Abstract

We numerically investigate the optical bistability effect in the metal-insulator-metal waveguide with a nanodisk resonator containing a Kerr nonlinear medium. It is found that the increase of the refractive index, which is induced by enhancing the incident intensity, can cause a redshift for the resonance wavelength. The local resonant field excited in the nanodisk cavity can significantly increase the Kerr nonlinear effect. In addition, an obvious bistability loop is observed in the proposed structure. This nonlinear structure can find important applications for all-optical switching in highly integrated optical circuits.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. Y. Gong, L. Wang, X. Hu, X. Li, and X. Liu, “Broad-bandgap and low-sidelobe surface plasmon polariton reflector with Bragg-grating-based MIM waveguide,” Opt. Express 17, 13727–13736 (2009).
    [CrossRef] [PubMed]
  4. J. Liu, L. Wang, M. He, W. Huang, D. Wang, B. Zou, and S. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express 16, 4888–4894 (2008).
    [CrossRef] [PubMed]
  5. Z. H. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
    [CrossRef]
  6. G. Wang, H. Lu, X. Liu, D. Mao, and L. Duan, “Tunable multi-channel wavelength demultiplexer based on MIM plasmonic nanodisk resonators at telecommunication regime,” Opt. Express 19, 3513–3518 (2011).
    [CrossRef] [PubMed]
  7. J. Tao, X. Huang, and J. Zhu, “A wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nano-capillary resonators,” Opt. Express 18, 11111–11116 (2010).
    [CrossRef] [PubMed]
  8. H. Lu, X. M. Liu, D. Mao, L. R. Wang, and Y. K. Gong, “Tunable band-pass plasmonic waveguide filters with nanodisk resonators,” Opt. Express 18, 17922–17927 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  31. H. Lu, X. Liu, L. Wang, Y. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express 19, 2910–2915 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  33. T. Wang, X. Wen, C. Yin, and H. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17, 24096–24101 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]

2011 (4)

2010 (9)

Z. Zhong, Y. Xu, S. Lan, Q. Dai, and L. Wu, “Sharp and asymmetric transmission response in metal-dielectric-metal plasmonic waveguides containing Kerr nonlinear media,” Opt. Express 18, 79–86 (2010).
[CrossRef] [PubMed]

A. V. Krasavin and A. V. Zayats, “Silicon-based plasmonic waveguides,” Opt. Express 18, 11791–11799 (2010).
[CrossRef] [PubMed]

F. R. Jeffrey and W. S. Steven, “The impact of nonlinearity on degenerate parametric amplifiers,” Appl. Phys. Lett. 96, 234101 (2010).
[CrossRef]

I. V. Kabakova, C. M. de Sterke, and B. J. Eggleton, “Performance of field-enhanced optical switching in fiber Bragg gratings,” J. Opt. Soc. Am. B 27, 1343–1352 (2010).
[CrossRef]

G. Tremblay and Y. L. Sheng, “Improving imaging performance of a metallic superlens using the long-range surface plasmon polariton mode cutoff technique,” Appl. Opt. 49, A36–A41 (2010).
[CrossRef] [PubMed]

J. Tao, X. Huang, and J. Zhu, “A wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nano-capillary resonators,” Opt. Express 18, 11111–11116 (2010).
[CrossRef] [PubMed]

H. Lu, X. M. Liu, D. Mao, L. R. Wang, and Y. K. Gong, “Tunable band-pass plasmonic waveguide filters with nanodisk resonators,” Opt. Express 18, 17922–17927 (2010).
[CrossRef] [PubMed]

Y. Gong, X. Liu, and L. Wang, “High channel-count plasmonic filter with the metal-insulator-metal Fibonacci-sequence gratings,” Opt. Lett. 35, 285–287 (2010).
[CrossRef] [PubMed]

M. Pu, N. Yao, C. Hu, X. Xin, Z. Zhao, C. Wang, and X. Luo, “Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide,” Opt. Express 18, 21030–21037 (2010).
[CrossRef] [PubMed]

2009 (4)

2008 (6)

2007 (3)

2006 (2)

G. Wurtz, R. Pollard, and A. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

2005 (3)

2004 (2)

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]

B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29, 1992–1994 (2004).
[CrossRef] [PubMed]

2003 (1)

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

Barnes, W. L.

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

Brongersma, M. L.

R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

Chang, C.

Chen, C.

Chen, H.

Chen, J.

