Abstract

In this article, an analytical theory to describe the nonlinear dynamic response characteristics of a typical SPP waveguide-cavity structure formed by a Kerr-type standing-wave cavity side-coupling to a metal-insulator-metal (MIM) waveguide is proposed by combining the temporal coupled mode theory and the Kerr nonlinearity. With the analytical theory, the optical bistability with the hysteresis behavior is successfully predicted, and the optical bistability evolutions and its dynamic physical mechanism are also phenomenologically analyzed. Moreover, the influence of the quality factors Q0 and Q1 on the first-turnning point (FTP) power of optical bistability and the bistable region width, the approaches to decrease the FTP power and to broaden the bistable region are also discussed in detail with our analytical theory. This work can help us understand the physical mechanism of the nonlinear dynamical response at nanoscale, and may be useful to design nonlinear nanophotonic systems for applications in ultra-compact all-optical devices and storages.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength scale localization,” Phys. Rev. B73, 035407 (2006).
    [CrossRef]
  4. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonic beyond the diffraction limit,” Nat. Photonics4, 83–90 (2010).
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  5. D. Y. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt.12, 015002 (2010).
    [CrossRef]
  6. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B75, 245405 (2007).
    [CrossRef]
  7. G. X. Wang, H. Lu, and X. M. Liu, “Trapping of surface plasmon waves in graded grating waveguide system,” Appl. Phys. Lett.101, 013111 (2012).
    [CrossRef]
  8. Q. Zhang, X. G. Huang, X. S. Lin, J. Tao, and X. P. Jin, “A subwavelength coupler-type MIM optical filter,” Opt. Express17, 7549–7555 (2009).
    [CrossRef]
  9. Y. Hwang, J. Kim, and H. Y. Park, “Frequency selective metal-insulator-metal splitters for surface plasmons,” Opt. Comm.284, 4778–4781 (2011).
    [CrossRef]
  10. A. Noual, A. Akjouj, Y. Pennec, J. N. Gillet, and B. D. Rouhani, “Modeling of two-dimensional nanoscale Y-bent plasmonic waveguides with cavities for demultiplexing of the telecommunication wavelengths,” New J. Phys.11, 103020 (2009).
    [CrossRef]
  11. G. X. Wang, H. Lu, X. M. Liu, D. Mao, and L. N. Duan, “Tunable multi-channel wavelength demultiplexer based on MIM plasmonic nanodisk resonators at telecommunication regime,” Opt. Express19, 3513–3518 (2011).
    [CrossRef] [PubMed]
  12. G. A. Wurtz and A. V. Zayats, “Nonlinear surface plasmon polaritonic crystals,” Laser Photon. Rev.2, 125–135 (2008).
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  13. J. Tao, Q. J. Wang, and X. G. Huang, “All-optical plasmonic switches based on coupled nano-disk cavity structures containing nonlinear material,” Plasmonics6, 753–759 (2011).
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  14. N. Nozhat and N. Granpayeh, “Switching power reduction in the ultra-compact Kerr nonlinear plasmonic directional coupler,” Opt. Comm.285, 1555–1559 (2012).
    [CrossRef]
  15. H. Lu, X. M. Liu, L. R. Wang, Y. K. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express19, 2910–2915 (2011).
    [CrossRef] [PubMed]
  16. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics3, 55–58 (2009).
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  17. J. J. Chen, Z. Li, S. Yue, and Q. H. Gong, “Highly efficient all-optical control of surface-plasmon-polariton generation based on a compact asymmetric single slit,” Nano Lett.11, 2933–2937 (2011).
    [CrossRef] [PubMed]
  18. J. X. Chen, P. Wang, X. L. Wang, Y. H. Lu, R. S. Zheng, H. Ming, and Q. W. 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]
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    [CrossRef]
  21. X. L. Wang, H. Q. Jiang, J. X. Chen, P. Wang, Y. H. Lu, and H. Ming, “Optical bistability effect in plasmonic racetrack resonator with high extinction ratio,” Opt. Express19, 19415–19421 (2011).
    [CrossRef] [PubMed]
  22. H. Lu, X. M. Liu, Y. K. Gong, D. Mao, and L. R. Wang, “Enhancement of transmission efficiency of nanoplasmonic wavelength demultiplexer based on channel drop filters and reflection nanocavities,” Opt. Express19, 12885–12890 (2011).
    [CrossRef] [PubMed]
  23. Y. Liu, F. Zhou, B. Yao, J. Cao, and Q. H. Mao, “High-extinction-ratio and low-insertion-loss plasmonic filter with coherent coupled nano-cavity array in a MIM waveguide,” Plasmonics8, 1035–1041 (2013).
    [CrossRef]
  24. L. Liu, X. Hao, Y. T. Ye, J. X. Liu, Z. L. Chen, Y. C. Song, Y. Luo, J. Zhang, and L. Tan, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
    [CrossRef]
  25. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Inc., 1999).
  26. R. S. Irving, Integers, Polynomials, and Rings (Springer, 2004).
  27. X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
    [CrossRef]
  28. Q. H. Mao and J. W. Y. Lit, “Optical bistability in an L-band dual-wavelength erbium-doped fiber laser with overlapping cavities,” IEEE Photon. Technol. Lett.14, 1252–1254 (2002).
    [CrossRef]
  29. P. Berini and I. Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics6, 16–23 (2012).
    [CrossRef]

