Abstract

The pseudo-spectral time domain (PSTD) and the discrete dipole approximation (DDA) are two popular and robust methods for the numerical simulation of dielectric particle light scattering. The present study compares the numerical performances of the two methods in the computation of the single-scattering properties of homogeneous dielectric spheres and spheroids for which the exact solutions can be obtained from the Lorenz-Mie theory and the T-matrix theory. The accuracy criteria for the extinction efficiency and the phase function are prescribed to be the same for the PSTD and DDA in order that the computational time can be compared in a fair manner. The computational efficiency and applicability of the two methods are each shown to depend on both the size parameter and the refractive index of the scattering particle. For a small refractive index, a critical size parameter, which decreases from 80 to 30 as the refractive index increases from 1.2 to 1.4, exists below which the DDA outperforms the PSTD. For large refractive indices (>1.4), the PSTD is more efficient than the DDA for a wide size parameter range and has a larger region of applicability. Furthermore, the accuracy shown by the two methods in the computation of backscatter, linear polarization, and asymmetry factor is comparable. The comparison was extended to include spheroids with typical refractive indices of ice and dust and similar conclusions were drawn.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
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  8. M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: An overview and recent developments,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 558–589 (2007).
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  9. Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, “Zero-backscatter cloak for aspherical particles using a generalized DDA formalism,” Opt. Express16(3), 2068–2079 (2008).
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  10. P. C. Chaumet and A. Rahmani, “Coupled-dipole method for magnetic and negative-refraction materials,” J. Quant. Spectrosc. Radiat. Transf.110(1-2), 22–29 (2009).
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  11. R. Alcaraz de la Osa, P. Albella, J. M. Saiz, F. González, and F. Moreno, “Extended discrete dipole approximation and its application to bianisotropic media,” Opt. Express18(23), 23865–23871 (2010).
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    [CrossRef] [PubMed]
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    [CrossRef]
  25. Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antenn. Propag.43(12), 1460–1463 (1995).
    [CrossRef]
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    [CrossRef]
  27. K. V. Gilev, E. Eremina, M. A. Yurkin, and V. P. Maltsev, “Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells,” Opt. Express18(6), 5681–5690 (2010).
    [CrossRef] [PubMed]
  28. S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: A revised compilation,” J. Geophys. Res.113(D14), D14220 (2008), doi:.
    [CrossRef]
  29. O. Muñoz, F. Moreno, D. Guirado, D. D. Dabrowska, H. Volten, and J. W. Hovenier, “The Amsterdam-Granada light scattering database,” J. Quant. Spectrosc. Radiat. Transf.113(7), 565–574 (2012).
    [CrossRef]
  30. B. Piller and O. J. F. Martin, “Increasing the performance of the coupled-dipole approximation: A spectral approach,” IEEE Trans. Antenn. Propag.46(8), 1126–1137 (1998).
    [CrossRef]
  31. M. A. Yurkin, M. Min, and A. G. Hoekstra, “Application of the discrete dipole approximation to very large refractive indices: Filtered coupled dipoles revived,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.82(3 Pt 2), 036703 (2010).
    [CrossRef] [PubMed]
  32. A. Bunse-Gerstner and R. Stover, “On a conjugate gradient-type method for solving complex symmetric linear systems,” Lin. Alg. Appl.287(1-3), 105–123 (1999).
    [CrossRef]
  33. I. Ayranci, R. Vaillon, and N. Selcuk, “Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles,” J. Quant. Spectrosc. Radiat. Transf.103(1), 83–101 (2007).
    [CrossRef]

2012

C. Liu, R. Lee Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properites for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Transf.113(13), 1728–1740 (2012).
[CrossRef]

O. Muñoz, F. Moreno, D. Guirado, D. D. Dabrowska, H. Volten, and J. W. Hovenier, “The Amsterdam-Granada light scattering database,” J. Quant. Spectrosc. Radiat. Transf.113(7), 565–574 (2012).
[CrossRef]

2011

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: Capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf.112(13), 2234–2247 (2011).
[CrossRef]

2010

2009

P. C. Chaumet and A. Rahmani, “Coupled-dipole method for magnetic and negative-refraction materials,” J. Quant. Spectrosc. Radiat. Transf.110(1-2), 22–29 (2009).
[CrossRef]

