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Applied Optics

Applied Optics


  • Vol. 37, Iss. 12 — Apr. 20, 1998
  • pp: 2483–2492

Controlled modification of the expansion order as a tool in Mie computations

Günther Roll, Thomas Kaiser, and Gustav Schweiger  »View Author Affiliations

Applied Optics, Vol. 37, Issue 12, pp. 2483-2492 (1998)

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In the framework of Mie theory the involved electromagnetic fields are expanded in an infinite series of multipoles. In numerical computations the summation has to be terminated after a finite number of terms (the expansion order N), which unavoidably produces errors. On the other hand, it is known that the contributions of terms of order l with x < l < N, where x is the dimensionless size parameter, are highly localized, i.e., these contributions appear as sharp peaks in resonance spectra. We show that it is possible to specify the expansion order in a controlled manner to extract certain features from Mie spectra. This controlled modification of the expansion order can be used as a high-pass, low-pass or bandpass filter. Formulas that serve as linewidth (frequency) and resonance-order filters are given, and their usage is demonstrated.

© 1998 Optical Society of America

OCIS Codes
(260.5740) Physical optics : Resonance
(290.0290) Scattering : Scattering
(290.3700) Scattering : Linewidth
(290.4020) Scattering : Mie theory

Original Manuscript: August 12, 1997
Revised Manuscript: December 18, 1997
Published: April 20, 1998

Günther Roll, Thomas Kaiser, and Gustav Schweiger, "Controlled modification of the expansion order as a tool in Mie computations," Appl. Opt. 37, 2483-2492 (1998)

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  1. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980). [CrossRef] [PubMed]
  2. V. Khare, “Short-wavelength scattering of electromagnetic waves by a homogeneous dielectric sphere,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1976).
  3. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Appendix A.
  4. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 4.
  5. S. C. Hill, R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), Chap. 1, pp. 1–63.
  6. M. L. Gorodetsky, A. A. Savchenkov, V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996). [CrossRef] [PubMed]
  7. G. Schweiger, “Raman scattering on microparticles: size dependence,” J. Opt. Soc. Am. B 8, 1770–1778 (1991). [CrossRef]
  8. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957), p. 208.
  9. B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993). [CrossRef]
  10. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, UK, 1992), Chap. 14. [CrossRef]
  11. C. C. Lam, P. T. Leung, K. Young, “Explicit asymptotic formulas for the positions, widths, and strength of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992). [CrossRef]
  12. M. Abramowitz, I. E. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), Chap. 10.
  13. J. B. Keller, “A geometrical theory of diffraction,” in Calculus of Variations and its Applications, Proceedings of Symposia in Applied Mathematics, L. M. Graves, ed. (McGraw-Hill, New York, 1958), Vol. 8. [CrossRef]
  14. P. Chyélek, “Resonance structure of Mie scattering: distance between resonances,” J. Opt. Soc. Am. A 7, 1609–1613 (1990). [CrossRef]
  15. J. B. Keller, S. I. Rubinow, “Asymptotic solution of eigenvalue problems,” Ann. Phys. (N.Y.) 9, 24–75 (1960). [CrossRef]

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