Abstract

The guided-mode resonance properties of planar dielectric waveguide gratings are presented and explained. It is shown that these structures function as filters that produce complete exchange of energy between forward- and backward-propagating diffracted waves with smooth line shapes and arbitrarily narrow filter linewidths. Simple expressions based on rigorous coupled-wave theory and on classical slab waveguide theory give a clear view and quantification of the inherent TE/TM polarization separation and the free spectral ranges of the filters. Furthermore, the resonance regimes, defining the parametric regions of the guided-mode resonances, can be directly visualized. It is shown that the linewidths of the resonances can be controlled by the grating modulation amplitude and by the degree of mode confinement (refractive-index difference at the boundaries). Examples presented of potential uses for these elements include a narrow-line polarized laser, a tunable polarized laser, a photorefractive tunable filter, and an electro-optic switch. The guided-mode resonance filter represents a basic new optical element with significant potential for practical applications.

© 1993 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, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470–1475 (1990).
    [CrossRef]
  2. S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.
  3. R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
    [CrossRef]
  4. A. Hessel, A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 10, 1275–1297 (1965).
    [CrossRef]
  5. T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik 38, 269–297 (1973).
  6. M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
    [CrossRef]
  7. M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonance of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
    [CrossRef]
  8. S. Zhang, T. Tamir, “Spatial modifications of Gaussian beams diffracted by reflection gratings,” J. Opt. Soc. Am. 6, 1368–1381 (1989).
    [CrossRef]
  9. M. T. Gale, “Diffraction, beauty and commerce,” Phys. World 2(10), 24–28 (1989).
  10. M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1210, 83–89 (1990).
  11. S. Mori, K. Mukai, J. Yamakita, K. Rokushima, “Analysis of dielectric lamellar gratings coated with anisotropic layers,” J. Opt. Soc. Am. A 7, 1661–1665 (1990).
    [CrossRef]
  12. 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]
  13. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [CrossRef]
  14. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  15. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991), Chap. 1, p. 7.
  16. A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470–479 (1978).

1992 (1)

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

1991 (1)

1990 (2)

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 8, 1470–1475 (1990).
[CrossRef]

S. Mori, K. Mukai, J. Yamakita, K. Rokushima, “Analysis of dielectric lamellar gratings coated with anisotropic layers,” J. Opt. Soc. Am. A 7, 1661–1665 (1990).
[CrossRef]

1989 (2)

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

M. T. Gale, “Diffraction, beauty and commerce,” Phys. World 2(10), 24–28 (1989).

1985 (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

1981 (1)

1978 (1)

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470–479 (1978).

1973 (3)

T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik 38, 269–297 (1973).

M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonance of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

1965 (1)

A. Hessel, A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 10, 1275–1297 (1965).
[CrossRef]

Bagby, J. S.

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 8, 1470–1475 (1990).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Cadilhac, M.

M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonance of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

DeSandre, L. F.

Elson, J. M.

Gale, M. T.

M. T. Gale, “Diffraction, beauty and commerce,” Phys. World 2(10), 24–28 (1989).

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1210, 83–89 (1990).

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

Glass, A. M.

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470–479 (1978).

Hessel, A.

A. Hessel, A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 10, 1275–1297 (1965).
[CrossRef]

Knop, K.

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1210, 83–89 (1990).

Magnusson, R.

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[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 8, 1470–1475 (1990).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991), Chap. 1, p. 7.

Moharam, M. G.

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 8, 1470–1475 (1990).
[CrossRef]

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” 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, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1210, 83–89 (1990).

Mori, S.

Mukai, K.

Neviere, M.

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonance of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

Oliner, A. A.

A. Hessel, A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 10, 1275–1297 (1965).
[CrossRef]

Petit, R.

M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonance of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Rokushima, K.

Tamir, T.

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

T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik 38, 269–297 (1973).

Vincent, P.

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonance of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Wang, S. S.

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[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 8, 1470–1475 (1990).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

Yamakita, J.

Zhang, S.

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

Appl. Opt. (1)

A. Hessel, A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 10, 1275–1297 (1965).
[CrossRef]

Appl. Phys. Lett. (1)

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

J. Opt. Soc. Am. (2)

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

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

J. Opt. Soc. Am. A (3)

Opt. Commun. (2)

M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonance of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Opt. Eng. (1)

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470–479 (1978).

Optik (1)

T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik 38, 269–297 (1973).

Phys. World (1)

M. T. Gale, “Diffraction, beauty and commerce,” Phys. World 2(10), 24–28 (1989).

Proc. IEEE (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Other (3)

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991), Chap. 1, p. 7.

