Abstract

Resonant grating filters have been proposed as a promising alternative to multilayer stacks for narrowband free-space filtering. The efficiency of such filters under normal incidence has been demonstrated. Unfortunately, under oblique incidence, the limited angular tolerance of the resonance forbids any filtering applications with use of standard collimated incident beams. Using a multimode planar waveguide and a bi-atom grating, we show how to increase the angular tolerance up to the divergence of standard beams (0.2 deg) without modifying the spectral bandwidth (0.1 nm), under any oblique angle of incidence.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. S. Peng, G. Morris, “Experimental demonstration of resonant anomalies in diffraction from two-dimensional gratings,” Opt. Lett. 21, 549–551 (1996).
    [CrossRef] [PubMed]
  5. A. Sharon, D. Rosenblatt, A. A. Friesem, “Narrow spectral bandwidths with grating waveguide structures,” Appl. Phys. Lett. 69, 4154–4156 (1996).
    [CrossRef]
  6. A. Sharon, D. Rosenblatt, A. A. Friesem, “Resonant grating-waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
    [CrossRef]
  7. F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1, 545–551 (1999).
    [CrossRef]
  8. E. Popov, L. Mashev, “Diffraction from planar corrugated waveguides at normal incidence,” Opt. Commun. 61, 176–180 (1987).
    [CrossRef]
  9. F. Lemarchand, A. Sentenac, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 23, 1149–1151 (1998).
    [CrossRef]
  10. D. Brundrett, E. Glytsis, T. Gaylord, J. Bendickson, “Effects of modulation strength in guided-mode resonant subwavelength gratings at normal incidence,” J. Opt. Soc. Am. A 17, 1221–1230 (2000).
    [CrossRef]
  11. D. Jacob, S. Dunn, M. Moharam, “Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams,” J. Opt. Soc. Am. A 18, 2109–2120 (2001).
    [CrossRef]
  12. P. Yeh, Optical Waves in Layered Media (Wiley Interscience, New York, 1988).
  13. N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, Pa., 1976).
  14. W. Barnes, T. Preist, S. Kitson, S. J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6243 (1996).
    [CrossRef]
  15. D. Lacour, J.-P. Plumey, G. Granet, A. Mure-Ravaud, “Resonant waveguide grating: analysis of polarization independent filtering,” Opt. Quantum Electron. 33, 451–470 (2001).
    [CrossRef]

2001

D. Lacour, J.-P. Plumey, G. Granet, A. Mure-Ravaud, “Resonant waveguide grating: analysis of polarization independent filtering,” Opt. Quantum Electron. 33, 451–470 (2001).
[CrossRef]

D. Jacob, S. Dunn, M. Moharam, “Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams,” J. Opt. Soc. Am. A 18, 2109–2120 (2001).
[CrossRef]

2000

1999

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1, 545–551 (1999).
[CrossRef]

1998

1997

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

1996

A. Sharon, D. Rosenblatt, A. A. Friesem, “Narrow spectral bandwidths with grating waveguide structures,” Appl. Phys. Lett. 69, 4154–4156 (1996).
[CrossRef]

S. Peng, G. Morris, “Experimental demonstration of resonant anomalies in diffraction from two-dimensional gratings,” Opt. Lett. 21, 549–551 (1996).
[CrossRef] [PubMed]

W. Barnes, T. Preist, S. Kitson, S. J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6243 (1996).
[CrossRef]

1990

1987

E. Popov, L. Mashev, “Diffraction from planar corrugated waveguides at normal incidence,” Opt. Commun. 61, 176–180 (1987).
[CrossRef]

1985

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

1979

P. Vincent, M. Nevière, “Corrugated dielectric waveguides: a numerical study of the second order stop bands,” Appl. Phys. 20, 345–351 (1979).
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, Pa., 1976).

Bagby, J.

Barnes, W.

W. Barnes, T. Preist, S. Kitson, S. J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6243 (1996).
[CrossRef]

Bendickson, J.

Brundrett, D.

Cambril, E.

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1, 545–551 (1999).
[CrossRef]

Dunn, S.

Friesem, A. A.

