Abstract

A developed two-dimensional Finite Difference Time Domain (FDTD) method has been performed to investigate the optical bistability in a subwavelength metallic grating coated by nonlinear material. Different bistability loops have been shown to depend on parameters of the structure. The influences of two key parameters, thickness of nonlinear material and slit width of metallic grating, have been studied in detail. The effect of optical bistability in the structure is explained by Surface Plasmons (SPs) mode and resonant waveguide theory.

© 2007 Optical Society of America

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References

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
    [CrossRef]
  2. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen,"Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
    [CrossRef] [PubMed]
  3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  4. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen,"Beaming light from a subwavelength aperture," Science 297, 220-222 (2002).
    [CrossRef]
  5. X. Jiao, P. Wang, L. Tang, Y. Lu, Q. Li, D. Zhang, P. Yao, H. Ming, and J. Xie, "Fabry-Pérot-like phenomenon in the surface plasmons resonant transmission of metallic gratings with very narrow slits," Appl. Phys. B 80, 301-305 (2005).
  6. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
    [CrossRef] [PubMed]
  7. E. Ozbay, "Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  8. I. I. Smolyaninov, "Quantum Fluctuations of the Refractive Index near the Interface between a metal and a Nonlinear Dielectric," Phys. Rev. Lett. 94, 057403 (2005).
    [CrossRef] [PubMed]
  9. 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 (2004).
  10. G. A. Wurtz, R. Pollard, and A. V. Zayats, "Optical Bistability in Nonlinear Surface-Plasmon Polaritonic Crystals," Phys. Rev. Lett. 97, 057402 (2006).
    [CrossRef] [PubMed]
  11. C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, "Beam manipulating by metallic nano-optic lens containing nonlinear media, " Opt. Express 15, 9541-9546 (2007)
    [CrossRef] [PubMed]
  12. M. Fujii, C. Koos, C. Poulton, I. Sakagami, J. Leuthold and W. Freude, "A simple and rigorous verification technique for nonlinear FDTD algorithms by optical parametric four-wave mixing," Microwave Opt. Technol. Lett. 48, 88-91 (2005).
    [CrossRef]
  13. J. B. Jubkins and 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]
  14. P. Harms, R. Mittra, and W. Ko, "Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures," IEEE Trans. Antennas Propagat. 42, 1317-1324 (1994).
    [CrossRef]
  15. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed., (Artech House, Boston, MA 2000).
  16. E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, London 1985).
  17. M. Born and E. Wolf, Principles of Optics, (Pergamon Press, 1975).
  18. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer, Berlin 1988).

2007

2006

G. A. Wurtz, R. Pollard, and A. V. Zayats, "Optical Bistability in Nonlinear Surface-Plasmon Polaritonic Crystals," Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

E. Ozbay, "Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

2005

I. I. Smolyaninov, "Quantum Fluctuations of the Refractive Index near the Interface between a metal and a Nonlinear Dielectric," Phys. Rev. Lett. 94, 057403 (2005).
[CrossRef] [PubMed]

M. Fujii, C. Koos, C. Poulton, I. Sakagami, J. Leuthold and W. Freude, "A simple and rigorous verification technique for nonlinear FDTD algorithms by optical parametric four-wave mixing," Microwave Opt. Technol. Lett. 48, 88-91 (2005).
[CrossRef]

X. Jiao, P. Wang, L. Tang, Y. Lu, Q. Li, D. Zhang, P. Yao, H. Ming, and J. Xie, "Fabry-Pérot-like phenomenon in the surface plasmons resonant transmission of metallic gratings with very narrow slits," Appl. Phys. B 80, 301-305 (2005).

2004

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 (2004).

