Abstract

We present a highly efficient semi-analytical and straightforward-to-implement model for the determination of plasmonic band edges of metallic nanowire arrays inside photonic crystal fibers. The model relies on the approximation of the hexagonal unit cell by a circle and using particular boundary conditions, showing an accurate agreement with finite element simulations. The model reduces simulation time by a factor of 100, thus representing an efficient tool for structure design. It further allows the calculation of all relevant modes in the system by slight changes of the entries in a 4 × 4 matrix.

© 2014 Optical Society of America

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  1. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, P. S. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004).
    [CrossRef] [PubMed]
  2. A. Argyros, T. Birks, S. Leon-Saval, C. M. Cordeiro, F. Luan, P. S. J. Russell, “Photonic bandgap with an index step of one percent,” Opt. Express 13, 309–314 (2005).
    [CrossRef] [PubMed]
  3. B. Kuhlmey, B. Eggleton, D. Wu, “Fluid-filled solid-core photonic bandgap fibers,” J. Lightwave Technol. 27, 1617–1630 (2009).
    [CrossRef]
  4. W. Y. W. Yuan, G. Town, O. Bang, “Refractive index sensing in an all-solid twin-core photonic bandgap fiber,” IEEE Sens. J. 10, 1192–1199 (2010).
    [CrossRef]
  5. S. Saitoh, K. Saitoh, M. Kashiwagi, S. Matsuo, L. Dong, “Design optimization of large-mode-area all-solid photonic bandgap fibers for high-power laser applications,” J. Lightwave Technol. 32, 440–449 (2013).
    [CrossRef]
  6. A. Isomäki, O. G. Okhotnikov, “Femtosecond soliton mode-locked laser based on ytterbium-doped photonic bandgap fiber,” Opt. Express 14, 9238–9243 (2006).
    [CrossRef] [PubMed]
  7. A. Wang, A. K. George, J. C. Knight, “Three-level neodymium fiber laser incorporating photonic bandgap fiber,” Opt. Lett. 31, 1388–1390 (2006).
    [CrossRef] [PubMed]
  8. C. C. Pfeiffer, E. E. Economou, K. K. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
    [CrossRef]
  9. L. Novotny, C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50, 4094–4106 (1994).
    [CrossRef]
  10. H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, P. S. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19, 12180–12189 (2011).
    [CrossRef] [PubMed]
  11. H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
    [CrossRef]
  12. H. K. Tyagi, H. W. Lee, P. Uebel, M. a. Schmidt, N. Joly, M. Scharrer, P. S. J. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. 35, 2573–2575 (2010).
    [CrossRef] [PubMed]
  13. A. Nagasaki, K. Saitoh, M. Koshiba, “Polarization characteristics of photonic crystal fibers selectively filled with metal wires into cladding air holes,” Opt. Express 19, 3799–3808 (2011).
    [CrossRef] [PubMed]
  14. M. A. Schmidt, P. S. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16, 13617–13623 (2008).
    [CrossRef] [PubMed]
  15. H. W. Lee, M. A. Schmidt, P. S. J. Russell, “Excitation of a nanowire molecule in gold-filled photonic crystal fiber,” Opt. Lett. 37, 2946–2948 (2012).
    [CrossRef] [PubMed]
  16. M. A. Schmidt, L. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. S. J. Russell, L. N. P. Sempere, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
    [CrossRef]
  17. C. G. Poulton, M. A. Schmidt, G. J. Pearce, G. Kakarantzas, P. S. J. Russell, “Numerical study of guided modes in arrays of metallic nanowires,” Opt. Lett. 32, 1647–1649 (2007).
    [CrossRef] [PubMed]
  18. T. A. Birks, G. J. Pearce, D. M. Bird, “Approximate band structure calculation for photonic bandgap fibres,” Opt. Express 14, 9483–9490 (2006).
    [CrossRef] [PubMed]
  19. L. Dong, “A vector boundary matching technique for efficient and accurate determination of photonic bandgaps in photonic bandgap fibers,” Opt. Express 19, 12582–12593 (2011).
    [CrossRef] [PubMed]
  20. Y. Li, Y. Yao, M. Hu, L. Chai, C. Wang, “Improved fully vectorial effective index method for photonic crystal fibers: evaluation and enhancement,” Appl. Optics 47, 399–406 (2008).
    [CrossRef]
  21. M. Midrio, M. Singh, C. Someda, “The space filling mode of holey fibers: an analytical vectorial solution,” J. Lightwave Technol. 18, 1031–1037 (2000).
    [CrossRef]
  22. P. W. Atkins, R. S. Friedman, Molecular quantum mechanics (Oxford University Press, 1997).
  23. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Lightwave Technol. 19, 2322–2330 (2002).
  24. “ www.comsol.com ,”.
  25. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1208 (1965).
    [CrossRef]
  26. P. G. Etchegoin, E. C. Le Ru, M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127, 189901 (2007).
    [CrossRef]
  27. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  28. F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University Press, 2010).
  29. J. Pottage, D. Bird, T. Hedley, J. Knight, T. Birks, P. Russell, P. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11, 2854–2861 (2003).
    [CrossRef] [PubMed]
  30. J. C. Flanagan, R. Amezcua, F. Poletti, J. R. Hayes, N. G. R. Broderick, D. J. Richardson, “The effect of periodicity on the defect modes of large mode area microstructured fibers,” Opt. Express 16, 18631–18645 (2008).
    [CrossRef]
  31. L. Kleinman, “Error in the tetrahedron integration scheme,” Phys. Rev. B 28, 1139–1141 (1983).
    [CrossRef]
  32. K. Busch, S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
    [CrossRef]

