Rigorous coupled-wave analysis of electromagnetic scattering from lamellar grating with defects

doi:10.1364/OE.19.025799

Rigorous coupled-wave analysis of electromagnetic scattering from lamellar grating with defects

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

Optics Express, Vol. 19, Issue 25, pp. 25799-25811 (2011)
http://dx.doi.org/10.1364/OE.19.025799

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Abstract

This paper proposes a spectral-domain approach to the electromagnetic scattering problem of lamellar grating with defects. The fields in imperfectly periodic structures have continuous spectra in the wavenumber space, and the main problem of the spectral-domain approach is connected to the discretization scheme on the wavenumber. The present approach introduces the pseudo-periodic Fourier transform to consider the discretization scheme in the Brillouin zone. This transformation also makes it possible to apply the conventional grating formulations to the problems of imperfectly periodic structures. The present formulation is based on the rigorous coupled-wave analysis with the help of pseudo-periodic Fourier transform.

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: September 2, 2011
Revised Manuscript: October 7, 2011
Manuscript Accepted: October 10, 2011
Published: December 2, 2011

Citation
Koki Watanabe, Jaromír Pištora, and Yoshimasa Nakatake, "Rigorous coupled-wave analysis of electromagnetic scattering from lamellar grating with defects," Opt. Express 19, 25799-25811 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25799

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References

O. Manyardo, R. Michaely, F. Schädelin, W. Noell, T. Overstolz, N. De Rooij, and H. P. Herzig, “Miniature lamellar grating interferometer based on silicon technology,” Opt. Lett.29, 1437–1439 (2004). [CrossRef]
Y. Hongbin, Z. Guangya, Ch. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” J. Micromech. Microeng.18, 055016 (2008). [CrossRef]
A. Sato, “Analysis of finite-sized guided-mode resonant gratings using the fast multipole boundary element method,” J. Opt. Soc. Am. A27, 1909–1919 (2010). [CrossRef]
F. Marquier, C. Arnold, M. Laroche, J. J. Greffet, and Y. Chen, “Degree of polarization of thermal light emitted by gratings supporting surface waves,” Opt. Express16, 5305–5313 (2008). [CrossRef] [PubMed]
N. Bonod, G. Tayeb, D. Maystre, S. Enoch, and E. Popov, “Total absorption of light by lamellar metallic gratings,” Opt. Express16, 15431–15438 (2008). [CrossRef] [PubMed]
W. T. Lu, Y. J. Huang, P. Vodo, R. K. Banyal, C. H. Perry, and S. Sridhar, “A new mechanism for negative refraction and focusing using selective diffraction from surface corrugation,” Opt. Express15, 9166–9175 (2007). [CrossRef] [PubMed]
L. Pajewski, R. Borghi, G. Schettini, F. Frezza, and M. Santarsiero, “Design of a binary grating with subwavelength features that acts as a polarizing beam splitter,” Appl. Opt.40, 5898–5905 (2001). [CrossRef]
T. Käpfe and O. Parriaux, “Parameter-tolerant binary gratings,” J. Opt. Soc. Am. A27, 2660–2669 (2010). [CrossRef]
T. Oonishi, T. Konishi, and K. Itoh, “Fabrication of phase only binary blazed grating with subwavelength structures designed by deterministic method based on electromagnetic analysis,” Jpn. J. Appl. Phys.46, 5435–5440 (2007). [CrossRef]
R. Antoš, J. Pištora, I. Ohlídal, K. Postava, J. Mistrík, T. Yamaguchi, Š. Višňovský, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys.97, 053107 (2005). [CrossRef]
W. Nakagawa, P.-Ch. Sun, Ch-H. Chen, and Y. Fainman, “Wide-field-of-view narrow-band spectral filters based on photonic crystal nanocavities,” Opt. Lett.27, 191–193 (2002). [CrossRef]
B. G. Zhai, Y. G. Cai, and Y. M. Huang, “Transmission spectra of one-dimensional photonic crystal with a centered defect,” Mat. Sci. For.663–665, 733–736 (2010).
K. Ren, X. Ren, R. Li, J. Zhou, and D. Liu, “Creating “defects” in photonic crystals by controlling polarizations,” Phys. Lett.325, 415–419 (2004). [CrossRef]
E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).
K. Watanabe and K. Yasumoto, “Two-dimensional electromagnetic scattering of non-plane incident waves by periodic structures,” Progress in Electromagnetic Res.PIER 74, 241–271 (2007). [CrossRef]
R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am.68, 1206–1210 (1978). [CrossRef]
M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am.72, 1385–1392 (1982). [CrossRef]
L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A13, 1870–1876 (1996). [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).
H. Takahasi and M. Mori, “Double exponential formulas for numerical integration,” Publ. RIMS, Kyoto Univ.9, 721–741 (1974). [CrossRef]
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd ed. (Academic Press, New York, 1984).

