Abstract

Directional coupler (DC) and nonlinear Mach-Zehnder interferometer (MZI) based on metal-insulator-metal (MIM) plasmonic waveguide are investigated numerically. We show that the coupling length increases almost linearly with the wavelength and this property is utilized in the design of wavelength division multiplexer (WDM). A nonlinear MZI, with one branch filled with Kerr nonlinear medium, is built to ensure controlling light with light. Employing nonlinear processes including self-phase modulation (SPM) and cross-phase modulation (XPM), intensity-based router and all-optical switch are realized.

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  9. H. Zhao, X. G. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008).
    [CrossRef]
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    [CrossRef]
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2010 (2)

Z. Han, A. Y. Elezzabi, and V. Van, “Wideband Y-splitter and aperture-assisted coupler based on sub-diffraction confined plasmonic slot waveguides,” Appl. Phys. Lett. 96(13), 131106 (2010).
[CrossRef]

Z.-J. Zhong, Y. Xu, S. Lan, Q.-F. Dai, and L.-J. Wu, “Sharp and asymmetric transmission response in metal-dielectric-metal plasmonic waveguides containing Kerr nonlinear media,” Opt. Express 18(1), 79–86 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (3)

2007 (1)

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007).
[CrossRef]

2006 (3)

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006).
[CrossRef]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

2005 (2)

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005).
[CrossRef] [PubMed]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

2004 (1)

C. Oubre and P. Nordlander, “Optical Properties of Metallodielectric Nanostructures Calculated Using the Finite Difference Time Domain Method,” J. Phys. Chem. B 108(46), 17740–17747 (2004).
[CrossRef]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2002 (1)

2000 (1)

1984 (1)

Abushagur, M. A. G.

R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic Directional Couplers and Mach-Zehnder Inerferometers,” Opt. Commun. 282(23), 4622–4626 (2009).
[CrossRef]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Aussenegg, F. R.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007).
[CrossRef]

Bader, M. A.

Bahtiar, A.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Berini, P.

Bozhevolnyi, S. I.

Brongersma, M. L.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
[CrossRef]

Bubeck, C.

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
[CrossRef]

Charbonneau, R.

Chen, C.

Chen, Z.

Chilwell, J.

Dai, Q.-F.

Deng, Y.

Dereux, A.

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Ditlbacher, H.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Elezzabi, A. Y.

Z. Han, A. Y. Elezzabi, and V. Van, “Wideband Y-splitter and aperture-assisted coupler based on sub-diffraction confined plasmonic slot waveguides,” Appl. Phys. Lett. 96(13), 131106 (2010).
[CrossRef]

Fan, S.

Feng, D.

Forsberg, E.

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006).
[CrossRef]

Fukui, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Gramotnev, D. K.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Guang, X. G.

H. Zhao, X. G. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008).
[CrossRef]

Han, Z.

Z. Han, A. Y. Elezzabi, and V. Van, “Wideband Y-splitter and aperture-assisted coupler based on sub-diffraction confined plasmonic slot waveguides,” Appl. Phys. Lett. 96(13), 131106 (2010).
[CrossRef]

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006).
[CrossRef]

Haraguchi, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Hodgkinson, I.

Hohenau, A.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007).
[CrossRef]

Holmgaard, T.

Hörhold, H.-H.

Huang, J.

H. Zhao, X. G. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008).
[CrossRef]

Koynov, K.

Krasavin, A. V.

Krenn, J. R.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007).
[CrossRef]

Lahoud, N.

Lan, S.

Leitner, A.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007).
[CrossRef]

Liu, L.

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006).
[CrossRef]

Lu, Y.

Lu, Z.

R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic Directional Couplers and Mach-Zehnder Inerferometers,” Opt. Commun. 282(23), 4622–4626 (2009).
[CrossRef]

Markey, L.

Marowsky, G.

Matsuzaki, Y.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Mattiussi, G.

Min, C.

Ming, H.

Ning, T.

Nordlander, P.

C. Oubre and P. Nordlander, “Optical Properties of Metallodielectric Nanostructures Calculated Using the Finite Difference Time Domain Method,” J. Phys. Chem. B 108(46), 17740–17747 (2004).
[CrossRef]

Ogawa, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Okamoto, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Oubre, C.

C. Oubre and P. Nordlander, “Optical Properties of Metallodielectric Nanostructures Calculated Using the Finite Difference Time Domain Method,” J. Phys. Chem. B 108(46), 17740–17747 (2004).
[CrossRef]

Pereira, S.

Pile, D. F. P.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Polman, A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Schuller, J. A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
[CrossRef]

Steinberger, B.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007).
[CrossRef]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Tanev, S.

