Abstract

An interference-waveguide approach is developed to predict the response of a resonant grating reflection filter and to provide a better understanding of the resonant process. An expression for the reflected field that accounts for all internal boundary reflections within the filter is developed. Under the assumption of an antireflective design, expressions characterizing the line shape of a filter of infinite length are first developed; then the effects of finite length on the response are determined. Expressions relating the length of the filter to the peak reflection efficiency and line width are developed. The degradation of the response as a function of filter length is evaluated. An equivalent waveguide representation is used to determine the location of the resonance as well as the spectral and angular linewidths of the filter. The minimum obtainable spectral linewidth for a filter of given length is determined to be on the order of Δλλ2/L. Rigorous analysis is used to verify the interference-waveguide approach.

© 2000 Optical Society of America

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    [CrossRef]
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  7. G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
    [CrossRef]
  8. I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).
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    [CrossRef]
  10. G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, E. Popov, L. Mashev, “Diffraction characteristics of planar corrugated waveguides,” Opt. Quantum Electron. 18, 123–128 (1986).
    [CrossRef]
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  12. S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
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  13. L. F. DeSandre, J. M. Elson, “Extinction-theorem analysis of diffraction anomalies in overcoated gratings,” J. Opt. Soc. Am. A 8, 763–777 (1991).
    [CrossRef]
  14. R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
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  15. M. Neviere, E. Popov, R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
    [CrossRef]
  16. T. Tamir, S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
    [CrossRef]
  17. T. Tamir, S. Zhang, “Resonant scattering by multilayered dielectric gratings,” J. Opt. Soc. Am. A 14, 1607–1616 (1997).
    [CrossRef]
  18. E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 8.
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  24. S. M. Norton, G. M. Morris, T. Erdogan, “Experimental investigation of resonant-grating filter lineshapes in comparison with theoretical models,” J. Opt. Soc. Am. A 15, 464–472 (1998).
    [CrossRef]
  25. I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527–1539 (1989).
    [CrossRef]
  26. S. Zhang, T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. A 6, 1368–1381 (1989).
    [CrossRef]
  27. J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
    [CrossRef]
  28. A. Sharon, S. Glasberg, D. Rosenblatt, A. A. Friesem, “Metal-based resonant grating waveguide structures,” J. Opt. Soc. Am. A 14, 588–595 (1997).
    [CrossRef]
  29. A. Sharon, D. Rosenblatt, A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14, 2985–2993 (1997).
    [CrossRef]
  30. D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
    [CrossRef]
  31. S. Glasberg, A. Sharon, D. Rosenblatt, A. A. Friesem, “Spectral shifts and line-shapes asymmetries in the resonant response of grating waveguide structures,” Opt. Commun. 145, 291–299 (1998).
    [CrossRef]
  32. H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin-film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
    [CrossRef]
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1998 (2)

S. M. Norton, G. M. Morris, T. Erdogan, “Experimental investigation of resonant-grating filter lineshapes in comparison with theoretical models,” J. Opt. Soc. Am. A 15, 464–472 (1998).
[CrossRef]

S. Glasberg, A. Sharon, D. Rosenblatt, A. A. Friesem, “Spectral shifts and line-shapes asymmetries in the resonant response of grating waveguide structures,” Opt. Commun. 145, 291–299 (1998).
[CrossRef]

1997 (5)

1996 (2)

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

1995 (4)

1994 (1)

1992 (1)

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

1991 (1)

1990 (1)

1989 (3)

H. L. Bertoni, L. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527–1539 (1989).
[CrossRef]

S. Zhang, T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. A 6, 1368–1381 (1989).
[CrossRef]

1986 (2)

E. Popov, L. Mashev, D. Maystre, “Theoretical study of anomalies of coated dielectric gratings,” Opt. Acta 32, 607–629 (1986).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, E. Popov, L. Mashev, “Diffraction characteristics of planar corrugated waveguides,” Opt. Quantum Electron. 18, 123–128 (1986).
[CrossRef]

1985 (3)

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

1984 (1)

L. Mashev, E. Popov, “Diffraction efficiency anomalies of multicoated dielectric gratings,” Opt. Commun. 51, 131–136 (1984).
[CrossRef]

1973 (2)

M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin-film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin-film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
[CrossRef]

1965 (1)

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), Chap. 2.

Avrutskii, I. D.

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

Avrutsky, I. A.

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527–1539 (1989).
[CrossRef]

Bagby, J. S.

Bertoni, H. L.

H. L. Bertoni, L. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

Cadilhac, M.

M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin-film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Cheo, L. S.

