Abstract

Photonic functions are programmed by designing the interference of local waves in inhomogeneous resonant guided wave networks composed of power-splitting elements arranged at the nodes of a nonuniform waveguide network. Using a compact, yet comprehensive, scattering matrix representation of the network, the desired photonic function is designed by fitting structural parameters according to an optimization procedure. This design scheme is demonstrated for plasmonic dichroic and trichroic routers in the infrared frequency range.

© 2010 OSA

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References

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  1. E. Yablonovitch, “Photonic crystals: semiconductors of light,” Sci. Am. 285(6), 46–51, 54–55 (2001).
    [CrossRef]
  2. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of light, 2’nd Ed. (New Jersey, Princeton, 2008).
  3. M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
    [CrossRef] [PubMed]
  4. J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, “Lasing from a circular Bragg nanocavity with an ultra small modal volume,” Appl. Phys. Lett. 86(25), 251101 (2005).
    [CrossRef]
  5. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
    [CrossRef] [PubMed]
  6. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
    [CrossRef]
  7. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  8. E. Feigenbaum and H. A. Atwater, “Resonant guided wave networks,” Phys. Rev. Lett. 104(14), 147402 (2010).
    [CrossRef] [PubMed]
  9. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [CrossRef] [PubMed]
  10. E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182(2), 539–554 (1969).
    [CrossRef]
  11. B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B Condens. Matter 44(24), 13556–13572 (1991).
    [CrossRef] [PubMed]
  12. 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]
  13. J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
    [CrossRef] [PubMed]
  14. E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol. 25(9), 2547–2562 (2007).
    [CrossRef]
  15. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).
    [CrossRef]
  16. E. Feigenbaum and M. Orenstein, “Perfect 4-way splitting in nano plasmonic X-junctions,” Opt. Express 15(26), 17948–17953 (2007).
    [CrossRef] [PubMed]
  17. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
    [CrossRef]
  18. S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-1-4 .
    [CrossRef] [PubMed]
  19. S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008).
    [CrossRef]
  20. E. D. Palik, Handbook of optical constants of solids, 2'nd Ed. (San-Diego, Academic, 1998).

2010

E. Feigenbaum and H. A. Atwater, “Resonant guided wave networks,” Phys. Rev. Lett. 104(14), 147402 (2010).
[CrossRef] [PubMed]

2008

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008).
[CrossRef]

2007

E. Feigenbaum and M. Orenstein, “Perfect 4-way splitting in nano plasmonic X-junctions,” Opt. Express 15(26), 17948–17953 (2007).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol. 25(9), 2547–2562 (2007).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

2006

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
[CrossRef] [PubMed]

2005

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

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[CrossRef] [PubMed]

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, “Lasing from a circular Bragg nanocavity with an ultra small modal volume,” Appl. Phys. Lett. 86(25), 251101 (2005).
[CrossRef]

2004

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

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]

2003

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

2001

E. Yablonovitch, “Photonic crystals: semiconductors of light,” Sci. Am. 285(6), 46–51, 54–55 (2001).
[CrossRef]

1998

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-1-4 .
[CrossRef] [PubMed]

1997

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

1991

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B Condens. Matter 44(24), 13556–13572 (1991).
[CrossRef] [PubMed]

1969

E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Asano, T.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[CrossRef] [PubMed]

Atwater, H. A.

E. Feigenbaum and H. A. Atwater, “Resonant guided wave networks,” Phys. Rev. Lett. 104(14), 147402 (2010).
[CrossRef] [PubMed]

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
[CrossRef] [PubMed]

Barnes, W. L.

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

Brongersma, M. L.

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]

Catrysse, P. B.

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]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Dereux, A.

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

DeRose, G. A.

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, “Lasing from a circular Bragg nanocavity with an ultra small modal volume,” Appl. Phys. Lett. 86(25), 251101 (2005).
[CrossRef]

Dionne, J. A.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
[CrossRef] [PubMed]

Ebbesen, T. W.

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

Economou, E. N.

E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Fan, S.

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008).
[CrossRef]

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

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-1-4 .
[CrossRef] [PubMed]

Feigenbaum, E.

E. Feigenbaum and H. A. Atwater, “Resonant guided wave networks,” Phys. Rev. Lett. 104(14), 147402 (2010).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Perfect 4-way splitting in nano plasmonic X-junctions,” Opt. Express 15(26), 17948–17953 (2007).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol. 25(9), 2547–2562 (2007).
[CrossRef]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Fujita, M.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[CrossRef] [PubMed]

Green, W. M.

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, “Lasing from a circular Bragg nanocavity with an ultra small modal volume,” Appl. Phys. Lett. 86(25), 251101 (2005).
[CrossRef]

Haus, H.

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-1-4 .
[CrossRef] [PubMed]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Joannopoulos, J.

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-1-4 .
[CrossRef] [PubMed]

Kocabas, S. E.

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008).
[CrossRef]

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Lezec, H. J.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
[CrossRef] [PubMed]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Miller, D.

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008).
[CrossRef]

Mysyrowicz, A.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B Condens. Matter 44(24), 13556–13572 (1991).
[CrossRef] [PubMed]

Noda, S.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[CrossRef] [PubMed]

Orenstein, M.

E. Feigenbaum and M. Orenstein, “Perfect 4-way splitting in nano plasmonic X-junctions,” Opt. Express 15(26), 17948–17953 (2007).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol. 25(9), 2547–2562 (2007).
[CrossRef]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Prade, B.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B Condens. Matter 44(24), 13556–13572 (1991).
[CrossRef] [PubMed]

Scheuer, J.

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, “Lasing from a circular Bragg nanocavity with an ultra small modal volume,” Appl. Phys. Lett. 86(25), 251101 (2005).
[CrossRef]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Selker, M. D.

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]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Takahashi, S.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[CrossRef] [PubMed]

Tanaka, Y.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[CrossRef] [PubMed]

Veronis, G.

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008).
[CrossRef]

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

Villeneuve, P.

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-1-4 .
[CrossRef] [PubMed]

Vinet, J. Y.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B Condens. Matter 44(24), 13556–13572 (1991).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, “Photonic crystals: semiconductors of light,” Sci. Am. 285(6), 46–51, 54–55 (2001).
[CrossRef]

Yariv, A.

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, “Lasing from a circular Bragg nanocavity with an ultra small modal volume,” Appl. Phys. Lett. 86(25), 251101 (2005).
[CrossRef]

Zia, R.

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]

Appl. Phys. Lett.

J. Scheuer, W. M. Green, G. A. DeRose, and A. Yariv, “Lasing from a circular Bragg nanocavity with an ultra small modal volume,” Appl. Phys. Lett. 86(25), 251101 (2005).
[CrossRef]

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

IEEE J. Sel. Top. Quantum Electron.

S. E. Kocabas, G. Veronis, D. Miller, and S. Fan, “Transmission Line and Equivalent Circuit Models for Plasmonic Waveguide Components,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1462–1472 (2008).
[CrossRef]

J. Lightwave Technol.

E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol. 25(9), 2547–2562 (2007).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

J. Opt. Soc. Am. A

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]

Nano Lett.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006).
[CrossRef] [PubMed]

Nat. Photonics

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Nature

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

Opt. Express

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-1-4 .
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Perfect 4-way splitting in nano plasmonic X-junctions,” Opt. Express 15(26), 17948–17953 (2007).
[CrossRef] [PubMed]

Phys. Rev.

E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Phys. Rev. B Condens. Matter

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B Condens. Matter 44(24), 13556–13572 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett.

E. Feigenbaum and H. A. Atwater, “Resonant guided wave networks,” Phys. Rev. Lett. 104(14), 147402 (2010).
[CrossRef] [PubMed]

Sci. Am.

E. Yablonovitch, “Photonic crystals: semiconductors of light,” Sci. Am. 285(6), 46–51, 54–55 (2001).
[CrossRef]

Science

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Other

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of light, 2’nd Ed. (New Jersey, Princeton, 2008).

E. D. Palik, Handbook of optical constants of solids, 2'nd Ed. (San-Diego, Academic, 1998).

Supplementary Material (5)

» Media 1: MPG (1605 KB)     
» Media 2: MPG (2427 KB)     
» Media 3: MPG (2670 KB)     
» Media 4: MPG (1679 KB)     
» Media 5: MPG (2522 KB)     

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Figures (7)

Fig. 1
Fig. 1

RGWNs basics: schematic illustration of (a) 4-terminals equal power splitting element and (b) local resonance forming in a 2x2 RGWN constructed from 4 splitting elements and 4 isolated waveguides. (c) Plasmonics implementation of RGWN as intersecting air gaps in Au matrix: (I) X-junction as power splitting element (II) illustration of two wave splits acquiring different phase/amplitude changes as they follow different trajectories in the network and then interfere with each other. (d) Illustration of possible inhomogeneous RGWN layout.

Fig. 2
Fig. 2

Mathematical representation reference of (a) 2x2 RGWN system and its components, (b) waveguide component (c) X-junction component

Fig. 3
Fig. 3

Tunabillity of the wave properties in RGWN components. TM0 modal effective index in an MIM waveguide plotted versus its width and excitation frequency - (a) Real and (b) imaginary parts. Transmission coefficients to the different terminals when wave power splitting occurs at an X-junction – (c) amplitude and (d) phase of the transmission coefficient. The variables width1 and width2 correspond to the air gap widths of two normally intersecting MIM waveguides at an X-junction. Two-dimensional contours of these plots can be found in appendix A.

