Abstract

We numerically investigate the polarization characteristics of photonic crystal fibers selectively filled with metal wires into cladding air holes, through a full-vector modal solver based on the finite-element method (FEM). Firstly, we investigate the fundamental coupling properties between the core guided light and surface plasmon polaritons (SPPs) excited on the surface of metal wire. Secondly, we show that we can obtain highly polarization-dependent transmission characteristics in PCFs by introducing several metal wires closely aligned into the cladding, and reveal the strongly polarization-dependent coupling properties between the core guided modes and the SPP supermodes, which consist of discrete SPP modes. Finally, we show the importance of arranging the metal wires close to each other for high polarization-dependence.

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    [CrossRef]
  2. D. Noordegraaf, L. Scolari, J. Lægsgaard, T. Tanggaard Alkeskjold, G. Tartarini, E. Borelli, P. Bassi, J. Li, and S.-T. Wu, “Avoided-crossing-based liquid-crystal photonic-bandgap notch filter,” Opt. Lett. 33(9), 986–988 (2008).
    [CrossRef] [PubMed]
  3. H. K. Tyagi, M. A. Schmidt, L. N. Prill Sempere, and P. St. J. Russell, “Optical properties of photonic crystal fiber with integral micron-sized Ge wire,” Opt. Express 16(22), 17227–17236 (2008).
    [CrossRef] [PubMed]
  4. M. Schmidt, L. Prill Sempere, H. Tyagi, C. Poulton, and P. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77(3), 033417 (2008).
    [CrossRef]
  5. M. A. Schmidt and P. St. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16(18), 13617–13623 (2008).
    [CrossRef] [PubMed]
  6. H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. N. Prill Sempere, and P. St. J. Russell, “Transmission properties of selectively gold-filled polarization-maintaining PCF,” Conference on Lasers and Electro-Optics / Quantum Electronics and Laser Science Conference (CLEO/QELS), paper CFO3 (2008).
  7. H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
    [CrossRef]
  8. X. Zhang, R. Wang, F. M. Cox, B. T. Kuhlmey, and M. C. J. Large, “Selective coating of holes in microstructured optical fiber and its application to in-fiber absorptive polarizers,” Opt. Express 15(24), 16270–16278 (2007).
    [CrossRef] [PubMed]
  9. H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, and P. St. J. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. 35(15), 2573–2575 (2010).
    [CrossRef] [PubMed]
  10. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. 38(7), 927–933 (2002).
    [CrossRef]
  11. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, CA, 1989).
  12. A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71(8), 085416 (2005).
    [CrossRef]
  13. Z. Zhang, Y. Shi, B. Bian, and J. Lu, “Dependence of leaky mode coupling on loss in photonic crystal fiber with hybrid cladding,” Opt. Express 16(3), 1915–1922 (2008).
    [CrossRef] [PubMed]

2010 (1)

2008 (6)

2007 (1)

2006 (1)

2005 (1)

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71(8), 085416 (2005).
[CrossRef]

2002 (1)

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. 38(7), 927–933 (2002).
[CrossRef]

Barchiesi, D.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71(8), 085416 (2005).
[CrossRef]

Bassi, P.

Bian, B.

Borelli, E.

Cox, F. M.

de la Chapelle, M.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71(8), 085416 (2005).
[CrossRef]

Grimault, A.-S.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71(8), 085416 (2005).
[CrossRef]

Joly, N.

Koshiba, M.

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. 38(7), 927–933 (2002).
[CrossRef]

Kuhlmey, B. T.

Lægsgaard, J.

Large, M. C. J.

Lee, H. W.

H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, and P. St. J. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. 35(15), 2573–2575 (2010).
[CrossRef] [PubMed]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
[CrossRef]

Li, J.

Lu, J.

Macías, D.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71(8), 085416 (2005).
[CrossRef]

Noordegraaf, D.

Poulton, C.

M. Schmidt, L. Prill Sempere, H. Tyagi, C. Poulton, and P. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77(3), 033417 (2008).
[CrossRef]

Prill Sempere, L.

M. Schmidt, L. Prill Sempere, H. Tyagi, C. Poulton, and P. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77(3), 033417 (2008).
[CrossRef]

Prill Sempere, L. N.

Russell, P.

M. Schmidt, L. Prill Sempere, H. Tyagi, C. Poulton, and P. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77(3), 033417 (2008).
[CrossRef]

Russell, P. S. J.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
[CrossRef]

Russell, P. St. J.

Saitoh, K.

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. 38(7), 927–933 (2002).
[CrossRef]

Scharrer, M.

Schmidt, M.

M. Schmidt, L. Prill Sempere, H. Tyagi, C. Poulton, and P. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77(3), 033417 (2008).
[CrossRef]

Schmidt, M. A.

Scolari, L.

Sempere, L. P.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
[CrossRef]

Shi, Y.

Tanggaard Alkeskjold, T.

Tartarini, G.

Tyagi, H.

M. Schmidt, L. Prill Sempere, H. Tyagi, C. Poulton, and P. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77(3), 033417 (2008).
[CrossRef]

Tyagi, H. K.

Uebel, P.

Vial, A.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71(8), 085416 (2005).
[CrossRef]

Wang, R.

Wu, S.-T.

Zhang, X.

Zhang, Z.

Appl. Phys. Lett. (1)

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. 38(7), 927–933 (2002).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. B (2)

M. Schmidt, L. Prill Sempere, H. Tyagi, C. Poulton, and P. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77(3), 033417 (2008).
[CrossRef]

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71(8), 085416 (2005).
[CrossRef]

Other (2)

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. N. Prill Sempere, and P. St. J. Russell, “Transmission properties of selectively gold-filled polarization-maintaining PCF,” Conference on Lasers and Electro-Optics / Quantum Electronics and Laser Science Conference (CLEO/QELS), paper CFO3 (2008).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, CA, 1989).

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Figures (10)

Fig. 1
Fig. 1

Schematic representation of a PCF with a metal wire.

Fig. 2
Fig. 2

Wavelength dependence of effective indices and losses of the x-polarized and y-polarized core modes in the PCFs for d=1.0 μm, Λ=2.0 μm, filled with a gold wire into the hole of (a) first air hole layer and (b) second air hole layer. The solid green lines represent SPP modes of the specific mode orders excited on an isolated gold wire embedded in silica surrounded by air hole lattice, and the dashed black line is the core mode index of the unfilled PCF with the same structural parameters, and the dotted line is the cladding mode index, and the dashed-dotted line is the silica index. The insets on dispersion diagrams represent the magnitude of electric field of the relevant modes. The shaded regions denote the resonance points of the core guided modes and SPP modes.

Fig. 3
Fig. 3

(a)-(c) x-component of the electric field distributions of the x-polarized core mode and (d)-(f) y-component of the electric field distributions of the y-polarized core mode at the peak wavelengths with plasmonic resonance achieved in Fig. 2(a).

Fig. 4
Fig. 4

(a) Wavelength dependence of effective indices and losses of the x-polarized and y-polarized core modes in the PCF for d=1.0 μm, Λ=2.0 μm, filled with two gold wires into cladding air hole of second and third air hole layer. The solid green lines represent SPP supermodes consisting of the two isolated SPP modes, and the dotted black line is the cladding mode index, and the dashed-dotted line is the silica index. (b) x-component of the electric field distributions of the x-polarized core mode and (c) y-component of the electric field distributions of the y-polarized core mode at wavelength 1.822 μm.

Fig. 5
Fig. 5

Transverse electric field vector distributions of SPP supermodes. Each SPP supermode consists of isolated SPP modes of (a),(b) fundamental, (c)-(f) 1st order, (g)-(j) 2nd order.

Fig. 6
Fig. 6

Wavelength dependence of modal losses of the x-polarized and y-polarized core modes in the PCF for d=1.0 μm, Λ=2.0 μm, selectively filled with gold wires into cladding air hole. The insets show the schematic representation of PCFs filled with gold wire in different arrangement.

Fig. 7
Fig. 7

(a) x-component of the electric field distributions of the x-polarized core mode and (b),(c) y-component of the electric field distributions of the y-polarized core mode at the peak wavelengths with plasmonic resonance achieved in Fig. 6(c).

Fig. 8
Fig. 8

Schematic representation of a PCF filled with three gold wires.

Fig. 9
Fig. 9

Wavelength dependence of effective indices and losses of the x-polarized and y-polarized core modes in the PCF for d=1.0 μm, Λ=2.0 μm, d m= (a) 1.0 μm, (b) 1.4 μm, filled with three gold wires into cladding air hole as shown in Fig. 8. The dotted black line is the cladding mode index, and the solid green lines represent SPP supermodes consist of three isolated SPP modes of 1st order.

Fig. 10
Fig. 10

Transverse electric field vector distributions of SPP supermodes consist of isolated SPP modes of 1st order in the PCF shown in Fig. 8 (d=1.0 μm, Λ=2.0 μm, d m= 1.0 μm).

Tables (1)

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Table 1 Values of the optimized parameters to fit the experimental data of bulk gold [12].

Equations (1)

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ε m = ε ω D 2 ω ( ω j γ D ) Δ ε Ω L 2 ( ω 2 Ω L 2 ) j Γ L ω

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