H. L. Bertoni, L. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

Day, R. W.

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

DeSandre, L. F.

Elson, J. M.

Erdogan, T.

Friesem, A. A.

S. Glasberg, A. Sharon, D. Rosenblatt, A. A. Friesem, “Spectral shifts and line-shapes asymmetries in the resonant response of grating waveguide structures,” Opt. Commun. 145, 291–299 (1998).
[CrossRef]

A. Sharon, S. Glasberg, D. Rosenblatt, A. A. Friesem, “Metal-based resonant grating waveguide structures,” J. Opt. Soc. Am. A 14, 588–595 (1997).
[CrossRef]

A. Sharon, D. Rosenblatt, A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14, 2985–2993 (1997).
[CrossRef]

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Gaylord, T. K.

Glasberg, S.

S. Glasberg, A. Sharon, D. Rosenblatt, A. A. Friesem, “Spectral shifts and line-shapes asymmetries in the resonant response of grating waveguide structures,” Opt. Commun. 145, 291–299 (1998).
[CrossRef]

A. Sharon, S. Glasberg, D. Rosenblatt, A. A. Friesem, “Metal-based resonant grating waveguide structures,” J. Opt. Soc. Am. A 14, 588–595 (1997).
[CrossRef]

Golubenko, G. A.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, E. Popov, L. Mashev, “Diffraction characteristics of planar corrugated waveguides,” Opt. Quantum Electron. 18, 123–128 (1986).
[CrossRef]

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

Grann, E. B.

Hessel, A.

Kogelnik, H.

H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin-film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
[CrossRef]

Loewen, E. G.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 8.

Magnusson, R.

Mashev, L.

E. Popov, L. Mashev, D. Maystre, “Theoretical study of anomalies of coated dielectric gratings,” Opt. Acta 32, 607–629 (1986).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, E. Popov, L. Mashev, “Diffraction characteristics of planar corrugated waveguides,” Opt. Quantum Electron. 18, 123–128 (1986).
[CrossRef]

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

L. Mashev, E. Popov, “Diffraction efficiency anomalies of multicoated dielectric gratings,” Opt. Commun. 51, 131–136 (1984).
[CrossRef]

Maystre, D.

E. Popov, L. Mashev, D. Maystre, “Theoretical study of anomalies of coated dielectric gratings,” Opt. Acta 32, 607–629 (1986).
[CrossRef]

D. Maystre, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), Chap. 1.

Moharam, M. G.

Morris, G. M.

Neviere, M.

Nevière, M.

M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin-film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Nevière, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 5.

Noponen, E.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Norton, S. M.

Oliner, A. A.

Petit, R.

M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin-film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Pommet, D. A.

Popov, E.

M. Neviere, E. Popov, R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
[CrossRef]

E. Popov, L. Mashev, D. Maystre, “Theoretical study of anomalies of coated dielectric gratings,” Opt. Acta 32, 607–629 (1986).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, E. Popov, L. Mashev, “Diffraction characteristics of planar corrugated waveguides,” Opt. Quantum Electron. 18, 123–128 (1986).
[CrossRef]

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

L. Mashev, E. Popov, “Diffraction efficiency anomalies of multicoated dielectric gratings,” Opt. Commun. 51, 131–136 (1984).
[CrossRef]

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 8.

Reinisch, R.

Rosenblatt, D.

S. Glasberg, A. Sharon, D. Rosenblatt, A. A. Friesem, “Spectral shifts and line-shapes asymmetries in the resonant response of grating waveguide structures,” Opt. Commun. 145, 291–299 (1998).
[CrossRef]

A. Sharon, D. Rosenblatt, A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14, 2985–2993 (1997).
[CrossRef]

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

A. Sharon, S. Glasberg, D. Rosenblatt, A. A. Friesem, “Metal-based resonant grating waveguide structures,” J. Opt. Soc. Am. A 14, 588–595 (1997).
[CrossRef]

Saarinen, J.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Sharon, A.

S. Glasberg, A. Sharon, D. Rosenblatt, A. A. Friesem, “Spectral shifts and line-shapes asymmetries in the resonant response of grating waveguide structures,” Opt. Commun. 145, 291–299 (1998).
[CrossRef]

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

A. Sharon, D. Rosenblatt, A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14, 2985–2993 (1997).
[CrossRef]

A. Sharon, S. Glasberg, D. Rosenblatt, A. A. Friesem, “Metal-based resonant grating waveguide structures,” J. Opt. Soc. Am. A 14, 588–595 (1997).
[CrossRef]

Sosnowski, T. P.

