OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 25, Iss. 12 — Dec. 1, 2008
  • pp: 2991–3000

Scattering of an electromagnetic plane wave by a Luneburg lens. III. Finely stratified sphere model

James A. Lock  »View Author Affiliations


JOSA A, Vol. 25, Issue 12, pp. 2991-3000 (2008)
http://dx.doi.org/10.1364/JOSAA.25.002991


View Full Text Article

Enhanced HTML    Acrobat PDF (474 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The parallel iteration procedure for computing scattering by a multilayer sphere is described. The procedure uses a successive doubling strategy applied to four sets of multiple-scattering amplitudes, which is reminiscent of the fast Fourier transform (FFT) algorithm. The procedure is then used to calculate scattering of a plane wave by a modified Luneburg lens. The evolution of the transmission rainbow for the Luneburg lens parameter f > 1 into an orbiting ray for f = 1 and into a series of morphology-dependent resonances for f < 1 is studied, and various features of the scattered intensity as a function of scattering angle are commented on. It is found that some resonances are formed without the presence of an exterior centrifugal barrier to confine them.

© 2008 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(260.5740) Physical optics : Resonance
(290.4020) Scattering : Mie theory

ToC Category:
Scattering

History
Original Manuscript: July 30, 2008
Manuscript Accepted: September 11, 2008
Published: November 12, 2008

Citation
James A. Lock, "Scattering of an electromagnetic plane wave by a Luneburg lens. III. Finely stratified sphere model," J. Opt. Soc. Am. A 25, 2991-3000 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-12-2991


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. A. Lock, “Scattering of an electromagnetic plane wave by a Luneburg lens. I. Ray theory,” J. Opt. Soc. Am. A 25, 2971-2979 (2008). [CrossRef]
  2. J. A. Lock, “Scattering of an electromagnetic plane wave by a Luneburg lens. II. Wave theory,” J. Opt. Soc. Am. A 25, 2980-2990 (2008). [CrossRef]
  3. O. B. Toon and T. P. Ackerman, “Algorithms for the calculation of scattering by stratified spheres,” Appl. Opt. 20, 3657-3660 (1981). [CrossRef] [PubMed]
  4. R. Bhandari, “Scattering coefficients for a multilayered sphere: analytic expressions and algorithms,” Appl. Opt. 24, 1960-1967 (1985). [CrossRef] [PubMed]
  5. D. W. Mackowski, R. A. Altenkirch, and M. P. Menguc, “Internal absorption cross sections in a stratified sphere,” Appl. Opt. 29, 1551-1559 (1990). [CrossRef] [PubMed]
  6. Z. S. Wu and Y. P. Wang, “Electromagnetic scattering for a multilayered sphere: recursive algorithms,” Radio Sci. 26, 1393-1401 (1991). [CrossRef]
  7. L. Kai and P. Massoli, “Scattering of electromagnetic-plane waves by radially inhomogeneous spheres: a finely stratified sphere model,” Appl. Opt. 33, 501-511 (1994). [CrossRef] [PubMed]
  8. B. R. Johnson, “Light scattering by a multilayer sphere,” Appl. Opt. 35, 3286-3296 (1996). [CrossRef] [PubMed]
  9. Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, and G. Grehan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188-5198 (1997). [CrossRef] [PubMed]
  10. J. A. Lock, “Debye series analysis of scattering of a plane wave by a spherical Bragg grating,” Appl. Opt. 44, 5594-5603 (2005). [CrossRef] [PubMed]
  11. R. C. Gonzalez, Digital Image Processing, 3rd ed. (Pearson/Prentice Hall, 2008), pp. 299-302.
  12. H. C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981), pp. 124-125.
  13. M.Abramowitz and I.A.Stegun, eds., Handbook of Mathematical Functions (National Bureau of Standards, 1964), p. 365, Eq. (9.3.1); p. 437, Eq. (10.1.1).
  14. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505-1509 (1980). [CrossRef] [PubMed]
  15. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983), pp. 127, 128, and 478.
  16. H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82-124 (1969). [CrossRef]
  17. H. C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981), pp. 176-178.
  18. H. C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981), pp. 209-210.
  19. P. Chylek, “Partial-wave resonances and the ripple structure in the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285-287 (1976). [CrossRef]
  20. P. Chylek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229-2233 (1978). [CrossRef]
  21. C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585-1592 (1992). [CrossRef]
  22. P. Chylek, J. D. Pendleton, and R. G. Pinnick, “Internal and near-surface scattered field of a spherical particle at resonant conditions,” Appl. Opt. 24, 3940-3942 (1985). [CrossRef] [PubMed]
  23. M. Schneider and E. D. Hirleman, “Influence of internal refractive index gradients on size measurements of spherically symmetric particles by phase Doppler anemometry,” Appl. Opt. 33, 2379-2388 (1994). [CrossRef] [PubMed]
  24. J. P. A. J. van Beeck and M. L. Reithmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259-2266 (1996). [CrossRef] [PubMed]
  25. P. Massoli, “Rainbow refractometry applied to radially inhomogeneous spheres: the critical case of evaporating droplets,” Appl. Opt. 37, 3227-3235 (1998). [CrossRef]
  26. D. Q. Chowdhury, S. C. Hill, and P. W. Barber, “Morphology-dependent resonances in radially inhomogeneous spheres,” J. Opt. Soc. Am. A 8, 1702-1705 (1991). [CrossRef]
  27. K. M. Lee, P. T. Leung, and K. M. Pang, “Iterative perturbation scheme for morphology-dependent resonances in dielectric spheres,” J. Opt. Soc. Am. A 15, 1383-1393 (1998). [CrossRef]
  28. P. L. Marston and E. Trinh, “Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops,” Nature 312, 529-531 (1984). [CrossRef]
  29. W. P. Arnott and P. L. Marston, “Unfolding axial caustics of glory scattering with harmonic angular perturbations of toroidal wave fronts,” J. Acoust. Soc. Am. 85, 1427-1440 (1989). [CrossRef]
  30. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187-5198 (1990). [CrossRef] [PubMed]
  31. J. A. Adam and P. Laven, “Rainbows from inhomogeneous transparent spheres: a ray-theoretic approach,” Appl. Opt. 46, 922-929 (2007). [CrossRef] [PubMed]
  32. C. L. Brockman and N. G. Alexopoulos, “Geometrical optics of inhomogeneous particles; glory ray and the rainbow revisited,” Appl. Opt. 16, 166-174 (1977). [CrossRef] [PubMed]
  33. A. Y. Perelman, “Scattering by particles with radially variable refractive indices,” Appl. Opt. 35, 5452-5460 (1996). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited