Abstract

Within the range in which light penetration depth is approximately the same as or less than the diameter of the particles in the medium, particulate media with considerable absorption behave as two-dimensional, rough-surface structures. As penetration depth increases, a complicated transition between volume and surface effects is seen. For these media, low-order scattering sequences have small spatial extent, making observation of polarization characteristics difficult. We present an experimental technique to access the low-order scattered photons by artificially reinjecting them through total internal reflections. Using a dielectric layer in contact with the high-absorption medium, we are able to observe fourfold polarization asymmetry in backscattering from highly absorbant media. We discuss the origin of the polarization patterns in a ray-optics approximation and suggest possibilities for solving practical problems encountered in characterizing composites with appreciable absorption.

© 1997 Optical Society of America

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References

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  1. S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
    [CrossRef]
  2. W. I. Kordonski, S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2937–2948 (1996).
    [CrossRef]
  3. I. V. Prohorov, W. I. Kordonski, L. K. Gleb, G. R. Gorodkin, M. L. Levin, “New high precision magnetorheological instrument-based method of polishing optics,” in Optical Fabrication and Testing, Vol. 24 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 135–136.
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  5. D. Elyiahu, M. Rosenbluh, I. Freund, “Angular intensity and polarization dependence of diffuse transmission through random media,” J. Opt. Soc. Am. A 10, 447–491 (1993).
  6. R. Berkovitz, M. Kaveh, “The vector memory effect for waves,” Europhys. Lett. 13, 97–101 (1992).
    [CrossRef]
  7. M. P. Albada, M. B. Van der Mark, A. Lagendjik, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2358 (1987).
    [CrossRef]
  8. M. Dogariu, T. Asakura, “Photon pathlength distribution from polarized backscattering in random media,” Opt. Eng. 35, 2234–2239 (1996).
    [CrossRef]
  9. C. J. Solomon, J. C. Dainty, “Use of polarization in double-passage imaging through a random screen,” Opt. Commun. 87, 207–211 (1992).
    [CrossRef]
  10. M. Dogariu, T. Asakura, “Polarization dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
    [CrossRef]
  11. M. Dogariu, T. Asakura, “Polarized light scattering in dielectric layers with rough interfaces,” Opt. Commun. 131, 1–7 (1996).
    [CrossRef]
  12. A. Carswell, S. R. Pal, “Polarization anisotropy in lidar multiple scattering from clouds,” Appl. Opt. 24, 3464–3471 (1980).
  13. D. Bicout, E. Akkermans, R. Maynard, “Dynamical correlations from multiple light scattering in laminar flow,” J. Phys. I (Paris) 1, 471–491 (1991).
  14. D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of size parameters,” Phys. Rev. E 49, 1767–1770 (1994).
    [CrossRef]

1996

W. I. Kordonski, S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2937–2948 (1996).
[CrossRef]

M. Dogariu, T. Asakura, “Photon pathlength distribution from polarized backscattering in random media,” Opt. Eng. 35, 2234–2239 (1996).
[CrossRef]

M. Dogariu, T. Asakura, “Polarized light scattering in dielectric layers with rough interfaces,” Opt. Commun. 131, 1–7 (1996).
[CrossRef]

1994

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of size parameters,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

1993

M. Dogariu, T. Asakura, “Polarization dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

D. Elyiahu, M. Rosenbluh, I. Freund, “Angular intensity and polarization dependence of diffuse transmission through random media,” J. Opt. Soc. Am. A 10, 447–491 (1993).

1992

R. Berkovitz, M. Kaveh, “The vector memory effect for waves,” Europhys. Lett. 13, 97–101 (1992).
[CrossRef]

C. J. Solomon, J. C. Dainty, “Use of polarization in double-passage imaging through a random screen,” Opt. Commun. 87, 207–211 (1992).
[CrossRef]

1991

D. Bicout, E. Akkermans, R. Maynard, “Dynamical correlations from multiple light scattering in laminar flow,” J. Phys. I (Paris) 1, 471–491 (1991).

1987

M. P. Albada, M. B. Van der Mark, A. Lagendjik, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2358 (1987).
[CrossRef]

1980

Akkermans, E.

D. Bicout, E. Akkermans, R. Maynard, “Dynamical correlations from multiple light scattering in laminar flow,” J. Phys. I (Paris) 1, 471–491 (1991).

