Abstract

A novel multiline filter using a two-dimensional guided-mode resonant (GMR) filter is proposed. The filter concept utilizes the multiple planes of diffraction produced by the two-dimensional grating. Multiple resonances are obtained by matching the guided modes in the different planes of diffraction to different wavelengths. It is shown that the location and the separation between resonances can be specifically controlled by modifying the periodicity of the grating and the other physical dimensions of the structure. This is in contrast to the one-dimensional GMR filters where the location of the resonances is material dependent. Two-line reflection filter designs with spectral linewidths less than 1 nm and a controllable spectral separation of up to 23% of the short resonance wavelength are presented using rectangular-grid grating GMR structures. Three-line filters are designed in hexagonal-grid grating GMR structures with two independently controllable resonance locations.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photon. Technol. Lett. 14, 1091-1093 (2002).
    [CrossRef]
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    [CrossRef]
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2004 (1)

G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser based applications," Laser Focus World 40(9), (September 2004).

2002 (1)

Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photon. Technol. Lett. 14, 1091-1093 (2002).
[CrossRef]

2000 (2)

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, "Dielectric frequency-selective structures incorporating waveguide gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

D. K. Jacob, S. C. Dunn, and M. G. Moharam, "Design considerations for narrow-band dielectric resonant grating reflection filters of finite length," J. Opt. Soc. Am. A 17, 1241-1249 (2000).
[CrossRef]

1998 (1)

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, "Thin-film optical filters with diffractive elements and waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

1997 (1)

1996 (3)

1995 (2)

M. G. Moharam, E. B. Grann, D. A. Pommet, and 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]

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 5, 1077-1086 (1995).
[CrossRef]

1992 (1)

R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
[CrossRef]

1986 (1)

M. G. Moharam and T. K. Gaylord, "Coupled-wave analysis of two-dimensional gratings," in- Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. SPIE 883, 8-11 (1986).

1965 (1)

Dunn, S. C.

Gaylord, T. K.

M. G. Moharam, E. B. Grann, D. A. Pommet, and 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]

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 5, 1077-1086 (1995).
[CrossRef]

M. G. Moharam and T. K. Gaylord, "Coupled-wave analysis of two-dimensional gratings," in- Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. SPIE 883, 8-11 (1986).

Grann, E. B.

Hessel, A.

Holzheimer, T. R.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, "Dielectric frequency-selective structures incorporating waveguide gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

Jacob, D. K.

Liu, Z. S.

Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photon. Technol. Lett. 14, 1091-1093 (2002).
[CrossRef]

Magnusson, R.

Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photon. Technol. Lett. 14, 1091-1093 (2002).
[CrossRef]

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, "Dielectric frequency-selective structures incorporating waveguide gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, "Thin-film optical filters with diffractive elements and waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

S. Tibuleac and R. Magnusson, "Reflection and transmission guided-mode resonance filters," J. Opt. Soc. Am. A 14, 1617-1626 (1997).
[CrossRef]

R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
[CrossRef]

Maldonado, T. A.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, "Dielectric frequency-selective structures incorporating waveguide gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, "Thin-film optical filters with diffractive elements and waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974), Chap. 1.

Minott, G.

G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser based applications," Laser Focus World 40(9), (September 2004).

Moharam, M. G.

Morris, G. M.

Oliner, A. A.

Peng, S.

Pommet, D. A.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 5, 1077-1086 (1995).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommet, and 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]

Shin, D.

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, "Thin-film optical filters with diffractive elements and waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

Shnapir, B.

G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser based applications," Laser Focus World 40(9), (September 2004).

Sprague, R.

G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser based applications," Laser Focus World 40(9), (September 2004).

Tibuleac, S.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, "Dielectric frequency-selective structures incorporating waveguide gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, "Thin-film optical filters with diffractive elements and waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

S. Tibuleac and R. Magnusson, "Reflection and transmission guided-mode resonance filters," J. Opt. Soc. Am. A 14, 1617-1626 (1997).
[CrossRef]

Wang, S. S.