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[1] O. Manyardo, R. Michaely, F. Schädelin, W. Noell, T. Overstolz, N. De Rooij, and H. P. Herzig, “Miniature lamellar grating interferometer based on silicon technology,” Opt. Lett.29, 1437–1439 (2004). [CrossRef]

[2] Y. Hongbin, Z. Guangya, Ch. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” J. Micromech. Microeng.18, 055016 (2008). [CrossRef]

[3] A. Sato, “Analysis of finite-sized guided-mode resonant gratings using the fast multipole boundary element method,” J. Opt. Soc. Am. A27, 1909–1919 (2010). [CrossRef]

[4] F. Marquier, C. Arnold, M. Laroche, J. J. Greffet, and Y. Chen, “Degree of polarization of thermal light emitted by gratings supporting surface waves,” Opt. Express16, 5305–5313 (2008). [CrossRef] [PubMed]

[5] N. Bonod, G. Tayeb, D. Maystre, S. Enoch, and E. Popov, “Total absorption of light by lamellar metallic gratings,” Opt. Express16, 15431–15438 (2008). [CrossRef] [PubMed]

[6] W. T. Lu, Y. J. Huang, P. Vodo, R. K. Banyal, C. H. Perry, and S. Sridhar, “A new mechanism for negative refraction and focusing using selective diffraction from surface corrugation,” Opt. Express15, 9166–9175 (2007). [CrossRef] [PubMed]

[7] L. Pajewski, R. Borghi, G. Schettini, F. Frezza, and M. Santarsiero, “Design of a binary grating with subwavelength features that acts as a polarizing beam splitter,” Appl. Opt.40, 5898–5905 (2001). [CrossRef]

[8] T. Käpfe and O. Parriaux, “Parameter-tolerant binary gratings,” J. Opt. Soc. Am. A27, 2660–2669 (2010). [CrossRef]

[9] T. Oonishi, T. Konishi, and K. Itoh, “Fabrication of phase only binary blazed grating with subwavelength structures designed by deterministic method based on electromagnetic analysis,” Jpn. J. Appl. Phys.46, 5435–5440 (2007). [CrossRef]

[10] R. Antoš, J. Pištora, I. Ohlídal, K. Postava, J. Mistrík, T. Yamaguchi, Š. Višňovský, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys.97, 053107 (2005). [CrossRef]

[11] W. Nakagawa, P.-Ch. Sun, Ch-H. Chen, and Y. Fainman, “Wide-field-of-view narrow-band spectral filters based on photonic crystal nanocavities,” Opt. Lett.27, 191–193 (2002). [CrossRef]

[12] B. G. Zhai, Y. G. Cai, and Y. M. Huang, “Transmission spectra of one-dimensional photonic crystal with a centered defect,” Mat. Sci. For.663–665, 733–736 (2010).

[13] K. Ren, X. Ren, R. Li, J. Zhou, and D. Liu, “Creating “defects” in photonic crystals by controlling polarizations,” Phys. Lett.325, 415–419 (2004). [CrossRef]

[14] E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

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

[16] R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).

[17] K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am.68, 1206–1210 (1978). [CrossRef]

[18] M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am.72, 1385–1392 (1982). [CrossRef]

[19] L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A13, 1870–1876 (1996). [CrossRef]

[20] 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).

[21] H. Takahasi and M. Mori, “Double exponential formulas for numerical integration,” Publ. RIMS, Kyoto Univ.9, 721–741 (1974). [CrossRef]

[22] P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd ed. (Academic Press, New York, 1984).

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Rigorous coupled-wave analysis of electromagnetic scattering from lamellar grating with defects