2013

2012

2011

2010

2009

2008

M. A. Schmidt, P. S. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16, 13617–13623 (2008).
[CrossRef] [PubMed]

J. C. Flanagan, R. Amezcua, F. Poletti, J. R. Hayes, N. G. R. Broderick, D. J. Richardson, “The effect of periodicity on the defect modes of large mode area microstructured fibers,” Opt. Express 16, 18631–18645 (2008).
[CrossRef]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

M. A. Schmidt, L. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. S. J. Russell, L. N. P. Sempere, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
[CrossRef]

Y. Li, Y. Yao, M. Hu, L. Chai, C. Wang, “Improved fully vectorial effective index method for photonic crystal fibers: evaluation and enhancement,” Appl. Optics 47, 399–406 (2008).
[CrossRef]

2007

P. G. Etchegoin, E. C. Le Ru, M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127, 189901 (2007).
[CrossRef]

C. G. Poulton, M. A. Schmidt, G. J. Pearce, G. Kakarantzas, P. S. J. Russell, “Numerical study of guided modes in arrays of metallic nanowires,” Opt. Lett. 32, 1647–1649 (2007).
[CrossRef] [PubMed]

2006

2005

2004

2003

2002

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Lightwave Technol. 19, 2322–2330 (2002).

2000

1998

K. Busch, S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

1994

L. Novotny, C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50, 4094–4106 (1994).
[CrossRef]

1983

L. Kleinman, “Error in the tetrahedron integration scheme,” Phys. Rev. B 28, 1139–1141 (1983).
[CrossRef]

1974

C. C. Pfeiffer, E. E. Economou, K. K. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

1965

Amezcua, R.

Argyros, A.

Atkins, P. W.

P. W. Atkins, R. S. Friedman, Molecular quantum mechanics (Oxford University Press, 1997).

Bang, O.

W. Y. W. Yuan, G. Town, O. Bang, “Refractive index sensing in an all-solid twin-core photonic bandgap fiber,” IEEE Sens. J. 10, 1192–1199 (2010).
[CrossRef]

Bird, D.

Bird, D. M.

Birks, T.

Birks, T. A.

Boisvert, R. F.

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University Press, 2010).

Botten, L. C.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Lightwave Technol. 19, 2322–2330 (2002).

Broderick, N. G. R.

Busch, K.

K. Busch, S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

Chai, L.

Y. Li, Y. Yao, M. Hu, L. Chai, C. Wang, “Improved fully vectorial effective index method for photonic crystal fibers: evaluation and enhancement,” Appl. Optics 47, 399–406 (2008).
[CrossRef]

Clark, C. W.

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University Press, 2010).

Cordeiro, C. M.

de Sterke, C. M.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Lightwave Technol. 19, 2322–2330 (2002).

Dong, L.

Economou, E. E.

C. C. Pfeiffer, E. E. Economou, K. K. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Eggleton, B.

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127, 189901 (2007).
[CrossRef]

Flanagan, J. C.

Friedman, R. S.

P. W. Atkins, R. S. Friedman, Molecular quantum mechanics (Oxford University Press, 1997).

George, A. K.

