrossRef]
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    [CrossRef]

2004 (1)

2003 (1)

2000 (3)

V. A. Loiko, V. P. Dick, A. P. Ivanov, “Features in coherent transmittance of a monolayer of particles,” J. Opt. Soc. Am. A 17, 2040–2045 (2000).
[CrossRef]

A. V. Konkolovich, V. V. Presnyakov, V. Ya Zyryanov, V. A. Loiko, V. F. Shabanov, “Interference quenching of light transmittance through a monolayer film of polymer-dispersed nematic liquid crystal,” JETP Lett. 71, 486–488 (2000).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, “Interference effect of coherent transmittance quenching: theoretical study of optical modulation by surface ferroelectric liquid crystal droplets,” J. Phys. D. 33, 2201–2210 (2000).
[CrossRef]

1996 (1)

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]

1994 (1)

1982 (2)

A. Ishimaru, Y. Kuga, “Attenuation constant of a coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
[CrossRef]

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

1980 (1)

1977 (1)

1971 (2)

E. A. Trabka, “Crowded emulsions: granularity theory for monolayers,” J. Opt. Soc. Am. 61, 800–810 (1971).
[CrossRef]

C. R. Berry, “On the need to apply electromagnetic theory to optical behavior of photographic emulsions,” Photogr. Sci. Eng. 15, 394–399 (1971).

1968 (1)

F. Lado, “Equation of state of the hard disk fluid from approximate integral equations,” J. Chem. Phys. 49, 3092–3096 (1968).
[CrossRef]

1961 (1)

P. C. Waterman, R. Truell, “Multiple scattering of waves,” J. Math. Phys. 2, 512–537 (1961).
[CrossRef]

1951 (1)

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
[CrossRef]

Aliev, F.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Arfken, G. V.

G. V. Arfken, H. J. Weber, Mathematical Methods for Physicists (Academic, 1995).

Astafyeva, L. A.

V. A. Babenko, L. A. Astafyeva, V. N. Kuzmin, Electromagnetic Scattering in Disperse Media (Springer, 2003).

Babenko, V. A.

V. A. Babenko, L. A. Astafyeva, V. N. Kuzmin, Electromagnetic Scattering in Disperse Media (Springer, 2003).

Berry, C. R.

C. R. Berry, “On the need to apply electromagnetic theory to optical behavior of photographic emulsions,” Photogr. Sci. Eng. 15, 394–399 (1971).

Bohren, C. F.

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

Cavalieri, S.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Chiu, Ch.-L.

Colocci, M.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Dal Negro, L.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Del Bianco, S.

Dick, V. P.

V. A. Loiko, V. P. Dick, A. P. Ivanov, “Features in coherent transmittance of a monolayer of particles,” J. Opt. Soc. Am. A 17, 2040–2045 (2000).
[CrossRef]

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

Ding, K.-H.

L. Tsang, J. A. Kong, K.-H. Ding, Scattering of Electromagnetic Waves: Theory of Microwave Remote Sensing (Wiley, 1985).

Gaburro, Z.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Ghulinyan, M.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Gottardo, S.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Hong, K. M.

Hovenier, J. W.

Huffman, D. R.

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

Ishimaru, A.

Ivanov, A. P.

V. A. Loiko, V. P. Dick, A. P. Ivanov, “Features in coherent transmittance of a monolayer of particles,” J. Opt. Soc. Am. A 17, 2040–2045 (2000).
[CrossRef]

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

Johnson, P. M.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[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. (USSR) 53, 1043–1048 (1982).

Khersonskii, V. K.

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum (Nauka, 1975;World Scientific, 1988).

Kong, J. A.

L. Tsang, J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics (Wiley, 2001).

L. Tsang, J. A. Kong, K.-H. Ding, Scattering of Electromagnetic Waves: Theory of Microwave Remote Sensing (Wiley, 1985).

Konkolovich, A. V.

