Abstract

The purpose of this work is to show that an appropriate multiple T-matrix formalism can be useful in performing qualitative studies of the optical properties of colloidal systems composed of nonspherical objects (despite limitations concerning nonspherical particle packing densities). In this work we have calculated the configuration averages of scattering and absorption cross sections of different clusters of dielectric particles. These clusters are characterized by their refraction index, particle shape, and filling fraction. Computations were performed with the recursive centered T-matrix algorithm (RCTMA), a previously established method for solving the multiple scattering equation of light from finite clusters of isotropic dielectric objects. Comparison of the average optical cross sections between the different systems highlights variations in the scattering and absorption properties due to the electromagnetic interactions, and we demonstrate that the magnitudes of these quantities are clearly modulated by the shape of the primary particles.

© 2007 Optical Society of America

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References

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2005 (1)

2003 (3)

J.-C. Auger and B. Stout, 'A recursive T-matrix algorithm to solve the multiple scattering equation: numerical validation,' J. Acoust. Soc. Am. 79-80, 533-547, (2003).

E. Zubkoa, Y. Shkuratova, M. Hart, J. Eversole, and G. Videen, 'Backscattering and negative polarization of agglomerate particles,' Opt. Lett. 28, 1504-1506 (2003).
[CrossRef]

J. Joshi, H. S. Shah, and R. V. Mehta, 'Application of multiflux theory based on scattering by nonspherical particles to the problem of modeling optical characteristics of pigmented paint film: part II,' Color Res. Appl. 28, 308-316 (2003).
[CrossRef]

2002 (2)

T. Wriedt, 'Using the T-Matrix method for light scattering computations by non-axisymmetric particles: superellipspoids and realistically shaped particles,' Part. Part. Syst. Charact. 19, 256-268 (2002).
[CrossRef]

B. Stout, J.-C. Auger, and J. Lafait, 'A transfer matrix approach to local field calculations in multiple-scattering problems,' J. Mod. Opt. 49, 2129-2152 (2002).
[CrossRef]

2001 (2)

B. Stout, J. C. Auger, and J. Lafait, 'Individual and aggregate scattering matrices and cross sections: conservation laws and reciprocity,' J. Mod. Opt. 48, 2105-2128 (2001).
[CrossRef]

F. M. Kahnert, J. J. Stamnes, and K. Stamnes, 'Application of the extended boundary condition method to homogeneous particles with point group symmetries,' Appl. Opt. 40, 3110-3123 (2001).
[CrossRef]

1998 (1)

1997 (1)

1996 (1)

1994 (1)

1991 (1)

1990 (1)

A.-K. Hamid, 'Electromagnetic scattering by an arbitrary configuration of dielectric spheres,' Can. J. Phys. 68, 1419-1428 (1990).
[CrossRef]

1988 (2)

K. A. Fuller, 'Consummate solution to the problem of classical electromagnetic scattering by an ensemble of spheres. I: Linear chains,' Opt. Lett. 13, 90-92 (1988).
[CrossRef] [PubMed]

B. T. Draine, 'The discrete-dipole approximation and its application to interstellar graphite grains,' Astrophys. J. 333, 848-872 (1988).
[CrossRef]

1981 (1)

1971 (1)

P. C. Waterman, 'Symmetry, unitary and geometry in electromagnetic scattering,' Phys. Rev. D 3, 825-839 (1971).
[CrossRef]

1962 (1)

O. R. Cruzan, 'Translation addition theorems for spherical vector wave functions,' Q. Appl. Math. 20, 33-40 (1962).

Appl. Opt. (3)

Astrophys. J. (1)

B. T. Draine, 'The discrete-dipole approximation and its application to interstellar graphite grains,' Astrophys. J. 333, 848-872 (1988).
[CrossRef]

Can. J. Phys. (1)

A.-K. Hamid, 'Electromagnetic scattering by an arbitrary configuration of dielectric spheres,' Can. J. Phys. 68, 1419-1428 (1990).
[CrossRef]

Color Res. Appl. (1)

J. Joshi, H. S. Shah, and R. V. Mehta, 'Application of multiflux theory based on scattering by nonspherical particles to the problem of modeling optical characteristics of pigmented paint film: part II,' Color Res. Appl. 28, 308-316 (2003).
[CrossRef]

J. Acoust. Soc. Am. (1)

J.-C. Auger and B. Stout, 'A recursive T-matrix algorithm to solve the multiple scattering equation: numerical validation,' J. Acoust. Soc. Am. 79-80, 533-547, (2003).

J. Mod. Opt. (2)

B. Stout, J. C. Auger, and J. Lafait, 'Individual and aggregate scattering matrices and cross sections: conservation laws and reciprocity,' J. Mod. Opt. 48, 2105-2128 (2001).
[CrossRef]

B. Stout, J.-C. Auger, and J. Lafait, 'A transfer matrix approach to local field calculations in multiple-scattering problems,' J. Mod. Opt. 49, 2129-2152 (2002).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Lett. (3)

Part. Part. Syst. Charact. (1)

T. Wriedt, 'Using the T-Matrix method for light scattering computations by non-axisymmetric particles: superellipspoids and realistically shaped particles,' Part. Part. Syst. Charact. 19, 256-268 (2002).
[CrossRef]

Phys. Rev. D (1)

P. C. Waterman, 'Symmetry, unitary and geometry in electromagnetic scattering,' Phys. Rev. D 3, 825-839 (1971).
[CrossRef]

Q. Appl. Math. (1)

O. R. Cruzan, 'Translation addition theorems for spherical vector wave functions,' Q. Appl. Math. 20, 33-40 (1962).

Other (4)

W. C. Chew, Waves and Field in Inhomogeneous Media, IEEE Press Series on Electromagnetic Waves (IEEE, 1990).

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

K. S. Kunz and R. J. Luebbers, Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge U. Press, 2002).

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Figures (9)

Fig. 1
Fig. 1

Spatial arrangements of aggregated nonspherical particles (a) without circumscribing sphere spatial constraints and (b) with circumscribing sphere spatial constraints.

