Abstract

We present approximate analytical expressions describing the optical bistability phenomenon in a plasmonic-gap-waveguide-based nonlinear device. The device is formed by a metal–dielectric–metal (MDM) waveguide perpendicularly coupled to a stub structure that is filled with an optically nonlinear medium. Among the recently reported studies on nonlinearity-induced bistability in plasmonic nanostructures, our work stands out because of its pure analytic approach and the considered device geometry. The scattered-field technique that we employ here is hinged on the concepts of circuit theory and the characteristic-impedance model for single-mode MDM waveguides. By properly accounting for surface-plasmon damping, multiple reflections, and the Kerr effect, we obtain a fairly accurate parametric relation connecting the input and output intensities of the device. The impact of changing the operating wavelength and geometrical parameters of the stub on the bistable switching thresholds and the hysteresis loop width is demonstrated using a number of numerical examples. The derived relation is useful for rapid design optimization of plasmonic switches and memories.

© 2011 Optical Society of America

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2011

2010

2009

N. J. Halas, “Connecting the dots: reinventing optics for nanoscale dimensions,” Proc. Natl. Acad. Sci. USA 106, 3643–3644(2009).
[CrossRef] [PubMed]

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photon. 3, 283–286(2009).
[CrossRef]

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal–oxide–Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef] [PubMed]

W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9, 4403–4411 (2009).
[CrossRef] [PubMed]

G. Veronis, S. E. Kocabaş, D. A. B. Miller, and S. Fan, “Modeling of plasmonic waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808–1826 (2009).
[CrossRef]

X. Lin and X. Huang, “Numerical modeling of a teeth-shaped nanoplasmonic waveguide filter,” J. Opt. Soc. Am. B 26, 1263–1268 (2009).
[CrossRef]

C. Min and G. Veronis, “Absorption switches in metal-dielectric-metal plasmonic waveguides,” Opt. Express 17, 10757–10766(2009).
[CrossRef] [PubMed]

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. Tao, X. Huang, X. Lin, Q. Zhang, and X. Jin, “A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure,” Opt. Express 17, 13989–13994(2009).
[CrossRef] [PubMed]

R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic couplers and splitters,” Opt. Express 17, 19033–19040 (2009).
[CrossRef]

2008

2007

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photon. 1, 641–648 (2007).
[CrossRef]

A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91, 083115 (2007).
[CrossRef]

M. U. González, A. L. Stepanov, J. C. Weeber, A. Hohenau, A. Dereux, R. Quidant, and J. R. Krenn, “Analysis of the angular acceptance of surface plasmon Bragg mirrors,” Opt. Lett. 32, 2704–2706 (2007).
[CrossRef] [PubMed]

G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25, 2511–2521 (2007).
[CrossRef]

2006

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach–Zehnder interferometers based on surface plasmon polariton,” Opt. Commun. 259, 690–695 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407(2006).
[CrossRef]

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[CrossRef]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

2005

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23, 413–422 (2005).
[CrossRef]

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005).
[CrossRef] [PubMed]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005).
[CrossRef] [PubMed]

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

2004

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (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

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

1998

Abushagur, M. A. G.

Agrawal, G. P.

Akjouj, A.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (2004).
[CrossRef]

Atwater, H. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal–oxide–Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407(2006).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Baida, F. I.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Barnes, W. L.

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

Belkhir, A.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Boltasseva, A.

Borghs, G.

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photon. 3, 283–286(2009).
[CrossRef]

Bouazaoui, M.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (2004).
[CrossRef]

Boyd, R.

R. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
[CrossRef]

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61, 44–50 (2008).
[CrossRef]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23, 413–422 (2005).
[CrossRef]

Brixner, T.

Brongersma, M. L.

M. L. Brongersma and V. M. Shalaev, “The case for plasmonics,” Science 328, 440–441 (2010).
[CrossRef] [PubMed]

W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9, 4403–4411 (2009).
[CrossRef] [PubMed]

Cai, W.

W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9, 4403–4411 (2009).
[CrossRef] [PubMed]

Capasso, F.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Chen, C.

Crozier, K. B.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Cubukcu, E.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Dai, Q.-F.

Deng, Y.

Dereux, A.

Diest, K.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal–oxide–Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef] [PubMed]

Dionne, J. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal–oxide–Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407(2006).
[CrossRef]

Djafari-Rouhani, B.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (2004).
[CrossRef]

Djurisic, A. B.

Dobrzynski, L.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (2004).
[CrossRef]

Dorpe, P. V.

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photon. 3, 283–286(2009).
[CrossRef]

Duzer, T. V.