2013

Y. Liu, F. Zhou, B. Yao, J. Cao, and Q. H. Mao, “High-extinction-ratio and low-insertion-loss plasmonic filter with coherent coupled nano-cavity array in a MIM waveguide,” Plasmonics8, 1035–1041 (2013).
[CrossRef]

2012

L. Liu, X. Hao, Y. T. Ye, J. X. Liu, Z. L. Chen, Y. C. Song, Y. Luo, J. Zhang, and L. Tan, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

N. Nozhat and N. Granpayeh, “Switching power reduction in the ultra-compact Kerr nonlinear plasmonic directional coupler,” Opt. Comm.285, 1555–1559 (2012).
[CrossRef]

G. X. Wang, H. Lu, and X. M. Liu, “Trapping of surface plasmon waves in graded grating waveguide system,” Appl. Phys. Lett.101, 013111 (2012).
[CrossRef]

P. Berini and I. Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics6, 16–23 (2012).
[CrossRef]

2011

Y. Hwang, J. Kim, and H. Y. Park, “Frequency selective metal-insulator-metal splitters for surface plasmons,” Opt. Comm.284, 4778–4781 (2011).
[CrossRef]

H. Lu, X. M. Liu, L. R. Wang, Y. K. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express19, 2910–2915 (2011).
[CrossRef] [PubMed]

G. X. Wang, H. Lu, X. M. Liu, D. Mao, and L. N. Duan, “Tunable multi-channel wavelength demultiplexer based on MIM plasmonic nanodisk resonators at telecommunication regime,” Opt. Express19, 3513–3518 (2011).
[CrossRef] [PubMed]

H. Lu, X. M. Liu, Y. K. Gong, D. Mao, and L. R. Wang, “Enhancement of transmission efficiency of nanoplasmonic wavelength demultiplexer based on channel drop filters and reflection nanocavities,” Opt. Express19, 12885–12890 (2011).
[CrossRef] [PubMed]

X. L. Wang, H. Q. Jiang, J. X. Chen, P. Wang, Y. H. Lu, and H. Ming, “Optical bistability effect in plasmonic racetrack resonator with high extinction ratio,” Opt. Express19, 19415–19421 (2011).
[CrossRef] [PubMed]

A. Pannipitiya, I. D. Rukhlenko, and M. Premaratne, “Analytical theory of optical bistability in plasmonic nanoresonators,” J. Opt. Soc. Am. B28, 2820–2826 (2011).
[CrossRef]

J. Tao, Q. J. Wang, and X. G. Huang, “All-optical plasmonic switches based on coupled nano-disk cavity structures containing nonlinear material,” Plasmonics6, 753–759 (2011).
[CrossRef]

J. J. Chen, Z. Li, S. Yue, and Q. H. Gong, “Highly efficient all-optical control of surface-plasmon-polariton generation based on a compact asymmetric single slit,” Nano Lett.11, 2933–2937 (2011).
[CrossRef] [PubMed]

2010

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonic beyond the diffraction limit,” Nat. Photonics4, 83–90 (2010).
[CrossRef]

D. Y. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt.12, 015002 (2010).
[CrossRef]

2009

J. X. Chen, P. Wang, X. L. Wang, Y. H. Lu, R. S. Zheng, H. Ming, and Q. W. 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]

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics3, 55–58 (2009).
[CrossRef]

X. S. Lin, J. H. Yan, Y. B. Zheng, L. J. Wu, and S. Lan, “Bistable switching in the lossy side-coupled plasmonic waveguide-cavity structrues,” Opt. Express19, 9594–9599 (2009).
[CrossRef]