Fig. 2
Fig. 2

Relations between the aspect ratio of the nonspherical particles and the maximum filling fraction obtainable for the system under the hypothesis of the smallest circumscribing spheres restriction (a) large aspect ratio (b) small aspect ratio.

Fig. 3
Fig. 3

Statistical treatment. (a) Representation of the extinction cross sections as function of the different random configurations of the system. (b) Gaussian adjustment from the previous set of data describing the probability for the system to possess a given value of the extinction cross section.

Fig. 4
Fig. 4

Frequency as a function of the extinction cross sections for the spherical, oblate, and prolate systems with index of refraction n p = 1.5 : (a) f p = 0.002 , (b) f p = 0.03 , (c) f p = 0.07 .

Fig. 5
Fig. 5

Frequency as function of the extinction cross sections for the spherical, oblate, and prolate systems with index of refraction n p = 2.8 : (a) f p = 0.002 , (b) f p = 0.03 , (c) f p = 0.07 .

Fig. 6
Fig. 6

Frequency as function of the scattering cross sections for the spherical, oblate, and prolate systems with index of refraction n p = 1.5 + i 1.0 : (a) f p = 0.002 , (b) f p = 0.03 , (c) f p = 0.07 .

Fig. 7
Fig. 7

Frequency as function of the absorption cross sections for the spherical, oblate, and prolate systems with index of refraction n p = 1.5 + i 1.0 : (a) f p = 0.002 , (b) f p = 0.03 , (c) f p = 0.07 .

Fig. 8
Fig. 8

Frequency as function of the scattering cross sections for the spherical, oblate, and prolate systems with index of refraction n p = 2.8 + i 1.0 : (a) f p = 0.002 , (b) f p = 0.03 , (c) f p = 0.07 .

Fig. 9
Fig. 9

Frequency as function of the absorption cross-sections for the spherical, oblate and prolate systems with index of refraction n p = 2.8 + i 1.0 : (a) f p = 0.002 , (b) f p = 0.03 , (c) f p = 0.07 .

Tables (8)

Tables Icon

Table 1 Values of the Average Extinction Cross Sections and Standard Deviations Obtained from Fig. 4 and Related to the Systems Having n p = 1.5

Tables Icon

Table 2 Values of the Average Extinction Cross Sections and Standard Deviations Obtained from Fig. 5 and Related to the Systems Having n p = 2.8

Tables Icon

Table 3 Values of the Average Absorption Cross Sections and Standard Deviation Obtained from Fig. 6 and Related to the Systems Having n p = 1.5 + i 1.0

Tables Icon

Table 4 Values of the Average Scattering Cross Sections and Standard Deviation Obtained from Fig. 7 and Related to the Systems Having n p = 1.5 + i 1.0

Tables Icon

Table 5 Values of the Average Absorption Cross Sections and Standard Deviation Obtained from Fig. 8 and Related to the Systems Having n p = 2.8 + i 1.0

Tables Icon

Table 6 Values of the Average Scattering Cross Sections and Standard Deviation Obtained from Fig. 9 and Related to the Systems Having n p = 2.8 + i 1.0

Tables Icon

Table 7 Values of the Average Extinction Cross Sections Assuming Independent Scatterers for the Three Systems Having n p = 1.5 and n p = 2.8

Tables Icon

Table 8 Values of the Average Scattering and Absorption Cross Sections Assuming Independent Scatterers for the Three Systems Having n p = 1.5 and n p = 2.8

Equations (5)

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E inc = E 0 n = 1 m = n n [ R g { Ψ 1 n m t ( k r ) } a 1 n m + R g { Ψ 2 n m t ( k r ) } a 2 n m ] E 0 R g { Ψ t ( k r ) } a ,
E sca ( i ) = E 0 n = 1 m = n n [ Ψ 1 n m t ( k r i ) f 1 n m ( i ) + Ψ 2 n m t ( k r i ) f 2 n m ( i ) ] E 0 Ψ t ( k r i ) f ( i ) ,
E exc ( i ) = R g { Ψ t ( k r i ) } [ J ( i , 0 ) a + j = 1 j i j = N H ( i , j ) f ( j ) ] R g { Ψ t ( k r i ) } e ( i ) ,
f ( i ) = T 1 ( i ) [ J ( i , 0 ) a + j = 1 j i j = N H ( i , j ) f ( j ) ] , i = 1 , , N .
T N ( i ) = T 1 ( i ) [ I + j = 1 j i N H ( i , j ) T N ( j ) J ( j , i ) ] , i = 1 , , N .

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