A. V. Konkolovich, V. V. Presnyakov, V. Ya Zyryanov, V. A. Loiko, V. F. Shabanov, “Interference quenching of light transmittance through a monolayer film of polymer-dispersed nematic liquid crystal,” JETP Lett. 71, 486–488 (2000).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, “Interference effect of coherent transmittance quenching: theoretical study of optical modulation by surface ferroelectric liquid crystal droplets,” J. Phys. D. 33, 2201–2210 (2000).
[CrossRef]

Kuga, Y.

Kuzmin, V. N.

V. A. Babenko, L. A. Astafyeva, V. N. Kuzmin, Electromagnetic Scattering in Disperse Media (Springer, 2003).

Lado, F.

F. Lado, “Equation of state of the hard disk fluid from approximate integral equations,” J. Chem. Phys. 49, 3092–3096 (1968).
[CrossRef]

Lagendijk, A.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Lax, M.

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
[CrossRef]

Lock, J. A.

Loiko, V. A.

V. A. Loiko, V. P. Dick, A. P. Ivanov, “Features in coherent transmittance of a monolayer of particles,” J. Opt. Soc. Am. A 17, 2040–2045 (2000).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, “Interference effect of coherent transmittance quenching: theoretical study of optical modulation by surface ferroelectric liquid crystal droplets,” J. Phys. D. 33, 2201–2210 (2000).
[CrossRef]

A. V. Konkolovich, V. V. Presnyakov, V. Ya Zyryanov, V. A. Loiko, V. F. Shabanov, “Interference quenching of light transmittance through a monolayer film of polymer-dispersed nematic liquid crystal,” JETP Lett. 71, 486–488 (2000).
[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]

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

Mackowsky, D. W.

Martelli, F.

Mishchenko, M. I.

Molochko, V. I.

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]

Moskalev, A. N.

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum (Nauka, 1975;World Scientific, 1988).

Mujumdar, S.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Oton, C.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Pavesi, L.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Presnyakov, V. V.

A. V. Konkolovich, V. V. Presnyakov, V. Ya Zyryanov, V. A. Loiko, V. F. Shabanov, “Interference quenching of light transmittance through a monolayer film of polymer-dispersed nematic liquid crystal,” JETP Lett. 71, 486–488 (2000).
[CrossRef]

Righini, R.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Sapienza, R.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Shabanov, V. F.

A. V. Konkolovich, V. V. Presnyakov, V. Ya Zyryanov, V. A. Loiko, V. F. Shabanov, “Interference quenching of light transmittance through a monolayer film of polymer-dispersed nematic liquid crystal,” JETP Lett. 71, 486–488 (2000).
[CrossRef]

Stark, H.

Trabka, E. A.

Truell, R.

P. C. Waterman, R. Truell, “Multiple scattering of waves,” J. Math. Phys. 2, 512–537 (1961).
[CrossRef]

Tsang, L.

L. Tsang, J. A. Kong, K.-H. Ding, Scattering of Electromagnetic Waves: Theory of Microwave Remote Sensing (Wiley, 1985).

L. Tsang, J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics (Wiley, 2001).

Tuchin, V.

V. Tuchin, Tissue Optics (SPIE Press, 2000).

Varshalovich, D. A.

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum (Nauka, 1975;World Scientific, 1988).

Vos, W. L.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Waterman, P. C.

P. C. Waterman, R. Truell, “Multiple scattering of waves,” J. Math. Phys. 2, 512–537 (1961).
[CrossRef]

Weber, H. J.

G. V. Arfken, H. J. Weber, Mathematical Methods for Physicists (Academic, 1995).

Wiersma, D. S.

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

Ya Zyryanov, V.

A. V. Konkolovich, V. V. Presnyakov, V. Ya Zyryanov, V. A. Loiko, V. F. Shabanov, “Interference quenching of light transmittance through a monolayer film of polymer-dispersed nematic liquid crystal,” JETP Lett. 71, 486–488 (2000).
[CrossRef]

Zaccanti, G.

Ziman, J. M.