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2002

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen,"Beaming light from a subwavelength aperture," Science 297, 220-222 (2002).
[CrossRef]

2001

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen,"Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

1995

J. B. Jubkins and 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]

1994

P. Harms, R. Mittra, and W. Ko, "Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures," IEEE Trans. Antennas Propagat. 42, 1317-1324 (1994).
[CrossRef]

Appl. Phys. B

X. Jiao, P. Wang, L. Tang, Y. Lu, Q. Li, D. Zhang, P. Yao, H. Ming, and J. Xie, "Fabry-Pérot-like phenomenon in the surface plasmons resonant transmission of metallic gratings with very narrow slits," Appl. Phys. B 80, 301-305 (2005).

IEEE Trans. Antennas Propagat.

P. Harms, R. Mittra, and W. Ko, "Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures," IEEE Trans. Antennas Propagat. 42, 1317-1324 (1994).
[CrossRef]

J. Opt. Soc. Am. A.

J. B. Jubkins and 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]

Microwave Opt. Technol. Lett.

M. Fujii, C. Koos, C. Poulton, I. Sakagami, J. Leuthold and W. Freude, "A simple and rigorous verification technique for nonlinear FDTD algorithms by optical parametric four-wave mixing," Microwave Opt. Technol. Lett. 48, 88-91 (2005).
[CrossRef]

Nature

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. B

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 (2004).

Phys. Rev. Lett.

G. A. Wurtz, R. Pollard, and A. V. Zayats, "Optical Bistability in Nonlinear Surface-Plasmon Polaritonic Crystals," Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen,"Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001).
[CrossRef] [PubMed]

I. I. Smolyaninov, "Quantum Fluctuations of the Refractive Index near the Interface between a metal and a Nonlinear Dielectric," Phys. Rev. Lett. 94, 057403 (2005).
[CrossRef] [PubMed]

Science

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen,"Beaming light from a subwavelength aperture," Science 297, 220-222 (2002).
[CrossRef]

E. Ozbay, "Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Other

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed., (Artech House, Boston, MA 2000).

E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, London 1985).

M. Born and E. Wolf, Principles of Optics, (Pergamon Press, 1975).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer, Berlin 1988).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic view of the nonlinear metallic structure under study: a metallic grating of period p, metallic film thickness h, slit width w, and nonlinear material layer thickness d. A TM-polarized plane wave is incident vertically from the top of the structure.

Fig. 2.
Fig. 2.

(a). The far-field transmission spectra of the structure corresponding to SPs excitation at intensities of incident light: I=1×1014, 2.25×1016 and 4×1016 V2/m2. The thickness of nonlinear layer is d=0.88µm. (b) Far-field transmission versus incident intensity in the structure at the wavelength λ=1.55µm. T1 and T2 denote the transmissions respective obtained from increasing and decreasing intensity of incident light.

Fig. 3.
Fig. 3.

(a). The far-field transmission spectra versus thickness d of nonlinear layer at intensities of incident light: I=1×1014, 2.25×1016 and 4×1016 V2/m2 with wavelength λ=1.55µm. The transmission versus incident intensity is shown at the chosen thickness (b) d=0.16µm and (c) d=1.62µm. (d) The transmission ratio (T2/T1) of upper and down branches of bistability loop is shown at different thicknesses d versus incident intensity.

Fig. 4.
Fig. 4.

The transmission versus incident intensity at the chosen slit width: (a) w=0.1µm (b) w=0.2µm (c) w=0.4µm. The thickness of nonlinear layer is fixed at d=0.88µm and the wavelength is λ=1.55µm. (d) The transmission ratio (T2/T1) of upper and lower branches of bistability loop is shown at different slit widths w versus incident intensity.

Equations (5)

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ε d = ε l + χ ( 3 ) E 2 ,
× H = ε E t + P l t + P nl t
λ sp = p m Re ( ε d ε m ε d + ε m ε d sin θ ) ( m = 1 , 2 , 3 )
d k 0 2 ε d k 2 = m π + ϕ 12 + ϕ 23 ( m = 0 , 1 , 2 )
Δ d = π k 0 2 ε d k

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