Abstract

Multilayer, multimode waveguides are utilized in resonant grating filters having a broadened angular acceptance bandwidth for multiple wavelengths at a single oblique angle of incidence. It is shown that the waveguide grating structure should support a few leaky modes in order to support a multiwavelength resonant filter at oblique incidence with broadened angle acceptance at each wavelength.

© 2007 Optical Society of America

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  1. R. Magnusson, D. Shin, and Z. S. Liu, "Guided-mode Resonance Brewster Filter," Opt. Lett. 23, 612-614 (1998).
    [CrossRef]
  2. R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
    [CrossRef]
  3. S. M. Norton, G. M. Morris, and T. Erdogan, "Experimental investigation of resonant-grating filter lineshapes in comparison with theoretical models," J. Opt. Soc. Am. A 15, 464-472 (1998).
    [CrossRef]
  4. E. Popov and B. Bozhkov, "Corrugated waveguides as resonance optical filters-advantages and limitations," J. Opt. Soc. Am. A. 18, 1758-1764 (2001).
    [CrossRef]
  5. D. K. Jacob, S. C. Dunn, and 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]
  6. M. Neviere, "The homogeneous problem," in Electromagnetic Theory of Gratings, R. Petit, ed., (Springer-Verlag, Berlin 1980).
  7. F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, "Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters," J. Opt. A: Pure Appl. Opt. 1, 545-551 (1999).
    [CrossRef]
  8. A. Sentenac and A. L. Fehrembach, "Angular tolerant resonant grating filters under oblique incidence," J. Opt. Soc. Am. A. 22, 475-480 (2005).
    [CrossRef]
  9. A. L. Fehrembach, S. Hernandez, and A. Sentenac, "k-gaps for multimode waveguide gratings," Phys. Rev. B. 73, 233405 (2006).
    [CrossRef]
  10. Q. Cao, P. Lalanne, and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A. 19, 335-338 (2002).
    [CrossRef]
  11. M. G. Moharam and A. B. Greenwell, "Efficient rigorous calculations of power flow in grating coupled surface-emitting devices," Proc. SPIE. 5456, 57-67 (2004).
    [CrossRef]
  12. S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133, (1975).
    [CrossRef]
  13. D. Shin, S. Tibuleac, T. A. Maldanado, and R. Magnusson, "Thin-film optical filterswith Diffractive Elements and Waveguides," Opt. Eng. 37, 2634-2646 (1998).
    [CrossRef]
  14. A. B. Greenwell, S. Boonruang, and M. G. Moharam, "Effect of Loss or Gain on Guided Mode Resonant Devices," in Integrated Photonics Research and Applications/Nanophotonics, Technical Digest (CD) (Optical Society of America, 2006), paper NThA1.

2006 (1)

A. L. Fehrembach, S. Hernandez, and A. Sentenac, "k-gaps for multimode waveguide gratings," Phys. Rev. B. 73, 233405 (2006).
[CrossRef]

2005 (1)

A. Sentenac and A. L. Fehrembach, "Angular tolerant resonant grating filters under oblique incidence," J. Opt. Soc. Am. A. 22, 475-480 (2005).
[CrossRef]

2004 (1)

M. G. Moharam and A. B. Greenwell, "Efficient rigorous calculations of power flow in grating coupled surface-emitting devices," Proc. SPIE. 5456, 57-67 (2004).
[CrossRef]

2002 (1)

Q. Cao, P. Lalanne, and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A. 19, 335-338 (2002).
[CrossRef]

2001 (2)

E. Popov and B. Bozhkov, "Corrugated waveguides as resonance optical filters-advantages and limitations," J. Opt. Soc. Am. A. 18, 1758-1764 (2001).
[CrossRef]

D. K. Jacob, S. C. Dunn, and 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]

1999 (1)

F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, "Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters," J. Opt. A: Pure Appl. Opt. 1, 545-551 (1999).
[CrossRef]

1998 (3)

1992 (1)

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

1975 (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133, (1975).
[CrossRef]

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133, (1975).
[CrossRef]

Bozhkov, B.

E. Popov and B. Bozhkov, "Corrugated waveguides as resonance optical filters-advantages and limitations," J. Opt. Soc. Am. A. 18, 1758-1764 (2001).
[CrossRef]

Cambril, E

F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, "Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters," J. Opt. A: Pure Appl. Opt. 1, 545-551 (1999).
[CrossRef]

Cao, Q.

