Abstract

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The results point toward the emerging feasibility of direct, exact Maxwell equations modeling of light propagation through many millimeters of biological tissues. More generally, our results have a wider implication: Namely, the study of electromagnetic wave propagation within random media is moving toward exact rather than approximate solutions of Maxwell’s equations.

© 2004 Optical Society of America

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References

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  1. A. J. Welch and M. J. C. van Gemert, in Lasers, Photonics, and Electro-Optics, H. Kogelnik, ed. (Plenum, New York, 1995).
  2. G. Mie, Ann. Phys. (Leipzig) 25, 377 (1908).
    [CrossRef]
  3. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).
  4. R. Drezek, A. Dunn, and R. Richards-Kortum, Opt. Express 6, 147 (2000), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  5. Q. H. Liu, Microwave Opt. Technol. Lett. 15, 158 (1997).
    [CrossRef]
  6. Q. H. Liu, IEEE Trans. Geosci. Remote Sens. 37, 917 (1999).
    [CrossRef]
  7. S. D. Gedney, IEEE Trans. Antennas Propag. 44, 1630 (1996).
    [CrossRef]
  8. G. Zhao and Q. H. Liu, IEEE Trans. Antennas Propag. 51, 619 (2003).
    [CrossRef]

2003

G. Zhao and Q. H. Liu, IEEE Trans. Antennas Propag. 51, 619 (2003).
[CrossRef]

2000

1999

Q. H. Liu, IEEE Trans. Geosci. Remote Sens. 37, 917 (1999).
[CrossRef]

1997

Q. H. Liu, Microwave Opt. Technol. Lett. 15, 158 (1997).
[CrossRef]

1996

S. D. Gedney, IEEE Trans. Antennas Propag. 44, 1630 (1996).
[CrossRef]

1908

G. Mie, Ann. Phys. (Leipzig) 25, 377 (1908).
[CrossRef]

Drezek, R.

Dunn, A.

Gedney, S. D.

S. D. Gedney, IEEE Trans. Antennas Propag. 44, 1630 (1996).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

Liu, Q. H.

G. Zhao and Q. H. Liu, IEEE Trans. Antennas Propag. 51, 619 (2003).
[CrossRef]

Q. H. Liu, IEEE Trans. Geosci. Remote Sens. 37, 917 (1999).
[CrossRef]

Q. H. Liu, Microwave Opt. Technol. Lett. 15, 158 (1997).
[CrossRef]

Mie, G.

G. Mie, Ann. Phys. (Leipzig) 25, 377 (1908).
[CrossRef]

Richards-Kortum, R.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

van Gemert, M. J. C.

A. J. Welch and M. J. C. van Gemert, in Lasers, Photonics, and Electro-Optics, H. Kogelnik, ed. (Plenum, New York, 1995).

Welch, A. J.

A. J. Welch and M. J. C. van Gemert, in Lasers, Photonics, and Electro-Optics, H. Kogelnik, ed. (Plenum, New York, 1995).

Zhao, G.

G. Zhao and Q. H. Liu, IEEE Trans. Antennas Propag. 51, 619 (2003).
[CrossRef]

Ann. Phys. (Leipzig)

G. Mie, Ann. Phys. (Leipzig) 25, 377 (1908).
[CrossRef]

IEEE Trans. Antennas Propag.

S. D. Gedney, IEEE Trans. Antennas Propag. 44, 1630 (1996).
[CrossRef]

G. Zhao and Q. H. Liu, IEEE Trans. Antennas Propag. 51, 619 (2003).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

Q. H. Liu, IEEE Trans. Geosci. Remote Sens. 37, 917 (1999).
[CrossRef]

Microwave Opt. Technol. Lett.

Q. H. Liu, Microwave Opt. Technol. Lett. 15, 158 (1997).
[CrossRef]

Opt. Express

Other

A. J. Welch and M. J. C. van Gemert, in Lasers, Photonics, and Electro-Optics, H. Kogelnik, ed. (Plenum, New York, 1995).

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

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Figures (4)

Fig. 1
Fig. 1

PSTD-computed TSCS of a 160µm overall-diameter cylindrical bundle of 34 randomly positioned, noncontacting n=1.2 dielectric cylinders of individual diameter d. Four cases [(a)–(c)] are shown, with the position of each cylinder fixed. As d exceeds approximately 10 µm, the TSCS above 60 THz saturates.

Fig. 2
Fig. 2

 PSTD-computed TSCS of a 160µm overall-diameter cylindrical bundle of N randomly positioned, noncontacting n=1.2 dielectric cylinders of fixed individual diameter d=5 µm. Five cases [(a)–(e)] are shown. As N exceeds approximately 200, the TSCS above 60 THz saturates at the level indicated in Fig. 1.

Fig. 3
Fig. 3

PSTD-computed TSCS of a 160µm overall-diameter cylindrical bundle of N randomly positioned, noncontacting n=1.2 dielectric cylinders of fixed individual diameter d=10 µm. Five cases [(a)–(e)] are shown. As N exceeds approximately 50, the TSCS above 60 THz saturates at the same level as in Figs. 1 and 2.

Fig. 4
Fig. 4

PSTD-computed TSCSs of (a) a 160µm overall-diameter cylindrical bundle of 120 randomly positioned, noncontacting n=1.2 dielectric cylinders of individual diameter d=10 µm; (b) as in (a) but for 480 cylinders of individual diameter d=5 µm; (c) a single cylinder of refractive index n=1.0938, the average refractive index for (a) and (b).

Equations (3)

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

Vxi=-F-1jk˜xFVi,
μHscatt+σ*Hscat=-×Escat-σ*Hinc-μ-μ0Hinct,
Escatt+σEscat=×Hscat-σEinc--0Einct

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