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

A. Sharon, D. Rosenblatt, A. A. Friesem, “Narrow spectral bandwidths with grating waveguide structures,” Appl. Phys. Lett. 69, 4154–4156 (1996).
[CrossRef]

Gaylord, T.

Giovannini, H.

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1, 545–551 (1999).
[CrossRef]

Glytsis, E.

Granet, G.

D. Lacour, J.-P. Plumey, G. Granet, A. Mure-Ravaud, “Resonant waveguide grating: analysis of polarization independent filtering,” Opt. Quantum Electron. 33, 451–470 (2001).
[CrossRef]

Jacob, D.

Kitson, S.

W. Barnes, T. Preist, S. Kitson, S. J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6243 (1996).
[CrossRef]

Lacour, D.

D. Lacour, J.-P. Plumey, G. Granet, A. Mure-Ravaud, “Resonant waveguide grating: analysis of polarization independent filtering,” Opt. Quantum Electron. 33, 451–470 (2001).
[CrossRef]

Lemarchand, F.

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1, 545–551 (1999).
[CrossRef]

F. Lemarchand, A. Sentenac, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 23, 1149–1151 (1998).
[CrossRef]

Magnusson, R.

Mashev, L.

E. Popov, L. Mashev, “Diffraction from planar corrugated waveguides at normal incidence,” Opt. Commun. 61, 176–180 (1987).
[CrossRef]

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

Mermin, N. D.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, Pa., 1976).

Moharam, M.

Morris, G.

Mure-Ravaud, A.

D. Lacour, J.-P. Plumey, G. Granet, A. Mure-Ravaud, “Resonant waveguide grating: analysis of polarization independent filtering,” Opt. Quantum Electron. 33, 451–470 (2001).
[CrossRef]

Nevière, M.

P. Vincent, M. Nevière, “Corrugated dielectric waveguides: a numerical study of the second order stop bands,” Appl. Phys. 20, 345–351 (1979).
[CrossRef]

Peng, S.

Plumey, J.-P.

D. Lacour, J.-P. Plumey, G. Granet, A. Mure-Ravaud, “Resonant waveguide grating: analysis of polarization independent filtering,” Opt. Quantum Electron. 33, 451–470 (2001).
[CrossRef]

Popov, E.

E. Popov, L. Mashev, “Diffraction from planar corrugated waveguides at normal incidence,” Opt. Commun. 61, 176–180 (1987).
[CrossRef]

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

Preist, T.

W. Barnes, T. Preist, S. Kitson, S. J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6243 (1996).
[CrossRef]

Rosenblatt, D.

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

A. Sharon, D. Rosenblatt, A. A. Friesem, “Narrow spectral bandwidths with grating waveguide structures,” Appl. Phys. Lett. 69, 4154–4156 (1996).
[CrossRef]

Sambles, S. J. R.

W. Barnes, T. Preist, S. Kitson, S. J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6243 (1996).
[CrossRef]

Sentenac, A.

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1, 545–551 (1999).
[CrossRef]

F. Lemarchand, A. Sentenac, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 23, 1149–1151 (1998).
[CrossRef]

Sharon, A.

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

A. Sharon, D. Rosenblatt, A. A. Friesem, “Narrow spectral bandwidths with grating waveguide structures,” Appl. Phys. Lett. 69, 4154–4156 (1996).
[CrossRef]

Vincent, P.

P. Vincent, M. Nevière, “Corrugated dielectric waveguides: a numerical study of the second order stop bands,” Appl. Phys. 20, 345–351 (1979).
[CrossRef]

Wang, S.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley Interscience, New York, 1988).

Appl. Phys.

P. Vincent, M. Nevière, “Corrugated dielectric waveguides: a numerical study of the second order stop bands,” Appl. Phys. 20, 345–351 (1979).
[CrossRef]

Appl. Phys. Lett.

A. Sharon, D. Rosenblatt, A. A. Friesem, “Narrow spectral bandwidths with grating waveguide structures,” Appl. Phys. Lett. 69, 4154–4156 (1996).
[CrossRef]

IEEE J. Quantum Electron.