A. Noual, A. Akjouj, Y. Pennec, J. N. Gillet, and B. D. Rouhani, “Modeling of two-dimensional nanoscale Y-bent plasmonic waveguides with cavities for demultiplexing of the telecommunication wavelengths,” New J. Phys.11, 103020 (2009).
[CrossRef]

Q. Zhang, X. G. Huang, X. S. Lin, J. Tao, and X. P. Jin, “A subwavelength coupler-type MIM optical filter,” Opt. Express17, 7549–7555 (2009).
[CrossRef]

2008

G. A. Wurtz and A. V. Zayats, “Nonlinear surface plasmon polaritonic crystals,” Laser Photon. Rev.2, 125–135 (2008).
[CrossRef]

2007

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B75, 245405 (2007).
[CrossRef]

2006

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength scale localization,” Phys. Rev. B73, 035407 (2006).
[CrossRef]

2005

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep.408, 131–314 (2005).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424, 824–830 (2003).
[CrossRef] [PubMed]

2002

Q. H. Mao and J. W. Y. Lit, “Optical bistability in an L-band dual-wavelength erbium-doped fiber laser with overlapping cavities,” IEEE Photon. Technol. Lett.14, 1252–1254 (2002).
[CrossRef]

Akjouj, A.

A. Noual, A. Akjouj, Y. Pennec, J. N. Gillet, and B. D. Rouhani, “Modeling of two-dimensional nanoscale Y-bent plasmonic waveguides with cavities for demultiplexing of the telecommunication wavelengths,” New J. Phys.11, 103020 (2009).
[CrossRef]

Arsenin, A. V.

D. Y. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt.12, 015002 (2010).
[CrossRef]

Atwater, H.

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength scale localization,” Phys. Rev. B73, 035407 (2006).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424, 824–830 (2003).
[CrossRef] [PubMed]

Berini, P.

P. Berini and I. Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics6, 16–23 (2012).
[CrossRef]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonic beyond the diffraction limit,” Nat. Photonics4, 83–90 (2010).
[CrossRef]

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B75, 245405 (2007).
[CrossRef]

Cao, J.

Y. Liu, F. Zhou, B. Yao, J. Cao, and Q. H. Mao, “High-extinction-ratio and low-insertion-loss plasmonic filter with coherent coupled nano-cavity array in a MIM waveguide,” Plasmonics8, 1035–1041 (2013).
[CrossRef]

Chen, J. J.

J. J. Chen, Z. Li, S. Yue, and Q. H. Gong, “Highly efficient all-optical control of surface-plasmon-polariton generation based on a compact asymmetric single slit,” Nano Lett.11, 2933–2937 (2011).
[CrossRef] [PubMed]

Chen, J. X.

X. L. Wang, H. Q. Jiang, J. X. Chen, P. Wang, Y. H. Lu, and H. Ming, “Optical bistability effect in plasmonic racetrack resonator with high extinction ratio,” Opt. Express19, 19415–19421 (2011).
[CrossRef] [PubMed]

J. X. Chen, P. Wang, X. L. Wang, Y. H. Lu, R. S. Zheng, H. Ming, and Q. W. 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]

Chen, Z. L.

L. Liu, X. Hao, Y. T. Ye, J. X. Liu, Z. L. Chen, Y. C. Song, Y. Luo, J. Zhang, and L. Tan, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424, 824–830 (2003).
[CrossRef] [PubMed]

Ding, C. Y.

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

Dionne, J.

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength scale localization,” Phys. Rev. B73, 035407 (2006).
[CrossRef]

Duan, L. N.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424, 824–830 (2003).
[CrossRef] [PubMed]

Fedyanin, D. Y.

D. Y. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt.12, 015002 (2010).
[CrossRef]

Gillet, J. N.

A. Noual, A. Akjouj, Y. Pennec, J. N. Gillet, and B. D. Rouhani, “Modeling of two-dimensional nanoscale Y-bent plasmonic waveguides with cavities for demultiplexing of the telecommunication wavelengths,” New J. Phys.11, 103020 (2009).
[CrossRef]

Gladun, A. D.

D. Y. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt.12, 015002 (2010).
[CrossRef]

Gong, Q. H.

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

J. J. Chen, Z. Li, S. Yue, and Q. H. Gong, “Highly efficient all-optical control of surface-plasmon-polariton generation based on a compact asymmetric single slit,” Nano Lett.11, 2933–2937 (2011).
[CrossRef] [PubMed]

Gong, Y. K.

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonic beyond the diffraction limit,” Nat. Photonics4, 83–90 (2010).
[CrossRef]

Granpayeh, N.

