Abstract

We show how fast-Fourier-transform methods can be used to accelerate computations of scattering and absorption by particles of arbitrary shape using the discrete-dipole approximation.

© 1991 Optical Society of America

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References

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  1. E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
    [Crossref]
  2. B. T. Draine, Astrophys. J. 333, 848 (1988).
    [Crossref]
  3. G. H. Goedecke, S. G. O’Brien, Appl. Opt. 28, 2431 (1988).
    [Crossref]
  4. J. I. Hage, J. M. Greenberg, Astrophys. J. 361, 251 (1990).
    [Crossref]
  5. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).
  6. A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, in Applications of the CG Method in EM and Signal Processing, T. K. Sarkar, ed., PIER Series (North Holland/Elsevier, Amsterdam, 1991).
  7. N. M. Brenner, IEEE Trans. Audio Electroacoust. AU-17, 128 (1969).
    [Crossref]
  8. C. J. Temperton, J. Comp. Phys. 52, 1 (1983).
    [Crossref]
  9. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

1990 (1)

J. I. Hage, J. M. Greenberg, Astrophys. J. 361, 251 (1990).
[Crossref]

1988 (2)

B. T. Draine, Astrophys. J. 333, 848 (1988).
[Crossref]

G. H. Goedecke, S. G. O’Brien, Appl. Opt. 28, 2431 (1988).
[Crossref]

1983 (1)

C. J. Temperton, J. Comp. Phys. 52, 1 (1983).
[Crossref]

1973 (1)

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[Crossref]

1969 (1)

N. M. Brenner, IEEE Trans. Audio Electroacoust. AU-17, 128 (1969).
[Crossref]

Bohren, C. F.

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

Brenner, N. M.

N. M. Brenner, IEEE Trans. Audio Electroacoust. AU-17, 128 (1969).
[Crossref]

Chan, C. H.

A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, in Applications of the CG Method in EM and Signal Processing, T. K. Sarkar, ed., PIER Series (North Holland/Elsevier, Amsterdam, 1991).

Draine, B. T.

B. T. Draine, Astrophys. J. 333, 848 (1988).
[Crossref]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Goedecke, G. H.

G. H. Goedecke, S. G. O’Brien, Appl. Opt. 28, 2431 (1988).
[Crossref]

Greenberg, J. M.

J. I. Hage, J. M. Greenberg, Astrophys. J. 361, 251 (1990).
[Crossref]

Hage, J. I.

J. I. Hage, J. M. Greenberg, Astrophys. J. 361, 251 (1990).
[Crossref]

Huffman, D. R.

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

Mittra, R.

A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, in Applications of the CG Method in EM and Signal Processing, T. K. Sarkar, ed., PIER Series (North Holland/Elsevier, Amsterdam, 1991).

O’Brien, S. G.

G. H. Goedecke, S. G. O’Brien, Appl. Opt. 28, 2431 (1988).
[Crossref]

Pennypacker, C. R.

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[Crossref]

Peterson, A. F.

A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, in Applications of the CG Method in EM and Signal Processing, T. K. Sarkar, ed., PIER Series (North Holland/Elsevier, Amsterdam, 1991).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[Crossref]

Ray, S. L.

A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, in Applications of the CG Method in EM and Signal Processing, T. K. Sarkar, ed., PIER Series (North Holland/Elsevier, Amsterdam, 1991).

Temperton, C. J.

C. J. Temperton, J. Comp. Phys. 52, 1 (1983).
[Crossref]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Appl. Opt. (1)

G. H. Goedecke, S. G. O’Brien, Appl. Opt. 28, 2431 (1988).
[Crossref]

Astrophys. J. (3)

J. I. Hage, J. M. Greenberg, Astrophys. J. 361, 251 (1990).
[Crossref]

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973).
[Crossref]

B. T. Draine, Astrophys. J. 333, 848 (1988).
[Crossref]

IEEE Trans. Audio Electroacoust. (1)

N. M. Brenner, IEEE Trans. Audio Electroacoust. AU-17, 128 (1969).
[Crossref]

J. Comp. Phys. (1)

C. J. Temperton, J. Comp. Phys. 52, 1 (1983).
[Crossref]

Other (3)

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

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

A. F. Peterson, S. L. Ray, C. H. Chan, R. Mittra, in Applications of the CG Method in EM and Signal Processing, T. K. Sarkar, ed., PIER Series (North Holland/Elsevier, Amsterdam, 1991).

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Figures (5)

Fig. 1
Fig. 1

CPU time per iteration for cubes represented by different numbers of dipoles for two different computers and two different FFT routines.

Fig. 2
Fig. 2

Scattering by a sphere with refractive index m = 1.33 + 0.01i for x = ka = 5. Exact results for S11 are compared with S11 results computed using the DDA with different numbers of dipoles N.

Fig. 3
Fig. 3

Same as Fig. 2 but for x = 10 and also showing S11 for scattering by a cube of equal volume.

Fig. 4
Fig. 4

Same as Fig. 2 but for x = 15.

Fig. 5
Fig. 5

Same as Fig. 2 but for m = 3 + 4i

Tables (1)

Tables Icon

Table 1 Number of Iterations Required for a Cube

Equations (7)

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E inc . i = E 0 exp ( i k r i i ω t ) ,
E self , i = j i A i j P j .
( α i ) 1 P i + j i A i j P j = E inc , i .
A i j P j = exp ( i k r i j ) r i j 3 { k 2 r i j × ( r i j × P j ) + ( 1 i k r i j ) r i j 2 × [ r i j 2 P j 3 r i j ( r i j P j ) ] } ( j i ) .
A i j { A i - j if i j 0 if i = j .
Y i = j x = 0 2 N x j y = 0 2 N y j z = 0 2 N z A i - j X j j A i - j X j .
Y n i Y i exp [ i ( n x i x 2 N x + n y i y 2 N y + n z i z 2 N z ) ] .

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