Albada, M. P.

M. P. Albada, M. B. Van der Mark, A. Lagendjik, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2358 (1987).
[CrossRef]

Asakura, T.

M. Dogariu, T. Asakura, “Photon pathlength distribution from polarized backscattering in random media,” Opt. Eng. 35, 2234–2239 (1996).
[CrossRef]

M. Dogariu, T. Asakura, “Polarized light scattering in dielectric layers with rough interfaces,” Opt. Commun. 131, 1–7 (1996).
[CrossRef]

M. Dogariu, T. Asakura, “Polarization dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

Berkovitz, R.

R. Berkovitz, M. Kaveh, “The vector memory effect for waves,” Europhys. Lett. 13, 97–101 (1992).
[CrossRef]

Bicout, D.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of size parameters,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

D. Bicout, E. Akkermans, R. Maynard, “Dynamical correlations from multiple light scattering in laminar flow,” J. Phys. I (Paris) 1, 471–491 (1991).

Brosseau, C.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of size parameters,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Carswell, A.

Dainty, J. C.

C. J. Solomon, J. C. Dainty, “Use of polarization in double-passage imaging through a random screen,” Opt. Commun. 87, 207–211 (1992).
[CrossRef]

Dogariu, M.

M. Dogariu, T. Asakura, “Polarized light scattering in dielectric layers with rough interfaces,” Opt. Commun. 131, 1–7 (1996).
[CrossRef]

M. Dogariu, T. Asakura, “Photon pathlength distribution from polarized backscattering in random media,” Opt. Eng. 35, 2234–2239 (1996).
[CrossRef]

M. Dogariu, T. Asakura, “Polarization dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

Elyiahu, D.

D. Elyiahu, M. Rosenbluh, I. Freund, “Angular intensity and polarization dependence of diffuse transmission through random media,” J. Opt. Soc. Am. A 10, 447–491 (1993).

Fess, E.

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

Freund, I.

D. Elyiahu, M. Rosenbluh, I. Freund, “Angular intensity and polarization dependence of diffuse transmission through random media,” J. Opt. Soc. Am. A 10, 447–491 (1993).

Gleb, L. K.

I. V. Prohorov, W. I. Kordonski, L. K. Gleb, G. R. Gorodkin, M. L. Levin, “New high precision magnetorheological instrument-based method of polishing optics,” in Optical Fabrication and Testing, Vol. 24 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 135–136.

Golini, D.

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

Gorodkin, G. R.

I. V. Prohorov, W. I. Kordonski, L. K. Gleb, G. R. Gorodkin, M. L. Levin, “New high precision magnetorheological instrument-based method of polishing optics,” in Optical Fabrication and Testing, Vol. 24 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 135–136.

Hsu, Y.

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

Ishimaru, A.

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

Jacobs, S. D.

W. I. Kordonski, S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2937–2948 (1996).
[CrossRef]

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

Kaveh, M.

R. Berkovitz, M. Kaveh, “The vector memory effect for waves,” Europhys. Lett. 13, 97–101 (1992).
[CrossRef]

Kordonski, V. W.

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

Kordonski, W. I.

W. I. Kordonski, S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2937–2948 (1996).
[CrossRef]

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

I. V. Prohorov, W. I. Kordonski, L. K. Gleb, G. R. Gorodkin, M. L. Levin, “New high precision magnetorheological instrument-based method of polishing optics,” in Optical Fabrication and Testing, Vol. 24 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 135–136.

Lagendjik, A.

M. P. Albada, M. B. Van der Mark, A. Lagendjik, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2358 (1987).
[CrossRef]

Levin, M. L.

I. V. Prohorov, W. I. Kordonski, L. K. Gleb, G. R. Gorodkin, M. L. Levin, “New high precision magnetorheological instrument-based method of polishing optics,” in Optical Fabrication and Testing, Vol. 24 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 135–136.

Martinez, A. S.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of size parameters,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Maynard, R.

D. Bicout, E. Akkermans, R. Maynard, “Dynamical correlations from multiple light scattering in laminar flow,” J. Phys. I (Paris) 1, 471–491 (1991).

Pal, S. R.

Pietrowski, D.

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

Prohorov, I. V.

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

I. V. Prohorov, W. I. Kordonski, L. K. Gleb, G. R. Gorodkin, M. L. Levin, “New high precision magnetorheological instrument-based method of polishing optics,” in Optical Fabrication and Testing, Vol. 24 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 135–136.

