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

JOSA A, Vol. 27, Issue 6, pp. 1404-1412 (2010)

http://dx.doi.org/10.1364/JOSAA.27.001404

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### 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

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### References

- J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).
- 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]
- 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]
- 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]
- H. S. Sözüer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994). [CrossRef]
- K. Ohtaka, “Scattering theory of low-energy photon diffraction,” J. Phys. C 13, 667–680 (1980). [CrossRef]
- A. Modinos, “Scattering of electromagnetic waves by a plane of spheres—formalism,” Physica A 141, 575–588 (1987). [CrossRef]
- P. A. Martin, Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles (Cambridge Univ. Press, 2006).
- M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).
- 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]
- N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys. Condens. Matter 4, 7389–7400 (1992). [CrossRef]
- 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]
- N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998). [CrossRef]
- 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]
- L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997). [CrossRef]
- 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).
- 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]
- 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]
- C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (SIAM, 1995). [CrossRef]

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