J. M. Ziman, Models of Disorder (Cambridge University, 1979).

Appl. Opt. (2)

J. Chem. Phys. (1)

F. Lado, “Equation of state of the hard disk fluid from approximate integral equations,” J. Chem. Phys. 49, 3092–3096 (1968).
[CrossRef]

J. Math. Phys. (1)

P. C. Waterman, R. Truell, “Multiple scattering of waves,” J. Math. Phys. 2, 512–537 (1961).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (2)

J. Phys. D. (1)

V. A. Loiko, A. V. Konkolovich, “Interference effect of coherent transmittance quenching: theoretical study of optical modulation by surface ferroelectric liquid crystal droplets,” J. Phys. D. 33, 2201–2210 (2000).
[CrossRef]

JETP Lett. (1)

A. V. Konkolovich, V. V. Presnyakov, V. Ya Zyryanov, V. A. Loiko, V. F. Shabanov, “Interference quenching of light transmittance through a monolayer film of polymer-dispersed nematic liquid crystal,” JETP Lett. 71, 486–488 (2000).
[CrossRef]

Opt. Spectrosc. (USSR) (1)

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

Part. Part. Syst. Charact. (1)

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]

Photogr. Sci. Eng. (1)

C. R. Berry, “On the need to apply electromagnetic theory to optical behavior of photographic emulsions,” Photogr. Sci. Eng. 15, 394–399 (1971).

Rev. Mod. Phys. (1)

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287–310 (1951).
[CrossRef]

Other (12)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol. 2.

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

L. Tsang, J. A. Kong, K.-H. Ding, Scattering of Electromagnetic Waves: Theory of Microwave Remote Sensing (Wiley, 1985).

V. Tuchin, Tissue Optics (SPIE Press, 2000).

G. P. Crawford, S. Zumer, eds., Liquid Crystals in Complex Geometries Formed by Polymer and Porous Networks (Taylor & Francis, 1996).

D. S. Wiersma, S. Gottardo, R. Sapienza, S. Mujumdar, S. Cavalieri, M. Colocci, R. Righini, L. Dal Negro, C. Oton, M. Ghulinyan, Z. Gaburro, L. Pavesi, F. Aliev, P. M. Johnson, A. Lagendijk, W. L. Vos, “Light transport in complex photonic systems,” in Wave Scattering in Complex Media: From Theory to Applications, B. A. Tiggelen, S. E. Skipetrov, eds. (Kluwer Academic, 2003).
[CrossRef]

J. M. Ziman, Models of Disorder (Cambridge University, 1979).

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

V. A. Babenko, L. A. Astafyeva, V. N. Kuzmin, Electromagnetic Scattering in Disperse Media (Springer, 2003).

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum (Nauka, 1975;World Scientific, 1988).

G. V. Arfken, H. J. Weber, Mathematical Methods for Physicists (Academic, 1995).

L. Tsang, J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics (Wiley, 2001).

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Figures (13)

Fig. 1
Fig. 1

Transmitted wave phase versus the refractive index n at various size parameters: solid curves, results of the calculations from the QCA (φtms); dashed curves, from the SSA (φtss). η = 0.5, κ = 5 × 10−5.

Fig. 2
Fig. 2

Dependence of the coherent transmission coefficient on the refractive index n at various size parameters: solid curves, results of the calculations with the QCA (|Tms|2); dashed curves, with the SSA (|Tss|2); η = 0.5, κ = 5 × 10−5.

Fig. 3
Fig. 3

Dependence of the phase of reflected wave on the refractive index n at different size parameters: solid curves, results of the calculations from the QCA (φrms); dashed curves, from the SSA (φrss); η = 0.5, κ = 5 × 10−5.

Fig. 4
Fig. 4

Dependence of the reflection coefficient on the refractive index n at various size parameters: solid curves, results of calculations from the QCA |Rms|2); dashed curves, from the SSA (|Rss|2); η = 0.5, κ = 5 × 10−5.

Fig. 5
Fig. 5

Solid curve, dependence of the coherent transmission coefficient |Tms|2; dashed curve, phase of transmitted wave φtms on size parameter x in the region of size parameters corresponding to the transmission minimum, which is due to interference from the incident and the transmitted waves. Calculation is from the QCA; η = 0.5, n = 1.6, κ = 5 × 10−5.

Fig. 6
Fig. 6

Dependence of the phase of transmitted wave φtms on the refractive index n in the region of size parameters corresponding to the transmission minimum, which is due to interference from the incident and the transmitted waves. Calculation is with the QCA; η = 0.5, κ = 5 × 10−5.

