Abstract

Yb-doped double-cladding large mode area rod-type photonic crystal fibers are a key component for power scaling in fiber laser systems. Recently, designs with 19-cell core defect, that is with 19 missing air-holes in the center of the photonic crystal cladding, have been proposed, with reported core diameter up to 100 μm. In this paper an analysis of the cut-off wavelength of the first high-order mode in such low-NA fibers is reported, accounting for different approaches for the definition of the cladding effective index. Results have shown that taking into account the finite fiber cross-section and considering the first cladding mode of the actual fiber is mandatory to obtain a correct estimate of the cut-off wavelength.

© 2011 OSA

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References

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  1. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, 63–92 (2010).
    [CrossRef]
  2. A. Tünnerman, T. Schreiber, and J. Limpert, “Fiber lasers and amplifiers: an ultrafast performance evolution,” Appl. Opt. 49, 71–78 (2010).
    [CrossRef]
  3. F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung,“High peak power operation of a 100 μm-core, Yb-doped rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
    [CrossRef]
  4. K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
    [CrossRef]
  5. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [CrossRef] [PubMed]
  6. B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal cutoff in microstructured optical fibers,” Opt. Lett. 27, 1684–1686 (2003).
    [CrossRef]
  7. 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).
    [CrossRef] [PubMed]
  8. M. Koshiba and K. Saitoh, “Applicability of classical optical fiber theories to holey fibers,” Opt. Lett. 29, 1739–1741 (2004).
    [CrossRef] [PubMed]
  9. S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, “New design of single-mode large-mode-area photonic crystal fibers,” Proc. SPIE 5950, 59500U (2005).
    [CrossRef]
  10. K. Saitoh, Y. Tsuchida, M. Koshiba, and N. A. Mortensen, “Endlessly singe-mode holey fibers: the influence of core design,” Opt. Express 13, 10833–10839 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-26-10833 .
    [CrossRef] [PubMed]
  11. F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fibers: Properties and Applications (Springer, 2007), Vol. 102.
  12. A. Cucinotta, F. Poli, S. Selleri, L. Vincetti, and M. Zoboli, “Amplification properties of Er3+-doped photonic crystal fibers,” J. Lightwave Technol. 21, 782–788 (2003).
    [CrossRef]
  13. F. Poli, A. Cucinotta, D. Passaro, S. Selleri, J. Lægsgaard, and J. Broeng, “Single mode regime in large mode area rare-earth doped rod-type PCFs,” IEEE IEEE J. Sel. Top. Quantum Electron. 15, 54–60 (2009).
    [CrossRef]
  14. D. A. Gaponov, S. Février, M. Devautour, P. Roy, M. E. Likhachev, S. S. Aleshkina, M. Y. Salganskii, M. V. Yashkov, and A. N. Guryanov, “Management of the high-order mode content in large (40 μm) core photonic bandgap Bragg fiber laser,” Opt. Lett. 35, 2233–2235 (2010).
    [CrossRef] [PubMed]
  15. S. G. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–179 (2001), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-3-173 .
    [CrossRef] [PubMed]
  16. F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, “Suppression of higher-order modes by segmented core doping in rod-type photonic crystal fibers,” J. Lightwave Technol. 27, 4935–4942 (2009).
    [CrossRef]
  17. Datasheet of Corning®SMF-28e+™ optical fiber, http://www.corning.com/WorkArea/linkit.aspx?LinkIdentifier=id&ItemID=27659

2010 (4)

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, 63–92 (2010).
[CrossRef]

A. Tünnerman, T. Schreiber, and J. Limpert, “Fiber lasers and amplifiers: an ultrafast performance evolution,” Appl. Opt. 49, 71–78 (2010).
[CrossRef]

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung,“High peak power operation of a 100 μm-core, Yb-doped rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

D. A. Gaponov, S. Février, M. Devautour, P. Roy, M. E. Likhachev, S. S. Aleshkina, M. Y. Salganskii, M. V. Yashkov, and A. N. Guryanov, “Management of the high-order mode content in large (40 μm) core photonic bandgap Bragg fiber laser,” Opt. Lett. 35, 2233–2235 (2010).
[CrossRef] [PubMed]