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

J. Opt. A, Pure Appl. Opt.

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1, 545–551 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

E. Popov, L. Mashev, “Diffraction from planar corrugated waveguides at normal incidence,” Opt. Commun. 61, 176–180 (1987).
[CrossRef]

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

Opt. Lett.

Opt. Quantum Electron.

D. Lacour, J.-P. Plumey, G. Granet, A. Mure-Ravaud, “Resonant waveguide grating: analysis of polarization independent filtering,” Opt. Quantum Electron. 33, 451–470 (2001).
[CrossRef]

Phys. Rev. B

W. Barnes, T. Preist, S. Kitson, S. J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6243 (1996).
[CrossRef]

Other

P. Yeh, Optical Waves in Layered Media (Wiley Interscience, New York, 1988).

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders College Publishing, Philadelphia, Pa., 1976).

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Figures (5)

Fig. 1
Fig. 1

(a) Illumination configuration and representation in the Fourier space of the phase-matching condition at a given wavelength. (b) Dispersion relation of the mode in the perturbed waveguide. (c), (d) Reflectivity of the grating versus the wavelength and incident angle. n sub = 1.448 , n sup = 1 , n layer = 2.07 , thickness e = 300   nm , d = 971   nm , h = 20   nm , a = 721   nm .

Fig. 2
Fig. 2

(a) Left, different examples of the geometry of a MBG waveguide plus grating coupler. In the bi-atom grating, the pattern consists of two ridges with different widths centered about one fourth and three fourths of the period. Right, representation in the Fourier space of the phase-matching condition when two modes are excited under normal incidence. (b) Dispersion relation in the vicinity of the second-order stop band. (c) Reflectivity of the bi-atom grating as a function of the wavelength at normal incidence. (d) Reflectivity of the bi-atom as a function of the incident angle for a wavelength corresponding to the maximum of reflectivity ( λ = 1572.3   nm ) .

Fig. 3
Fig. 3

Geometry of the bi-atom grating whose reflectivity spectra are plotted in Figs. 2(c) and 2(d). The substrate and superstrate are the same as in Fig. 1; the planar waveguide is a multilayer with refractive indices 2.07, 1.47, 2.07 and thicknesses 79.1, 263.5, 62.5 nm from bottom to top. The bi-atom grating is defined by a = 241.25   nm , b = 281.25   nm , d = 1047.5   nm , h = 382.6   nm , n = 2.07 . The Fourier coefficients of the relative permittivity of the grating are 1 = 0.093 and 2 = 1.037 .

Fig. 4
Fig. 4

(a) Top, illumination configuration and bottom, representation in the Fourier space of the phase-matching condition when two different modes are excited at a given wavelength under oblique incidence. (b) Top, dispersion relation when the waveguide supports two TE modes in the limit h tends to 0. Bottom, zoom-in of the mini-stop band when the TE 1 branch intersects the TE 2 branch obtained by calculating the reflectivity of the grating as a function of the angle of incidence and wavelength. (c) Reflectivity of the grating as a function of the wavelength for θ = 5   deg . (d) Reflectivity of the grating as a function of the angle of incidence for a wavelength corresponding to the maximum of reflectivity ( λ = 1555   nm ) .

Fig. 5
Fig. 5

Geometry of the bi-atom grating whose reflectivity spectra are plotted in Figs. 4(c) and 4(d). The substrate and superstrate are the same as in Fig. 1; the planar waveguide is a multilayer with refraction indices 2.07, 1.47, 2.07 and thicknesses 346.3, 217.9, 309.8 nm from top to bottom. The bi-atom grating is defined by a = 225.5   nm , b = 185.5   nm , d = 902   nm , h = 100   nm , n = 2.07 . The effective indices of the TE 1 and TE 2 modes of the imperturbed structure are, respectively, 1.6236 and 1.8120.

Equations (3)

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( x ) = q = - q exp ( iqKx ) ,
α + K α m 2 ( λ 0 ) , α - K - α m 1 ( λ 0 ) ,
sin ( θ ) = [ n eff 1 ( λ 0 ) - n eff 2 ( λ 0 ) ] / 2 .

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