Hafner, C.

L. Novotny, C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50, 4094–4106 (1994).
[CrossRef]

Hayes, J. R.

Hedley, T.

Hedley, T. D.

Hu, M.

Y. Li, Y. Yao, M. Hu, L. Chai, C. Wang, “Improved fully vectorial effective index method for photonic crystal fibers: evaluation and enhancement,” Appl. Optics 47, 399–406 (2008).
[CrossRef]

Isomäki, A.

John, S.

K. Busch, S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

Joly, N.

Joly, N. Y.

Kakarantzas, G.

Kashiwagi, M.

Kleinman, L.

L. Kleinman, “Error in the tetrahedron integration scheme,” Phys. Rev. B 28, 1139–1141 (1983).
[CrossRef]

Knight, J.

Knight, J. C.

Koshiba, M.

Kuhlmey, B.

Kuhlmey, B. T.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Lightwave Technol. 19, 2322–2330 (2002).

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127, 189901 (2007).
[CrossRef]

Lee, H. W.

Leon-Saval, S.

Li, Y.

Y. Li, Y. Yao, M. Hu, L. Chai, C. Wang, “Improved fully vectorial effective index method for photonic crystal fibers: evaluation and enhancement,” Appl. Optics 47, 399–406 (2008).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Lozier, D. W.

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University Press, 2010).

Luan, F.

Malitson, I. H.

Matsuo, S.

Maystre, D.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Lightwave Technol. 19, 2322–2330 (2002).

McPhedran, R. C.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Lightwave Technol. 19, 2322–2330 (2002).

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127, 189901 (2007).
[CrossRef]

Midrio, M.

Nagasaki, A.

Ngai, K. K.

C. C. Pfeiffer, E. E. Economou, K. K. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Novotny, L.

L. Novotny, C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50, 4094–4106 (1994).
[CrossRef]

Okhotnikov, O. G.

Olver, F. W. J.

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University Press, 2010).

Pearce, G. J.

Pfeiffer, C. C.

C. C. Pfeiffer, E. E. Economou, K. K. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Poletti, F.

Pottage, J.

Poulton, C. G.

M. A. Schmidt, L. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. S. J. Russell, L. N. P. Sempere, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
[CrossRef]

C. G. Poulton, M. A. Schmidt, G. J. Pearce, G. Kakarantzas, P. S. J. Russell, “Numerical study of guided modes in arrays of metallic nanowires,” Opt. Lett. 32, 1647–1649 (2007).
[CrossRef] [PubMed]

Prill Sempere, L.

M. A. Schmidt, L. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. S. J. Russell, L. N. P. Sempere, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
[CrossRef]

Renversez, G.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Lightwave Technol. 19, 2322–2330 (2002).

Richardson, D. J.

Roberts, P.

Russell, P.

Russell, P. S. J.

H. W. Lee, M. A. Schmidt, P. S. J. Russell, “Excitation of a nanowire molecule in gold-filled photonic crystal fiber,” Opt. Lett. 37, 2946–2948 (2012).
[CrossRef] [PubMed]

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, P. S. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19, 12180–12189 (2011).
[CrossRef] [PubMed]

H. K. Tyagi, H. W. Lee, P. Uebel, M. a. Schmidt, N. Joly, M. Scharrer, P. S. J. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. 35, 2573–2575 (2010).
[CrossRef] [PubMed]

M. A. Schmidt, P. S. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16, 13617–13623 (2008).
[CrossRef] [PubMed]

M. A. Schmidt, L. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. S. J. Russell, L. N. P. Sempere, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
[CrossRef]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

C. G. Poulton, M. A. Schmidt, G. J. Pearce, G. Kakarantzas, P. S. J. Russell, “Numerical study of guided modes in arrays of metallic nanowires,” Opt. Lett. 32, 1647–1649 (2007).
[CrossRef] [PubMed]

A. Argyros, T. Birks, S. Leon-Saval, C. M. Cordeiro, F. Luan, P. S. J. Russell, “Photonic bandgap with an index step of one percent,” Opt. Express 13, 309–314 (2005).
[CrossRef] [PubMed]

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, P. S. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004).
[CrossRef] [PubMed]

Russell, R. F.

Saitoh, K.

Saitoh, S.

Scharrer, M.

Schmidt, M. A.