Q. Cao, P. Lalanne, and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A. 19, 335-338 (2002).
[CrossRef]

Dunn, S. C.

D. K. Jacob, S. C. Dunn, and 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]

Erdogan, T.

Fehrembach, A. L.

A. L. Fehrembach, S. Hernandez, and A. Sentenac, "k-gaps for multimode waveguide gratings," Phys. Rev. B. 73, 233405 (2006).
[CrossRef]

A. Sentenac and A. L. Fehrembach, "Angular tolerant resonant grating filters under oblique incidence," J. Opt. Soc. Am. A. 22, 475-480 (2005).
[CrossRef]

Giovannini, H

F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, "Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters," J. Opt. A: Pure Appl. Opt. 1, 545-551 (1999).
[CrossRef]

Greenwell, A. B.

M. G. Moharam and A. B. Greenwell, "Efficient rigorous calculations of power flow in grating coupled surface-emitting devices," Proc. SPIE. 5456, 57-67 (2004).
[CrossRef]

Hernandez, S.

A. L. Fehrembach, S. Hernandez, and A. Sentenac, "k-gaps for multimode waveguide gratings," Phys. Rev. B. 73, 233405 (2006).
[CrossRef]

Hugonin, J. P.

Q. Cao, P. Lalanne, and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A. 19, 335-338 (2002).
[CrossRef]

Jacob, D. K.

D. K. Jacob, S. C. Dunn, and 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]

Lalanne, P.

Q. Cao, P. Lalanne, and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A. 19, 335-338 (2002).
[CrossRef]

Lemarchand, F.

F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, "Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters," J. Opt. A: Pure Appl. Opt. 1, 545-551 (1999).
[CrossRef]

Liu, Z. S.

Magnusson, R.

R. Magnusson, D. Shin, and Z. S. Liu, "Guided-mode Resonance Brewster Filter," Opt. Lett. 23, 612-614 (1998).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldanado, and R. Magnusson, "Thin-film optical filterswith Diffractive Elements and Waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

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

Maldanado, T. A.

D. Shin, S. Tibuleac, T. A. Maldanado, and R. Magnusson, "Thin-film optical filterswith Diffractive Elements and Waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

Moharam, M. G.

M. G. Moharam and A. B. Greenwell, "Efficient rigorous calculations of power flow in grating coupled surface-emitting devices," Proc. SPIE. 5456, 57-67 (2004).
[CrossRef]

D. K. Jacob, S. C. Dunn, and 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]

Morris, G. M.

Norton, S. M.

Peng, S. T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133, (1975).
[CrossRef]

Popov, E.

E. Popov and B. Bozhkov, "Corrugated waveguides as resonance optical filters-advantages and limitations," J. Opt. Soc. Am. A. 18, 1758-1764 (2001).
[CrossRef]

Sentenac, A

F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, "Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters," J. Opt. A: Pure Appl. Opt. 1, 545-551 (1999).
[CrossRef]

Sentenac, A.

A. L. Fehrembach, S. Hernandez, and A. Sentenac, "k-gaps for multimode waveguide gratings," Phys. Rev. B. 73, 233405 (2006).
[CrossRef]

A. Sentenac and A. L. Fehrembach, "Angular tolerant resonant grating filters under oblique incidence," J. Opt. Soc. Am. A. 22, 475-480 (2005).
[CrossRef]

Shin, D.

D. Shin, S. Tibuleac, T. A. Maldanado, and R. Magnusson, "Thin-film optical filterswith Diffractive Elements and Waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

R. Magnusson, D. Shin, and Z. S. Liu, "Guided-mode Resonance Brewster Filter," Opt. Lett. 23, 612-614 (1998).
[CrossRef]

Tamir, T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133, (1975).
[CrossRef]

Tibuleac, S.

D. Shin, S. Tibuleac, T. A. Maldanado, and R. Magnusson, "Thin-film optical filterswith Diffractive Elements and Waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

Wang, S. S.