J. Chen, P. Wang, X. Wang, Y. Lu, R. Zheng, H. Ming, and Q. Zhan, “Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure,” Appl. Phys. Lett. 94, 081117(2009).
[CrossRef]

Dai, Q.

de Sterke, C. M.

Deng, Q.

Deng, Y.

Dereux, A.

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

Donghyun, K.

Du, C.

Duan, L.

Ebbesen, T. W.

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

Eggleton, B. J.

Fan, S.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Forsberg, E.

Z. H. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

Gao, H.

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]

Gong, Y.

Gong, Y. K.

Guang, X.

H. Zhao, X. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40, 3025–3029 (2008).
[CrossRef]

Hagness, S. C.

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

Han, Z. H.

Z. H. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

He, M.

He, S.

Z. H. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

Hu, C.

Hu, X.

Huang, J.

H. Zhao, X. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40, 3025–3029 (2008).
[CrossRef]

Huang, W.

Huang, W. P.

Huang, X.

Jeffrey, F. R.

F. R. Jeffrey and W. S. Steven, “The impact of nonlinearity on degenerate parametric amplifiers,” Appl. Phys. Lett. 96, 234101 (2010).
[CrossRef]

Jiao, X.

Kabakova, I. V.

Kim, H.

Krasavin, A. V.

Kuo, W.

Lan, S.

Lee, B.

Li, X.

Lin, X.

Liu, J.

Liu, X.

Liu, X. M.

Lu, H.

Lu, Y.

J. Chen, P. Wang, X. Wang, Y. Lu, R. Zheng, H. Ming, and Q. Zhan, “Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure,” Appl. Phys. Lett. 94, 081117(2009).
[CrossRef]

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, 869–871 (2008).
[CrossRef] [PubMed]

Luo, X.

Lv, Y.

Mao, D.

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.

Mu, J. W.

Ning, T.

Park, J.

Pollard, R.

G. Wurtz, R. Pollard, and A. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

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]

Pu, M.

Schuller, J. A.

R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

Shen, Y.

Sheng, Y. L.

Shi, H.

Steven, W. S.

F. R. Jeffrey and W. S. Steven, “The impact of nonlinearity on degenerate parametric amplifiers,” Appl. Phys. Lett. 96, 234101 (2010).
[CrossRef]

Su, J.

Taflove, A.

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

Tao, J.

Tremblay, G.

Veronis, G.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Wang, B.

Wang, C.

Wang, D.

Wang, G.

Wang, G. P.

Wang, H.

Wang, J.

Wang, L.

Wang, L. R.

Wang, P.

Wang, T.

Wang, X.

J. Chen, P. Wang, X. Wang, Y. Lu, R. Zheng, H. Ming, and Q. Zhan, “Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure,” Appl. Phys. Lett. 94, 081117(2009).
[CrossRef]

Wen, S.

Wen, X.

Wu, L.

Wurtz, G.

G. Wurtz, R. Pollard, and A. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Xin, X.

Xu, Y.

Yang, G.

Yao, H.

Yao, N.

Yin, C.

Zayats, A.

G. Wurtz, R. Pollard, and A. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Zayats, A. V.

Zhan, Q.

J. Chen, P. Wang, X. Wang, Y. Lu, R. Zheng, H. Ming, and Q. Zhan, “Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure,” Appl. Phys. Lett. 94, 081117(2009).
[CrossRef]

Zhao, H.

H. Zhao, X. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40, 3025–3029 (2008).
[CrossRef]

Zhao, X.

Zhao, Z.

Zheng, R.

J. Chen, P. Wang, X. Wang, Y. Lu, R. Zheng, H. Ming, and Q. Zhan, “Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure,” Appl. Phys. Lett. 94, 081117(2009).
[CrossRef]

Zhong, Z.

Zhou, Y.

Zhu, J.

Zia, R.

R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

Zou, B.