2008

2007

P. Zhai, C. Li, G. W. Kattawar, and P. Yang, “FDTD far-field scattering amplitudes: Comparison of surface and volume integration methods,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 590–594 (2007).
[CrossRef]

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express15(26), 17902–17911 (2007).
[CrossRef] [PubMed]

I. Ayranci, R. Vaillon, and N. Selcuk, “Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles,” J. Quant. Spectrosc. Radiat. Transf.103(1), 83–101 (2007).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 546–557 (2007).
[CrossRef]

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: An overview and recent developments,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 558–589 (2007).
[CrossRef]

2005

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE93(2), 216–231 (2005).
[CrossRef]

2000

1999

W. Sun, Q. Fu, and Z. Chen, “Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition,” Appl. Opt.38(15), 3141–3151 (1999).
[CrossRef] [PubMed]

A. Bunse-Gerstner and R. Stover, “On a conjugate gradient-type method for solving complex symmetric linear systems,” Lin. Alg. Appl.287(1-3), 105–123 (1999).
[CrossRef]

1998

B. Piller and O. J. F. Martin, “Increasing the performance of the coupled-dipole approximation: A spectral approach,” IEEE Trans. Antenn. Propag.46(8), 1126–1137 (1998).
[CrossRef]

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transf.60(3), 309–324 (1998).
[CrossRef]

1997

Q. H. Liu, “The PSTD algorithm: A time-domain method requiring only two cells per wavelength,” Microw. Opt. Technol. Lett.15(3), 158–165 (1997).
[CrossRef]

1996

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transf.55(5), 535–575 (1996).
[CrossRef]

P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A13(10), 2072–2085 (1996).
[CrossRef]

1995

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antenn. Propag.43(12), 1460–1463 (1995).
[CrossRef]

1994

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.114(2), 185–200 (1994).
[CrossRef]

1988

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J.333, 848–872 (1988).
[CrossRef]

1973

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J.186, 705–714 (1973).
[CrossRef]

1966

K. S. Yee, “Numerical solutin of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

1908

G. Mie, “Beitrȁge zur optik trȕber medien, speziell kolloidaler metallȍsungen,” Ann. Phys.330(3), 377–445 (1908).
[CrossRef]

Albella, P.

Alcaraz de la Osa, R.

Ayranci, I.

I. Ayranci, R. Vaillon, and N. Selcuk, “Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles,” J. Quant. Spectrosc. Radiat. Transf.103(1), 83–101 (2007).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.114(2), 185–200 (1994).
[CrossRef]

Brandt, R. E.

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: A revised compilation,” J. Geophys. Res.113(D14), D14220 (2008), doi:.
[CrossRef]

Brock, R. S.

Bunse-Gerstner, A.

A. Bunse-Gerstner and R. Stover, “On a conjugate gradient-type method for solving complex symmetric linear systems,” Lin. Alg. Appl.287(1-3), 105–123 (1999).
[CrossRef]

Chaumet, P. C.

P. C. Chaumet and A. Rahmani, “Coupled-dipole method for magnetic and negative-refraction materials,” J. Quant. Spectrosc. Radiat. Transf.110(1-2), 22–29 (2009).
[CrossRef]

Chen, G.

Chen, Z.

Dabrowska, D. D.

O. Muñoz, F. Moreno, D. Guirado, D. D. Dabrowska, H. Volten, and J. W. Hovenier, “The Amsterdam-Granada light scattering database,” J. Quant. Spectrosc. Radiat. Transf.113(7), 565–574 (2012).
[CrossRef]

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J.333, 848–872 (1988).
[CrossRef]

Eremina, E.

Frigo, M.

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE93(2), 216–231 (2005).
[CrossRef]

Fu, Q.

Gilev, K. V.

González, F.

Guirado, D.

