Abstract

Techniques for controlling spectral width are used in conjunction with thin-film techniques in the design of guided-mode resonance (GMR) filters to provide simultaneous control over line-shape symmetry, sideband levels, and spectral width. Several factors that could limit the minimum spectral width are discussed. We used interference effects for passband shaping by stacking multiple GMR filters on top of one another. A design is presented for a 200-GHz telecommunications filter along with a tolerance analysis. Compared with a conventional thin-film filter, the GMR filter has fewer layers and looser thickness tolerances. Grating fabrication tolerances are also discussed.

© 2003 Optical Society of America

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References

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    [CrossRef]
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2002 (1)

2001 (1)

2000 (4)

1998 (3)

1997 (1)

1996 (3)

1995 (3)

1994 (1)

1992 (1)

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

1990 (1)

P. D. Townsend, “An overview of ion-implanted optical waveguide profiles,” Nucl. Instrum. Methods Phys. Res. B 46, 18–25 (1990).
[CrossRef]

1989 (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]

1985 (1)

G. A. Golubenko, V. A. Sychugov, A. V. Tishchenko, “The phenomenon of full ‘external’ reflection of light from the surface of a corrugated dielectric waveguide and its use in narrow band filters,” Sov. Phys. Lebedev Inst. Rep. 1(11), 36–40 (1985).

1981 (1)

1977 (1)

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

1973 (1)

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

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

1941 (1)

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]

Boye, R. R.

Brazas, J. C.

C. Dunn, S.

D. K. Jacob, S. C. Dunn, M. G. Moharam, “Resonant grating reflection filters for normally incident Gaussian beams,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 41 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 23–25.

Cadilhac, M.

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

Cox, J. A.

J. A. Cox, R. A. Morgan, R. Wilke, C. M. Ford, “Guided-mode grating resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
[CrossRef]

Cunn, S. C.

Dunn, S. C.

Engel, H.

Erdogan, T.

Fano, U.

Ford, C. M.

J. A. Cox, R. A. Morgan, R. Wilke, C. M. Ford, “Guided-mode grating resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
[CrossRef]

Friesem, A. A.

G. Levy-Yurista, A. A. Friesem, “Very narrow spectral filters with multilayered grating/waveguide structures,” Appl. Phys. Lett. 77, 1596–1598 (2000).
[CrossRef]

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

A. Sharon, D. Rosenblatt, A. A. Friesem, H. G. Weber, H. Engel, R. Steingrueber, “Light modulation with resonant grating-waveguide structures,” Opt. Lett. 21, 1564–1566 (1996).
[CrossRef]

Gale, M. T.

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. SPIE1210, 83–89 (1990).
[CrossRef]

Gaylord, T. K.

Giovannini, H.

Golubenko, G. A.

G. A. Golubenko, V. A. Sychugov, A. V. Tishchenko, “The phenomenon of full ‘external’ reflection of light from the surface of a corrugated dielectric waveguide and its use in narrow band filters,” Sov. Phys. Lebedev Inst. Rep. 1(11), 36–40 (1985).

Haruna, M.

H. Nishihara, M. Haruna, T. Suhara, “Materials and fabrication techniques,” in Optical Integrated Circuits (McGraw-Hill, New York, 1989), pp. 138–171.

Hegedus, Z.

Jacob, D. K.

D. K. Jacob, S. C. Dunn, M. G. Moharam, “Flat-top narrow-band spectral response obtained from cascaded resonant grating reflection filters,” Appl. Opt. 41, 1241–1245 (2002).
[CrossRef] [PubMed]

D. K. Jacob, S. C. Cunn, 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]

D. K. Jacob, S. C. Dunn, M. G. Moharam, “Resonant grating reflection filters for normally incident Gaussian beams,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 41 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 23–25.

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. SPIE1210, 83–89 (1990).
[CrossRef]

Kostuk, R. K.

Lemarchand, F.

Levy-Yurista, G.