Appl. Opt. (3)

Appl. Phys. Lett. (3)

F. R. Jeffrey and W. S. Steven, “The impact of nonlinearity on degenerate parametric amplifiers,” Appl. Phys. Lett. 96, 234101 (2010).
[CrossRef]

J. Chen, P. Wang, X. Wang, Y. Lu, R. Zheng, H. Ming, and Q. Zhan, “Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure,” Appl. Phys. Lett. 94, 081117(2009).
[CrossRef]

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. H. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

J. Lightwave Technol. (1)

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

Mater. Today (1)

R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006).
[CrossRef]

Nature (1)

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

Opt. Express (16)

Y. Gong, L. Wang, X. Hu, X. Li, and X. Liu, “Broad-bandgap and low-sidelobe surface plasmon polariton reflector with Bragg-grating-based MIM waveguide,” Opt. Express 17, 13727–13736 (2009).
[CrossRef] [PubMed]

J. Liu, L. Wang, M. He, W. Huang, D. Wang, B. Zou, and S. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express 16, 4888–4894 (2008).
[CrossRef] [PubMed]

G. Wang, H. Lu, X. Liu, D. Mao, and L. Duan, “Tunable multi-channel wavelength demultiplexer based on MIM plasmonic nanodisk resonators at telecommunication regime,” Opt. Express 19, 3513–3518 (2011).
[CrossRef] [PubMed]

J. Tao, X. Huang, and J. Zhu, “A wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nano-capillary resonators,” Opt. Express 18, 11111–11116 (2010).
[CrossRef] [PubMed]

H. Lu, X. M. Liu, D. Mao, L. R. Wang, and Y. K. Gong, “Tunable band-pass plasmonic waveguide filters with nanodisk resonators,” Opt. Express 18, 17922–17927 (2010).
[CrossRef] [PubMed]

H. Chen, J. Su, J. Wang, and X. Zhao, “Optically-controlled high-speed terahertz wave modulator based on nonlinear photonic crystals,” Opt. Express 19, 3599–3603 (2011).
[CrossRef] [PubMed]

M. Pu, N. Yao, C. Hu, X. Xin, Z. Zhao, C. Wang, and X. Luo, “Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide,” Opt. Express 18, 21030–21037 (2010).
[CrossRef] [PubMed]

H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express 13, 10795–10800 (2005).
[CrossRef] [PubMed]

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16, 413–425 (2008).
[CrossRef] [PubMed]

Y. Shen and G. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16, 8421–8426 (2008).
[CrossRef] [PubMed]

H. Lu, X. Liu, L. Wang, Y. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express 19, 2910–2915 (2011).
[CrossRef] [PubMed]

C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Optical bistability in subwavelength metallic grating coated by nonlinear material,” Opt. Express 15, 12368–12373 (2007).
[CrossRef] [PubMed]

A. V. Krasavin and A. V. Zayats, “Silicon-based plasmonic waveguides,” Opt. Express 18, 11791–11799 (2010).
[CrossRef] [PubMed]

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]

T. Wang, X. Wen, C. Yin, and H. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17, 24096–24101 (2009).
[CrossRef]

Z. Zhong, Y. Xu, S. Lan, Q. Dai, and L. Wu, “Sharp and asymmetric transmission response in metal-dielectric-metal plasmonic waveguides containing Kerr nonlinear media,” Opt. Express 18, 79–86 (2010).
[CrossRef] [PubMed]

Opt. Lett. (4)

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. Lett. (1)

G. Wurtz, R. Pollard, and A. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Physica E (1)

H. Zhao, X. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40, 3025–3029 (2008).
[CrossRef]

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the MIM plasmonic waveguide with a nanodisk resonator. r: the radius of the resonator, w: the width of the waveguide, d t : the coupling length between the waveguide and resonator.

Fig. 2
Fig. 2

(a) Transmission spectra with different refractive indices with r = 150 nm , w = 50 nm , and d t = 20 nm . (b) Transmitted-peak wavelength of the nanodisk resonator versus refractive index. Contour profiles of field | H z | 2 at the wavelength of 1025 nm with n = 1.6 (c) and n = 1.5 (d).

Fig. 3
Fig. 3

(a) Transmission spectra at the incident intensities of 1 × 10 14 , 1 × 10 16 , and 3 × 10 16 V 2 / m 2 . The inset is the transmitted-peak wavelength versus the incident intensity. (b) Transmission contrast ratio between the intensity of 1 × 10 14 V 2 / m 2 and 3 × 10 16 V 2 / m 2 . Contour profiles of field | H z | 2 with the incident electric intensity of (c)  1 × 10 14 V 2 / m 2 and (d)  3 × 10 16 V 2 / m 2 at the wavelength of 988 nm .

Fig. 4
Fig. 4

Transmission coefficients by increasing (blue curve) and decreasing (red curve) the incident intensity with different radii of the nanodisk resonator.

Equations (2)

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ε m ( ω ) = ε ω p 2 ω ( ω + i γ ) .
ε d = ε l + χ ( 3 ) | E | 2 ,

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