H. W. Lee, M. A. Schmidt, P. S. J. Russell, “Excitation of a nanowire molecule in gold-filled photonic crystal fiber,” Opt. Lett. 37, 2946–2948 (2012).
[CrossRef] [PubMed]

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, P. S. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19, 12180–12189 (2011).
[CrossRef] [PubMed]

H. K. Tyagi, H. W. Lee, P. Uebel, M. a. Schmidt, N. Joly, M. Scharrer, P. S. J. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. 35, 2573–2575 (2010).
[CrossRef] [PubMed]

M. A. Schmidt, P. S. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16, 13617–13623 (2008).
[CrossRef] [PubMed]

M. A. Schmidt, L. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. S. J. Russell, L. N. P. Sempere, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
[CrossRef]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

C. G. Poulton, M. A. Schmidt, G. J. Pearce, G. Kakarantzas, P. S. J. Russell, “Numerical study of guided modes in arrays of metallic nanowires,” Opt. Lett. 32, 1647–1649 (2007).
[CrossRef] [PubMed]

Sempere, L. N. P.

M. A. Schmidt, L. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. S. J. Russell, L. N. P. Sempere, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
[CrossRef]

Sempere, L. P.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

Singh, M.

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Someda, C.

Town, G.

W. Y. W. Yuan, G. Town, O. Bang, “Refractive index sensing in an all-solid twin-core photonic bandgap fiber,” IEEE Sens. J. 10, 1192–1199 (2010).
[CrossRef]

Tyagi, H. K.

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, P. S. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19, 12180–12189 (2011).
[CrossRef] [PubMed]

H. K. Tyagi, H. W. Lee, P. Uebel, M. a. Schmidt, N. Joly, M. Scharrer, P. S. J. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. 35, 2573–2575 (2010).
[CrossRef] [PubMed]

M. A. Schmidt, L. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. S. J. Russell, L. N. P. Sempere, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
[CrossRef]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

Uebel, P.

Wang, A.

Wang, C.

Y. Li, Y. Yao, M. Hu, L. Chai, C. Wang, “Improved fully vectorial effective index method for photonic crystal fibers: evaluation and enhancement,” Appl. Optics 47, 399–406 (2008).
[CrossRef]

White, T. P.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Lightwave Technol. 19, 2322–2330 (2002).

Wu, D.

Yao, Y.

Y. Li, Y. Yao, M. Hu, L. Chai, C. Wang, “Improved fully vectorial effective index method for photonic crystal fibers: evaluation and enhancement,” Appl. Optics 47, 399–406 (2008).
[CrossRef]

Yuan, W. Y. W.

W. Y. W. Yuan, G. Town, O. Bang, “Refractive index sensing in an all-solid twin-core photonic bandgap fiber,” IEEE Sens. J. 10, 1192–1199 (2010).
[CrossRef]

Appl. Optics

Y. Li, Y. Yao, M. Hu, L. Chai, C. Wang, “Improved fully vectorial effective index method for photonic crystal fibers: evaluation and enhancement,” Appl. Optics 47, 399–406 (2008).
[CrossRef]

Appl. Phys. Lett.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[CrossRef]

IEEE Sens. J.

W. Y. W. Yuan, G. Town, O. Bang, “Refractive index sensing in an all-solid twin-core photonic bandgap fiber,” IEEE Sens. J. 10, 1192–1199 (2010).
[CrossRef]

J. Chem. Phys.

P. G. Etchegoin, E. C. Le Ru, M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127, 189901 (2007).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am.

Opt. Express

J. Pottage, D. Bird, T. Hedley, J. Knight, T. Birks, P. Russell, P. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11, 2854–2861 (2003).
[CrossRef] [PubMed]

J. C. Flanagan, R. Amezcua, F. Poletti, J. R. Hayes, N. G. R. Broderick, D. J. Richardson, “The effect of periodicity on the defect modes of large mode area microstructured fibers,” Opt. Express 16, 18631–18645 (2008).
[CrossRef]

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, P. S. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19, 12180–12189 (2011).
[CrossRef] [PubMed]

A. Argyros, T. Birks, S. Leon-Saval, C. M. Cordeiro, F. Luan, P. S. J. Russell, “Photonic bandgap with an index step of one percent,” Opt. Express 13, 309–314 (2005).
[CrossRef] [PubMed]

A. Isomäki, O. G. Okhotnikov, “Femtosecond soliton mode-locked laser based on ytterbium-doped photonic bandgap fiber,” Opt. Express 14, 9238–9243 (2006).
[CrossRef] [PubMed]

