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

  • Editor: Franco Gori
  • Vol. 27, Iss. 6 — Jun. 1, 2010
  • pp: 1404–1412

Improved spherical wave least squares method for analyzing periodic arrays of spheres

Huan Xie and Ya Yan Lu  »View Author Affiliations


JOSA A, Vol. 27, Issue 6, pp. 1404-1412 (2010)
http://dx.doi.org/10.1364/JOSAA.27.001404


View Full Text Article

Enhanced HTML    Acrobat PDF (189 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

For analyzing plane wave scattering from a multilayer periodic structure where each layer consists of a two-dimensional periodic array of spheres, a spherical wave least squares method is developed which extends and improves the earlier work by Matsushima et al. [PIER 69, 305 (2007)] . A number of techniques are used to speed up the method and to reduce the memory requirement. Spherical wave expansions are used in one unit cell containing a sphere in each layer, and quasi-periodic conditions are imposed on lateral surfaces of the unit cell in the least squares sense. Unlike the layer-Korringa–Kohn–Rostoker method [ Physica A 141, 575 (1987) ], the method does not need lattice sums and it is relatively simple to implement.

© 2010 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Diffraction and Gratings

History
Original Manuscript: February 10, 2010
Manuscript Accepted: April 23, 2010
Published: May 21, 2010

Citation
Huan Xie and Ya Yan Lu, "Improved spherical wave least squares method for analyzing periodic arrays of spheres," J. Opt. Soc. Am. A 27, 1404-1412 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-6-1404


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).
  2. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990). [CrossRef] [PubMed]
  3. E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991). [CrossRef] [PubMed]
  4. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994). [CrossRef]
  5. H. S. Sözüer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994). [CrossRef]
  6. K. Ohtaka, “Scattering theory of low-energy photon diffraction,” J. Phys. C 13, 667–680 (1980). [CrossRef]
  7. A. Modinos, “Scattering of electromagnetic waves by a plane of spheres—formalism,” Physica A 141, 575–588 (1987). [CrossRef]
  8. P. A. Martin, Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles (Cambridge Univ. Press, 2006).
  9. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).
  10. N. Stafanou and A. Modinos, “Scattering of light from a two-dimensional array of spherical particles on a substrate,” J. Phys. Condens. Matter 3, 8135–8148 (1991). [CrossRef]
  11. N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys. Condens. Matter 4, 7389–7400 (1992). [CrossRef]
  12. K. Ohtaka and Y. Tanabe, “Photonic bands using vector spherical waves. II. Reflectivity, coherence and local field,” J. Phys. Soc. Jpn. 65, 2276–2284 (1996). [CrossRef]
  13. N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998). [CrossRef]
  14. N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM 2: a new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000). [CrossRef]
  15. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997). [CrossRef]
  16. G. Bao, P. Li, and H. Wu, “An adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures,” Math. Comput. 70, 1–34 (2010).
  17. E. Popov and M. Nevière, “Maxwell equations in Fourier space: a fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001). [CrossRef]
  18. A. Matsushima, Y. Momoka, M. Ohtsu, and Y. Okuno, “Efficient numerical approach to electromagnetic scattering from three-dimensional periodic array of dielectric spheres using sequential accumulation,” PIER 69, 305–322 (2007). [CrossRef]
  19. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (SIAM, 1995). [CrossRef]

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited