Abstract

New reflection and transmission optical filters based on guided-mode resonances in multilayer waveguide gratings are characterized and compared with homogeneous thin-film filters. These guided-mode resonance filters are implemented by integration of diffraction gratings into classical thin-film multilayers to produce high-efficiency filter response and arbitrarily low sidebands extended over a large spectral range. Compared with homogeneous thin-film reflection filters, guided-mode resonance reflection filters require significantly fewer layers for a narrow linewidth and a high peak response to be obtained. The single-grating transmission filters presented have a narrower linewidth than Fabry–Perot filters with an equal number of layers and similar materials while maintaining high peak transmittance and low sidebands.

© 1997 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, “Waveguide mode-induced resonances in planar diffraction gratings,” in OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.
  2. H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
    [CrossRef]
  3. 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]
  4. R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
    [CrossRef]
  5. S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
    [CrossRef] [PubMed]
  6. S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
    [CrossRef] [PubMed]
  7. S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
    [CrossRef] [PubMed]
  8. R. Magnusson, S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Opt. 34, 8106–8109 (1995).
    [CrossRef] [PubMed]
  9. 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]
  10. S. Peng, G. M. Morris, “Sub-nanometer linewidth resonant grating filters,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 257–260.
  11. V. V. Meriakri, I. P. Nikitin, M. P. Parkhomenko “Frequency characteristics of metal-dielectric gratings,” Radiotekh. Elektron. 4, 604–611 (1992).
  12. 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. 42, 567–569 (1994).
    [CrossRef]
  13. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  14. M. G. Moharam, T. K. Gaylord “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  15. H. A. Macleod, Thin-Film Optical Filters (McGraw-Hill, New York, 1989).
  16. J. D. Rancourt, Optical Thin Films Users’ Handbook (Macmillan, New York, 1987).
  17. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989).
  18. J. A. Dombrowolski, Coatings and Filters. Handbook of Optics (McGraw-Hill, New York, 1978).
  19. TFCalc Manual, Thin Film Design Software for Windows Version 3.0 (Software Spectra, Inc., Portland, Ore., 1995).
  20. R. Magnusson, S. Tibuleac, Z. Liu, D. Shin, P. P. Young, S. S. Wang, “Thin-film filters with diffractive and waveguiding layers,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 246–248.
  21. Sh. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontieres, Paris, 1992).
  22. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  23. S. Tibuleac, R. Magnusson, S. S. Wang, T. A. Maldonado, A. E. Oberhofer, “Linewidth broadening mechanisms of guided-mode resonance filters,” presented at OSA Annual Meeting, Portland, Ore., Sept. 10–15, 1995 (Optical Society of America, Washington, D.C., 1995), p. 154.

1995

1994

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. 42, 567–569 (1994).
[CrossRef]

S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
[CrossRef] [PubMed]

1993

1992

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

V. V. Meriakri, I. P. Nikitin, M. P. Parkhomenko “Frequency characteristics of metal-dielectric gratings,” Radiotekh. Elektron. 4, 604–611 (1992).

1990

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]

1989

H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

1985

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

1982

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 OSA 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, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (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. 42, 567–569 (1994).
[CrossRef]

Cheo, L.

H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

Dombrowolski, J. A.

J. A. Dombrowolski, Coatings and Filters. Handbook of Optics (McGraw-Hill, New York, 1978).

Furman, Sh. A.

Sh. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontieres, Paris, 1992).

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.

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 “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
[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. SPIE1210, 83–89 (1990).
[CrossRef]

Liu, Z.

R. Magnusson, S. Tibuleac, Z. Liu, D. Shin, P. P. Young, S. S. Wang, “Thin-film filters with diffractive and waveguiding layers,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 246–248.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (McGraw-Hill, New York, 1989).

Magnusson, R.

S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
[CrossRef] [PubMed]

R. Magnusson, S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Opt. 34, 8106–8109 (1995).
[CrossRef] [PubMed]

S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
[CrossRef] [PubMed]

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. 42, 567–569 (1994).
[CrossRef]

S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
[CrossRef] [PubMed]

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 OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

R. Magnusson, S. Tibuleac, Z. Liu, D. Shin, P. P. Young, S. S. Wang, “Thin-film filters with diffractive and waveguiding layers,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 246–248.