N. Nozhat and N. Granpayeh, “Switching power reduction in the ultra-compact Kerr nonlinear plasmonic directional coupler,” Opt. Comm.285, 1555–1559 (2012).
[CrossRef]

Hao, X.

L. Liu, X. Hao, Y. T. Ye, J. X. Liu, Z. L. Chen, Y. C. Song, Y. Luo, J. Zhang, and L. Tan, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

Holmgaard, T.

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B75, 245405 (2007).
[CrossRef]

Hu, X. Y.

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

Huang, X. G.

J. Tao, Q. J. Wang, and X. G. Huang, “All-optical plasmonic switches based on coupled nano-disk cavity structures containing nonlinear material,” Plasmonics6, 753–759 (2011).
[CrossRef]

Q. Zhang, X. G. Huang, X. S. Lin, J. Tao, and X. P. Jin, “A subwavelength coupler-type MIM optical filter,” Opt. Express17, 7549–7555 (2009).
[CrossRef]

Hwang, Y.

Y. Hwang, J. Kim, and H. Y. Park, “Frequency selective metal-insulator-metal splitters for surface plasmons,” Opt. Comm.284, 4778–4781 (2011).
[CrossRef]

Irving, R. S.

R. S. Irving, Integers, Polynomials, and Rings (Springer, 2004).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Inc., 1999).

Jiang, H. Q.

Jiang, P.

X. Y. Hu, P. Jiang, C. Y. Ding, H. Yang, and Q. H. Gong, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

Jin, X. P.

Kim, J.

Y. Hwang, J. Kim, and H. Y. Park, “Frequency selective metal-insulator-metal splitters for surface plasmons,” Opt. Comm.284, 4778–4781 (2011).
[CrossRef]

Lan, S.

Leiman, V. G.

D. Y. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt.12, 015002 (2010).
[CrossRef]

Leon, I.

P. Berini and I. Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics6, 16–23 (2012).
[CrossRef]

Li, Z.

J. J. Chen, Z. Li, S. Yue, and Q. H. Gong, “Highly efficient all-optical control of surface-plasmon-polariton generation based on a compact asymmetric single slit,” Nano Lett.11, 2933–2937 (2011).
[CrossRef] [PubMed]

Lin, X. S.

Lit, J. W. Y.

Q. H. Mao and J. W. Y. Lit, “Optical bistability in an L-band dual-wavelength erbium-doped fiber laser with overlapping cavities,” IEEE Photon. Technol. Lett.14, 1252–1254 (2002).
[CrossRef]

Liu, J. X.

L. Liu, X. Hao, Y. T. Ye, J. X. Liu, Z. L. Chen, Y. C. Song, Y. Luo, J. Zhang, and L. Tan, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

Liu, L.

L. Liu, X. Hao, Y. T. Ye, J. X. Liu, Z. L. Chen, Y. C. Song, Y. Luo, J. Zhang, and L. Tan, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

Liu, X. M.

Liu, Y.

Y. Liu, F. Zhou, B. Yao, J. Cao, and Q. H. Mao, “High-extinction-ratio and low-insertion-loss plasmonic filter with coherent coupled nano-cavity array in a MIM waveguide,” Plasmonics8, 1035–1041 (2013).
[CrossRef]

Lu, H.

Lu, Y. H.

X. L. Wang, H. Q. Jiang, J. X. Chen, P. Wang, Y. H. Lu, and H. Ming, “Optical bistability effect in plasmonic racetrack resonator with high extinction ratio,” Opt. Express19, 19415–19421 (2011).
[CrossRef] [PubMed]

J. X. Chen, P. Wang, X. L. Wang, Y. H. Lu, R. S. Zheng, H. Ming, and Q. W. 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]

Luo, Y.

L. Liu, X. Hao, Y. T. Ye, J. X. Liu, Z. L. Chen, Y. C. Song, Y. Luo, J. Zhang, and L. Tan, “Systematical research on the characteristics of a vertical coupled Fabry-Perot plasmonic filter,” Opt. Comm.285, 2558–2562 (2012).
[CrossRef]

MacDonald, K. F.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics3, 55–58 (2009).
[CrossRef]

Mao, D.

Mao, Q. H.

Y. Liu, F. Zhou, B. Yao, J. Cao, and Q. H. Mao, “High-extinction-ratio and low-insertion-loss plasmonic filter with coherent coupled nano-cavity array in a MIM waveguide,” Plasmonics8, 1035–1041 (2013).
[CrossRef]

Q. H. Mao and J. W. Y. Lit, “Optical bistability in an L-band dual-wavelength erbium-doped fiber laser with overlapping cavities,” IEEE Photon. Technol. Lett.14, 1252–1254 (2002).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep.408, 131–314 (2005).
[CrossRef]

Ming, H.

