Abstract

Finite-difference time-domain numerical experiments and supporting analyses demonstrate that the spectral dependence of the total scattering cross sections of randomly inhomogeneous dielectric spheres of sizes in the resonant range closely resemble those of their homogeneous counterparts that have a volume-averaged refractive index. This result holds even for the extreme case in which the refractive index within an inhomogeneous sphere varies randomly over the range 1.0–2.0.

© 2003 Optical Society of America

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References

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  1. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, Calif., 2000).
  2. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  3. M. Kerker, The Scattering of Light (Academic, New York, 1969).
  4. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).
  5. P. Yang and K. N. Liou, J. Opt. Soc. Am. A 13, 2072 (1996).
    [CrossRef]
  6. A. Dunn and R. Richards-Kortum, IEEE J. Sel. Top. Quantum Electron. 2, 898 (1996).
    [CrossRef]
  7. J.-P. Berenger, J. Comput. Phys. 114, 185 (1994).
    [CrossRef]
  8. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN 77: The Art of Scientific Computing (Cambridge U. Press, New York, 1992).
  9. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  10. S. A. Ackerman and G. L. Stephens, J. Atmos. Sci. 44, 1574 (1987).
    [CrossRef]

1996

A. Dunn and R. Richards-Kortum, IEEE J. Sel. Top. Quantum Electron. 2, 898 (1996).
[CrossRef]

P. Yang and K. N. Liou, J. Opt. Soc. Am. A 13, 2072 (1996).
[CrossRef]

1994

J.-P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

1987

S. A. Ackerman and G. L. Stephens, J. Atmos. Sci. 44, 1574 (1987).
[CrossRef]

Ackerman, S. A.

S. A. Ackerman and G. L. Stephens, J. Atmos. Sci. 44, 1574 (1987).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Dunn, A.

A. Dunn and R. Richards-Kortum, IEEE J. Sel. Top. Quantum Electron. 2, 898 (1996).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN 77: The Art of Scientific Computing (Cambridge U. Press, New York, 1992).

Hagness, S.

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

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, Calif., 2000).

Ishimaru, A.

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

Kerker, M.

M. Kerker, The Scattering of Light (Academic, New York, 1969).

Liou, K. N.

Mishchenko, M. I.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, Calif., 2000).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN 77: The Art of Scientific Computing (Cambridge U. Press, New York, 1992).

Richards-Kortum, R.

A. Dunn and R. Richards-Kortum, IEEE J. Sel. Top. Quantum Electron. 2, 898 (1996).
[CrossRef]

Stephens, G. L.

S. A. Ackerman and G. L. Stephens, J. Atmos. Sci. 44, 1574 (1987).
[CrossRef]

Taflove, A.

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

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN 77: The Art of Scientific Computing (Cambridge U. Press, New York, 1992).

Travis, L. D.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, Calif., 2000).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN 77: The Art of Scientific Computing (Cambridge U. Press, New York, 1992).

Yang, P.

IEEE J. Sel. Top. Quantum Electron.

A. Dunn and R. Richards-Kortum, IEEE J. Sel. Top. Quantum Electron. 2, 898 (1996).
[CrossRef]

J. Atmos. Sci.

S. A. Ackerman and G. L. Stephens, J. Atmos. Sci. 44, 1574 (1987).
[CrossRef]

J. Comput. Phys.

J.-P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN 77: The Art of Scientific Computing (Cambridge U. Press, New York, 1992).

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

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, Calif., 2000).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

M. Kerker, The Scattering of Light (Academic, New York, 1969).

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

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Figures (3)

Fig. 1
Fig. 1

Typical assignment of randomly distributed refractive indices along a cut through the center of the 5-µm spherical particle; each FDTD grid cell has a size of 25 nm: (a) fine-grained and (b) coarse-grained inhomogeneity.

Fig. 2
Fig. 2

Total scattering cross section versus wavelength for 1.45n1.55. The ten FDTD simulations are represented by filled circles; the corresponding Mie result, by a dotted curve: (a) fine-grained and (b) coarse-grained inhomogeneity.

Fig. 3
Fig. 3

Total scattering cross section versus wavelength for 1.0n2.0. The two FDTD simulations are represented by the filled circles; corresponding Mie result, by a dotted curve: (a) fine-grained (b) coarse-grained inhomogeneity.

Equations (2)

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σsν=2 ReA1-expiξrd2r,
σs=2πd/221+2n0-1/ρ2/3-2n0 sin ρ/ρ+4n0 sin2ρ/2/ρ2+βρ,

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