R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
[CrossRef]

Young, P. P.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, "Dielectric frequency-selective structures incorporating waveguide gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photon. Technol. Lett. 14, 1091-1093 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, "Dielectric frequency-selective structures incorporating waveguide gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

J. Opt. Soc. Am. A (6)

Laser Focus World (1)

G. Minott, R. Sprague, and B. Shnapir, "Rugate notch filters find use in laser based applications," Laser Focus World 40(9), (September 2004).

Opt. Eng. (1)

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, "Thin-film optical filters with diffractive elements and waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

M. G. Moharam and T. K. Gaylord, "Coupled-wave analysis of two-dimensional gratings," in- Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. SPIE 883, 8-11 (1986).

Other (1)

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974), Chap. 1.

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Figures (10)

Fig. 1
Fig. 1

Guided-mode resonant filters.

Fig. 2
Fig. 2

(Color online) Diffraction-guiding plane in a 1D-GMR structure.

Fig. 3
Fig. 3

General two-dimensional crossed diffraction grating and a 2D-GMR structure.

Fig. 4
Fig. 4

Planes of diffraction in a 2D-GMR with rectangular- and hexagonal-grid structures.

Fig. 5
Fig. 5

Spectral response of the two-line 1D-GMR filter for the normal incident TE wave from air. The structure parameters are grating (n H n L = 1.5∕1, fill factor = 0.6, Λ a = 320 nm, t g = 105 nm), film (n f = 1.7, t f = 343 nm), AR layer (n AR = n f n s , t AR = 475 4 n AR ), and substrate (n s = 1.47).

Fig. 6
Fig. 6

Resonance separations for two-line 1D-GMR filters (Fig. 5) versus film refractive index and film thickness.

Fig. 7
Fig. 7

Spectral response of the two-line 2D-GMR filters with a rectangular-grid structure. (a) Λ b ∕Λ a = 0.89; (b) Λ b ∕Λ a = 0.96; (c) Λ b ∕Λ a = 1.03; (d) Λ b ∕Λ a = 1.1 for a normal incident TE wave (polarized along the y axis) from air. The structure parameters are grating (n H n L = 1.5∕1, airhole radius = 50 nm, Λ a = 281 nm, t g = 100 nm), film (n f = 2.5, t f = 50 nm), AR layer (n AR = n f n s , t AR = 475 4 n AR ), and substrate (n s = 1.47).

Fig. 8
Fig. 8

Shift in the location of the second resonance in two-line 2D-GMR filters (Fig. 7) with a rectangular-grid structure versus the ratio of the grating periods.

Fig. 9
Fig. 9

(a) Film thickness versus the ratio of the two grating periods (Λ b ∕Λ a ). (b) Location of the three resonances in the three-line 2D-GMR filters with a hexagonal-grid structure versus the ratio of the grating periods for a normal incident TE wave (polarized along the y axis) from air. The structure parameters are grating (n H n L = 1.5∕1, airhole radius = 50 nm, Λ a = 280 nm, t g = 100 nm), film (n f = 2.5), AR layer (n AR = n f n s , t AR = 475 4 n AR ), and substrate (n s = 1.47).

Fig. 10
Fig. 10

Spectral response of the three-line 2D GMR filters (Fig. 9) with a hexagonal-grid structure: (a) Λ b ∕Λ a = 0.96, t f = 100.49 nm; (b) Λ b ∕Λ a = 1.07, tf = 88.97 nm; (c) Λ b ∕Λ a = 1.14, t f = 83.76 nm; (d) Λ b ∕Λ a = 1.21, t f = 79.71 nm.

Equations (6)

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k x , p = k x , inc p 2 π Λ a , k y = 0 ,
k x , p q = k x , inc [ p 2 π Λ b sec ( ζ ) + q 2 π Λ a tan ( ζ ) ] ,
k y , p q = k y , inc ( q 2 π Λ a ) ,
β k x , p q               2 + k y , p q               2 ,
V = k 0 t f n f     2 n s     2 ,
Δ λ λ 1 = C ( Λ b Λ a 1 ) + Δ λ wg λ 1 , C = 1 λ 1 d ( Δ λ ) d ( Λ b / Λ a ) .

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