Abstract

We show that ideal reflection filters can be designed by combining guided-mode resonance effects in waveguide gratings with antireflection effects of thin-film structures. Since the guided-mode resonance effect overrides the antireflection effect this filter provides a symmetrical line shape with near-zero reflectivity over appreciable wavelength bands adjacent to the resonance wavelength. In the single-layer filter the same layer functions as the waveguide grating supporting the resonance and as the antireflection layer suppressing reflection around the resonance. A multilayer design allows the filter resonance peak to have a wide surrounding region of low reflectance. The central resonance wavelength, the filter linewidth, the range of the low sidebands, and the resonance line shape are all under the control of the designer.

© 1994 Optical Society of America

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References

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  1. S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, J. Opt. Soc. Am. A 7, 1470 (1990).
    [CrossRef]
  2. S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, in Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.
  3. A. Hessel, A. A. Oliner, Appl. Opt. 10, 1275 (1965).
    [CrossRef]
  4. L. Mashev, E. Popov, Opt. Commun. 55, 377 (1985).
    [CrossRef]
  5. H. Bertoni, L. Cheo, T. Tamir, IEEE Trans. Antennas Propag. 37, 78 (1989).
    [CrossRef]
  6. M. T. Gale, K. Knop, R. H. Morf, Proc. Soc. Photo-Opt. Instrum. Eng. 1210, 83 (1990).
  7. R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHZ,”IEEE Trans. Antennas Propag. (to be publsihed).
  8. R. Magnusson, S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
    [CrossRef]
  9. S. S. Wang, R. Magnusson, Appl. Opt. 32, 2606 (1993).
    [CrossRef] [PubMed]
  10. T. K. Gaylord, M. G. Moharam, Proc. IEEE 73, 894 (1985).
    [CrossRef]

1993

1992

R. Magnusson, S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

1990

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, J. Opt. Soc. Am. A 7, 1470 (1990).
[CrossRef]

M. T. Gale, K. Knop, R. H. Morf, Proc. Soc. Photo-Opt. Instrum. Eng. 1210, 83 (1990).

1989

H. Bertoni, L. Cheo, T. Tamir, IEEE Trans. Antennas Propag. 37, 78 (1989).
[CrossRef]

1985

L. Mashev, E. Popov, Opt. Commun. 55, 377 (1985).
[CrossRef]

T. K. Gaylord, M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

1965

A. Hessel, A. A. Oliner, Appl. Opt. 10, 1275 (1965).
[CrossRef]

Bagby, J. S.

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, J. Opt. Soc. Am. A 7, 1470 (1990).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, in Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Bertoni, H.

H. Bertoni, L. Cheo, T. Tamir, IEEE Trans. Antennas Propag. 37, 78 (1989).
[CrossRef]

Black, T. D.

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHZ,”IEEE Trans. Antennas Propag. (to be publsihed).

Cheo, L.

H. Bertoni, L. Cheo, T. Tamir, IEEE Trans. Antennas Propag. 37, 78 (1989).
[CrossRef]

Gale, M. T.

M. T. Gale, K. Knop, R. H. Morf, Proc. Soc. Photo-Opt. Instrum. Eng. 1210, 83 (1990).

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Hessel, A.

A. Hessel, A. A. Oliner, Appl. Opt. 10, 1275 (1965).
[CrossRef]

Knop, K.

M. T. Gale, K. Knop, R. H. Morf, Proc. Soc. Photo-Opt. Instrum. Eng. 1210, 83 (1990).

Magnusson, R.

S. S. Wang, R. Magnusson, Appl. Opt. 32, 2606 (1993).
[CrossRef] [PubMed]

R. Magnusson, S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, J. Opt. Soc. Am. A 7, 1470 (1990).
[CrossRef]

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHZ,”IEEE Trans. Antennas Propag. (to be publsihed).

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, in Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Mashev, L.

L. Mashev, E. Popov, Opt. Commun. 55, 377 (1985).
[CrossRef]

Moharam, M. G.

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, J. Opt. Soc. Am. A 7, 1470 (1990).
[CrossRef]

T. K. Gaylord, M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, in Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Morf, R. H.

