Accurate analysis of electromagnetic scattering from periodic circular cylinder array with defects

doi:10.1364/OE.20.010646

Accurate analysis of electromagnetic scattering from periodic circular cylinder array with defects

Koki Watanabe, Yoshimasa Nakatake, and Jaromír Pištora »View Author Affiliations

Optics Express, Vol. 20, Issue 10, pp. 10646-10657 (2012)
http://dx.doi.org/10.1364/OE.20.010646

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Abstract

This paper considers the two-dimensional electromagnetic scattering from periodic array of circular cylinders in which some cylinders are removed, and presents a formulation based on the recursive transition-matrix algorithm (RTMA). The RTMA was originally developed as an accurate approach to the scattering problem of a finite number of cylinders, and an approach to the problem of periodic cylinder array was then developed with the help of the lattice sums technique. This paper introduces the concept of the pseudo-periodic Fourier transform to the RTMA with the lattice sums technique, and proposes a spectral-domain approach to the problem of periodic cylinder array with defects.

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Diffraction and Gratings

History
Original Manuscript: January 26, 2012
Revised Manuscript: March 13, 2012
Manuscript Accepted: March 23, 2012
Published: April 24, 2012

Citation
Koki Watanabe, Yoshimasa Nakatake, and Jaromír Pištora, "Accurate analysis of electromagnetic scattering from periodic circular cylinder array with defects," Opt. Express 20, 10646-10657 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-10646

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References

S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics2, 52–56 (2007). [CrossRef]
J. Ouellette, “Seeing the future in photonic crystals,” Ind. Phys. 7, 14–17 (2001).
Ch. Kang and S. M. Weiss, “Photonic crystal with multi-hole defect for sensor applications,” Opt. Express16, 18188–18193 (2008). [CrossRef] [PubMed]
A. V. Giannopoulos, J. D. Sulkin, Ch. M. Long, J. J. Coleman, and K. D. Choquette, “Decimated photonic crystal defect cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 17, 1693–1694 (2011). [CrossRef]
W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).
D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A11, 2526–2538 (1994). [CrossRef]
H. Roussel, W. C. Chew, F. Jouvie, and W. Tabbara, “Electromagnetic scattering from dielectric and magnetic gratings of fibers — a T-matrix solution,” J. Electromagn. Waves Appl. 10, 109–127 (1996). [CrossRef]
K. Watanabe and K. Yasumoto, “Two-dimensional electromagnetic scattering of non-plane incident waves by periodic structures,” Prog. Electromagn. Res. PIER 74, 241–271 (2007). [CrossRef]
K. Watanabe and Y. Nakatake, “Spectral-domain formulation of electromagnetic scattering from circular cylinders located near periodic cylinder array,” Prog. Electromagn. Res. B31, 219–237 (2011).
K. Watanabe, J. Pištora, and Y. Nakatake, “Rigorous coupled-wave analysis of electromagnetic scattering from lamellar grating with defects,” Opt. Express19, 25799–25811 (2011). [CrossRef]
K. Watanabe, J. Pištora, and Y. Nakatake, “Coordinate transformation formulation of electromagnetic scattering from imperfectly periodic surfaces,” Opt. Express(to be published). [PubMed]
N. A. Nicorovici and R. C. McPhedran, “Lattice sums for off-axis electromagnetic scattering by gratings,” Phys. Rev. E50, 3143–3160 (1994). [CrossRef]
K. Yasumoto and K. Yoshitomi, “Efficient calculation of lattice sums for free-space periodic Green’s function,” IEEE Trans. Antennas Propag. 47, 1050–1055 (1999). [CrossRef]
C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989).

IEEE J. Sel. Top. Quantum Electron

A. V. Giannopoulos, J. D. Sulkin, Ch. M. Long, J. J. Coleman, and K. D. Choquette, “Decimated photonic crystal defect cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 17, 1693–1694 (2011). [CrossRef]

IEEE Trans. Antennas Propag

K. Yasumoto and K. Yoshitomi, “Efficient calculation of lattice sums for free-space periodic Green’s function,” IEEE Trans. Antennas Propag. 47, 1050–1055 (1999). [CrossRef]

Ind. Phys

J. Ouellette, “Seeing the future in photonic crystals,” Ind. Phys. 7, 14–17 (2001).

J. Electromagn. Waves Appl

H. Roussel, W. C. Chew, F. Jouvie, and W. Tabbara, “Electromagnetic scattering from dielectric and magnetic gratings of fibers — a T-matrix solution,” J. Electromagn. Waves Appl. 10, 109–127 (1996). [CrossRef]

J. Opt. Soc. Am. A

D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A11, 2526–2538 (1994). [CrossRef]

Nat. Photonics

S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics2, 52–56 (2007). [CrossRef]

Opt. Express

Phys. Rev. E

N. A. Nicorovici and R. C. McPhedran, “Lattice sums for off-axis electromagnetic scattering by gratings,” Phys. Rev. E50, 3143–3160 (1994). [CrossRef]

Prog. Electromagn. Res

K. Watanabe and K. Yasumoto, “Two-dimensional electromagnetic scattering of non-plane incident waves by periodic structures,” Prog. Electromagn. Res. PIER 74, 241–271 (2007). [CrossRef]

Prog. Electromagn. Res. B

K. Watanabe and Y. Nakatake, “Spectral-domain formulation of electromagnetic scattering from circular cylinders located near periodic cylinder array,” Prog. Electromagn. Res. B31, 219–237 (2011).

Other

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).
K. Watanabe, J. Pištora, and Y. Nakatake, “Coordinate transformation formulation of electromagnetic scattering from imperfectly periodic surfaces,” Opt. Express(to be published). [PubMed]
C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989).

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