Fig. 4
Fig. 4

2x2 RGWN programmed to function as a dichroic router: (a) schematic drawing, and snapshots of the H-field at the two operation frequencies: (b) λ1 (Media 1) and (c) λ2 (Media 2). The movies show the right half of the RGWN.

Fig. 5
Fig. 5

3x3 RGWN programmed to function as a trichroic router. Snapshots of the H-field at the three operation frequencies: (a) λ1 (Media 3), (b) λ2 (Media 4) and (c) λ2 (Media 5). The movies show the right half of the RGWN.

Fig. A1
Fig. A1

Tunability of the wave properties in RGWN components.

Fig. C1
Fig. C1

Flow chart of the optimization procedure

Tables (4)

Tables Icon

Table 1 Dichroic router set of parameters for 2x2 RGWN

Tables Icon

Table 2 Trichroic router set of parameters for 3x3 RGWN

Tables Icon

Table C1 Amplitudes of output terminals of the Dichroic router

Tables Icon

Table C2 Amplitudes of output terminals of the Trichroic router

Equations (6)

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A ¯ o u t t r = { a 1 ( 1 ) o , a 1 ( 2 ) o , a 3 ( 3 ) o , a 3 ( 2 ) o , a 2 ( 1 ) o , a 2 ( 4 ) o , a 4 ( 3 ) o , a 4 ( 4 ) o } ; A ¯ i n t r = { a 1 ( 1 ) i , a 1 ( 2 ) i , a 3 ( 3 ) i , a 3 ( 2 ) i , a 2 ( 1 ) i , a 2 ( 4 ) i , a 4 ( 3 ) i , a 4 ( 4 ) i } ; A ¯ n e t t r = { a 1 ( 3 ) i , a 1 ( 4 ) i , a 3 ( 1 ) i , a 3 ( 4 ) i , a 3 ( 3 ) i , a 3 ( 2 ) i , a 4 ( 1 ) i , a 4 ( 2 ) i } ;
{ A ¯ o u t = M ¯ ¯ F S A ¯ n e t + M ¯ ¯ R S A ¯ i n 0 ¯ = ( M ¯ ¯ R S K ¯ ¯ ) A ¯ n e t + M ¯ ¯ F S A ¯ i n
M ¯ ¯ F S = D i a g { S ¯ ¯ F S 1 , S ¯ ¯ F S 3 , S ¯ ¯ F S 2 , S ¯ ¯ F S 4 } , M ¯ ¯ R S = D i a g { S ¯ ¯ R S 1 , S ¯ ¯ R S 3 , S ¯ ¯ R S 2 , S ¯ ¯ R S 4 } S ¯ ¯ F S i = ( ( t F V ) i ( t S H ) i ( t S V ) i ( t F H ) i ) S ¯ ¯ R S i = ( ( t R V ) i ( t S H ) i ( t S V ) i ( t R H ) i ) K ¯ ¯ = { K ( 1 , 3 ) = K ( 3 , 1 ) = κ 1 3 K ( 2 , 6 ) = K ( 6 , 2 ) = κ 1 2 K ( 4 , 8 ) = K ( 8 , 4 ) = κ 3 4 K ( 5 , 7 ) = K ( 7 , 5 ) = κ 2 4 o t h e r m a t r i x e l e m e n t s = 0 , κ i m = exp { j ( β L ) i m }
S ¯ ¯ 2 x 2 R G W N = M ¯ ¯ R S M ¯ ¯ F S ( M ¯ ¯ R S K ) 1 M ¯ ¯ F S
O 1 = | O u t 6 ( λ 1 ) | / | O u t 5 ( λ 1 ) | O 2 = | O u t 5 ( λ 2 ) | / | O u t 6 ( λ 2 ) | 1 f = [ | O u t 6 ( λ 1 ) | | O u t 5 ( λ 2 ) | ] [ O 1 O 2 ] [ 1 | O 1 O 2 O 1 + O 2 | ]
O 1 = | O u t 9 ( λ 1 ) | / ( | O u t 7 ( λ 1 ) | + | O u t 8 ( λ 1 ) | ) O 2 = | O u t 8 ( λ 2 ) | / ( | O u t 7 ( λ 2 ) | + | O u t 9 ( λ 2 ) | ) O 3 = | O u t 7 ( λ 3 ) | / ( | O u t 8 ( λ 3 ) | + | O u t 9 ( λ 3 ) | ) 1 f = [ | O u t 9 ( λ 1 ) | | O u t 8 ( λ 2 ) | | O u t 7 ( λ 3 ) | ] [ O 1 O 2 O 3 ]     [ ( 1 | O 1 O 2 O 1 + O 2 | ) ( 1 | O 1 O 3 O 1 + O 3 | ) ] ( 1 | O 2 O 3 O 2 + O 3 | )

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