Abstract

The design and analysis of a dielectric guided-mode resonance filter (GMRF) utilizing a nonlinear material for the waveguide is presented. Small changes to the parameters of a GMRF have a large impact on its resonance. A nonlinear material can provide a small change in the refractive index of the waveguide, altering the resonance of the device and resulting in modulation of the transmitted and reflected output of the filter. Numerical results show that nonlinear switching from 100% transmission to 100% reflection can be accomplished with less than 100 kW/cm2 using a simple design.

© 1999 Optical Society of America

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  1. 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]
  2. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Stable implementation of the rigorous couple-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
    [CrossRef]
  3. A. Taflove, Computational Electrodynamics (Artech House, Norwood, Mass., 1995).
  4. J. B. Judkins, R. W. Ziolkowski, “Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings,” J. Opt. Soc. Am. A 12, 1974–1983 (1995).
    [CrossRef]
  5. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).
    [CrossRef]
  6. A. Hessel, A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275–1297 (1965).
    [CrossRef]
  7. L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
    [CrossRef]
  8. R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
    [CrossRef]
  9. S. S. Wang, R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
    [CrossRef] [PubMed]
  10. S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
    [CrossRef] [PubMed]
  11. S. Peng, G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A 13, 993–1005 (1996).
    [CrossRef]
  12. Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998).
    [CrossRef]
  13. I. A. Avrutskii, V. A. Sychugov, “Reflection of a Gaussian light beam from the surface of a corrugated waveguide,” Sov. J. Quantum. Electron. 16, 1558–1559 (1986).
    [CrossRef]
  14. M. T. Gale, K. Knop, R. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagan, ed., Proc. SPIE1210, 83–89 (1990).
    [CrossRef]
  15. A. Sharon, D. Rosenblatt, A. A. Friesem, H. G. Weber, H. Engel, R. Steingrueber, “Light modulation with resonant grating-wavelength structures,” Opt. Lett. 21, 1564–1566 (1996).
    [CrossRef] [PubMed]
  16. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  17. S. Ohtsuka, T. Koyama, K. Tsunetomo, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
    [CrossRef]
  18. B. Yu, C. Zhu, H. Xia, H. Chen, F. Gan, “Optical non-linearities of PbSe microcrystallites doped in glass,” J. Mater. Sci. Lett. 16, 2001–2004 (1997).
    [CrossRef]
  19. A. Taflove, Advances in Computational Electrodynamics (Artech House, Norwood, Mass., 1998).

1998

1997

B. Yu, C. Zhu, H. Xia, H. Chen, F. Gan, “Optical non-linearities of PbSe microcrystallites doped in glass,” J. Mater. Sci. Lett. 16, 2001–2004 (1997).
[CrossRef]

1996

1995

1993

1992

S. Ohtsuka, T. Koyama, K. Tsunetomo, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

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

1986

I. A. Avrutskii, V. A. Sychugov, “Reflection of a Gaussian light beam from the surface of a corrugated waveguide,” Sov. J. Quantum. Electron. 16, 1558–1559 (1986).
[CrossRef]

1985

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

1965

1902

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).
[CrossRef]

Avrutskii, I. A.

I. A. Avrutskii, V. A. Sychugov, “Reflection of a Gaussian light beam from the surface of a corrugated waveguide,” Sov. J. Quantum. Electron. 16, 1558–1559 (1986).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Chen, H.

B. Yu, C. Zhu, H. Xia, H. Chen, F. Gan, “Optical non-linearities of PbSe microcrystallites doped in glass,” J. Mater. Sci. Lett. 16, 2001–2004 (1997).
[CrossRef]

Engel, H.

Friesem, A. A.

Gale, M. T.

M. T. Gale, K. Knop, R. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagan, ed., Proc. SPIE1210, 83–89 (1990).
[CrossRef]

Gan, F.

B. Yu, C. Zhu, H. Xia, H. Chen, F. Gan, “Optical non-linearities of PbSe microcrystallites doped in glass,” J. Mater. Sci. Lett. 16, 2001–2004 (1997).
[CrossRef]

Gaylord, T. K.

Grann, E. B.

Hessel, A.

Judkins, J. B.

Knop, K.

M. T. Gale, K. Knop, R. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagan, ed., Proc. SPIE1210, 83–89 (1990).
[CrossRef]

Koyama, T.

S. Ohtsuka, T. Koyama, K. Tsunetomo, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Liu, Z. S.

Magnusson, R.

Mashev, L.

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Moharam, M. G.

Morf, R.