2009 (2)

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, “Suppression of higher-order modes by segmented core doping in rod-type photonic crystal fibers,” J. Lightwave Technol. 27, 4935–4942 (2009).
[CrossRef]

F. Poli, A. Cucinotta, D. Passaro, S. Selleri, J. Lægsgaard, and J. Broeng, “Single mode regime in large mode area rare-earth doped rod-type PCFs,” IEEE IEEE J. Sel. Top. Quantum Electron. 15, 54–60 (2009).
[CrossRef]

2008 (1)

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

2005 (1)

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, “New design of single-mode large-mode-area photonic crystal fibers,” Proc. SPIE 5950, 59500U (2005).
[CrossRef]

2004 (1)

2003 (3)

1997 (1)

Aleshkina, S. S.

Birks, T. A.

Bottacini, M.

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, “New design of single-mode large-mode-area photonic crystal fibers,” Proc. SPIE 5950, 59500U (2005).
[CrossRef]

Broeng, J.

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, “Suppression of higher-order modes by segmented core doping in rod-type photonic crystal fibers,” J. Lightwave Technol. 27, 4935–4942 (2009).
[CrossRef]

F. Poli, A. Cucinotta, D. Passaro, S. Selleri, J. Lægsgaard, and J. Broeng, “Single mode regime in large mode area rare-earth doped rod-type PCFs,” IEEE IEEE J. Sel. Top. Quantum Electron. 15, 54–60 (2009).
[CrossRef]

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

Cheung, E. C.

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung,“High peak power operation of a 100 μm-core, Yb-doped rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

Clarkson, W. A.

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, 63–92 (2010).
[CrossRef]

Cucinotta, A.

F. Poli, A. Cucinotta, D. Passaro, S. Selleri, J. Lægsgaard, and J. Broeng, “Single mode regime in large mode area rare-earth doped rod-type PCFs,” IEEE IEEE J. Sel. Top. Quantum Electron. 15, 54–60 (2009).
[CrossRef]

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, “Suppression of higher-order modes by segmented core doping in rod-type photonic crystal fibers,” J. Lightwave Technol. 27, 4935–4942 (2009).
[CrossRef]

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, “New design of single-mode large-mode-area photonic crystal fibers,” Proc. SPIE 5950, 59500U (2005).
[CrossRef]

A. Cucinotta, F. Poli, S. Selleri, L. Vincetti, and M. Zoboli, “Amplification properties of Er3+-doped photonic crystal fibers,” J. Lightwave Technol. 21, 782–788 (2003).
[CrossRef]

F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fibers: Properties and Applications (Springer, 2007), Vol. 102.

de Sterke, C. M.

Denninger, M.

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

Devautour, M.

Di Teodoro, F.

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung,“High peak power operation of a 100 μm-core, Yb-doped rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

Février, S.

Folkenberg, J. R.

Foroni, M.

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, “New design of single-mode large-mode-area photonic crystal fibers,” Proc. SPIE 5950, 59500U (2005).
[CrossRef]

Gaponov, D. A.

Guryanov, A. N.

Hansen, K. P.

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

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).
[CrossRef] [PubMed]

Hemmat, M. K.

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung,“High peak power operation of a 100 μm-core, Yb-doped rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

Jakobsen, C.

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

Knight, J. C.

Koshiba, M.

Kuhlmey, B. T.

Lægsgaard, J.

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, “Suppression of higher-order modes by segmented core doping in rod-type photonic crystal fibers,” J. Lightwave Technol. 27, 4935–4942 (2009).
[CrossRef]

F. Poli, A. Cucinotta, D. Passaro, S. Selleri, J. Lægsgaard, and J. Broeng, “Single mode regime in large mode area rare-earth doped rod-type PCFs,” IEEE IEEE J. Sel. Top. Quantum Electron. 15, 54–60 (2009).
[CrossRef]

Likhachev, M. E.

Limpert, J.

Mattson, K.

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

McPhedran, R. C.

Morais, J.

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung,“High peak power operation of a 100 μm-core, Yb-doped rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

Mortensen, N. A.

Nielsen, M. D.

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

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).
[CrossRef] [PubMed]

Nikolajsen, T.