G. Levy-Yurista, A. A. Friesem, “Very narrow spectral filters with multilayered grating/waveguide structures,” Appl. Phys. Lett. 77, 1596–1598 (2000).
[CrossRef]

Li, L.

Liu, Z. S.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (American Elsevier, New York, 1969).

H. A. Macleod, “Challenges in the design and production of narrow-band filters for optical fiber telecommunications,” in Optical and Infrared Thin Films, M. L. Fulton, ed., Proc. SPIE4094, 46–57 (2000).
[CrossRef]

Magnusson, R.

Main, I. G.

I. G. Main, “Forced vibrations,” in Vibrations and Waves in Physics (Cambridge University Cambridge, England1993), pp. 56–77.
[CrossRef]

Moharam, M. G.

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. SPIE1210, 83–89 (1990).
[CrossRef]

Morgan, R. A.

J. A. Cox, R. A. Morgan, R. Wilke, C. M. Ford, “Guided-mode grating resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
[CrossRef]

Morris, G. M.

Netterfield, R.

Nevière, M.

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

Nishihara, H.

H. Nishihara, M. Haruna, T. Suhara, “Materials and fabrication techniques,” in Optical Integrated Circuits (McGraw-Hill, New York, 1989), pp. 138–171.

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.

Peng, S.

Peng, S. T.

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Petit, R.

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

Rosenblatt, D.

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

A. Sharon, D. Rosenblatt, A. A. Friesem, H. G. Weber, H. Engel, R. Steingrueber, “Light modulation with resonant grating-waveguide structures,” Opt. Lett. 21, 1564–1566 (1996).
[CrossRef]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Saarinen, J.

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

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley-/Interscience, New York, 1991), pp. 80–107.
[CrossRef]

Sentenac, A.

Sharon, A.

A. Sharon, D. Rosenblatt, A. A. Friesem, H. G. Weber, H. Engel, R. Steingrueber, “Light modulation with resonant grating-waveguide structures,” Opt. Lett. 21, 1564–1566 (1996).
[CrossRef]

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

Shin, D.

Steingrueber, R.

Suhara, T.

H. Nishihara, M. Haruna, T. Suhara, “Materials and fabrication techniques,” in Optical Integrated Circuits (McGraw-Hill, New York, 1989), pp. 138–171.

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, V. A. Sychugov, A. V. Tishchenko, “The phenomenon of full ‘external’ reflection of light from the surface of a corrugated dielectric waveguide and its use in narrow band filters,” Sov. Phys. Lebedev Inst. Rep. 1(11), 36–40 (1985).

Tamir, T.

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley-/Interscience, New York, 1991), pp. 80–107.
[CrossRef]

Thurman, S. T.

S. T. Thurman, G. M. Morris, “Resonant-grating filter design: the appropriate effective-index model,” presented at the OSA Annual Meeting, Providence, R.I., 22–26 Oct. 2000.

Tibuleac, S.

Tishchenko, A. V.

G. A. Golubenko, V. A. Sychugov, A. V. Tishchenko, “The phenomenon of full ‘external’ reflection of light from the surface of a corrugated dielectric waveguide and its use in narrow band filters,” Sov. Phys. Lebedev Inst. Rep. 1(11), 36–40 (1985).

Townsend, P. D.

P. D. Townsend, “An overview of ion-implanted optical waveguide profiles,” Nucl. Instrum. Methods Phys. Res. B 46, 18–25 (1990).
[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. G.

Wilke, R.

J. A. Cox, R. A. Morgan, R. Wilke, C. M. Ford, “Guided-mode grating resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
[CrossRef]

Young, P. P.