M. T. Gale, K. Knop, R. H. Morf, Proc. Soc. Photo-Opt. Instrum. Eng. 1210, 83 (1990).

Oliner, A. A.

A. Hessel, A. A. Oliner, Appl. Opt. 10, 1275 (1965).
[CrossRef]

Popov, E.

L. Mashev, E. Popov, Opt. Commun. 55, 377 (1985).
[CrossRef]

Sohn, A.

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHZ,”IEEE Trans. Antennas Propag. (to be publsihed).

Tamir, T.

H. Bertoni, L. Cheo, T. Tamir, IEEE Trans. Antennas Propag. 37, 78 (1989).
[CrossRef]

Wang, S. S.

S. S. Wang, R. Magnusson, Appl. Opt. 32, 2606 (1993).
[CrossRef] [PubMed]

R. Magnusson, S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, J. Opt. Soc. Am. A 7, 1470 (1990).
[CrossRef]

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHZ,”IEEE Trans. Antennas Propag. (to be publsihed).

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, in Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Appl. Opt.

Appl. Phys. Lett.

R. Magnusson, S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

IEEE Trans. Antennas Propag.

H. Bertoni, L. Cheo, T. Tamir, IEEE Trans. Antennas Propag. 37, 78 (1989).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

L. Mashev, E. Popov, Opt. Commun. 55, 377 (1985).
[CrossRef]

Proc. IEEE

T. K. Gaylord, M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

M. T. Gale, K. Knop, R. H. Morf, Proc. Soc. Photo-Opt. Instrum. Eng. 1210, 83 (1990).

Other

R. Magnusson, S. S. Wang, T. D. Black, A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHZ,”IEEE Trans. Antennas Propag. (to be publsihed).

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, in Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the multiple-layer, square-wave-profile waveguide-grating model used. The angles θi′ represent the angles of the wave vector of the ith backward-diffracted wave with respect to the z axis, and θi″ are the corresponding angles for the forward-diffracted waves. The angle of incidence (θ′) is arbitrary.

Fig. 2
Fig. 2

TE spectral response of a single-layer waveguide-grating filter for which the resonance wavelength is λc ≅ 610 nm and the grating thickness is d = 200 nm. The other parameters are ɛa = 1.0, ɛH = 4.0, ɛL = 3.61, ɛs = 2.31, Λ = 350 nm, and θ′ = 0°.

Fig. 3
Fig. 3

TE spectral response of a single-layer waveguide-grating filter for which the resonance wavelength is λc ≅ 587.8 nm and the grating thickness is d = 148 nm (near a half-wavelength). The other parameters are the same as in Fig. 2.

Fig. 4
Fig. 4

TE spectral response of a single-layer waveguide-grating filter for which the resonance wavelength is λc ≅ 604 nm and the grating thickness is d = 155 nm (half-wavelength). The other parameters are ɛa = ɛs = 2.31 (i.e., AR design), ɛH = 4.0, ɛL = 3.61, Λ = 350 nm, and θ′ = 0°.

Fig. 5
Fig. 5

TE spectral response of a triple-layer waveguide-grating filter. The parameters are ɛa = 1.0, ɛ1 = 1.904, ɛH = 5.76, ɛL = 4.0, ɛ3 = 2.89, ɛs = 2.31, Λ = 350 nm, θ′ = 0°, and d2 = 125 nm (half-wavelength). The thicknesses are determined at the wavelength of 550 nm. Curve (a) was obtained with the AR design; d1 = 100 nm (quarter-wavelength) and d3 = 81 nm (quarter-wavelength). Curve (b) was obtained with the non-AR design; d1 = 200 nm (half-wavelength) and d3 = 162 nm (half-wavelength).

Equations (2)

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R = ε eff ( ε a ε s ) 2 cos 2 k eff d + ( ε a ε s ε eff ) 2 sin 2 k eff d ε eff ( ε a + ε s ) 2 cos 2 k eff d + ( ε a ε s + ε eff ) 2 sin 2 k eff d ,
R = ( ε a ε s ) 2 ( ε a + ε s ) 2 ,

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