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics, 3rd ed. (Wiley, 1994).

Ebbesen, T. W.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61, 44–50 (2008).
[CrossRef]

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

Elazar, J. M.

Enoch, S.

Fan, S.

G. Veronis, S. E. Kocabaş, D. A. B. Miller, and S. Fan, “Modeling of plasmonic waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808–1826 (2009).
[CrossRef]

G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25, 2511–2521 (2007).
[CrossRef]

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. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach–Zehnder interferometers based on surface plasmon polariton,” Opt. Commun. 259, 690–695 (2006).
[CrossRef]

Genet, C.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61, 44–50 (2008).
[CrossRef]

Gong, Y.

González, M. U.

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
[CrossRef]

Hahn, J.

Halas, N. J.

N. J. Halas, “Connecting the dots: reinventing optics for nanoscale dimensions,” Proc. Natl. Acad. Sci. USA 106, 3643–3644(2009).
[CrossRef] [PubMed]

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photon. 1, 641–648 (2007).
[CrossRef]

Han, Z.

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach–Zehnder interferometers based on surface plasmon polariton,” Opt. Commun. 259, 690–695 (2006).
[CrossRef]

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005).
[CrossRef] [PubMed]

Handapangoda, D.

Hattori, H. T.

He, S.

Hecht, B.

Hiller, J. M.

A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91, 083115 (2007).
[CrossRef]

Hohenau, A.

Hu, X.

Huang, J.-S.

Huang, X.

Imre, A.

A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91, 083115 (2007).
[CrossRef]

Jagadish, C.

Jin, X.

Kim, H.

Kjaer, K.

Kocabas, S. E.

G. Veronis, S. E. Kocabaş, D. A. B. Miller, and S. Fan, “Modeling of plasmonic waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808–1826 (2009).
[CrossRef]

Kort, E. A.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Krenn, J. R.

Labeke, D. V.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Lagae, L.

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photon. 3, 283–286(2009).
[CrossRef]

Lal, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photon. 1, 641–648 (2007).
[CrossRef]

Lamrous, O.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Lan, S.

Larsen, M. S.

Lee, B.

Leosson, K.

Li, X.

Lin, X.

Lin, X.-S.

Link, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photon. 1, 641–648 (2007).
[CrossRef]

Liu, L.

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach–Zehnder interferometers based on surface plasmon polariton,” Opt. Commun. 259, 690–695 (2006).
[CrossRef]

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005).
[CrossRef] [PubMed]

Liu, X.

Liu, Z.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005).
[CrossRef] [PubMed]

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Lu, Y.

Lu, Z.

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S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Majewski, M. L.

Mao, D.

Mayy, M.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

Miller, D. A. B.

G. Veronis, S. E. Kocabaş, D. A. B. Miller, and S. Fan, “Modeling of plasmonic waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808–1826 (2009).
[CrossRef]

Min, C.

Ming, H.

Neutens, P.

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photon. 3, 283–286(2009).
[CrossRef]

Nikolajsen, T.

Ning, T.

Noginov, M. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

Noginova, N.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

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E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
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A. Pannipitiya, I. D. Rukhlenko, and M. Premaratne, “Analytical modeling of resonant cavities for plasmonic-slot-waveguide junctions,” IEEE J. Photon. 3, 220–233 (2011).
[CrossRef]

A. Pannipitiya, I. D. Rukhlenko, M. Premaratne, H. T. Hattori, and G. P. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express 18, 6191–6204 (2010).
[CrossRef] [PubMed]

Park, J.

Pearson, J.

A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91, 083115 (2007).
[CrossRef]

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Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005).
[CrossRef] [PubMed]

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M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
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Renger, J.

Ritzo, B. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
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P. A. Rizzi, Microwave Engineering: Passive Circuits (Prentice-Hall, 1988).

Rukhlenko, I. D.

Shalaev, V. M.

M. L. Brongersma and V. M. Shalaev, “The case for plasmonics,” Science 328, 440–441 (2010).
[CrossRef] [PubMed]

Shen, Y.

Srituravanich, W.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Steele, J. M.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Stepanov, A. L.

Sun, C.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Sweatlock, L. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal–oxide–Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407(2006).
[CrossRef]

Tao, J.

Vasseur, J. O.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (2004).
[CrossRef]

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C. Min and G. Veronis, “Absorption switches in metal-dielectric-metal plasmonic waveguides,” Opt. Express 17, 10757–10766(2009).
[CrossRef] [PubMed]

G. Veronis, S. E. Kocabaş, D. A. B. Miller, and S. Fan, “Modeling of plasmonic waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808–1826 (2009).
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G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25, 2511–2521 (2007).
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G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Vigneron, J. P.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (2004).
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Vilcot, J. P.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (2004).
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P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photon. 3, 283–286(2009).
[CrossRef]

Vlasko-Vlasov, V. K.

