Abstract

Multimode interference (MMI) effect in metal-insulator-metal (MIM) waveguides is studied in this paper. Theoretical calculation based on the self-imaging principle and the finite element method (FEM) simulation are used to analyze the effect and further guide the design of plasmonic MMI devices. We show that wavelength-selective routing and splitting with high extinction ratios can be realized in the multimode waveguides, and active control by refractive index modulation is also demonstrated.

© 2011 OSA

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  1. P. Berini, “Plasmon-polariton modes guided by a metal film of finite width bounded by different dielectrics,” Opt. Express 7(10), 329–335 (2000).
    [CrossRef] [PubMed]
  2. T. Holmgaard and S. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
    [CrossRef]
  3. A. Krasavin and A. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008).
    [CrossRef]
  4. J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999).
    [CrossRef]
  5. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
    [CrossRef] [PubMed]
  6. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004).
    [CrossRef]
  7. J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
    [CrossRef]
  8. L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
    [CrossRef]
  9. J. Leuthold, J. Eckner, E. Gamper, P. A. Besse, and H. Melchior, “Multimode Interference Couplers for the Conversion and Combining of Zero- and First-Order Modes,” J. Lightwave Technol. 16(7), 1228–1239 (1998).
    [CrossRef]
  10. Y. J. Tsai, A. Degiron, N. M. Jokerst, and D. R. Smith, “Plasmonic multi-mode interference couplers,” Opt. Express 17(20), 17471–17482 (2009).
    [CrossRef] [PubMed]
  11. G. Yuan, P. Wang, Y. Lu, and H. Ming, “Multimode interference splitter based on dielectric-loaded surface plasmon polariton waveguides,” Opt. Express 17(15), 12594–12600 (2009).
    [CrossRef] [PubMed]
  12. I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-clad optical waveguides: analytical and experimental study,” Appl. Opt. 13(2), 396–405 (1974).
    [CrossRef] [PubMed]
  13. E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, Inc., 1985).
  14. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).
    [CrossRef]
  15. T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
    [CrossRef]
  16. E. M. McKenna, A. S. Lin, A. R. Mickelson, R. Dinu, and D. Jin, “Comparison of r33 values for AJ404 films prepared with parallel plate and corona poling,” J. Opt. Soc. Am. B 24(11), 2888–2892 (2007).
    [CrossRef]

2009 (2)

2008 (1)

A. Krasavin and A. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008).
[CrossRef]

2007 (2)

T. Holmgaard and S. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[CrossRef]

E. M. McKenna, A. S. Lin, A. R. Mickelson, R. Dinu, and D. Jin, “Comparison of r33 values for AJ404 films prepared with parallel plate and corona poling,” J. Opt. Soc. Am. B 24(11), 2888–2892 (2007).
[CrossRef]

2006 (2)

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

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

2005 (2)

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).
[CrossRef]

2004 (1)

2000 (1)

1999 (1)

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999).
[CrossRef]

1998 (1)

1995 (1)

L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[CrossRef]

1974 (1)

Atwater, H.

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

Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Berini, P.

Besse, P. A.

Bozhevolnyi, S.

T. Holmgaard and S. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[CrossRef]

Brongersma, M. L.

Catrysse, P. B.

Degiron, A.

Dereux, A.

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999).
[CrossRef]

Dinu, R.

Dionne, J.

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

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Eckner, J.

Fan, S.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).
[CrossRef]

Gamper, E.

Girard, C.

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999).
[CrossRef]

Goudonnet, J. P.

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999).
[CrossRef]

Hau, S.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Hohenau, A.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Holmgaard, T.

T. Holmgaard and S. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[CrossRef]

Jang, S. H.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Jen, A. K.-Y.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Jin, D.

Jokerst, N. M.

Ka, J. W.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Kaminow, I. P.

Kang, J. W.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Kim, T. D.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Krasavin, A.

A. Krasavin and A. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008).
[CrossRef]

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Krenn, J. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999).
[CrossRef]

Leuthold, J.

Lin, A. S.

Lu, Y.

Luo, J.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Mammel, W. L.

McKenna, E. M.

Melchior, H.

Mickelson, A. R.

Ming, H.

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[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. B 73(3), 035407 (2006).
[CrossRef]

Rogers, M.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Selker, M. D.

Shi, Z.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Smith, D. R.

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[CrossRef]

Sweatlock, L.

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

Tian, Y.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Tsai, Y. J.

Tucker, N. M.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Veronis, G.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).
[CrossRef]

Wagner, D.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Wang, P.

Weber, H. P.

Weeber, J. C.

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999).
[CrossRef]

Yuan, G.

Zayats, A.

A. Krasavin and A. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008).
[CrossRef]

Zia, R.

Adv. Mater. (Deerfield Beach Fla.) (1)

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K.-Y. Jen, “Ultralarge and Thermally Stable Electro-optic Activities from Diels-Alder Crosslinkable Polymers Containing Binary Chromophore Systems,” Adv. Mater. (Deerfield Beach Fla.) 18(22), 3038–3042 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).
[CrossRef]

J. Lightwave Technol. (2)

L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[CrossRef]

J. Leuthold, J. Eckner, E. Gamper, P. A. Besse, and H. Melchior, “Multimode Interference Couplers for the Conversion and Combining of Zero- and First-Order Modes,” J. Lightwave Technol. 16(7), 1228–1239 (1998).
[CrossRef]

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

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

Opt. Express (3)

Phys. Rev. B (4)

T. Holmgaard and S. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[CrossRef]

A. Krasavin and A. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B 78(4), 045425 (2008).
[CrossRef]

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999).
[CrossRef]

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

Phys. Rev. Lett. (1)

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Other (1)

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

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Figures (5)

Fig. 1
Fig. 1

(a) The dispersion relation of the MIM waveguides (shown in the inset). (b) The field profile of the first four TM modes in a 0.8μm-wide waveguide.

Fig. 2
Fig. 2

The time-averaged poynting vector distribution in the multimode waveguides. The width of the waveguide is (a) wm = 0.8μm, (b) wm = 1.6μm and (c) wm = 4μm.

Fig. 3
Fig. 3

The magnetic field intensity |Hy | in the MMI demultiplexer at the wavelength of (a) λ = 1.55μm and (b) λ = 1.31μm.

Fig. 4
Fig. 4

The magnetic field intensity |Hy | in the 3 × 3 coupler structure when light is (a)-(b) centre-launched from port B or (c)-(d) symmetrically launched from port A&C.

Fig. 5
Fig. 5

The magnetic field intensity |Hy | in the MMI tunable splitter at the wavelength of λ = 1.55μm. The refractive index in the multimode region is (a) n = 1.5, (b) n = 1.472 and (c) n = 1.458.

Tables (2)

Tables Icon

Table 1 The transmittance at the three output ports of the 3 × 3 coupler

Tables Icon

Table 2 The transmittance at the three output ports of the tunable splitter

Equations (2)

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

κ 1 w = m π + 2 arctan ( ε 1 α 2 ε 2 κ 1 )   with   m = 0 ,  1 ,  2 ......
( k + 1 ) L π 1.55 k L π 1.31

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