Fig. 7
Fig. 7

Dependence of the coherent transmission coefficient |Tms|2 of the monolayer on the refractive index n in the size-parameter region corresponding to the transmission minimum, which is due to interference from the incident and the transmitted waves. Calculation is with the QCA. η = 0.5, κ = 5 × 10−5.

Fig. 8
Fig. 8

Dependence of the amplitude transmission coefficient |Tms|, Re Tms, and Im Tms on the refractive index n in the size-parameter region corresponding to the transmission minimum that is due to interference from the incident and the transmitted waves. Calculation is from the QCA; η = 0.5, κ = 5 × 10−5. (a), (b) Change in the phase by −π. (c), (d) Change in the phase by +π.

Fig. 9
Fig. 9

Solid curve, dependence of the coherent reflection coefficient |Rms|2; dashed curve, phase of transmitted wave φrms on the size parameter x in the size-parameter region corresponding to the reflection minimum. Calculation is with the QCA; η = 0.5, n = 1.2, κ = 5 × 10−5.

Fig. 10
Fig. 10

Dependence of the phase of reflected wave φrms on the refractive index n in the size-parameter region corresponding to the reflection minimum. Calculation is with the QCA; φ = 0.5, κ = 5 × 10−5.

Fig. 11
Fig. 11

Dependence of the coherent reflectance coefficient |Rms|2 of the monolayer on the refractive index n in the size-parameter region corresponding to the reflection minimum. Calculation is from the QCA; η = 0.5, κ = 5 × 10−5.

Fig. 12
Fig. 12

Dependences of the amplitude reflection coefficient |Rms|, Re Rms, and Im Rms on the refractive index n in the size-parameter region corresponding to the reflection minimum. Calculation is from the QCA; η = 0.5, κ = 5 × 10−5: (a), (b) Change in the phase by π; (c), (d) change in the phase by +π.

Fig. 13
Fig. 13

Dependence of the coherent transmission coefficient and phase of the transmitted wave on the refractive index n at the different size parameters. Calculation is with the QCA; η = 0.5, κ = 5 × 10−5.

Equations (37)

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E ( r ) = E inc ( r ) + S d r i n s ( r i ) T ̂ · E ( r | r i ) .
T ̂ i · E ( r | r i ) f ( n ̂ ) h 0 ( k | r r i ) ,
E ( r | r i ) = E inc ( r ) + S d r j n ( r j | r i ) T ̂ j · E ( r | r j ) ,
E inc ( r ) = ( e z + i e y ) exp [ i k · ( r r i ) ] exp ( i k · r ) = exp ( i k · r i ) n = 1 C n 1 [ M n 1 ( i ) ( r r i ) + N n 1 ( i ) ( r r i ) ] ,
C n 1 = i n 1 2 n + 1 n ( n + 1 ) ,
E inc ( r ) = n = 1 C n 1 [ M n 1 ( i ) ( r r i ) + N n 1 ( i ) ( r r i ) ] .
T ̂ i · E ( r | r i ) = n [ b n z n 1 M n 1 ( 3 ) ( r r i ) + a n y n 1 N n 1 ( 3 ) ( r r i ) ] .
a i = m ψ i ( m x ) ψ i ( x ) ψ i ( x ) ψ i ( m x ) m ψ i ( m x ) χ i ( x ) χ i ( x ) ψ i ( m x ) ,
b i = ψ i ( m x ) ψ i ( x ) m ψ i ( x ) ψ i ( m x ) ψ i ( m x ) χ i ( x ) m χ i ( x ) ψ i ( m x ) ,
E ( r | r i ) = n [ z n 1 M n 1 ( 1 ) ( r r i ) + y n 1 N n 1 ( i ) ( r r i ) ] .
T = 1 η x 2 i = 1 N ( 2 i + 1 ) ( z i + y i ) ,
R = η x 2 i = 1 N ( 1 ) i ( 2 i + 1 ) ( z i + y i ) ,
z i = b i + b i η k 2 π x 2 j = 1 N ( A i j z j + B i j y j ) y i = a i + a i η k 2 π x 2 j = 1 N ( A i j y j + B i j z j ) } ,
A m n = 2 n + 1 2 1 [ m ( m + 1 ) n ( n + 1 ) ] 1 / 2 × p = 0 , 2 N i p ( 2 p + 1 ) [ m ( m + 1 ) + n ( n + 1 ) ] p ( p + 1 ) ] P p ( 0 ) ( m n p 0 0 0 ) ( m n p 1 1 0 ) H p ,
B m n = 2 n + 1 2 1 [ m ( m + 1 ) n ( n + 1 ) ] 1 / 2 × p = 0 , 2 N i p ( 2 p + 1 ) [ ( p + m n ) ( p m + n ) × ( m + n + 1 + p ) ( m + n + 1 p ) ] 1 / 2 × P p ( 0 ) ( m n p 1 0 0 0 ) ( m n p 1 1 0 ) H p ; ( j 1 j 2 j 3 m 1 m 2 m 3 )
H p = 2 π D d R R g 2 ( R / D ) h p ( 1 ) ( k R ) ,
g 2 ( R ) = 1 + 1 8 η 0 C 2 ( z / 2 ) 1 + C ( z / 2 ) J 0 ( z R ) z d z ,
C ( t ) = 4 η 1 η 2 J 1 ( 2 t ) 2 t + 4 η 2 ( 1 η ) 2 J 0 ( t ) 2 J 1 ( t ) t + [ η 2 ( 1 η ) 2 + 2 η 3 ( 1 η 3 ) ] [ 2 J 1 ( t ) t ] 2 ,
P p ( 0 ) = i p ( p 1 ) ! ! p ! ! ,
H 1 p = D d R R h p ( 1 ) ( k R ) ,
H 2 p = D d R R [ g ( R ) 1 ] h p ( 1 ) ( k R ) .
H 1 p = k 2 { k D h p + 1 ( 1 ) ( k D ) + q = 0 , 2 p [ 2 ( p q ) + 1 ] × p ! ! ( p q 1 ) ! ! ( p 1 ) ! ! ( p q ) ! ! h p q ( 1 ) ( k D ) } ,
( m n p 1 1 0 ) ,
( m n p 1 1 0 ) = 1 2 [ ( p + m n ) ( p m + n ) ( m + n + 1 + p ) ( m + n + 1 p ) m ( m + 1 ) n ( n + 1 ) ] 1 2 ( m n p 1 0 0 0 )
( m n p 1 1 0 ) = 1 2 m ( m + 1 ) + n ( n + 1 ) p ( p + 1 ) [ m ( m + 1 ) n ( n + 1 ) ] × ( m n p 0 0 0 )
( m n p 0 0 0 )
[ m n p 0 0 0 ] = { 0 , m + n + p = 2 d + 1 , ( 1 ) d p ( 2 p + 1 ) 1 / 2 d ! ( d m ) ! ( d n ) ! ( d p ) ! × [ ( 2 d 2 m ) ! ( 2 d 2 n ) ! ( 2 d 2 p ) ! ( 2 d + 1 ) ! ] 1 / 2 , m + n + p = 2 d ,
( m n p 0 0 0 ) = ( 1 ) p + 2 m 1 ( 2 p + 1 ) 1 / 2 [ m n p 0 0 0 ] .
[ j 1 j 2 j 3 m 1 m 2 m 3 ]
T m s = 1 η x 2 i = 1 N ( 2 i + 1 ) ( z i + y i ) ,
R m s = η x 2 i = 1 N ( 1 ) i ( 2 i + 1 ) ( z i + y i ) ,
T s s = 1 η x 2 i = 1 N ( 2 i + 1 ) ( a i + b i ) ,
R s s = η x 2 i = 1 N ( 1 ) i ( 2 i + 1 ) ( a i b i ) .
φ t m s = arctan Im ( T m s ) Re ( T m s ) ,
φ r m s = arctan Im ( R m s ) Re ( R m s ) ,
φ t s s = arctan Im ( T s s ) Re ( T s s ) ,
φ r s s = arctan Im ( R s s ) Re ( R s s ) .

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