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Applied Optics

Applied Optics


  • Vol. 42, Iss. 21 — Jul. 20, 2003
  • pp: 4381–4388

Method for integrating the absorption cross sections of spheres over wavelength or diameter

Steven C. Hill  »View Author Affiliations

Applied Optics, Vol. 42, Issue 21, pp. 4381-4388 (2003)

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The absorption cross sections of spherical particles and droplets must be integrated over frequency or droplet size or both for various applications. Morphology-dependent resonances (MDRs) of the spheres can make evaluation of such integrals difficult because the MDRs can contribute significantly to the integrals even when their linewidths are extremely narrow, especially when the absorption is weak. A method of evaluating these integrals by use of Lorentzian approximations near MDRs is described. Calculated frequency-integrated absorption cross sections illustrate how the method obtains accurate cross sections with far fewer integration points than a method that uses equally spaced points. The method reported here suggests a way to integrate over frequency in more-complicated scattering and emission problems and should also be useful for integrating scattering and absorption by other shapes, e.g., spheroids and cylinders, for which the MDR positions and linewidths can be calculated.

© 2003 Optical Society of America

OCIS Codes
(260.5740) Physical optics : Resonance
(290.1310) Scattering : Atmospheric scattering
(290.2200) Scattering : Extinction
(290.4020) Scattering : Mie theory
(290.5850) Scattering : Scattering, particles

Original Manuscript: December 18, 2002
Revised Manuscript: March 26, 2003
Published: July 20, 2003

Steven C. Hill, "Method for integrating the absorption cross sections of spheres over wavelength or diameter," Appl. Opt. 42, 4381-4388 (2003)

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