S. Tibuleac, R. Magnusson, S. S. Wang, T. A. Maldonado, A. E. Oberhofer, “Linewidth broadening mechanisms of guided-mode resonance filters,” presented at OSA Annual Meeting, Portland, Ore., Sept. 10–15, 1995 (Optical Society of America, Washington, D.C., 1995), p. 154.

Maldonado, T. A.

S. Tibuleac, R. Magnusson, S. S. Wang, T. A. Maldonado, A. E. Oberhofer, “Linewidth broadening mechanisms of guided-mode resonance filters,” presented at OSA Annual Meeting, Portland, Ore., Sept. 10–15, 1995 (Optical Society of America, Washington, D.C., 1995), p. 154.

Meriakri, V. V.

V. V. Meriakri, I. P. Nikitin, M. P. Parkhomenko “Frequency characteristics of metal-dielectric gratings,” Radiotekh. Elektron. 4, 604–611 (1992).

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 “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, M. G. Moharam, “Waveguide mode-induced resonances in planar diffraction gratings,” in OSA 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. SPIE1210, 83–89 (1990).
[CrossRef]

Morris, G. M.

S. Peng, G. M. Morris, “Sub-nanometer linewidth resonant grating filters,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 257–260.

Nikitin, I. P.

V. V. Meriakri, I. P. Nikitin, M. P. Parkhomenko “Frequency characteristics of metal-dielectric gratings,” Radiotekh. Elektron. 4, 604–611 (1992).

Oberhofer, A. E.

S. Tibuleac, R. Magnusson, S. S. Wang, T. A. Maldonado, A. E. Oberhofer, “Linewidth broadening mechanisms of guided-mode resonance filters,” presented at OSA Annual Meeting, Portland, Ore., Sept. 10–15, 1995 (Optical Society of America, Washington, D.C., 1995), p. 154.

Parkhomenko, M. P.

V. V. Meriakri, I. P. Nikitin, M. P. Parkhomenko “Frequency characteristics of metal-dielectric gratings,” Radiotekh. Elektron. 4, 604–611 (1992).

Peng, S.

S. Peng, G. M. Morris, “Sub-nanometer linewidth resonant grating filters,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 257–260.

Rancourt, J. D.

J. D. Rancourt, Optical Thin Films Users’ Handbook (Macmillan, New York, 1987).

Shin, D.

R. Magnusson, S. Tibuleac, Z. Liu, D. Shin, P. P. Young, S. S. Wang, “Thin-film filters with diffractive and waveguiding layers,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 246–248.

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. 42, 567–569 (1994).
[CrossRef]

Tamir, T.

H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[CrossRef]

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989).

Tibuleac, S.

R. Magnusson, S. Tibuleac, Z. Liu, D. Shin, P. P. Young, S. S. Wang, “Thin-film filters with diffractive and waveguiding layers,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 246–248.

S. Tibuleac, R. Magnusson, S. S. Wang, T. A. Maldonado, A. E. Oberhofer, “Linewidth broadening mechanisms of guided-mode resonance filters,” presented at OSA Annual Meeting, Portland, Ore., Sept. 10–15, 1995 (Optical Society of America, Washington, D.C., 1995), p. 154.

Tikhonravov, A. V.

Sh. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontieres, Paris, 1992).

Wang, S. S.

S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
[CrossRef] [PubMed]

R. Magnusson, S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Opt. 34, 8106–8109 (1995).
[CrossRef] [PubMed]

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. 42, 567–569 (1994).
[CrossRef]

S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
[CrossRef] [PubMed]

S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
[CrossRef] [PubMed]

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 OSA Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 117.

R. Magnusson, S. Tibuleac, Z. Liu, D. Shin, P. P. Young, S. S. Wang, “Thin-film filters with diffractive and waveguiding layers,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 246–248.