Pucherbner, B. E.

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

Rosenbluh, M.

D. Elyiahu, M. Rosenbluh, I. Freund, “Angular intensity and polarization dependence of diffuse transmission through random media,” J. Opt. Soc. Am. A 10, 447–491 (1993).

Schmitt, J. M.

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of size parameters,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Solomon, C. J.

C. J. Solomon, J. C. Dainty, “Use of polarization in double-passage imaging through a random screen,” Opt. Commun. 87, 207–211 (1992).
[CrossRef]

Strafford, D.

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

Van der Mark, M. B.

M. P. Albada, M. B. Van der Mark, A. Lagendjik, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2358 (1987).
[CrossRef]

Appl. Opt.

Europhys. Lett.

R. Berkovitz, M. Kaveh, “The vector memory effect for waves,” Europhys. Lett. 13, 97–101 (1992).
[CrossRef]

Int. J. Mod. Phys. B

W. I. Kordonski, S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10, 2937–2948 (1996).
[CrossRef]

J. Opt. (Paris)

M. Dogariu, T. Asakura, “Polarization dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

J. Opt. Soc. Am. A

D. Elyiahu, M. Rosenbluh, I. Freund, “Angular intensity and polarization dependence of diffuse transmission through random media,” J. Opt. Soc. Am. A 10, 447–491 (1993).

J. Phys. I (Paris)

D. Bicout, E. Akkermans, R. Maynard, “Dynamical correlations from multiple light scattering in laminar flow,” J. Phys. I (Paris) 1, 471–491 (1991).

Opt. Commun.

M. Dogariu, T. Asakura, “Polarized light scattering in dielectric layers with rough interfaces,” Opt. Commun. 131, 1–7 (1996).
[CrossRef]

C. J. Solomon, J. C. Dainty, “Use of polarization in double-passage imaging through a random screen,” Opt. Commun. 87, 207–211 (1992).
[CrossRef]

Opt. Eng.

M. Dogariu, T. Asakura, “Photon pathlength distribution from polarized backscattering in random media,” Opt. Eng. 35, 2234–2239 (1996).
[CrossRef]

Phys. Rev. B

M. P. Albada, M. B. Van der Mark, A. Lagendjik, “Vector character of light in weak localization: spatial anisotropy in coherent backscattering from a random medium,” Phys. Rev. B 36, 2353–2358 (1987).
[CrossRef]

Phys. Rev. E

D. Bicout, C. Brosseau, A. S. Martinez, J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: influence of size parameters,” Phys. Rev. E 49, 1767–1770 (1994).
[CrossRef]

Other

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Pucherbner, D. Strafford, W. I. Kordonski, I. V. Prohorov, E. Fess, D. Pietrowski, V. W. Kordonski, “Magnetorheological finishing a deterministic process for optics manufacturing,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 372–382 (1995).
[CrossRef]

I. V. Prohorov, W. I. Kordonski, L. K. Gleb, G. R. Gorodkin, M. L. Levin, “New high precision magnetorheological instrument-based method of polishing optics,” in Optical Fabrication and Testing, Vol. 24 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 135–136.

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

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Figures (5)

Fig. 1
Fig. 1

Experimental setup used to record polarization return pattern from media with high absorption.

Fig. 2
Fig. 2

Contours of equal intensity in backscattering from highly absorbant media. The penetration depths in panels a, b, c, and d are 7, 12, 20, and 40 µm, respectively. The scales are in millimeters.

Fig. 3
Fig. 3

Schematic of an in-plane, multiple-scattering sequence developed inside a dielectric layer in contact with a strongly absorbant medium.

Fig. 4
Fig. 4

Geometrical depolarization determined by two cornerlike scattering events.

Fig. 5
Fig. 5

Contours of equal intensity as derived from Eq. (5) for 〈cos γ〉 proportional to the penetration depths in Fig. 4.

Equations (5)

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

EoutexEoutsin 2φ+eyEoutcos 2φ,
IoutφEout221-cos 4φ.
Eout=Eout sin2φ+γ.
Iout=Eout2/21+1-2cos2 γ×cos 4φ+sin 2γsin 4φ.
Iout=Eout2/21+1-2cos2 γcos 4φ.

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