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1210, 83–89 (1990).

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” 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 (12)

Fig. 1
Fig. 1

Basic planar 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; θi″ are the corresponding angles for the forward-diffracted waves. The angle of incidence (θ′) is arbitrary.

Fig. 2
Fig. 2

Diagram showing the TE/TM polarization separation and the normalized resonance-free ranges in wavelength and in thickness for a guide-mode resonance filter. The parameters are ∊1 = 1, ∊g = 3, ∊3 = 2.161, and θ′ = 0° (normal incidence).

Fig. 3
Fig. 3

Resonance regimes of waveguide gratings. The parameters are ∊1 = 1, ∊g = 3, and ∊3 = 2.161.

Fig. 4
Fig. 4

TE spectral response of a symmetric guided-mode resonance filter. The parameters are ∊1 = ∊3 = 2.5, ∊g = 3, θ′ = 0° (normal incidence), Λ = d = 1.0 μm, Δ∊/∊g = 0.05, center free-space wavelength λ0 = 1669 nm, and linewidth of ~0.01 nm; DE10 and DE30 represent diffraction efficiencies.

Fig. 5
Fig. 5

TE spectral response of an asymmetric guided-mode resonance filter. The parameters are ∊1 = 1, ∊3 = 2.161, ∊g = 3, θ′ = 0° (normal incidence), Λ = d = 0.33 μm, Δ∊/∊g = 0.05, center free-space wavelength λ0 = 547 nm, and linewidth of ~0.02 nm.

Fig. 6
Fig. 6

Calculated relation between the modulation index and the linewidth of a guided-mode resonance filter for TE polarization. The parameters are ∊1 = 1, ∊3 = 2.161, ∊g = 3, and d/Λ = 1 at normal incidence.

Fig. 7
Fig. 7

Calculated relation between the refractive-index difference g 1 and the linewidth of a symmetric guided-mode resonance filter for TE polarization. The parameters are ∊g = 3, Δ∊/∊g = 0.05, θ′ = 0°, and Λ = d = 1 μm, with ∊1 (=∊3) varying from 1.0 to 2.95.

Fig. 8
Fig. 8

Resonance line in terms of the average relative permittivity of the waveguide grating for TE polarization. The Bragg condition λ/Λ = 2 sin θ′ is satisfied. The parameters for this example are Δ∊/∊g = 0.005, d = 0.32 μm, ∊1 = 1, ∊3 = 2.161, Λ = 1 μm, and θ′ = 31°; DE10, DE11, DE30, and DE31 are diffraction efficiencies.

Fig. 9
Fig. 9

TE filter reflectivity for a waveguide grating with square-wave grating shape. The angle θ′ is the external (air) angle of incidence. The parameters are ∊1 = ∊3 = 2.25, ∊g = 3.125, Λ = 0.4 μm, and d = 0.15 μm.

Fig. 10
Fig. 10

Resonance regime for the waveguide grating described in Fig. 9.

Fig. 11
Fig. 11

TM filter reflectivity for the waveguide grating described in Fig. 9.

Fig. 12
Fig. 12

Some potential applications of guided-mode resonance filters (GMRF’s): (a) narrow-line polarized laser, (b) tunable polarized laser, (c) photorefractive tunable filter, (d) electro-optic switch.

Equations (9)

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d 2 S ˆ i ( z ) d z 2 + [ k 2 g k 2 ( g sin θ i λ / Λ ) 2 S ˆ i ( z ) + 1 2 k 2 Δ [ S ˆ i + 1 ( z ) + S ˆ i 1 ( z ) ] = 0 ,
d 2 E ( z ) d z 2 + ( k 2 g β 2 ) E ( z ) = 0 ,
max { 1 , 3 } | N | < g .
β β i = k ( g sin θ i λ / Λ ) ,
tan ( κ i d ) = κ i ( γ i + δ i ) κ i 2 γ i δ i ,
tan ( κ i d ) = g κ i ( 3 γ i + 1 δ i ) 1 3 κ i 2 g 2 γ i δ i .
Δ d = π / κ i = λ 2 [ g ( g sin θ i λ / Λ ) 2 ] 1 / 2 .
tan [ κ i ( λ ) d ] = [ γ i ( λ ) + δ i ( λ ) ] κ i ( λ ) κ i 2 ( λ ) γ i ( λ ) δ i ( λ )
max { 1 , 3 } | 1 sin θ i λ / Λ | < g ,

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