S. Tibuleac, R. Magnusson, S. S. Wang, T. A. Maldonado, A. E. Oberhofer, “Linewidth broadening mechanisms of guided-mode resonance filters,” presented at OSA Annual Meeting, Portland, Ore., Sept. 10–15, 1995 (Optical Society of America, Washington, D.C., 1995), p. 154.

Yeh, P.

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

Young, P. P.

R. Magnusson, S. Tibuleac, Z. Liu, D. Shin, P. P. Young, S. S. Wang, “Thin-film filters with diffractive and waveguiding layers,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 246–248.

Appl. Opt.

Appl. Phys. Lett.

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

IEEE Trans. Antennas Propag.

H. Bertoni, L. Cheo, T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
[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. 42, 567–569 (1994).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

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]

Opt. Lett.

Proc. IEEE

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

Radiotekh. Elektron.

V. V. Meriakri, I. P. Nikitin, M. P. Parkhomenko “Frequency characteristics of metal-dielectric gratings,” Radiotekh. Elektron. 4, 604–611 (1992).

Other

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

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]

S. Peng, G. M. Morris, “Sub-nanometer linewidth resonant grating filters,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 257–260.

H. A. Macleod, Thin-Film Optical Filters (McGraw-Hill, New York, 1989).

J. D. Rancourt, Optical Thin Films Users’ Handbook (Macmillan, New York, 1987).

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989).

J. A. Dombrowolski, Coatings and Filters. Handbook of Optics (McGraw-Hill, New York, 1978).

TFCalc Manual, Thin Film Design Software for Windows Version 3.0 (Software Spectra, Inc., Portland, Ore., 1995).

R. Magnusson, S. Tibuleac, Z. Liu, D. Shin, P. P. Young, S. S. Wang, “Thin-film filters with diffractive and waveguiding layers,” in Diffractive Optics and Micro-optics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 246–248.

Sh. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontieres, Paris, 1992).

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

S. Tibuleac, R. Magnusson, S. S. Wang, T. A. Maldonado, A. E. Oberhofer, “Linewidth broadening mechanisms of guided-mode resonance filters,” presented at OSA Annual Meeting, Portland, Ore., Sept. 10–15, 1995 (Optical Society of America, Washington, D.C., 1995), p. 154.

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Figures (17)

Fig. 1
Fig. 1

Single-layer guided-mode resonance filter consisting of a grating with rectangular refractive-index profile of high (εH) and low (εL) dielectric constants with period Λ and thickness d.

Fig. 2
Fig. 2

Reflectance of the single-layer guided-mode resonance filter over the entire visible range. The refractive indices are nH=2.1, nL=2.0, nC=1, nS=1.52; the thickness is d =134 nm (half-wave at λ=550 nm); and the grating period is Λ=314 nm.

Fig. 3
Fig. 3

Reflectance of a double-layer waveguide-grating filter with V-type AR coating. The layer thicknesses are d1 =73 nm (0.73quarter-wave thickness) and d2=115 nm (1.72   quarter-wave thickness). The refractive indices are n1=1.38, nH,2=2.1, nL,2=2.0, nC=1.0, nS=1.52. The grating period is Λ=317 nm.

Fig. 4
Fig. 4

Reflectance of a double-layer waveguide-grating filter with W-type AR coating. The layer thicknesses are d1 =100 nm (quarter-wave thickness) and d2=134 nm (half-wave thickness). The refractive indices are n1=1.38, nH,2 =2.1, nL,2=2.0, nC=1.0, nS=1.52. The grating period is Λ=310 nm.

Fig. 5
Fig. 5

Reflectance of a double-layer structure with a surface-relief grating. The parameters are Λ=360 nm, d1=93.6 nm (quarter-wave), d2=75.5 nm (quarter-wave), nH,1=1.8, nL,1 =1.0, n2=1.8, nS=1.52, nC=1.0.

Fig. 6
Fig. 6

Triple-layer waveguide-grating filter response. The grating periods are a: Λ=290 nm, b: Λ= 310 nm, and c:Λ=330 nm. The optical thicknesses of the layers are λ/4λ/2λ/4 at 550 nm. The refractive indices are n1=1.38, nH,2=2.1, nL,2 =2.0, n3=1.62, nC=1.0, nS=1.52.