Appl. Opt. (4)

Appl. Phys. (1)

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Appl. Phys. Lett. (3)

G. Levy-Yurista, A. A. Friesem, “Very narrow spectral filters with multilayered grating/waveguide structures,” Appl. Phys. Lett. 77, 1596–1598 (2000).
[CrossRef]

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

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[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. (2)

J. Opt. Soc. Am. A (4)

Nucl. Instrum. Methods Phys. Res. B (1)

P. D. Townsend, “An overview of ion-implanted optical waveguide profiles,” Nucl. Instrum. Methods Phys. Res. B 46, 18–25 (1990).
[CrossRef]

Opt. Commun. (1)

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating coupler/waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[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. (6)

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Sov. Phys. Lebedev Inst. Rep. (1)

G. A. Golubenko, V. A. Sychugov, A. V. Tishchenko, “The phenomenon of full ‘external’ reflection of light from the surface of a corrugated dielectric waveguide and its use in narrow band filters,” Sov. Phys. Lebedev Inst. Rep. 1(11), 36–40 (1985).

Other (10)

S. M. Norton, “Resonant grating structures: theory, design, and applications,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1997).

J. A. Cox, R. A. Morgan, R. Wilke, C. M. Ford, “Guided-mode grating resonant filters for VCSEL applications,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 70–76 (1998).
[CrossRef]

H. A. Macleod, Thin-Film Optical Filters (American Elsevier, New York, 1969).

H. A. Macleod, “Challenges in the design and production of narrow-band filters for optical fiber telecommunications,” in Optical and Infrared Thin Films, M. L. Fulton, ed., Proc. SPIE4094, 46–57 (2000).
[CrossRef]

S. T. Thurman, G. M. Morris, “Resonant-grating filter design: the appropriate effective-index model,” presented at the OSA Annual Meeting, Providence, R.I., 22–26 Oct. 2000.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley-/Interscience, New York, 1991), pp. 80–107.
[CrossRef]

D. K. Jacob, S. C. Dunn, M. G. Moharam, “Resonant grating reflection filters for normally incident Gaussian beams,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 41 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 23–25.

I. G. Main, “Forced vibrations,” in Vibrations and Waves in Physics (Cambridge University Cambridge, England1993), pp. 56–77.
[CrossRef]

H. Nishihara, M. Haruna, T. Suhara, “Materials and fabrication techniques,” in Optical Integrated Circuits (McGraw-Hill, New York, 1989), pp. 138–171.

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. SPIE1210, 83–89 (1990).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Illustration of a three-layer GMR filter; n s , n 1, n 2, and n c are the indices of the substrate, layer 1, layer 2, and the cover region; d 1, d 2, and d 3 are the layer thicknesses; n 3hi and n 3lo represent the high and low indices of the grating layer; Λ is the grating period; f is the grating fill factor, and θ is the angle of incidence.

Fig. 2
Fig. 2

Spectral response for two three-layer GMR filters. Both filters are based on the thin-film method: the dashed curve represents a filter taken from Fig. 3 of Ref. 4, which is based on the zeroth-order effective-index model with f = 50%; the solid curve represents a filter based on the exact effective-index model with f = 42%. The remaining design parameters are the same for both filters: n s = 1.453, n 1 = 2.005, n 2 = 2.106, n 3hi = 1.490, n 3lo = n c = 1.000, d 1 = 106 nm, d 2 = 101 nm, d 3 = 168 nm, Λ = 483 nm, and θ = 0 deg.

Fig. 3
Fig. 3

Spectral response for a series of three-layer GMR filters with various buffer layer thicknesses. The solid curve represents a filter with d 2 = 0 nm and Λ = 855 nm; the dashed curve represents a filter with d 2 = 150 nm and Λ = 846 nm; the dotted curve represents a filter with d 2 = 300 nm and Λ = 843 nm; the dash-dot curve represents a filter with d 2 = 500 nm and Λ = 842 nm. The remaining design parameters are the same for each filter: n s = n 2 = n 3hi = 1.500, n 1 = 2.000, n 3lo = n c = 1.000, d 1 = 388 nm, d 3 = 317 nm, f = 33%, and θ = 5 deg.

Fig. 4
Fig. 4

Relationship between spectral width and buffer layer thickness for the series of GMR filters in Fig. 3. The squares represent data from RCWA calculations and the line represents calculations based on Eq. (4), where a waveguide perturbation method20 is used to estimate the loss of leaky mode γ. The design parameters are the same as for the filters in Fig. 3.

