Abstract

We investigate properties of nonlinear resonant gratings with emphasis on optical bistability. Slab waveguide gratings with various quality factors are designed and their characteristics analyzed with a finite-difference time-domain method. Considerable field enhancements are observed in the gratings and the performance compares favorably with metallic bistable devices. Bistabilitiy based on coupled gratings is also treated. Mechanically controllable switching intensity realized by varying a gap distance between two gratings is demonstrated. Resonant nonlinear elements in this work may find applications in all-optical information processing and optical switching, and our investigation on the dependence of the normalized switching intensity and the response time on quality factor will provide a general guide line for grating-based bistable device design.

© 2009 OSA

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  1. H. M. Gibbs, Optical bistability: Controlling Light with Light (Academic, 1985).
  2. S. F. Mingaleev and Y. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B 19(9), 2241 (2002).
    [CrossRef]
  3. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
    [CrossRef]
  4. M. Soljacić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28(8), 637–639 (2003).
    [CrossRef] [PubMed]
  5. S. Radic, N. George, and G. P. Agrawal, “Optical switching in λ/4-shifted nonlinear periodic structures,” Opt. Lett. 19(21), 1789–1791 (1994).
    [CrossRef] [PubMed]
  6. S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67(8), 1051 (1995).
    [CrossRef]
  7. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
    [CrossRef]
  8. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004).
    [CrossRef] [PubMed]
  9. R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
    [CrossRef] [PubMed]
  10. K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
    [CrossRef]
  11. D. Wawro, S. Tibuleac, and R. Magnusson, “Optical waveguide-mode resonant biosensors Optical,” Imaging Sensors and Systems for Homeland Security Applications, (Springer New York, 2006).
  12. H. Y. Song, S. Kim, and R. Magnusson, “Tunable guided-mode resonances in coupled gratings,” Opt. Express to be published
    [CrossRef] [PubMed]
  13. G. Purvinis, P. S. Priambodo, M. Pomerantz, M. Zhou, T. A. Maldonado, and R. Magnusson, “Second-harmonic generation in resonant waveguide gratings incorporating ionic self-assembled monolayer polymer films,” Opt. Lett. 29(10), 1108–1110 (2004).
    [CrossRef] [PubMed]
  14. P. Vincent, N. Paraire, M. Neviere, A. Koster, and R. Reinisch, “Grating in nonlinear optics and optical bistability,” J. Opt. Soc. Am. B 2(7), 1106 (1985).
    [CrossRef]
  15. I. A. Avrutskii and V. A. Sychugov, “Optical bistability in an excited nonlinear corrugated waveguide,” Sov. J. Quantum. Electron. 20(7), 856–859 (1990).
    [CrossRef]
  16. J. A. Porto, L. Martin-Moreno, and F. J. Garcia-Vidal, “Optical bistability in subwavelength slit apertures containing nonlinear media,” Phys. Rev. B 70, 081402(R) (2004).
    [CrossRef]
  17. C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning, Y. Zhou, and G. Yang, “All-optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33(8), 869–871 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  20. H. A. Haus, Waves and Field in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall, 1984).
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    [CrossRef]
  22. I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
    [CrossRef]
  23. H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998).
    [CrossRef]
  24. Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
    [CrossRef]

2008 (3)

2006 (2)

2005 (1)

2004 (3)

2003 (1)

2002 (2)

S. F. Mingaleev and Y. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B 19(9), 2241 (2002).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

1998 (1)

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998).
[CrossRef]

1995 (1)

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67(8), 1051 (1995).
[CrossRef]

1994 (1)

1992 (1)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

1990 (1)

I. A. Avrutskii and V. A. Sychugov, “Optical bistability in an excited nonlinear corrugated waveguide,” Sov. J. Quantum. Electron. 20(7), 856–859 (1990).
[CrossRef]

1989 (1)

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

1985 (1)

Agrawal, G. P.

Avrutskii, I. A.

I. A. Avrutskii and V. A. Sychugov, “Optical bistability in an excited nonlinear corrugated waveguide,” Sov. J. Quantum. Electron. 20(7), 856–859 (1990).
[CrossRef]

Avrutsky, I. A.

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

Bermel, P.

Britton, B.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Burr, G.

Cada, M.

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67(8), 1051 (1995).
[CrossRef]

Chen, C.

Deng, Y.

Ding, Y.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
[CrossRef]

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004).
[CrossRef] [PubMed]

Donkor, E.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Fan, S.

Farjadpour, A.

Fink, Y.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

Garcia-Vidal, F. J.

J. A. Porto, L. Martin-Moreno, and F. J. Garcia-Vidal, “Optical bistability in subwavelength slit apertures containing nonlinear media,” Phys. Rev. B 70, 081402(R) (2004).
[CrossRef]

George, N.

He, J.

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67(8), 1051 (1995).
[CrossRef]

Ho, N.

Ibanescu, M.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972 (2006).
[CrossRef] [PubMed]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

Jans, S.

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67(8), 1051 (1995).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972 (2006).
[CrossRef] [PubMed]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

Kim, S.

H. Y. Song, S. Kim, and R. Magnusson, “Tunable guided-mode resonances in coupled gratings,” Opt. Express to be published
[CrossRef] [PubMed]

Kivshar, Y. S.

Koster, A.

Lacomb, R.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Laniel, J. M.

Lee, K. J.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Liao, H. B.

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998).
[CrossRef]

Lu, Y.

Luo, C.