Fig. 7
Fig. 7

Triple-layer filter response with surface-relief grating. The thicknesses are all quarter-wave at 550 nm. The other parameters are Λ=330 nm, nH,1=1.6, nL,1=1.0, n2=2.0, n3 =1.85, nC=1.0, nS=1.52.

Fig. 8
Fig. 8

Transmittance of a 6-layer structure with the grating in the first layer and 5 high/low homogeneous quarter-wave layers. The grating parameters are Λ=330 nm, d=58.4 nm, nH =2.5, nL=2.2. The thicknesses and the refractive indices of the homogeneous layers are d=58.5 nm, n=2.35 (odd layers), d=100 nm, n=1.38 (even layers).

Fig. 9
Fig. 9

Spectral response of a 9-layer transmission filter with gratings in the top and the bottom layers. The gratings’ parameters are Λ=330 nm, nH,1=nH,9=2.5, nL,1=nL,9=2.2, d1 =d9=58.4 nm. Homogeneous layers have n=2.35 (odd layers) and n=1.38 (even layers) and quarter-wave thicknesses d =58.5 nm (odd layers) and d=100 nm (even layers).

Fig. 10
Fig. 10

Grating-enclosed guided-mode transmission filter (top) and its spectral response (bottom). The thicknesses and the refractive indices are the same as in the structure shown in Fig. 9 with two additional homogeneous high/low quarter-wave layers. The grating period is Λ=345 nm.

Fig. 11
Fig. 11

Transmittance of a 9-layer structure with one grating in the center layer. All the layers are a quarter-wave thick at 550 nm. The grating has the parameters Λ=330 nm, nH,5 =2.5, nL,5=2.2, d5=58.4 nm. The homogeneous layers have the following parameters: n=2.35 and d=58.5 nm (odd layers); n=1.38 and d=99.6 nm (even layers); nC=1.0, ns =1.52.

Fig. 12
Fig. 12

Transmittance of a 9-layer single-grating resonance filter that uses only two materials. The parameters are Λ =340 nm, nH=nodd=2.35, nL=neven=1.38, nS=1.52, nC=1.0. The grating fill factor f is indicated. All the optical layer thicknesses are a quarter-wave at 550 nm.  

Fig. 13
Fig. 13

Spectral response of a Boudot reflection filter, a computer-optimized design with 34 layers of alternating materials with nodd=1.46 and neven=2.3; nC=1.0 (cover), nS =1.52 (substrate) (following Ref. 19).

Fig. 14
Fig. 14

Spectral response of a rugate coating centered at 1066 nm. There are 491 layers (24.5 periods) simulating a sinusoidal variation of the refractive index with values between 1.9 and 2.1 (following Ref. 19).

Fig. 15
Fig. 15

Reflectance of a notch filter with 150 alternating layers with refractive indices nodd=1.52 and neven=1.47; optical thicknesses are three quarter-wave.  

Fig. 16
Fig. 16

Transmittance of a Fabry–Perot filter with 11 layers of alternating ZnS (nodd=2.35) and MgF2 (neven=1.38); nC =1.0, nS=1.52. The center layer is a half-wave thick; the other layer thicknesses are all a quarter-wave at 550 nm.

Fig. 17
Fig. 17

Spectral response of an 11-layer waveguide-grating filter with gratings in layers 1 and 11 (left) and a 9-layer waveguide-grating filter with one grating in layer 5. The grating periods are Λ=336 nm (left) and Λ=330 nm (right). The refractive indices and thicknesses are the same in both cases. The grating layers have the parameters nH=2.5, nL=2.2, d =58.4 nm. For odd-numbered layers, d=58.5 nm and n =2.35. For even-numbered layers, d=99.6 nm and n=1.38. The substrate is silica (nS=1.52), and the cover is air (nC =1.0).

Tables (1)

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Table 1 Comparison between a Single-Grating Resonance Filter and Fabry–Perot Filters a

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