Fig. 5
Fig. 5

Illustration of a five-layer GMR filter made up of a V coat, a waveguide layer, and another V coat that includes a grating layer.

Fig. 6
Fig. 6

Spectral response for a series of five-layer GMR filters based on the geometry of Fig. 5 with various waveguide layer thicknesses. The solid curve represents a filter with d 3 = 1000 nm, Λ = 739 nm, and f = 41.2%; the dashed curve represents a filter with d 3 = 1500 nm, Λ = 727 nm, and f = 41.3%; the dotted curve represents a filter with d 3 = 2000 nm, Λ = 722 nm, and f = 41.4%. The remaining design parameters are the same for each filter: n s = n 2 = n 4 = n 5hi = 1.500, n 1 = n 3 = 2.000, n 5lo = n c = 1.000, d 1 = 64 nm, d 2 = 86 nm, d 4 = 186 nm, d 5 = 160 nm, and θ = 10 deg.

Fig. 7
Fig. 7

Relationship between spectral width and waveguide layer thickness for the series of GMR filters in Fig. 6. The squares represent data from RCWA calculations and the curve represents calculations based on Eq. (4), where a waveguide perturbation method20 is used to estimate the loss of leaky mode γ. The design parameters are the same as for the filters in Fig. 6.

Fig. 8
Fig. 8

Illustration of a stack of four GMR filters. Each filter is identical and made up of a V coat, a waveguide layer, and an antireflective grating layer. d s1, d s2, d s3, and d s4 represent the thicknesses of the spacer layers between the filters. An additional V coat is on top of the stack. The design parameters are n s = n 2 = n 4lo = n v2 = 1.500, n 1 = n 3 = n 4hi = n v1 = 2.000, n c = 1.000, d 1 = 64 nm, d 2 = 85 nm, d 3 = 1027 nm, d 4 = 238 nm, Λ = 769 nm, f = 30%, d s1 = 1520 nm, d s2 = 1808 nm, d s3 = 1520 nm, d s4 = 600 nm, d v1 = 292 nm, d v2 = 195 nm, and θ = 5 deg.

Fig. 9
Fig. 9

Spectral response of two 200-GHz WDM filters. The solid curve represents the stacked GMR filter of Fig. 9, which operates in reflection, whereas the dashed curve represents a three-cavity Fabry-Perot thin-film filter, which operates in transmission. The design of the thin-film filter is taken from Ref. 2: A |LH (HL)7 6H (LH)7 L (HL)7 6H (LH)7 L (HL)7 6H (LH)7| G, where L = 303.51 nm, H = 94.4 nm, each H and L represents a quarter-wave layer of the high- and low-index materials, and the indices of refraction are n A = 1.000, n L = 1.444, n H = 2.100, and n G = 1.500. The design wavelength is λ0 = 1550 nm and the angle of incidence is θ = 0 deg. The dotted lines indicate the filter specifications.

Fig. 10
Fig. 10

Spectral response for an ensemble of GMR filters based on the design of Fig. 8 with random fabrication errors. Table 2 shows the nominal value and standard deviation for each design parameter. The dotted lines indicate the filter specifications.

Tables (2)

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Table 1 Estimated Size of GMR Filters for Telecommunication Applications

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Table 2 Tolerance Analysis of GMR 200-GHz Telecommunication Filter

Equations (13)

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nhi2-neff21/2tanπnhi2-neff21/2fΛ/λ=-nlo2-neff21/2tanπnlo2-neff21/2×1-fΛ/λ,
neff=fnhi2+1-fnlo21/2.
β=β0+iγ,
ΔλFWHM=λ0Λγ/π,
γd  γc,
γd=L/20 log10e.
ΔλFWHM  0.0044 nm
N=Cλ0/ΔλFWHM,
wΛλ0/ΔλFWHM=π/γ,
aγ  1,
Δθ=λ0γ/π cosθ,
δθ=4λ/πa,
a  4 cosθ/γ,

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