Abstract

Cascaded identical resonant grating reflection filters are shown to exhibit flattened spectral responses when the individual filter elements are cascaded π out of phase. Off resonance, the net response of a cascaded arrangement is given approximately by the sum of the individual filter responses. Cascading filters π out of phase thus result in a reduction in the off-resonance reflection levels and correspondingly an increase in the spectral bandpass ratio. The spectral bandpass ratio is a figure of merit used to gauge the flatness of a response and is defined as the ratio of the linewidth at an efficiency of 90% to the linewidth at an efficiency of 10%. Cascading two and three filters in this manner results in respective increases in the spectral bandpass ratio of three times and more than five times that of a single filter.

© 2002 Optical Society of America

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References

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  1. R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815 (1996).
    [CrossRef]
  2. M. Nevière, E. Popov, R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
    [CrossRef]
  3. T. Tamir, S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
    [CrossRef]
  4. S. M. Norton, T. Erdogan, G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A 14, 629–639 (1997).
    [CrossRef]
  5. D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
    [CrossRef]
  6. D. K. Jacob, S. C. Dunn, M. G. Moharam, “Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams,” J. Opt. Soc. Am. A 18, 2109–2120 (2001).
    [CrossRef]
  7. D. K. Jacob, S. C. Dunn, 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]
  8. S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
    [CrossRef] [PubMed]
  9. S. Tibuleac, R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14, 1470–1474 (1997).
    [CrossRef]
  10. F. Lemarchand, A. Sentenac, H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 23, 1149–1151 (1998).
    [CrossRef]
  11. D. K. Jacob, S. C. Dunn, M. G. Moharam, “Interference approach applied to dual-grating dielectric resonant grating reflection filters,” Opt. Lett. 26, 1749–1751 (2001).
    [CrossRef]
  12. M. G. Moharam, E. B. Grann, D. A. Pommet, 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]

2001

2000

1998

1997

S. M. Norton, T. Erdogan, G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A 14, 629–639 (1997).
[CrossRef]

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

S. Tibuleac, R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14, 1470–1474 (1997).
[CrossRef]

1996

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815 (1996).
[CrossRef]

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

1995

Day, R. W.

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815 (1996).
[CrossRef]

Dunn, S. C.

Erdogan, T.

Friesem, A. A.

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Gaylord, T. K.

Giovannini, H.

Grann, E. B.

Jacob, D. K.

Lemarchand, F.

Magnusson, R.

S. Tibuleac, R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14, 1470–1474 (1997).
[CrossRef]

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815 (1996).
[CrossRef]

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

Moharam, M. G.

Morris, G. M.

Nevière, M.

Norton, S. M.

Pommet, D. A.

Popov, E.

Reinisch, R.

Rosenblatt, D.

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Sentenac, A.

Sharon, A.

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Tamir, T.

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

Tibuleac, S.

S. Tibuleac, R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14, 1470–1474 (1997).
[CrossRef]

Wang, S. S.

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815 (1996).
[CrossRef]

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

Zhang, S.

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

J. Lightwave Technol.

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815 (1996).
[CrossRef]

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

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Figures (5)

Fig. 1
Fig. 1

Two cascaded identical dielectric resonant grating reflection filters.

Fig. 2
Fig. 2

Comparison of calculated spectral responses of two and three resonant grating reflection filter elements cascaded in phase and π out of phase to the response of a single filter.

Fig. 3
Fig. 3

Comparison of the spectral and angular (in air) line shapes of a single resonant grating reflection filter to two and three cascaded filter elements for δ = 2mπ, d sep/λ = 2.012.

Fig. 4
Fig. 4

Comparison of the spectral and angular (in air) line shapes of a single resonant grating reflection filter to two and three cascaded filter elements for δ = (2m + 1/2)π, d sep/λ = 2.075.

Fig. 5
Fig. 5

Comparison of the spectral and angular (in air) line shapes of a single resonant grating reflection filter to two and three cascaded filter elements for δ = (2m + 1)π, d sep/λ = 2.138.

Equations (4)

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Er=ηd expiΔϕ1-1-ηdexpiΔϕ,
Et=1-ηd1-Er,
δ=2δg+δf+δAR+δsep,
δf,AR,sep=2πλ nf,AR,sepdf,AR,sep

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