H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin-film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
[CrossRef]

Svakhin, A. S.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, E. Popov, L. Mashev, “Diffraction characteristics of planar corrugated waveguides,” Opt. Quantum Electron. 18, 123–128 (1986).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

Sychugov, V. A.

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527–1539 (1989).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, E. Popov, L. Mashev, “Diffraction characteristics of planar corrugated waveguides,” Opt. Quantum Electron. 18, 123–128 (1986).
[CrossRef]

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

Tamir, T.

T. Tamir, S. Zhang, “Resonant scattering by multilayered dielectric gratings,” J. Opt. Soc. Am. A 14, 1607–1616 (1997).
[CrossRef]

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

H. L. Bertoni, L. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

S. Zhang, T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. A 6, 1368–1381 (1989).
[CrossRef]

Tischenko, A. V.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, E. Popov, L. Mashev, “Diffraction characteristics of planar corrugated waveguides,” Opt. Quantum Electron. 18, 123–128 (1986).
[CrossRef]

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

Turunen, J.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Wang, S. S.

Weber, H. P.

H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin-film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
[CrossRef]

Zhang, S.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

H. Kogelnik, T. P. Sosnowski, H. P. Weber, “A ray-optical analysis of thin-film polarization converters,” IEEE J. Quantum Electron. QE-9, 795–800 (1973).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

H. L. Bertoni, L. S. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

J. Lightwave Technol. (2)

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

J. Mod. Opt. (1)

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527–1539 (1989).
[CrossRef]

J. Opt. Soc. Am. A (10)

S. Zhang, T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. A 6, 1368–1381 (1989).
[CrossRef]

A. Sharon, S. Glasberg, D. Rosenblatt, A. A. Friesem, “Metal-based resonant grating waveguide structures,” J. Opt. Soc. Am. A 14, 588–595 (1997).
[CrossRef]

A. Sharon, D. Rosenblatt, A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14, 2985–2993 (1997).
[CrossRef]

S. M. Norton, T. Erdogan, G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A 14, 629–639 (1997).
[CrossRef]

S. M. Norton, G. M. Morris, T. Erdogan, “Experimental investigation of resonant-grating filter lineshapes in comparison with theoretical models,” J. Opt. Soc. Am. A 15, 464–472 (1998).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

T. Tamir, S. Zhang, “Resonant scattering by multilayered dielectric gratings,” J. Opt. Soc. Am. A 14, 1607–1616 (1997).
[CrossRef]

M. Neviere, E. Popov, R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
[CrossRef]

L. F. DeSandre, J. M. Elson, “Extinction-theorem analysis of diffraction anomalies in overcoated gratings,” J. Opt. Soc. Am. A 8, 763–777 (1991).
[CrossRef]

Opt. Acta (1)

E. Popov, L. Mashev, D. Maystre, “Theoretical study of anomalies of coated dielectric gratings,” Opt. Acta 32, 607–629 (1986).
[CrossRef]

Opt. Commun. (4)

M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin-film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

L. Mashev, E. Popov, “Diffraction efficiency anomalies of multicoated dielectric gratings,” Opt. Commun. 51, 131–136 (1984).
[CrossRef]

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

S. Glasberg, A. Sharon, D. Rosenblatt, A. A. Friesem, “Spectral shifts and line-shapes asymmetries in the resonant response of grating waveguide structures,” Opt. Commun. 145, 291–299 (1998).
[CrossRef]

Opt. Eng. (1)

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, E. Popov, L. Mashev, “Diffraction characteristics of planar corrugated waveguides,” Opt. Quantum Electron. 18, 123–128 (1986).
[CrossRef]

Sov. J. Quantum Electron. (1)

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, A. V. Tischenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

Sov. Tech. Phys. Lett. (1)

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

Other (4)

M. Nevière, in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 5.

D. Maystre, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), Chap. 1.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 8.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), Chap. 2.

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Figures (8)

Fig. 1
Fig. 1

Resonant grating reflection filter geometry.

Fig. 2
Fig. 2

Multiple-wave interference in resonant grating structure.

Fig. 3
Fig. 3

Resonant grating filter incorporating AR layers.

Fig. 4
Fig. 4

Line-shape dependence on the finite filter length.

Fig. 5
Fig. 5

Number of externally diffracted field components N required to achieve peak reflection efficiencies ηr,peak=99%, 95%, 85%, and 75% as a function of grating strength ηd.

Fig. 6
Fig. 6

Five-layer equivalent waveguide representation of resonant grating filter.

Fig. 7
Fig. 7

Ψ versus ηr,peak.

