Abstract

The discrete dipole approximation (DDA) has been widely used to study light scattering by nonmagnetic objects. The electric field inside an arbitrary scatterer is found by solving a dense, symmetric, linear system using, in general, an iterative approach. However, when the scatterer has a nonzero magnetic susceptibility, the linear system becomes nonsymmetric, and some of the most commonly used iterative methods fail to work. We study the scattering of light by objects with both electric and magnetic linear responses and discuss the efficiency of several iterative solvers for the nonsymmetric DDA.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (2)

P. C. Chaumet and A. Rahmani, J. Quant. Spectrosc. Radiat. Transf. 110, 22 (2009).
[CrossRef]

P. C. Chaumet and A. Rahmani, Opt. Express 17, 2224 (2009).
[CrossRef] [PubMed]

2007 (1)

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
[CrossRef]

2006 (1)

Z. H. Fan, D. X. Wang, R. S. Chan, and E. K. N. Yung, Microwave Opt. Technol. Lett. 48, 1741 (2006).
[CrossRef]

2004 (2)

P. C. Chaumet, A. Sentenac, and A. Rahmani, Phys. Rev. E 70, 036606-6 (2004).
[CrossRef]

J. Tang, Y. Shen, Y. Zheng, and D. Qiu, Coastal Eng. 51, 143 (2004).
[CrossRef]

1997 (1)

1995 (1)

R. D. Da Cunha and T. Hopkins, Appl. Numer. Math. 19, 33 (1995).
[CrossRef]

1994 (2)

T. F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto, and C. H. Tong, SIAM J. Sci. Comput. (USA) 15, 338 (1994).
[CrossRef]

B. T. Draine and P. J. Flatau, J. Opt. Soc. Am. A 11, 1491 (1994).
[CrossRef]

1988 (1)

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

1975 (1)

G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
[CrossRef]

1973 (1)

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

Agarwal, G. S.

G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
[CrossRef]

Chan, R. S.

Z. H. Fan, D. X. Wang, R. S. Chan, and E. K. N. Yung, Microwave Opt. Technol. Lett. 48, 1741 (2006).
[CrossRef]

Chan, T. F.

T. F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto, and C. H. Tong, SIAM J. Sci. Comput. (USA) 15, 338 (1994).
[CrossRef]

Chaumet, P. C.

P. C. Chaumet and A. Rahmani, Opt. Express 17, 2224 (2009).
[CrossRef] [PubMed]

P. C. Chaumet and A. Rahmani, J. Quant. Spectrosc. Radiat. Transf. 110, 22 (2009).
[CrossRef]

P. C. Chaumet, A. Sentenac, and A. Rahmani, Phys. Rev. E 70, 036606-6 (2004).
[CrossRef]

Da Cunha, R. D.

R. D. Da Cunha and T. Hopkins, Appl. Numer. Math. 19, 33 (1995).
[CrossRef]

Draine, B. T.

Fan, Z. H.

Z. H. Fan, D. X. Wang, R. S. Chan, and E. K. N. Yung, Microwave Opt. Technol. Lett. 48, 1741 (2006).
[CrossRef]

Flatau, P. J.

Gallopoulos, E.

T. F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto, and C. H. Tong, SIAM J. Sci. Comput. (USA) 15, 338 (1994).
[CrossRef]

Hoekstra, A. G.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
[CrossRef]

Hopkins, T.

R. D. Da Cunha and T. Hopkins, Appl. Numer. Math. 19, 33 (1995).
[CrossRef]

Maltsev, V. P.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
[CrossRef]

Pennypacker, C. R.

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

Purcell, E. M.

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

Qiu, D.

J. Tang, Y. Shen, Y. Zheng, and D. Qiu, Coastal Eng. 51, 143 (2004).
[CrossRef]

Rahmani, A.

P. C. Chaumet and A. Rahmani, Opt. Express 17, 2224 (2009).
[CrossRef] [PubMed]

P. C. Chaumet and A. Rahmani, J. Quant. Spectrosc. Radiat. Transf. 110, 22 (2009).
[CrossRef]

P. C. Chaumet, A. Sentenac, and A. Rahmani, Phys. Rev. E 70, 036606-6 (2004).
[CrossRef]

Saad, Y.

Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, 2003).

Sentenac, A.

P. C. Chaumet, A. Sentenac, and A. Rahmani, Phys. Rev. E 70, 036606-6 (2004).
[CrossRef]

Shen, Y.

J. Tang, Y. Shen, Y. Zheng, and D. Qiu, Coastal Eng. 51, 143 (2004).
[CrossRef]

Simoncini, V.

T. F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto, and C. H. Tong, SIAM J. Sci. Comput. (USA) 15, 338 (1994).
[CrossRef]

Szeto, T.

T. F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto, and C. H. Tong, SIAM J. Sci. Comput. (USA) 15, 338 (1994).
[CrossRef]

Tang, J.

J. Tang, Y. Shen, Y. Zheng, and D. Qiu, Coastal Eng. 51, 143 (2004).
[CrossRef]

Tong, C. H.

T. F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto, and C. H. Tong, SIAM J. Sci. Comput. (USA) 15, 338 (1994).
[CrossRef]

Wang, D. X.

Z. H. Fan, D. X. Wang, R. S. Chan, and E. K. N. Yung, Microwave Opt. Technol. Lett. 48, 1741 (2006).
[CrossRef]

Yung, E. K. N.

Z. H. Fan, D. X. Wang, R. S. Chan, and E. K. N. Yung, Microwave Opt. Technol. Lett. 48, 1741 (2006).
[CrossRef]

Yurkin, M. A.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
[CrossRef]

Zheng, Y.

J. Tang, Y. Shen, Y. Zheng, and D. Qiu, Coastal Eng. 51, 143 (2004).
[CrossRef]

Appl. Numer. Math. (1)

R. D. Da Cunha and T. Hopkins, Appl. Numer. Math. 19, 33 (1995).
[CrossRef]

Astrophys. J. (2)

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

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

Coastal Eng. (1)

J. Tang, Y. Shen, Y. Zheng, and D. Qiu, Coastal Eng. 51, 143 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Radiat. Transf. (2)

P. C. Chaumet and A. Rahmani, J. Quant. Spectrosc. Radiat. Transf. 110, 22 (2009).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, J. Quant. Spectrosc. Radiat. Transf. 106, 546 (2007).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

Z. H. Fan, D. X. Wang, R. S. Chan, and E. K. N. Yung, Microwave Opt. Technol. Lett. 48, 1741 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
[CrossRef]

Phys. Rev. E (1)

P. C. Chaumet, A. Sentenac, and A. Rahmani, Phys. Rev. E 70, 036606-6 (2004).
[CrossRef]

SIAM J. Sci. Comput. (USA) (1)

T. F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto, and C. H. Tong, SIAM J. Sci. Comput. (USA) 15, 338 (1994).
[CrossRef]

Other (1)

Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, 2003).

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Figures (3)

Fig. 1
Fig. 1

Number of MVPs versus ε = μ for a homogenous sphere (see text for detail). (a) The sphere has no absorption: Im ( ε ) = Im ( μ ) = 0 . (b) Im ( ε ) = Im ( μ ) = 1 .

Fig. 2
Fig. 2

Number of MVPs versus ε 1 = μ 2 ( ε 2 = μ 1 = 1 ) for an inhomogeneous sphere (see text for detail). (a) The sphere has no absorption. (b) Im ( ε 1 ) = Im ( μ 2 ) = 1 .

Fig. 3
Fig. 3

Sphere of radius a = 2 λ . (a) Im ( ε ) = Im ( μ ) = 1 . (b) Im ( ε 1 ) = Im ( μ 2 ) = 1

Equations (5)

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

E ( r i ) = E inc ( r i ) + j i [ G ee ( r i , r j ) α e ( r j ) E ( r j ) + G em ( r i , r j ) α m ( r j ) H ( r j ) ]
H ( r i ) = H inc ( r i ) + j i [ G me ( r i , r j ) α e ( r j ) E ( r j ) + G mm ( r i , r j ) α m ( r j ) H ( r j ) ] ,
A x = b ,
A = ( I 0 0 I ) ( M K K M ) ( α e 0 0 α m ) ,
r = A x * b b .

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