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

Appl. Phys. Lett. (1)

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

IEEE Trans. Microwave Theory Tech. (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133, (1975).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, "Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters," J. Opt. A: Pure Appl. Opt. 1, 545-551 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

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

A. Sentenac and A. L. Fehrembach, "Angular tolerant resonant grating filters under oblique incidence," J. Opt. Soc. Am. A. 22, 475-480 (2005).
[CrossRef]

E. Popov and B. Bozhkov, "Corrugated waveguides as resonance optical filters-advantages and limitations," J. Opt. Soc. Am. A. 18, 1758-1764 (2001).
[CrossRef]

D. K. Jacob, S. C. Dunn, and 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]

Q. Cao, P. Lalanne, and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A. 19, 335-338 (2002).
[CrossRef]

Opt. Eng. (1)

D. Shin, S. Tibuleac, T. A. Maldanado, and R. Magnusson, "Thin-film optical filterswith Diffractive Elements and Waveguides," Opt. Eng. 37, 2634-2646 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B. (1)

A. L. Fehrembach, S. Hernandez, and A. Sentenac, "k-gaps for multimode waveguide gratings," Phys. Rev. B. 73, 233405 (2006).
[CrossRef]

Proc. SPIE. (1)

M. G. Moharam and A. B. Greenwell, "Efficient rigorous calculations of power flow in grating coupled surface-emitting devices," Proc. SPIE. 5456, 57-67 (2004).
[CrossRef]

Other (2)

A. B. Greenwell, S. Boonruang, and M. G. Moharam, "Effect of Loss or Gain on Guided Mode Resonant Devices," in Integrated Photonics Research and Applications/Nanophotonics, Technical Digest (CD) (Optical Society of America, 2006), paper NThA1.

M. Neviere, "The homogeneous problem," in Electromagnetic Theory of Gratings, R. Petit, ed., (Springer-Verlag, Berlin 1980).

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Figures (12)

Fig.  1.
Fig. 1.

A drawing of a waveguide grating that supports two leaky modes, as well as the material and structural parameters for the material and geometry.

Fig.2.
Fig.2.

The complex band structure, as well as the 0th order reflection response for all of the resonances of the system at a 0° angle of incidence for the two leaky mode resonant grating.

Fig. 3.
Fig. 3.

The complex modal dispersion, as well as the 0th order reflection response for all of the resonances of the system at a 1° angle of incidence for the two leaky mode resonant grating.

Fig. 4.
Fig. 4.

The complex modal dispersion, as well as the 0th order reflection response, for all of the resonances of the system at a ∼5° angle of incidence for the two leaky mode resonant grating.

Fig. 5.
Fig. 5.

The complex modal dispersion for the two leaky mode resonant grating structure showing the difference in slope and angular location of the upper and lower band edges at oblique incidence.

Fig. 6.
Fig. 6.

A drawing of a waveguide grating that supports three leaky modes, as well as the material and structural parameters for the material and geometry.

Fig. 7.
Fig. 7.

The complex modal dispersion, as well as the 0th order reflection response, for all of the resonances of the system at a ∼2.5° angle of incidence for the three leaky mode resonant grating. At this angle of incidence, the upper band edge resonances are nearly, but not quite aligned in their central angles.

Fig. 8.
Fig. 8.

A drawing of a grating waveguide structure that supports three leaky modes, as well as the material and geometric parameters for the grating waveguide, and the two layers that were varied in tandem to modify the device’s dispersion properties.

Fig. 9.
Fig. 9.

Plots showing different views of the change of the real (a) & (c) and imaginary (b) & (d) parts of the waveguide grating’s modal dispersion as a function of Δh.

Fig. 10.
Fig. 10.

Plots showing the dispersion band edges involved in the angular alignment problem. (a) Plot showing the dispersion curves for the entire range of Δh. (b) Plot showing the dispersion curves at Δh = -100 nm, 0 nm, and 100 nm.

Fig. 11.
Fig. 11.

The wavelength reflection spectrum and complex modal dispersion for the optimized multilayer waveguide grating (Δh ∼ 64 nm) having two collcated, broadened angular spectrum resonances at separate wavelengths.

Fig. 12.
Fig. 12.

(a) Plot showing the angular resonances associated with the optimized multilayer resonant grating structure. The resonances at wavelengths of 1.507m and 1.604 μm are both centered at an input angle of 3.17° and have broadened angular bandwidth due to the simultaneous interactions of separate pairs of leaky modes. (b) The real part of the modal dispersion diagram showing the band edges of interest. The circles are numbered and color-coded to the resonance curves from (a).

Tables (1)

Tables Icon

Table 1. Resonance property values at ~3.17º and ~3.24º angle of incidence for the resonance in Fig. 12.

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