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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 10 — Oct. 1, 2006
  • pp: 2578–2591

Convergence of the discrete dipole approximation. I. Theoretical analysis

Maxim A. Yurkin, Valeri P. Maltsev, and Alfons G. Hoekstra  »View Author Affiliations


JOSA A, Vol. 23, Issue 10, pp. 2578-2591 (2006)
http://dx.doi.org/10.1364/JOSAA.23.002578


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Abstract

We perform a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear term and a quadratic term in the size of a dipole d when the latter is in the range of DDA applicability. Moreover, the linear term is significantly smaller for cubically than for noncubically shaped scatterers. Therefore, for small d, errors for cubically shaped particles are much smaller than for noncubically shaped ones. The relative importance of the linear term decreases with increasing size; hence convergence of DDA for large enough scatterers is quadratic in the common range of d. Extensive numerical simulations are carried out for a wide range of d. Finally, we discuss a number of new developments in DDA and their consequences for convergence.

© 2006 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(260.2110) Physical optics : Electromagnetic optics
(290.5850) Scattering : Scattering, particles

ToC Category:
Scattering

History
Original Manuscript: January 23, 2006
Manuscript Accepted: April 18, 2006

Citation
Maxim A. Yurkin, Valeri P. Maltsev, and Alfons G. Hoekstra, "Convergence of the discrete dipole approximation. I. Theoretical analysis," J. Opt. Soc. Am. A 23, 2578-2591 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-10-2578

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