O. Muñoz, F. Moreno, D. Guirado, D. D. Dabrowska, H. Volten, and J. W. Hovenier, “The Amsterdam-Granada light scattering database,” J. Quant. Spectrosc. Radiat. Transf.113(7), 565–574 (2012).
[CrossRef]

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: Capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf.112(13), 2234–2247 (2011).
[CrossRef]

M. A. Yurkin, M. Min, and A. G. Hoekstra, “Application of the discrete dipole approximation to very large refractive indices: Filtered coupled dipoles revived,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.82(3 Pt 2), 036703 (2010).
[CrossRef] [PubMed]

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express15(26), 17902–17911 (2007).
[CrossRef] [PubMed]

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: An overview and recent developments,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 558–589 (2007).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 546–557 (2007).
[CrossRef]

Hovenier, J. W.

O. Muñoz, F. Moreno, D. Guirado, D. D. Dabrowska, H. Volten, and J. W. Hovenier, “The Amsterdam-Granada light scattering database,” J. Quant. Spectrosc. Radiat. Transf.113(7), 565–574 (2012).
[CrossRef]

Johnson, S. G.

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE93(2), 216–231 (2005).
[CrossRef]

Kattawar, G. W.

Kingsland, D. M.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antenn. Propag.43(12), 1460–1463 (1995).
[CrossRef]

Lee, J.-F.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antenn. Propag.43(12), 1460–1463 (1995).
[CrossRef]

Lee, R.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antenn. Propag.43(12), 1460–1463 (1995).
[CrossRef]

Lee Panetta, R.

C. Liu, R. Lee Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properites for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Transf.113(13), 1728–1740 (2012).
[CrossRef]

Li, C.

P. Zhai, C. Li, G. W. Kattawar, and P. Yang, “FDTD far-field scattering amplitudes: Comparison of surface and volume integration methods,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 590–594 (2007).
[CrossRef]

Liou, K. N.

Liu, C.

C. Liu, R. Lee Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properites for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Transf.113(13), 1728–1740 (2012).
[CrossRef]

Liu, Q. H.

Q. H. Liu, “The PSTD algorithm: A time-domain method requiring only two cells per wavelength,” Microw. Opt. Technol. Lett.15(3), 158–165 (1997).
[CrossRef]

Lu, J. Q.

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transf.55(5), 535–575 (1996).
[CrossRef]

Maltsev, V. P.

K. V. Gilev, E. Eremina, M. A. Yurkin, and V. P. Maltsev, “Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells,” Opt. Express18(6), 5681–5690 (2010).
[CrossRef] [PubMed]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 546–557 (2007).
[CrossRef]

Martin, O. J. F.

B. Piller and O. J. F. Martin, “Increasing the performance of the coupled-dipole approximation: A spectral approach,” IEEE Trans. Antenn. Propag.46(8), 1126–1137 (1998).
[CrossRef]

Mie, G.

G. Mie, “Beitrȁge zur optik trȕber medien, speziell kolloidaler metallȍsungen,” Ann. Phys.330(3), 377–445 (1908).
[CrossRef]

Min, M.

M. A. Yurkin, M. Min, and A. G. Hoekstra, “Application of the discrete dipole approximation to very large refractive indices: Filtered coupled dipoles revived,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.82(3 Pt 2), 036703 (2010).
[CrossRef] [PubMed]

Mishchenko, M. I.

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transf.60(3), 309–324 (1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transf.55(5), 535–575 (1996).
[CrossRef]

Moreno, F.

O. Muñoz, F. Moreno, D. Guirado, D. D. Dabrowska, H. Volten, and J. W. Hovenier, “The Amsterdam-Granada light scattering database,” J. Quant. Spectrosc. Radiat. Transf.113(7), 565–574 (2012).
[CrossRef]

R. Alcaraz de la Osa, P. Albella, J. M. Saiz, F. González, and F. Moreno, “Extended discrete dipole approximation and its application to bianisotropic media,” Opt. Express18(23), 23865–23871 (2010).
[CrossRef] [PubMed]

Muñoz, O.

O. Muñoz, F. Moreno, D. Guirado, D. D. Dabrowska, H. Volten, and J. W. Hovenier, “The Amsterdam-Granada light scattering database,” J. Quant. Spectrosc. Radiat. Transf.113(7), 565–574 (2012).
[CrossRef]

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J.186, 705–714 (1973).
[CrossRef]

Piller, B.

B. Piller and O. J. F. Martin, “Increasing the performance of the coupled-dipole approximation: A spectral approach,” IEEE Trans. Antenn. Propag.46(8), 1126–1137 (1998).
[CrossRef]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J.186, 705–714 (1973).
[CrossRef]

Rahmani, A.