A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91, 083115 (2007).
[CrossRef]

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L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (2004).
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Wahsheh, R. A.

Wang, B.

Wang, G. P.

Wang, L.

Wang, P.

Weeber, J. C.

Welp, U.

A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91, 083115 (2007).
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Whinnery, J. R.

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics, 3rd ed. (Wiley, 1994).

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W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9, 4403–4411 (2009).
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Xu, Y.

Yan, J.-H.

Yang, G.

Zhang, Q.

Zhang, X.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Zheng, Y.-B.

Zhong, Z.-J.

Zhou, Y.

Zhu, G.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef] [PubMed]

Zielinski, P.

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (2004).
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Appl. Opt.

Appl. Phys. Lett.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

A. Imre, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, and U. Welp, “Multiplexing surface plasmon polaritons on nanowires,” Appl. Phys. Lett. 91, 083115 (2007).
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G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

IEEE J. Photon.

A. Pannipitiya, I. D. Rukhlenko, and M. Premaratne, “Analytical modeling of resonant cavities for plasmonic-slot-waveguide junctions,” IEEE J. Photon. 3, 220–233 (2011).
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J. Appl. Phys.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
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J. Comput. Theor. Nanosci.

G. Veronis, S. E. Kocabaş, D. A. B. Miller, and S. Fan, “Modeling of plasmonic waveguide components and networks,” J. Comput. Theor. Nanosci. 6, 1808–1826 (2009).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Nano Lett.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005).
[CrossRef] [PubMed]

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal–oxide–Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef] [PubMed]

W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9, 4403–4411 (2009).
[CrossRef] [PubMed]

Nat. Photon.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photon. 1, 641–648 (2007).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
[CrossRef]

P. Neutens, P. V. Dorpe, I. D. Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photon. 3, 283–286(2009).
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Nature

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

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach–Zehnder interferometers based on surface plasmon polariton,” Opt. Commun. 259, 690–695 (2006).
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Opt. Express

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).
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H. Kim, J. Hahn, and B. Lee, “Focusing properties of surface plasmon polariton floating dielectric lenses,” Opt. Express 16, 3049–3057 (2008).
[CrossRef] [PubMed]

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005).
[CrossRef] [PubMed]

C. Min and G. Veronis, “Absorption switches in metal-dielectric-metal plasmonic waveguides,” Opt. Express 17, 10757–10766(2009).
[CrossRef] [PubMed]

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).
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J. Tao, X. Huang, X. Lin, Q. Zhang, and X. Jin, “A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure,” Opt. Express 17, 13989–13994(2009).
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R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic couplers and splitters,” Opt. Express 17, 19033–19040 (2009).
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A. Pannipitiya, I. D. Rukhlenko, M. Premaratne, H. T. Hattori, and G. P. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express 18, 6191–6204 (2010).
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A. A. Reiserer, J.-S. Huang, B. Hecht, and T. Brixner, “Subwavelength broadband splitters and switches for femtosecond plasmonic signals,” Opt. Express 18, 11810–11820 (2010).
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S. Randhawa, M. U. González, J. Renger, S. Enoch, and R. Quidant, “Design and properties of dielectric surface plasmon Bragg mirrors,” Opt. Express 18, 14496–14510 (2010).
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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).
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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 structures,” Opt. Express 19, 9594–9599 (2011).
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D. Handapangoda, M. Premaratne, I. D. Rukhlenko, and C. Jagadish, “Optimal design of composite nanowires for extended reach of surface plasmon-polaritons,” Opt. Express 19, 16058–16074 (2011).
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Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16, 8421–8426 (2008).
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Opt. Lett.

Phys. Rev. B

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407(2006).
[CrossRef]

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: role of the plasmonic modes,” Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Phys. Rev. E

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, J. O. Vasseur, M. Bouazaoui, J. P. Vilcot, H. A. Wahsh, P. Zielinski, and J. P. Vigneron, “Simple nanometric plasmon multiplexer,” Phys. Rev. E 69, 035601 (2004).
[CrossRef]

Phys. Rev. Lett.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
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Phys. Today

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Science

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef] [PubMed]

M. L. Brongersma and V. M. Shalaev, “The case for plasmonics,” Science 328, 440–441 (2010).
[CrossRef] [PubMed]

Other

M. Premaratne and G. P. Agrawal, Light Propagation in Gain Media (Cambridge University Press, 2011).

P. A. Rizzi, Microwave Engineering: Passive Circuits (Prentice-Hall, 1988).

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics, 3rd ed. (Wiley, 1994).