X. L. Wang, H. Q. Jiang, J. X. Chen, P. Wang, Y. H. Lu, and H. Ming, “Optical bistability effect in plasmonic racetrack resonator with high extinction ratio,” Opt. Express19, 19415–19421 (2011).
[CrossRef] [PubMed]

J. X. Chen, P. Wang, X. L. Wang, Y. H. Lu, R. S. Zheng, H. Ming, and Q. W. 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]

Noual, A.

A. Noual, A. Akjouj, Y. Pennec, J. N. Gillet, and B. D. Rouhani, “Modeling of two-dimensional nanoscale Y-bent plasmonic waveguides with cavities for demultiplexing of the telecommunication wavelengths,” New J. Phys.11, 103020 (2009).
[CrossRef]

Nozhat, N.

N. Nozhat and N. Granpayeh, “Switching power reduction in the ultra-compact Kerr nonlinear plasmonic directional coupler,” Opt. Comm.285, 1555–1559 (2012).
[CrossRef]

Pannipitiya, A.

Park, H. Y.

Y. Hwang, J. Kim, and H. Y. Park, “Frequency selective metal-insulator-metal splitters for surface plasmons,” Opt. Comm.284, 4778–4781 (2011).
[CrossRef]

Pennec, Y.

A. Noual, A. Akjouj, Y. Pennec, J. N. Gillet, and B. D. Rouhani, “Modeling of two-dimensional nanoscale Y-bent plasmonic waveguides with cavities for demultiplexing of the telecommunication wavelengths,” New J. Phys.11, 103020 (2009).
[CrossRef]

Polman, A.

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength scale localization,” Phys. Rev. B73, 035407 (2006).
[CrossRef]

Premaratne, M.

Rouhani, B. D.

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Figures (4)

Fig. 1
Fig. 1

Typical plasmonic structure with a Kerr nonlinear cavity side-coupling to a MIM waveguide.

Fig. 2
Fig. 2

(a) Transmissions as a function of incident power for different incident light wavelengths; (b) The comparisons of the bistable curves obtained by our analytical theory (solid line) and the FDTD numerical simulations (red circles).

Fig. 3
Fig. 3

(a) Schematic diagram for the linear transmission properties when the incident wavelength is larger or less than λM respectively; (b) and (c) Transmissions (black line) and non-linear resonant wavelengths (red line) as a function of incident light power for the incident light wavelength of 1580 and 1610 nm, respectively. The linear resonant wavelength and the incident light wavelengths are displayed with blue dot lines in (b) and (c).

Fig. 4
Fig. 4

The critical wavelength of optical bistability as a function of (a) Q0 and (b) Q1 for a fixed Q1 and Q0, respectively. Bistable properties at 1610 nm for (c) different Q0 and (d) different Q1 when Q1 and Q0 are fixed, respectively.

Equations (11)

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

d A d t = ( j ω c ω c Q 0 ω c 2 Q 1 ) A + ω c 2 Q 1 e j θ S + 1 ,
S 1 = S + 1 ω c 2 Q 1 e j θ A S 1 = ω c 2 Q 1 e j θ A
T = | S 1 S + 1 | 2 = ( ω ω c 1 ) 2 + ( 1 Q 0 ) 2 ( ω ω c 1 ) 2 + ( 1 Q 0 + 1 2 Q 1 ) 2 .
| A | 2 = 1 2 ω c Q 1 ( ω ω c 1 ) 2 + ( 1 Q 0 + 1 2 Q 1 ) 2 | S + 1 | 2 .
λ c = λ c 0 + 2 n 2 | E b | 2 L eff = λ c 0 + 2 n 2 L eff | A | 2 ε S
λ c 3 + B λ c 2 + ( C 1 C 2 P in ) λ c + D = 0 ,
λ c 3 + B 2 λ c 2 D 2 = 0 .
x 3 27 ζ 2 + 15 8 x 2 + 3 4 x + 1 8 = 0
x 1 , 2 = B 3 + e ± i 2 π 3 q 2 + Δ 3 + e i 2 π 3 q 2 Δ 3
x 1 , 2 = 1 ± 3 ζ
λ λ c 0 = ± 3 λ c 0 ( 1 Q 0 + 1 2 Q 1 ) = ± 3 Δ λ 2

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