P. C. Chaumet and A. Rahmani, “Coupled-dipole method for magnetic and negative-refraction materials,” J. Quant. Spectrosc. Radiat. Transf.110(1-2), 22–29 (2009).
[CrossRef]

Sacks, Z. S.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antenn. Propag.43(12), 1460–1463 (1995).
[CrossRef]

Saiz, J. M.

Selcuk, N.

I. Ayranci, R. Vaillon, and N. Selcuk, “Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles,” J. Quant. Spectrosc. Radiat. Transf.103(1), 83–101 (2007).
[CrossRef]

Stover, R.

A. Bunse-Gerstner and R. Stover, “On a conjugate gradient-type method for solving complex symmetric linear systems,” Lin. Alg. Appl.287(1-3), 105–123 (1999).
[CrossRef]

Sun, W.

Travis, L. D.

M. I. Mishchenko and L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transf.60(3), 309–324 (1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transf.55(5), 535–575 (1996).
[CrossRef]

Vaillon, R.

I. Ayranci, R. Vaillon, and N. Selcuk, “Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles,” J. Quant. Spectrosc. Radiat. Transf.103(1), 83–101 (2007).
[CrossRef]

Volten, H.

O. Muñoz, F. Moreno, D. Guirado, D. D. Dabrowska, H. Volten, and J. W. Hovenier, “The Amsterdam-Granada light scattering database,” J. Quant. Spectrosc. Radiat. Transf.113(7), 565–574 (2012).
[CrossRef]

Warren, S. G.

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: A revised compilation,” J. Geophys. Res.113(D14), D14220 (2008), doi:.
[CrossRef]

Yang, P.

C. Liu, R. Lee Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properites for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Transf.113(13), 1728–1740 (2012).
[CrossRef]

Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, “Zero-backscatter cloak for aspherical particles using a generalized DDA formalism,” Opt. Express16(3), 2068–2079 (2008).
[CrossRef] [PubMed]

G. Chen, P. Yang, and G. W. Kattawar, “Application of the pseudospectral time-domain method to the scattering of light by nonspherical particles,” J. Opt. Soc. Am. A25(3), 785–790 (2008).
[CrossRef] [PubMed]

P. Zhai, C. Li, G. W. Kattawar, and P. Yang, “FDTD far-field scattering amplitudes: Comparison of surface and volume integration methods,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 590–594 (2007).
[CrossRef]

P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A13(10), 2072–2085 (1996).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solutin of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

You, Y.

Yurkin, M. A.

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: Capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf.112(13), 2234–2247 (2011).
[CrossRef]

K. V. Gilev, E. Eremina, M. A. Yurkin, and V. P. Maltsev, “Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells,” Opt. Express18(6), 5681–5690 (2010).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

The relative performances of the PSTD and DDA on the (x, m) plane. The light area corresponds to the DDA-preferred region and the dark area to the PSTD-preferred region.

Fig. 2
Fig. 2

Comparison of the PSTD and DDA results with the exact (Lorenz-Mie) solutions for simulation of P11 (left panel) for spheres with x = 40 and a refractive index increase from 1.2 to 2.0 from the top to lower panel. The right panels show the relative errors.

Fig. 3
Fig. 3

Same as Fig. 2 but for P12/P11 (left panels) and the absolute errors (right panels).

Fig. 4
Fig. 4

Same as Fig. 2 but for spheroids with x = 30, aspect ratios of 0.5 and 2.0, and refractive indices of 1.312 + 1.489 × 10−9i and 1.55 + 0.001i.

Fig. 5
Fig. 5

Same as Fig. 4 but for P12/P11 (left panels) and the absolute errors (right panels).

Tables (3)

Tables Icon

Table 1 The Comparison of Numerical Performances of the PSTD and ADDA Methods for Spheres with Different x and m.

Tables Icon

Table 2 Same as Table 1 but for Some Accuracy Results

Tables Icon

Table 3 Same as Table 1 but for Spheroids with Size Parameters from 10 to 50, Aspect Ratios of 0.5 and 2.0, and Refractive Indices of 1.313 + 1.489 × 10−9i and 1.55 + 0.001i.

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