M. T. Gale, K. Knop, R. 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.

Nagata, H.

S. Ohtsuka, T. Koyama, K. Tsunetomo, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Ohtsuka, S.

S. Ohtsuka, T. Koyama, K. Tsunetomo, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Oliner, A. A.

Peng, S.

Pommet, D. A.

Popov, E.

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Rosenblatt, D.

Sharon, A.

Shin, D.

Steingrueber, R.

Sychugov, V. A.

I. A. Avrutskii, V. A. Sychugov, “Reflection of a Gaussian light beam from the surface of a corrugated waveguide,” Sov. J. Quantum. Electron. 16, 1558–1559 (1986).
[CrossRef]

Taflove, A.

A. Taflove, Advances in Computational Electrodynamics (Artech House, Norwood, Mass., 1998).

A. Taflove, Computational Electrodynamics (Artech House, Norwood, Mass., 1995).

Tanaka, S.

S. Ohtsuka, T. Koyama, K. Tsunetomo, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Tibuleac, S.

Tsunetomo, K.

S. Ohtsuka, T. Koyama, K. Tsunetomo, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Wang, S. S.

Weber, H. G.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).
[CrossRef]

Xia, H.

B. Yu, C. Zhu, H. Xia, H. Chen, F. Gan, “Optical non-linearities of PbSe microcrystallites doped in glass,” J. Mater. Sci. Lett. 16, 2001–2004 (1997).
[CrossRef]

Young, P. P.

Yu, B.

B. Yu, C. Zhu, H. Xia, H. Chen, F. Gan, “Optical non-linearities of PbSe microcrystallites doped in glass,” J. Mater. Sci. Lett. 16, 2001–2004 (1997).
[CrossRef]

Zhu, C.

B. Yu, C. Zhu, H. Xia, H. Chen, F. Gan, “Optical non-linearities of PbSe microcrystallites doped in glass,” J. Mater. Sci. Lett. 16, 2001–2004 (1997).
[CrossRef]

Ziolkowski, R. W.

Appl. Opt.

Appl. Phys. Lett.

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

S. Ohtsuka, T. Koyama, K. Tsunetomo, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

J. Mater. Sci. Lett.

B. Yu, C. Zhu, H. Xia, H. Chen, F. Gan, “Optical non-linearities of PbSe microcrystallites doped in glass,” J. Mater. Sci. Lett. 16, 2001–2004 (1997).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Opt. Lett.

Philos. Mag.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).
[CrossRef]

Sov. J. Quantum. Electron.

I. A. Avrutskii, V. A. Sychugov, “Reflection of a Gaussian light beam from the surface of a corrugated waveguide,” Sov. J. Quantum. Electron. 16, 1558–1559 (1986).
[CrossRef]

Other

M. T. Gale, K. Knop, R. Morf, “Zero-order diffractive microstructures for security applications,” in Optical Security and Anticounterfeiting Systems, W. F. Fagan, ed., Proc. SPIE1210, 83–89 (1990).
[CrossRef]

A. Taflove, Advances in Computational Electrodynamics (Artech House, Norwood, Mass., 1998).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

A. Taflove, Computational Electrodynamics (Artech House, Norwood, Mass., 1995).

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Figures (6)

Fig. 1
Fig. 1

Design used for analysis. The input is assumed to be a normally incident TE wave, and all dimensions are given in micrometers.

Fig. 2
Fig. 2

RCWA shows the resonance of the device assuming a constant index. The resonance wavelength does not exactly match the wavelength of minimum reflection resulting from the approximate AR coating provided by the grating.

Fig. 3
Fig. 3

Effect of index changes on the resonance. (a) Changing the index of the grating ridges requires a large index change to create noticeable changes in the device output. (b) Conversely, the waveguide index has a large influence over the output. The wavelength was held constant just off resonance at 638.4 nm.

Fig. 4
Fig. 4

Gray-scale image of the field amplitude distribution calculated by FDTD modeling. Large positive amplitudes are white and large negative amplitudes are black.

Fig. 5
Fig. 5

Output of the GMRF versus input intensity with a normally incident TE plane wave.

Fig. 6
Fig. 6

FDTD predicted time dependence of the field amplitude at a sample point within the waveguide. Large deviations occur as the interference pattern develops, but they settle out in approximately 50 fs.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

tanκih=κiγi+δiκi2-γiδi,
βi=kng sin θ-iλ/Λ,
ng=n0+n2I,
n2=4π2 Reχ3/n02.
neff=f11+f221/2,

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