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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 11 — Nov. 1, 2008
  • pp: 2693–2703

Discrete-dipole approximation for periodic targets: theory and tests

Bruce T. Draine and Piotr J. Flatau  »View Author Affiliations

JOSA A, Vol. 25, Issue 11, pp. 2693-2703 (2008)

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The discrete-dipole approximation (DDA) is a powerful method for calculating absorption and scattering by targets that have sizes smaller than or comparable to the wavelength of the incident radiation. The DDA can be extended to targets that are singly or doubly periodic. We generalize the scattering amplitude matrix and the 4 × 4 Mueller matrix to describe scattering by singly and doubly periodic targets and show how these matrices can be calculated using the DDA. The accuracy of DDA calculations using the open-source code DDSCAT is demonstrated by comparison with exact results for infinite cylinders and infinite slabs. A method for using the DDA solution to obtain fields within and near the target is presented, with results shown for infinite slabs.

© 2008 Optical Society of America

OCIS Codes
(260.0260) Physical optics : Physical optics
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(050.5298) Diffraction and gratings : Photonic crystals
(290.5825) Scattering : Scattering theory

ToC Category:
Diffraction and Gratings

Original Manuscript: June 24, 2008
Manuscript Accepted: August 19, 2008
Published: October 14, 2008

Bruce T. Draine and Piotr J. Flatau, "Discrete-dipole approximation for periodic targets: theory and tests," J. Opt. Soc. Am. A 25, 2693-2703 (2008)

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  1. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973). [CrossRef]
  2. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848-872 (1988). [CrossRef]
  3. B. T. Draine and P. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491-1499 (1994). [CrossRef]
  4. B. T. Draine, “The discrete dipole approximation for light scattering by irregular targets,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M.I.Mishchenko, J.W.Hovenier, and L.D.Travis, eds. (Academic, 2000), pp. 131-145.
  5. R. Schmehl, B. M. Nebeker, and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A 14, 3026-3036 (1997). [CrossRef]
  6. M. Paulus and O. J. F. Martin, “Green's tensor technique for scattering in two-dimensional stratified media,” Phys. Rev. E 63, 066615 (2001). [CrossRef]
  7. P. Yang and K. N. Liou, “Finite difference time domain method for light scattering by nonspherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M.I.Mishchenko, J.W.Hovenier, and L.D.Travis, eds. (Academic, 2000), pp. 173-221. [CrossRef]
  8. A. Taflove and S. C. Hagness, Advances in Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2005).
  9. V. A. Markel, “Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure,” J. Mod. Opt. 40, 2281-2291 (1993). [CrossRef]
  10. P. C. Chaumet, A. Rahmani, and G. W. Bryant, “Generalization of the coupled dipole method to periodic structures,” Phys. Rev. B 67, 165404 (2003). [CrossRef]
  11. P. C. Chaumet and A. Sentenac, “Numerical simulations of the electromagnetic field scattered by defects in a double-periodic structure,” Phys. Rev. B 72, 205437 (2005). [CrossRef]
  12. B. T. Draine and P. Flatau, “User Guide for the Discrete Dipole Approximation Code DDSCAT6.1,” http://arXiv.org/abs/astro-ph/0409262 (2004).
  13. B. T. Draine and J. Goodman, “Beyond Clausius-Mossotti--Wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685-697 (1993). [CrossRef]
  14. D. Gutkowicz-Krusin and B. T. Draine, “Propagation of electromagnetic waves on a rectangular lattice of polarizable points,” http://arXiv.org/abs/astro-ph/0403082 (2004).
  15. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  16. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  17. D. Mackowski, private communication (2007).
  18. Z. N. Utegulov, J. M. Shaw, B. T. Draine, S. A. Kim, and W. L. Johnson, “Surface-plasmon enhancement of Brillouin light scattering from gold-nanodisk arrays on glass,” Proc. SPIE 6641, 66411M (2007). [CrossRef]
  19. W. L. Johnson, S. A. Kim, Z. N. Utegulov, and B. T. Draine, “Surface-plasmon fields in two-dimensional arrays of gold nanodisks,” Proc. SPIE7032(2008) (to be published).
  20. http://www.astro.princeton.edu/~draine/DDSCAT.html (2008).
  21. M. A. Botchev, SUBROUTINE ZBCG2, http://www.math.uu.nl/people/vorst/zbcg2.f90 (2001).
  22. J. J. Goodman, B. T. Draine, and P. J. Flatau, “Application of fast-Fourier transform techniques to the discrete dipole approximation,” Opt. Lett. 16, 1198-1200 (1990). [CrossRef]
  23. B. T. Draine and P. Flatau, “User Guide for the Discrete Dipole Approximation Code DDSCAT 7.0,” http://arXiv.org/abs/0809.0337 (2008).
  24. http://ddscat.wikidot.com.

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