T. A. Birks, G. J. Pearce, D. M. Bird, “Approximate band structure calculation for photonic bandgap fibres,” Opt. Express 14, 9483–9490 (2006).
[CrossRef] [PubMed]

L. Dong, “A vector boundary matching technique for efficient and accurate determination of photonic bandgaps in photonic bandgap fibers,” Opt. Express 19, 12582–12593 (2011).
[CrossRef] [PubMed]

A. Nagasaki, K. Saitoh, M. Koshiba, “Polarization characteristics of photonic crystal fibers selectively filled with metal wires into cladding air holes,” Opt. Express 19, 3799–3808 (2011).
[CrossRef] [PubMed]

M. A. Schmidt, P. S. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16, 13617–13623 (2008).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. B

L. Kleinman, “Error in the tetrahedron integration scheme,” Phys. Rev. B 28, 1139–1141 (1983).
[CrossRef]

C. C. Pfeiffer, E. E. Economou, K. K. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

M. A. Schmidt, L. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. S. J. Russell, L. N. P. Sempere, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
[CrossRef]

Phys. Rev. E

L. Novotny, C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50, 4094–4106 (1994).
[CrossRef]

K. Busch, S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998).
[CrossRef]

Other

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University Press, 2010).

“ www.comsol.com ,”.

P. W. Atkins, R. S. Friedman, Molecular quantum mechanics (Oxford University Press, 1997).

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Figures (5)

Fig. 1:
Fig. 1:

(a) Schematic of a metallic nanowire array with central defect (core) in an optical fiber. (b) Cross section of the array and the corresponding real-space unit cell (lattice vectors v⃗1 and v⃗2, hole diameter d and pitch Λ)

Fig. 2:
Fig. 2:

Approximation of the hexagonal unit cell (left) by a circular unit cell (right). ε1 and ε2 are the permittivities of the metal wire and the cladding, respectively. The red arrows indicate the transverse unit vectors and θ̂ of the cylindrical coordinate system.

Fig. 3:
Fig. 3:

Comparison of the DOS calculated using a finite element method (left-hand column) and the presented semi-analytic model (right-hand column) for a wire diameter of d = 800nm. White and green regions correspond to zero DOS. The approximation on the right-hand side is composed from the refractive index of silica (blue line), the FSM (black dashed line), the plasmonic bands (yellow shaded regions) as well as the effective indices of the corresponding isolated surface plasmons (black lines). The vertical black dotted line indicates the wavelength (λ = 1000nm) of the fields presented in Fig. 4. (a, b) Λ = 4μm; (c, d) Λ = 2μm.

Fig. 4:
Fig. 4:

Comparison of the radial electric field distributions in the real-space unit cells of model and FEM calculations (The top scale bar refers to the amplitude of the electric field). Each row refers to different plasmonic mode order. Left-hand side: bottom band edge. Right-hand side: top band edge.

Fig. 5:
Fig. 5:

Hexagonal unit cell of the reciprocal lattice. Γ, M and K indicate the points of symmetry. The red grid lines illustrate the mesh of Bloch wave vectors in the irreducible wedge of the first Brillouin zone we have used in the FEM simulations. The red numbers correspond to the symmetry-induced weighting factors of the mesh points.

Tables (4)

Tables Icon

Table 1: Boundary conditions corresponding to the top and bottom band edge of a plasmonic band.

Tables Icon

Table 2: Definition of the boundary-related parameters ηe and ηh. To address a desired mode it is simply required to use the entries of the respective row of this table in Eqs. (1) and (2).

Tables Icon

Table 3: Numerical results of the band edges shown in Fig. 3(d) at a wavelength λ = 1000 nm (vertical black dotted line).

Tables Icon

Table 4: Matrix elements of Eq. (13) in the wire (j = 1) and the cladding (j = 2).

