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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 4 — Feb. 14, 2011
  • pp: 3799–3808
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Polarization characteristics of photonic crystal fibers selectively filled with metal wires into cladding air holes

Akira Nagasaki, Kunimasa Saitoh, and Masanori Koshiba  »View Author Affiliations


Optics Express, Vol. 19, Issue 4, pp. 3799-3808 (2011)
http://dx.doi.org/10.1364/OE.19.003799


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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.

© 2011 OSA

1. Introduction

Photonic crystal fibers (PCFs) [1

1. P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [CrossRef]

], also called holey fibers (HFs) or microstructured optical fibers (MOFs), basically composed of two-dimentional triangular lattice arrays of air holes running along the entire length and confine light in the defects of the periodic structure, have extraordinary properties not achievable in conventional optical fibers such as endlessly single-mode operation, unusual chromatic dispersion, high birefringence, high or low non-linearity, etc. Additionally, optical properties of silica-air PCFs can be extended by filling the cladding air holes with materials such as liquid crystal [2

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]

], semiconductor [3

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]

], or metal [4

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]

], etc. In metal-filled PCFs, surface plasmon polaritons (SPPs) can form on the metal wires [5

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]

], and the core guided light can be coupled with SPPs when the phases of them match. Metal-filled PCFs have strongly wavelength-dependent transmissions because the core guided light couples to leaky SPPs at particular frequencies. Selective filling of individual air holes with metal bring polarization-dependent transmission [6

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).

8

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]

]. Lee et al. have reported polarization-dependent characteristics of polarization-maintaining PCFs with a gold wire [7

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]

], and Zhang et al. have demonstrated selective silver coating in PCFs, expected to be applicable as absorptive polarizers [8

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]

]. H. K. Tyagi et al. have reported step-index fibers with a gold wire adjacent to the core [9

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]

]. However, these reported fibers do not have sufficient performance for polarizers. Moreover, there have not been any reports of concrete design methods for polarizers based on metal-filled PCFs.

2. Fundamental properties of metal-filled PCFs

Firstly, we show the polarization characteristics of PCFs with a metal wire into cladding air holes, in order to understand the fundamental property of metal-filled PCFs. Figure 1
Fig. 1 Schematic representation of a PCF with a metal wire.
illustrates the schematic of a PCF with a metal wire, whose cladding is composed of a triangular lattice of air holes with the parameters of lattice constant Λ and the hole diameters d, with four layers of air holes. The background material is pure silica. A metal wire is introduced into the cladding air hole. In the numerical calculation, the material dispersion of both silica and metal are included, and refractive index of air is 1. We have used Sellmeier equation for the dispersion of silica [11

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

], and Drude-Lorentz model for metal [12

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]

] defined as
εm=εωD2ω(ωjγD)ΔεΩL2(ω2ΩL2)jΓLω
(1)
where ε m is the permittivity of the metal, ε is the permittivity in the high frequency, Δε can be interpreted as a weighting factor, and ω is the angular frequency of guided light, ω D and γ D are the plasma frequency and damping frequency, ΩL and ΓL represent the frequency and the spectral width of the Lorentz oscillator. In this report, we assume metal as gold, using the parameters presented in Table 1

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

table-icon
View This Table
, which gives good agreement with measured values at optical frequencies [12

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]

].

3. Polarization characteristics of PCFs with several metal wires

particular SPP supermode whose parity matches, and the another does not couple. In Fig. 4, high polarization extinction ratio is achieved at wavelength 1.822 μm, where the losses of x-polarized and y-polarized modes are 296.57 dB/cm and 1.58 dB/cm, respectively. This is caused by the phase matching of the x-polarized mode to the SPP supermode which has the electric field distributions of Fig. 5(f), consists of two isolated 1st-order SPP modes. Surprisingly, 1st-order SPP modes can be coupled to the PCF core modes when the SPP modes become supermodes and get as lower effective index as the core modes have, whereas isolated 1st-order SPP modes can be never coupled as discussed in the Section 2. The electric field distributions of the two polarized core modes at wavelength 1.822 μm are shown in Fig. 4(b) and (c). It is evident from the figures that the x-polarized mode strongly couples to the SPP supermode, whereas the y-polarized mode is strongly confined into the central core. Thus, it is possible to realize a polarizer by metal-filled PCFs with sufficient extinction ratio.

So far, we have shown the importance of arranging the several gold wires close to each other for high polarization-dependence. Finally, we show the influence of varying the value of the wire diameter d m. Figure 8
Fig. 8 Schematic representation of a PCF filled with three gold wires.
shows the schematic of a PCF whose location of gold wires is the same as represented in Fig. 6(d), and the effective index and loss dependence on the operating wavelength of the x-polarized and y-polarized core modes in the PCFs for d=1.0 μm, Λ=2.0 μm, d m= (a) 1.0 μm, (b) 1.4 μm are plotted in Fig. 9(a) and (b)
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.
, respectively. The SPP supermodes consisting of 1st-order SPP modes are represented by the green curves, and their transverse electric field vector distributions are shown in 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).
for d m= 1.0 μm. The figures in Fig. 10 are arranged according to the value of the effective index, and their effective indices are (a) 1.475422, (b) 1.467014, (c) 1.464523, (d) 1.461778, (e) 1.461643, (f) 1.446053, at wavelength 1.3 μm. There are six SPP supermodes consisted of isolated SPP modes of 1st order, and the two-polarized core modes can only couple to particular SPP supermode whose parity matches, as we discussed the coupling characteristics in Fig. 4. In the PCF represented in Fig. 8, the x-polarized core mode couples to SPP supermodes (a), (e), (f) in Fig. 10, whereas the y-polarized core mode couples to SPP supermodes (b), (c), (d) in Fig. 10. The dashed green lines in Fig. 9 represent the dispersion curves of SPP supermodes which couple to the x-polarized core mode ((a), (e), (f) in Fig. 10), and solid green lines in Fig. 9 represent the curves of SPP supermodes which couple to the y-polarized core mode ((b), (c), (d) in Fig. 10). The dashed green curves are separated from each other, whereas the solid green curves are closer to each other. In addition, when the value of d m become larger, the dashed green curves become more separated from each other, but the solid green curves do not shift so much. As a consequence, we can achieve larger extinction ratio over wide range of wavelengths as shown in Fig. 9(b), expect to operate as a polarizer at communication wavelength.

4. Conclusion

References and links

1.

P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [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]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(240.6680) Optics at surfaces : Surface plasmons
(060.5295) Fiber optics and optical communications : Photonic crystal fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: January 4, 2011
Revised Manuscript: February 2, 2011
Manuscript Accepted: February 2, 2011
Published: February 11, 2011

Citation
Akira Nagasaki, Kunimasa Saitoh, and Masanori Koshiba, "Polarization characteristics of photonic crystal fibers selectively filled with metal wires into cladding air holes," Opt. Express 19, 3799-3808 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-3799


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References

  1. P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [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]

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