D. M. Pozar, Microwave Engineering, 2nd ed. (Wiley, 1998).

R. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

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Figures (6)

Fig. 1
Fig. 1

Schematic of a plasmonic-gap-waveguide resonator formed by an MDM waveguide of width h and a single stub of width w and length d. The permittivity of the material in the stub is ε n l . The rest of the parameters are specified in the text.

Fig. 2
Fig. 2

Three-port waveguide splitters: input is through port 1 in (a) and port 3 in (b). Equivalent transmission-line representations of (a) and (b) are shown by (c) and (d), respectively. The scattered electric, magnetic, and voltage components in the figure are detailed in the text.

Fig. 3
Fig. 3

Schematic of the waveguide geometry employed. Input and output electric field components are denoted by E in and E out , E 3 ± are the counterpropagating waves in the stub, E 1 + is the electric field in the input arm just before entering into the stub, and E 2 is the electric field in the output arm just after leaving the stub. Reflection-induced phase shift and attenuation are taken into account by the factor R 3 .

Fig. 4
Fig. 4

(a) Transmission spectra for MDM waveguide with a single stub in the case of linear dielectric materials. Solid curves represent the values for transmittance calculated through Eq. (10) for two different sets of parameters. Corresponding FDTD results are shown by open and closed circles. (b) Transmittance spectra when a Kerr medium in the stub, calculated analytically (solid curves) and numerically (symbols), for three average electric field intensities. Key parameters are mentioned therein.

Fig. 5
Fig. 5

Input/output characteristics of the resonator geometry in concern at λ = 1.55 μm . The solid green curve depicts the analytical predictions, while the blue open circles represent the FDTD simulation data. The nonlinear material parameters are ε l = 2.25 and χ ( 3 ) = 2 × 10 4 μm 2 / V 2 .

Fig. 6
Fig. 6

Bistable curves for three different (a) stub lengths, (b) stub widths, and (c) operating wavelengths. Geometrical parameters of the structure are shown in the figures themselves. For other parameters, refer to the text.

Equations (15)

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

tanh ( k d h 2 ) = k m ε d k d ε m ,
R 1 = Z S 2 Z 0 + Z S .
V 3 , 1 V 2 , 1 = Z S Z 0 ,
S 1 = 2 Z S 2 Z 0 + Z S , T 1 = 2 Z 0 2 Z 0 + Z S .
E 1 , 1 = R 1 E 1 + , E 2 , 1 = T 1 E 1 + , E 3 , 1 = ( h / w ) S 1 E 1 + .
R 2 = 2 Z 0 Z S 2 Z 0 + Z S , S 2 = 2 Z 0 2 Z 0 + Z S .
E 1 , 2 = E 2 , 2 = ( w / h ) S 2 E 3 + , E 3 , 2 = R 2 E 3 + .
E 3 = ( h / w ) S 1 E 1 + 1 R 2 R 3 exp ( i ϕ ) , E 3 + = ( h / w ) S 1 R 3 exp ( i ϕ ) E 1 + 1 R 2 R 3 exp ( i ϕ ) .
E S ( z ) = E 3 exp ( i β n l z ) + E 3 + exp ( i β n l z ) .
| E 1 + ( E ¯ S ) | 2 = | 1 R 2 R 3 exp ( i ϕ ) | 2 E ¯ S 2 ( | S 1 | h / w ) 2 ( Φ + Ψ ) ,
Φ = ( 1 + | R 3 | 2 exp ϕ ) ( exp ϕ 1 ) / ϕ , Ψ = 2 Im { R 3 [ exp ( i ϕ ) 1 ] } exp ϕ / ϕ .
| E 2 ( E ¯ S ) | 2 = | 1 R 3 exp ( i ϕ ) 1 R 2 R 3 exp ( i ϕ ) | 2 | T 1 E 1 + ( E ¯ S ) | 2 .
| E in ( E ¯ S ) | 2 = | E 1 + ( E ¯ S ) | 2 exp ( L 1 / L SPP ) ,
| E out ( E ¯ S ) | 2 = | E 2 ( E ¯ S ) | 2 exp ( L 2 / L SPP ) ,
T = | T 1 S 1 S 2 R 3 exp ( i ϕ ) 1 R 2 R 3 exp ( i ϕ ) | 2 exp ( L L SPP ) ,

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