Equations (28)

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M ^ = ( I m ( α 1 ) K m ( α 2 ) Γ e 0 0 m n eff α 1 2 I m ( α 1 ) m n eff α 2 2 K m ( α 2 ) Γ e Z 0 α 1 I m ( α 1 ) Z 0 α 2 K m ( α 2 ) Γ h 0 0 I m ( α 1 ) K m ( α 2 ) Γ h ε 1 α 1 Z 0 I m ( α 1 ) ε 2 α 2 Z 0 K m ( α 2 ) Γ e m n eff α 1 2 I m ( α 1 ) m n eff α 2 2 K m ( α 2 ) Γ h )
Γ e = 1 + η e I m ( α 2 ) K m ( α 2 ) Γ e = 1 + η e I m ( α 2 ) K m ( α 2 )
Γ h = 1 + η h I m ( α 2 ) K m ( α 2 ) Γ h = 1 + η h I m ( α 2 ) K m ( α 2 )
Δ E + k 0 2 ε j E = 0
Δ H + k 0 2 ε j H = 0
E z j = [ A j I m ( κ j r ) + B j K m ( κ j r ) ] p m ( θ )
H z j = [ C j I m ( κ j r ) + D j K m ( κ j r ) ] q m ( θ )
p m ( θ ) = p m = { cos ( m θ ) even modes sin ( m θ ) odd modes
q m ( θ ) = q m = { sin ( m θ ) even modes cos ( m θ ) odd modes
E r ( j ) = i k 0 κ j 2 ( n eff E z ( j ) r + 1 r μ 0 ε 0 H z ( j ) θ )
E θ ( j ) = i k 0 κ j 2 ( n eff r E z ( j ) θ μ 0 ε 0 H z ( j ) r )
H r ( j ) = i k 0 κ j 2 ( n eff H z ( j ) r ε j r ε 0 μ 0 E z ( j ) θ )
H θ ( j ) = i k 0 κ j 2 ( n eff r H z ( j ) θ + ε j ε 0 μ 0 E z ( j ) r ) .
( E z j E θ j H z j H θ j ) = ( a j ( r ) p m a j ( r ) p m 0 0 b j ( r ) q m b j ( r ) q m c j ( r ) q m c j ( r ) q m 0 0 a j ( r ) q m a j ( r ) q m d j ( r ) p m d j ( r ) p m b j ( r ) p m b j ( r ) p m ) ( A j B j C j D j ) ,
A 2 B 2 = η e = { K m ( κ 2 R ) I m ( κ 2 R ) bottom band edge K m ( κ 2 R ) I m ( κ 2 R ) top band edge
C 2 D 2 = η h = { K m ( κ 2 R ) I m ( κ 2 R ) bottom band edge K m ( κ 2 R ) / κ 2 R K m ( κ 2 R ) I m ( κ 2 R ) / κ 2 R I m ( κ 2 R ) top band edge
I m ( z ) = 1 2 ( I m 1 ( z ) + I m + 1 ( z ) )
K m ( z ) = 1 2 ( K m 1 ( z ) + K m + 1 ( z ) )
I m ( z ) = 1 4 ( I m 2 ( z ) + 2 I m ( z ) + I m + 2 ( z ) )
K m ( z ) = 1 4 ( K m 2 ( z ) + 2 K m ( z ) + K m + 2 ( z ) ) ,
( a 1 ( a ) [ a 2 ( a ) + η e a 2 ( a ) ] 0 0 b 1 ( a ) [ b 2 ( a ) + η e b 2 ( a ) ] c 1 ( a ) [ c 2 ( a ) + η h c 2 ( a ) ] 0 0 a 1 ( a ) [ a 2 ( a ) + η h a 2 ( a ) ] d 1 ( a ) [ d 2 ( a ) + η e d 2 ( a ) ] b 1 ( a ) [ b 2 ( a ) + η h b 2 ( a ) ] ) ( A 1 B 2 C 1 D 2 ) = 0 .
( A 1 B 1 C 1 D 1 ) = ( 1 0 m 0 m 34 m 12 0 ) A 1 ( A 2 B 2 C 2 D 2 ) = ( η e m 11 / m 12 m 11 / m 12 η h m 0 m 33 / m 12 m 0 m 33 / m 12 ) A 1
m 0 = m 11 m 22 m 12 m 21 m 23 m 34 m 24 m 33
v 1 = Λ ( 1 0 0 ) and v 2 = Λ ( 1 / 2 3 / 2 0 ) .
w 1 = 2 π Λ ( 1 1 / 3 0 ) and w 2 = 2 π Λ ( 0 2 / 3 0 ) .
u 1 = 2 π Λ ( 1 / 2 1 / ( 2 3 ) 0 ) and u 2 = 2 π Λ ( 1 / 6 1 / ( 2 3 ) 0 ) .
k F = j ( u 1 + l u 2 )
DOS ( λ , n eff ) = k w k i δ ( n n eff i , k ) ,

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