Magnusson, R.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
[CrossRef]

G. Purvinis, P. S. Priambodo, M. Pomerantz, M. Zhou, T. A. Maldonado, and R. Magnusson, “Second-harmonic generation in resonant waveguide gratings incorporating ionic self-assembled monolayer polymer films,” Opt. Lett. 29(10), 1108–1110 (2004).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004).
[CrossRef] [PubMed]

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

H. Y. Song, S. Kim, and R. Magnusson, “Tunable guided-mode resonances in coupled gratings,” Opt. Express to be published
[CrossRef] [PubMed]

Maldonado, T. A.

Martin-Moreno, L.

J. A. Porto, L. Martin-Moreno, and F. J. Garcia-Vidal, “Optical bistability in subwavelength slit apertures containing nonlinear media,” Phys. Rev. B 70, 081402(R) (2004).
[CrossRef]

Min, C.

Ming, H.

Mingaleev, S. F.

Neviere, M.

Ning, T.

Paraire, N.

Pomerantz, M.

Porto, J. A.

J. A. Porto, L. Martin-Moreno, and F. J. Garcia-Vidal, “Optical bistability in subwavelength slit apertures containing nonlinear media,” Phys. Rev. B 70, 081402(R) (2004).
[CrossRef]

Priambodo, P. S.

Purvinis, G.

Radic, S.

Reinisch, R.

Rodriguez, A.

Roundy, D.

Shokooh-Saremi, M.

R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
[CrossRef] [PubMed]

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Silva, H.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Soljacic, M.

M. Soljacić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28(8), 637–639 (2003).
[CrossRef] [PubMed]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

Song, H. Y.

H. Y. Song, S. Kim, and R. Magnusson, “Tunable guided-mode resonances in coupled gratings,” Opt. Express to be published
[CrossRef] [PubMed]

Sychugov, V. A.

I. A. Avrutskii and V. A. Sychugov, “Optical bistability in an excited nonlinear corrugated waveguide,” Sov. J. Quantum. Electron. 20(7), 856–859 (1990).
[CrossRef]

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

Vallee, R.

Vincent, P.

Wang, H.

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998).
[CrossRef]

Wang, P.

Wang, S. S.

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

Wasilewski, Z. R.

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67(8), 1051 (1995).
[CrossRef]

Wong, G. K. L.

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998).
[CrossRef]

Wong, K. S.

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998).
[CrossRef]

Xiao, R. F.

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998).
[CrossRef]

Yang, G.

Zhou, M.

Zhou, Y.

Appl. Phys. Lett. (3)

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67(8), 1051 (1995).
[CrossRef]

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[CrossRef]

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
[CrossRef]

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

J. Mod. Opt. (1)

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. B (1)

J. A. Porto, L. Martin-Moreno, and F. J. Garcia-Vidal, “Optical bistability in subwavelength slit apertures containing nonlinear media,” Phys. Rev. B 70, 081402(R) (2004).
[CrossRef]

Phys. Rev. E (1)

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[CrossRef]

Sov. J. Quantum. Electron. (1)

I. A. Avrutskii and V. A. Sychugov, “Optical bistability in an excited nonlinear corrugated waveguide,” Sov. J. Quantum. Electron. 20(7), 856–859 (1990).
[CrossRef]

Other (4)

H. M. Gibbs, Optical bistability: Controlling Light with Light (Academic, 1985).

D. Wawro, S. Tibuleac, and R. Magnusson, “Optical waveguide-mode resonant biosensors Optical,” Imaging Sensors and Systems for Homeland Security Applications, (Springer New York, 2006).

A. Taflove, Computational Electrodynamics, (Artech House, Boston, 1995).

H. A. Haus, Waves and Field in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall, 1984).

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Figures (7)

Fig. 1
Fig. 1

(a) Slab waveguide grating structure with input light of normal incidence. (b) Reflection spectra for various grating depths (δ). For each grating depth, waveguiding layer thickness is optimized to minimize the background reflection. The insets in (b) show field distributions at resonance. In this example, TE polarized light is used, that is, the electric-field is normal to the incident plane.

Fig. 2
Fig. 2

Bistability in the nonlinear gratings depicted in Fig. 1(a). (a) δ = 90 nm, (b) δ = 50 nm, (c) δ = 10 nm, (d) transmission for δ = 10 nm.

Fig. 3
Fig. 3

Optical incident intensity, optical intensity in the grating, and intensity enhancement factor for switching of bistable devices based on gratings of various quality factors. The optical intensity is normalized by (1/n2). The solid lines are fitting curves and their equations are noted.

Fig. 4
Fig. 4

Temporal response of bistable devices based on gratings of (a) δ = 90 nm and (b) δ = 10 nm.

Fig. 5
Fig. 5

(a) Slab waveguide grating whose guiding layer is made with a highly nonlinear material (n = 2.4), (b) reflection spectrum, (c) bistability curves, and (d) temporal response.

Fig. 6
Fig. 6

(a) Coupled identical slab waveguide gratings with a gap of d, (b) reflection spectrum for d = 50nm, (c) bistability curves for d = 50 nm, (d) temporal response for d = 50 nm. The inset in (b) is an enlarged spectrum of the shorter wavelength peak.

Fig. 7
Fig. 7

(a) Reflection spectra and (b) bistability curves of the coupled gratings depicted in Fig. 6(a) for various d. The gap d is varied from 50 to 49.5 nm.

Tables (1)

Tables Icon

Table 1 Characteristics of guided-mode resonances in the example design

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