Fig. 8
Fig. 8

Comparison of normalized spectral line shapes obtained by using RCWA and the interference-waveguide approach for coupling to the TE0 mode for θ=14° (neff=1.508) and θ=10° (neff=1.576).

Tables (4)

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Table 1 Resonant Grating Structure Parameters

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Table 2 Comparison of the Spectral and Angular Linewidths Obtained by Using RCWA and the Interference-Waveguide Approach for Resonance into the TE0 Mode

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Table 3 Comparison of the Spectral and Angular Linewidths Obtained by Using RCWA and the Interference-Waveguide Approach for Resonance into the TE1 Mode

Tables Icon

Table 4 Normalized Length Required to Achieve 99% Peak Reflection Efficiency

Equations (49)

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E1=r12,00.
E2=t12,01t21,10 H,
E3=t12,01t21,00 FH,
H=RqH=0(r21,01 FR)qH,
R=exp(iϕ)qR=0r21,11qR exp(iqRϕ),
F=exp(iδ)qF=0r21,10qFr23,00qF exp(iqFδ).
E4=t12,00t21,10r21,01r21,10FH,
E5=t12,00t21,00r21,01r21,10F2H.
E6=t12,00t21,00r21,10 F.
 ER=r12,00-t12,01+t12,00 r21,01r21,10 F(t21,10+t21,00 F)r21,11-r21,01F-exp(-iϕ)+t12,00t21,00r21,10 F.
ER=t12,01t21,10R.
ER=t12,01t21,10 exp(iϕ)1-r21,11 exp(iϕ).
IR=|t12,01|2|t21,10|2(1-r21,11)2+4r21,11 sin2(ϕ/2).
|t12,01|2=ηd=|t21,10|2=1-r21,11,
IR=ηd2ηd2+4(1-ηd)sin2(ϕ/2),
Δϕ,FWHM=4 sin-1ηd21-ηd.
β=k0nc sin θ-2πΛ,
ϕ(x0+Δx)=ϕ(x0)+Δx dϕdxx=x0+12 Δx2 d2ϕdx2x=x0+ .
ΔϕΔβ dϕdββ=β0Δλ dϕdλλ=λ0Δθdϕdθθ=θ0.
ΔβFWHMΔϕ,FWHM/dϕdββ=β0,
ER=t12,01t21,10 exp(iϕ) 1-r21,11N exp(iNϕ)1-r21,11 exp(iϕ),
IR=ηd2ηd2+4(1-ηd)sin2(ϕ/2)×[1-(1-ηd)N]2+4(1-ηd)N sin2 Nϕ2.
IRIR=[1-(1-ηd)N]2+4(1-ηd)N sin2 NΔϕ2.
ηr,peak=[1-(1-ηd)N]2.
N=log(1-ηr,peak)log(1-ηd)
l=dϕdβ,
N=Ll=L/dϕdβ.
ΔϕFWHMΔϕ,FWHMσb,
σb2χ2-1,
χ=2ηr,peak-1.
ΔβFWHMΔϕ,FWHMσb/dϕdββ=β0.
2κdf+2ϕc+2ϕs=2mπ,
ϕs=tan-1γARκ tanh[tanh-1(γs/γAR)+γAR dAR],
ϕc=tan-1γgκ tanh[tanh-1(γc/γg)+γgdg],
γc,s,g,AR=β2-kc,s,g,AR2,
ϕ=2κdf+2ϕc+2ϕs.
ΔλFWHMλΔϕ,FWHMσb/λdϕdλ,
ΔθFWHMΔϕ,FWHMσb/dϕdθ,
λdϕdλλ=λ0λΛ k0dϕdβ+2dfkf2-β2β=β0,
dϕdθθ=θ0=k0nc(cos θ)dϕdββ=β0,
dϕdλλ=λ0k0Λ dϕdββ=β0,
ΔλFWHMλΔϕ,FWHMσbΛλ/k0dϕdβ,
ΔθFWHMΔϕ,FWHMσb 1nc cos θ/k0dϕdβ,
ΔλFWHM(min)λΨΛλλL,
Ψ=log(1-ηr,peak)[2(2/ηr,peak-1)2-1]1/2π[(1-ηd)/ηd2]1/2 log(1-ηd).
ΔλFWHMλ2/L.
Llog(1-ηr,max)=|dϕ/dβ|log(1-ηd).
ϕ=2df (kf2-β2)1/2-2 tan-1β2-ks2kf2-β21/2-2 tan-1β2-kc2kf2-β21/2,
dϕdβ=2β(kf2-β2)1/2×df+1(β2-kc2)1/2+1(β2-ks2)1/2,

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