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

Nilsson, J.

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, 63–92 (2010).
[CrossRef]

Olausson, C. B.

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

Passaro, D.

F. Poli, A. Cucinotta, D. Passaro, S. Selleri, J. Lægsgaard, and J. Broeng, “Single mode regime in large mode area rare-earth doped rod-type PCFs,” IEEE IEEE J. Sel. Top. Quantum Electron. 15, 54–60 (2009).
[CrossRef]

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, “Suppression of higher-order modes by segmented core doping in rod-type photonic crystal fibers,” J. Lightwave Technol. 27, 4935–4942 (2009).
[CrossRef]

Poli, F.

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, “Suppression of higher-order modes by segmented core doping in rod-type photonic crystal fibers,” J. Lightwave Technol. 27, 4935–4942 (2009).
[CrossRef]

F. Poli, A. Cucinotta, D. Passaro, S. Selleri, J. Lægsgaard, and J. Broeng, “Single mode regime in large mode area rare-earth doped rod-type PCFs,” IEEE IEEE J. Sel. Top. Quantum Electron. 15, 54–60 (2009).
[CrossRef]

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, “New design of single-mode large-mode-area photonic crystal fibers,” Proc. SPIE 5950, 59500U (2005).
[CrossRef]

A. Cucinotta, F. Poli, S. Selleri, L. Vincetti, and M. Zoboli, “Amplification properties of Er3+-doped photonic crystal fibers,” J. Lightwave Technol. 21, 782–788 (2003).
[CrossRef]

F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fibers: Properties and Applications (Springer, 2007), Vol. 102.

Richardson, D. J.

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, 63–92 (2010).
[CrossRef]

Roy, P.

Russell, P. St. J.

Saitoh, K.

Salganskii, M. Y.

Schreiber, T.

Selleri, S.

F. Poli, J. Lægsgaard, D. Passaro, A. Cucinotta, S. Selleri, and J. Broeng, “Suppression of higher-order modes by segmented core doping in rod-type photonic crystal fibers,” J. Lightwave Technol. 27, 4935–4942 (2009).
[CrossRef]

F. Poli, A. Cucinotta, D. Passaro, S. Selleri, J. Lægsgaard, and J. Broeng, “Single mode regime in large mode area rare-earth doped rod-type PCFs,” IEEE IEEE J. Sel. Top. Quantum Electron. 15, 54–60 (2009).
[CrossRef]

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, “New design of single-mode large-mode-area photonic crystal fibers,” Proc. SPIE 5950, 59500U (2005).
[CrossRef]

A. Cucinotta, F. Poli, S. Selleri, L. Vincetti, and M. Zoboli, “Amplification properties of Er3+-doped photonic crystal fibers,” J. Lightwave Technol. 21, 782–788 (2003).
[CrossRef]

F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fibers: Properties and Applications (Springer, 2007), Vol. 102.

Simonsen, H. R.

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

Skovgaard, P. M. W.

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

Sørensen, M. H.

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

Tünnerman, A.

Vincetti, L.

Yashkov, M. V.

Zoboli, M.

Appl. Opt. (1)

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

F. Poli, A. Cucinotta, D. Passaro, S. Selleri, J. Lægsgaard, and J. Broeng, “Single mode regime in large mode area rare-earth doped rod-type PCFs,” IEEE IEEE J. Sel. Top. Quantum Electron. 15, 54–60 (2009).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, 63–92 (2010).
[CrossRef]

Opt. Lett. (5)

Proc. SPIE (3)

S. Selleri, A. Cucinotta, M. Foroni, F. Poli, and M. Bottacini, “New design of single-mode large-mode-area photonic crystal fibers,” Proc. SPIE 5950, 59500U (2005).
[CrossRef]

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung,“High peak power operation of a 100 μm-core, Yb-doped rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

K. P. Hansen, C. B. Olausson, J. Broeng, K. Mattson, M. D. Nielsen, T. Nikolajsen, P. M. W. Skovgaard, M. H. Sørensen, M. Denninger, C. Jakobsen, and H. R. Simonsen, “Airclad fiber laser technology,” Proc. SPIE 6873, 687307 (2008).
[CrossRef]

Other (4)

K. Saitoh, Y. Tsuchida, M. Koshiba, and N. A. Mortensen, “Endlessly singe-mode holey fibers: the influence of core design,” Opt. Express 13, 10833–10839 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-26-10833 .
[CrossRef] [PubMed]

F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fibers: Properties and Applications (Springer, 2007), Vol. 102.