Tillmann, H.

Tzolov, V.

Van, V.

Z. Han, A. Y. Elezzabi, and V. Van, “Wideband Y-splitter and aperture-assisted coupler based on sub-diffraction confined plasmonic slot waveguides,” Appl. Phys. Lett. 96(13), 131106 (2010).
[CrossRef]

Vernon, K. C.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Veronis, G.

Wahsheh, R. A.

R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic Directional Couplers and Mach-Zehnder Inerferometers,” Opt. Commun. 282(23), 4622–4626 (2009).
[CrossRef]

Wang, P.

Wu, L.-J.

Xu, Y.

Yamaguchi, K.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Yang, G.

Zayats, A. V.

Zhao, H.

H. Zhao, X. G. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008).
[CrossRef]

Zhong, Z.-J.

Zhou, Y.

Zia, R.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007).
[CrossRef]

Z. Han, A. Y. Elezzabi, and V. Van, “Wideband Y-splitter and aperture-assisted coupler based on sub-diffraction confined plasmonic slot waveguides,” Appl. Phys. Lett. 96(13), 131106 (2010).
[CrossRef]

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

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

J. Phys. Chem. B (1)

C. Oubre and P. Nordlander, “Optical Properties of Metallodielectric Nanostructures Calculated Using the Finite Difference Time Domain Method,” J. Phys. Chem. B 108(46), 17740–17747 (2004).
[CrossRef]

Mater. Today (1)

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006).
[CrossRef]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Opt. Commun. (2)

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006).
[CrossRef]

R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic Directional Couplers and Mach-Zehnder Inerferometers,” Opt. Commun. 282(23), 4622–4626 (2009).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. B (1)

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[CrossRef]

Physica E (1)

H. Zhao, X. G. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008).
[CrossRef]

Other (3)

A. Yariv, and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, New York, NY, 2006), 6th ed.

C. L. Chen, Foundations for Guided-Wave Optics (Wiley, 2006), chap.6.

B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (Wiley Intersceince, Hoboken, NJ, 2007), 2nd ed.

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Figures (7)

Fig. 1
Fig. 1

Propagation lengths of MIM waveguide versus the wavelength for different silver layer widths.

Fig. 2
Fig. 2

Effective mode refractive indexes of the symmetrical and antisymmetrical supermodes versus wavelength. Inset depicts the schematic of the directional coupler (n = 1.535, λ = 1.064μm, w = 100nm, d = 20nm) and the magnetic field distribution of the supermodes.

Fig. 3
Fig. 3

Coupling lengths versus wavelength calculated for different dielectric refractive indexes and separations.

Fig. 4
Fig. 4

Spectral response of the DC when excited by a pulse with central wavelength 632.8 nm and half width 0.2fs. The coupling ratio is 50% at 1064nm. The input pulse is shown in the inset.

Fig. 5
Fig. 5

Schematic of the plasmonic nonlinear Mach-Zehnder interferometer. Two identical directional couplers are connected by two branch arms. Arm-2 is filled with nonlinear Kerr medium. Four ports are illustrated to replace the port number in Fig. 2.

Fig. 6
Fig. 6

(a) Normalized signal power at port-3 and port-4 versus input power. The maximum power position at Port-4 is not consistent with the minimum power position at Port-3 because of the extreme power position offset effect of the directional couplers. (b, c) Scaled magnetic field distributions for input signal power 5e8 W/m (b) and 4.45e9 W/m (c).

Fig. 7
Fig. 7

Transmittances of signal and pump light at Port-3 and Port-4 versus the input pump power. The amplitude of the signal source is fixed at 1e8 W/m. The maximum signal power at Port-3(4) is not consistent with the minimum signal power at Port-4(3) because of the extreme power position offset effect of the directional coupler.

Equations (7)

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

tanh ( β 2 ε d k 0 2 w / 2 ) = ε d β 2 ε m k 0 2 ε m β 2 ε d k 0 2 ,
H ( x ) = H s ( x ) exp ( j β s z ) + H a ( x ) exp ( j β a z ) ,
a ( z ) = exp ( j β a z ) + exp ( j β s z ) 2 = cos ( κ z ) exp ( j β z ) ,
b ( z ) = exp ( j β a z ) exp ( j β s z ) 2 = j sin ( κ z ) exp ( j β z ) ,
L c = π 2 Re ( κ ) = π Re ( β a β s ) .
κ exp ( 2 π n e f f 2 ε m λ d ) .
Δ φ = 2 π × Δ n e f f ( n ) × l 3 λ s ,

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