Abstract

The germanium-doped photonic crystal fiber (PCF) has some characteristics that differentiate it from pure-silica PCF for a germanium element being doped in the core, such as the intensified nonlinearity, the enhanced photosensitivity, and so on. To pave the way for the application of the Ge-doped PCF successfully, it is necessary to study its properties. We investigated the modal cutoff properties of Ge-doped PCF quantitatively by using the beam propagation method. The numerical results show that the effective refractive indices and the normalized frequency V of Ge-doped PCF not only depend on the normalized pitch Λ/λ but also depend on the normalized hole size d/Λ, the modal cutoff boundary for the single mode–multimode of the Ge-doped PCF shift to the low d/Λ side in contrast to the pure-silica PCF.

© 2006 Optical Society of America

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  1. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt Lett. 21, 1547-1549 (1996).
    [PubMed]
  2. T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt Lett. 22, 961-963 (1997).
    [PubMed]
  3. K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, "Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion," Opt. Express 11, 843-852 (2003).
    [PubMed]
  4. N. A. Mortensen, "Effective area of photonic crystal fibers," Opt. Express 10, 341-348 (2002).
    [PubMed]
  5. L. Zou, X. Bao, and L. Chen, "Brillouin scattering spectrum in photonic crystal fiber with a partially germanium-doped core," Opt. Lett. 28, 2022-2024 (2003).
    [PubMed]
  6. T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
    [PubMed]
  7. B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, "Microstructured optical fiber devices," Opt. Express 9, 698-713 (2001).
    [PubMed]
  8. C. Martelli, J. Canning, N. Groothoff, and K. Lyytikainen, "Strain and temperature characterization of photonic crystal fiber Bragg gratings," Opt. Lett. 30, 1785-1787 (2005).
    [PubMed]
  9. B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windeler, and G. L. Burdge, "Cladding-mode-resonances in air-silica microstructure optical fibers," J. Lightwave Technol. 18, 1084-1100 (2000).
  10. N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, "Modal cutoff and the V parameter in photonic crystal fibers," Opt. Lett. 28, 1879-1881 (2003).
    [PubMed]
  11. B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, "Modal cutoff in microstructured optical fibers," Opt. Lett. 27, 1684-1686 (2002).
    [PubMed]
  12. M. D. Nielsen, N. A. Mortensen, J. R. Folkenberg, and A. Bjarklev, "Mode-field radius of photonic crystal fibers expressed by the V parameter," Opt. Lett. 28, 2309-2311 (2003).
    [PubMed]
  13. K. Saitoh and M. Koshiba, "Empirical relations for simple design of photonic crystal fibers," Opt. Express 13, 267-273 (2005).
    [PubMed]
  14. M. D. Felt and J. J. A. Fleck, "Computation of mode eigen functions in graded index optical fibers by the propagating beam method," Appl. Opt. 19, 2240-2246 (1980).
    [PubMed]
  15. D. Yevick and W. Bardyszewski, "Correspondance of variational finite-difference (relaxation) and imaginary-distance propagation for modal analysis," Opt. Lett. 17, 329-330 (1992).
    [PubMed]
  16. R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques formodeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).

Atkin, D. M.

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt Lett. 21, 1547-1549 (1996).
[PubMed]

Bao, X.

Bardyszewski, W.

Birks, T. A.

T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt Lett. 22, 961-963 (1997).
[PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt Lett. 21, 1547-1549 (1996).
[PubMed]

Bjarklev, A.

Burdge, G. L.

Canning, J.

Chen, L.

de Sterke, C. M.

Dong, X.

T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
[PubMed]

Eggleton, B. J.

Felt, M. D.

Fleck, J. J. A.

Folkenberg, J. R.

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques formodeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).

Groothoff, N.

Hale, A.

Hansen, K. P.

Hasegawa, T.

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques formodeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).

Kai, G.

T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
[PubMed]

Kerbage, C.

Knight, J. C.

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt Lett. 21, 1547-1549 (1996).
[PubMed]

T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt Lett. 22, 961-963 (1997).
[PubMed]

Koshiba, M.

Kuhlmey, B. T.

Liu, Y.

T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
[PubMed]

Lyytikainen, K.

Martelli, C.

McPhedran, R. C.

Mortensen, N. A.

Nielsen, M. D.

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques formodeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).

Russell, P. St. J.

T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt Lett. 22, 961-963 (1997).
[PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt Lett. 21, 1547-1549 (1996).
[PubMed]

Saitoh, K.

Sasaoka, E.

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques formodeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).

Sun, T.

T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
[PubMed]

Wang, C.

T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
[PubMed]

Wang, Z.

T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
[PubMed]

Westbrook, P. S.

White, C. A.

Windeler, R. S.

Yevick, D.

Yuan, S.

T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
[PubMed]

Zhang, C.

T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
[PubMed]

Zhang, W.

T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
[PubMed]

Zou, L.

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques formodeling guided-wave photonic devices," IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).

J. Lightwave Technol. (1)

Microwave Opt. Technol. Lett. (1)

T. Sun, G. Kai, Z. Wang, C. Wang, C. Zhang, Y. Liu, W. Zhang, S. Yuan, and X. Dong, "Multi-wavelength erbium-doped fiber laser based on a microstructure fiber Bragg grating," Microwave Opt. Technol. Lett. 20, 162-164 (2005).
[PubMed]

Opt Lett. (2)

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt Lett. 21, 1547-1549 (1996).
[PubMed]

T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt Lett. 22, 961-963 (1997).
[PubMed]

Opt. Express (4)

Opt. Lett. (6)

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Figures (8)

Fig. 1
Fig. 1

Transverse section scheme of a Ge-doped PCF.

Fig. 2
Fig. 2

Effective index as a function of the normalized pitch Λ∕λ.

Fig. 3
Fig. 3

NA as a function of the normalized pitch Λ∕λ.

Fig. 4
Fig. 4

Effective refractive indices as a function of the normalized hole size d∕Λ.

Fig. 5
Fig. 5

NA as a function of the normalized hole size d∕Λ.

Fig. 6
Fig. 6

V PCF as a function of the normalized pitch Λ∕λ.

Fig. 7
Fig. 7

Single-mode–multimode boundary curve.

Fig. 8
Fig. 8

V PCF as a function of the normalized hole size d∕Λ.

Equations (4)

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V = ( 2 π ρ / λ ) ( n co     2 n cl     2 ) 1 2 ,
V PCF = ( 2 π Λ λ ) ( n co 2 n cl 2 ) 1 2 ,
V PCF < π .
λ * / Λ = α ( d / Λ d * / Λ ) β ,

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