S. G. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–179 (2001), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-3-173 .
[CrossRef] [PubMed]

Datasheet of Corning®SMF-28e+™ optical fiber, http://www.corning.com/WorkArea/linkit.aspx?LinkIdentifier=id&ItemID=27659

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Figures (11)

Fig. 1
Fig. 1

(a) Cross-section of the 19-cell Yb-doped double-cladding PCF with 5 air-hole rings. Cross-section quarter, considered for the numerical analysis, of the fiber with (b) 4 and (c) 3 air-hole rings in the inner cladding.

Fig. 2
Fig. 2

Dispersion curves of the guided-modes and of the first mode of the infinite cladding and of the finite one, without core defect, for the 19-cell PCF with (a) 5, (b) 4 and (c) 3 air-hole rings in the inner cladding.

Fig. 3
Fig. 3

Magnetic field modulus distribution of the first mode of the finite cladding without defect at 1250 nm for the 19-cell PCF with (a) 5, (b) 4 and (c) 3 air-hole rings in the inner cladding.

Fig. 4
Fig. 4

Magnetic field modulus distribution of the FM at (a) 1225 nm, (b) 1230 nm, (c) 1235 nm, (d) 1240 nm, and (e) 1245 nm for the 19-cell PCF with 4 air-hole rings in the inner cladding.

Fig. 5
Fig. 5

Overlap integral on the hexagonal doped core of the FM and the HOM for the 19-cell PCF with (a) 5, (b) 4 and (c) 3 air-hole rings in the inner cladding. Vertical lines and symbols show the range between the FM and the HOM cut-off wavelengths, obtained with the methods based on the mode of the infinite cladding (black lines) and of the finite cladding without defect (pink lines).

Fig. 6
Fig. 6

(a) Effective index and (b) overlap integral on the core of the FM and the HOM of a conventional step-index fiber similar to Corning®SMF-28™ with core refractive index of 1.4547.

Fig. 7
Fig. 7

(a) Effective index and (b) overlap integral on the hexagonal doped core of the guided-modes and of the first mode of the finite cladding with core defect, for the 19-cell PCF with 5 air-hole rings in the inner cladding.

Fig. 8
Fig. 8

Magnetic field modulus distribution of (a) FM and (b) cladding mode at the FM cut-off wavelength, that is about 1078 nm, and of (c) HOM and (d) cladding mode at the HOM cut-off wavelength, that is about 1149 nm.

Fig. 9
Fig. 9

Dispersion curves of the guided-modes and of the first mode of the finite cladding with core defect, for the 19-cell PCF with (a) 4 and (b) 3 air-hole rings in the inner cladding.

Fig. 10
Fig. 10

Overlap integral on the hexagonal doped core of the guided-modes for the 19-cell PCF with (a) 4 and (b) 3 air-hole rings in the inner cladding. Vertical lines and symbols show the range between the FM and the HOM cut-off wavelengths, obtained with the methods based on the mode of the finite cladding with defect.

Fig. 11
Fig. 11

(a) HOM cut-off wavelength, (b) HOM overlap integral at cut-off, (c) single-mode wavelength range and (d) FM overlap integral at HOM cut-off wavelength for the 19-cell PCF with 5, 4 and 3 air-hole rings and d/Λ = 0.1, as a function of the core refractive index. The values of the same parameters for a 19-cell PCF with 5 air-hole rings and d/Λ = 0.05 are also shown.

Tables (2)

Tables Icon

Table 1 FM and HOM cut-off wavelengths and single-mode bandwidth for the 19-cell PCFs with 5, 4 and 3 air-hole rings calculated with the method based on the mode of the infinite cladding and of the finite cladding without defect.

Tables Icon

Table 2 FM and HOM cut-off wavelengths and single-mode bandwidth for the 19-cell PCFs with 5, 4 and 3 air-hole rings calculated with the avoided-crossing method.

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