Abstract

The influence of the internal temperature gradient in rare-earth-doped low-numerical-aperture fibers on modal properties is analyzed for step-index and photonic crystal fibers. We provide guidelines when a single-mode fiber turns into a multimode fiber and how the mode-field-diameter is affected.

© 2006 Optical Society of America

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References

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  1. Y. Jeong, J.K. Sahu, D.N. Payne, and J. Nilsson, "Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power," Opt. Express 12,6088-6092 (2004).
    [CrossRef] [PubMed]
  2. http://www.ipgphotonics.com
  3. A. Tünnermann, T. Schreiber, F. Röser, A. Liem, S. Höfer, H. Zellmer, S. Nolte and J. Limpert, "The renaissance and bright future of fibre lasers," J. Phys. B: At. Mol. Opt. Phys. 38, 681-693 (2005).
    [CrossRef]
  4. J. Limpert, A. Liem, M. Reich, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, "Low-nonlinearity single-transverse-mode ytterbium-doped photonic crystal fiber amplifier," Opt. Express 12,1313-1319 (2004).
    [CrossRef] [PubMed]
  5. http://www.sciner.com/Opticsland/FS.htm
  6. J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, and A. Tünnermann, "Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation," Opt. Express 11,2982-2990 (2003).
    [CrossRef] [PubMed]
  7. D.C. Brown and H.J. Hoffmann, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quantum Electron.,  37,207-217 (2001).
    [CrossRef]
  8. J. Riishede, N. A. Mortensen and J. Lægsgaard, "RGB A ‘poor man´s approach’ to modelling micro-structured optical fibers," J. Opt. A: Pure Appl.Opt. 5534-538(2003).
    [CrossRef]
  9. M. Koshiba and K. Saitoh, "Applicability of classical optical fiber theories to holey fibers," Opt. Lett. 29, 15, 1739 (2004).
    [CrossRef] [PubMed]
  10. N. Mortensen, J. R. Folkenberg, M. D. Nielsen, K.P. Hansen, "Modal cutoff and the V parameter in photonic crystal fibers," Opt. Lett. 28, 1879 (2003).
    [CrossRef] [PubMed]

2005 (1)

A. Tünnermann, T. Schreiber, F. Röser, A. Liem, S. Höfer, H. Zellmer, S. Nolte and J. Limpert, "The renaissance and bright future of fibre lasers," J. Phys. B: At. Mol. Opt. Phys. 38, 681-693 (2005).
[CrossRef]

2004 (3)

2003 (3)

2001 (1)

D.C. Brown and H.J. Hoffmann, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quantum Electron.,  37,207-217 (2001).
[CrossRef]

Broeng, J.

Brown, D.C.

D.C. Brown and H.J. Hoffmann, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quantum Electron.,  37,207-217 (2001).
[CrossRef]

Folkenberg, J. R.

Guyenot, V.

Hansen, K.P.

Höfer, S.

A. Tünnermann, T. Schreiber, F. Röser, A. Liem, S. Höfer, H. Zellmer, S. Nolte and J. Limpert, "The renaissance and bright future of fibre lasers," J. Phys. B: At. Mol. Opt. Phys. 38, 681-693 (2005).
[CrossRef]

Hoffmann, H.J.

D.C. Brown and H.J. Hoffmann, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quantum Electron.,  37,207-217 (2001).
[CrossRef]

Jakobsen, C.

Jeong, Y.

Koshiba, M.

Lægsgaard, J.

J. Riishede, N. A. Mortensen and J. Lægsgaard, "RGB A ‘poor man´s approach’ to modelling micro-structured optical fibers," J. Opt. A: Pure Appl.Opt. 5534-538(2003).
[CrossRef]

Liem, A.

Limpert, J.

Mortensen, N.

Mortensen, N. A.

J. Riishede, N. A. Mortensen and J. Lægsgaard, "RGB A ‘poor man´s approach’ to modelling micro-structured optical fibers," J. Opt. A: Pure Appl.Opt. 5534-538(2003).
[CrossRef]

Nielsen, M. D.

Nilsson, J.

Nolte, S.

Payne, D.N.

Peschel, T.

Petersson, A.

Reich, M.

Riishede, J.

J. Riishede, N. A. Mortensen and J. Lægsgaard, "RGB A ‘poor man´s approach’ to modelling micro-structured optical fibers," J. Opt. A: Pure Appl.Opt. 5534-538(2003).
[CrossRef]

Röser, F.

A. Tünnermann, T. Schreiber, F. Röser, A. Liem, S. Höfer, H. Zellmer, S. Nolte and J. Limpert, "The renaissance and bright future of fibre lasers," J. Phys. B: At. Mol. Opt. Phys. 38, 681-693 (2005).
[CrossRef]

Sahu, J.K.

Saitoh, K.

Schreiber, T.

Tünnermann, A.

Zellmer, H.

IEEE J. Quantum Electron. (1)

D.C. Brown and H.J. Hoffmann, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quantum Electron.,  37,207-217 (2001).
[CrossRef]

J. Opt. A: Pure Appl.Opt. (1)

J. Riishede, N. A. Mortensen and J. Lægsgaard, "RGB A ‘poor man´s approach’ to modelling micro-structured optical fibers," J. Opt. A: Pure Appl.Opt. 5534-538(2003).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys. (1)

A. Tünnermann, T. Schreiber, F. Röser, A. Liem, S. Höfer, H. Zellmer, S. Nolte and J. Limpert, "The renaissance and bright future of fibre lasers," J. Phys. B: At. Mol. Opt. Phys. 38, 681-693 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Other (2)

http://www.ipgphotonics.com

http://www.sciner.com/Opticsland/FS.htm

Supplementary Material (1)

» Media 1: AVI (1461 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Illustration of the “cold” index profile (a), typical temperature profile according to Eq. (1) and Eq. (2) (b), temperature induced index deformation (c).

Fig. 2.
Fig. 2.

Behaviour of the mode-field-diameter of the LP01 mode and the overlap of the LP11 mode in dependence on the thermal load for a photonic crystal fiber.(NA=0.03, V=2.0). [Media 1]

Fig. 3.
Fig. 3.

Simulated overlap of the LP11 mode with the core region (black) and the MFD of the LP01 (red) for a SIF with a NA of 0.03 (a) and NA of 0.04 (b). The dashed line is the single-mode condition described in the text.

Fig. 4.
Fig. 4.

Simulated overlap of the LP11 mode with the core region (black) and the MFD of the LP01 (red) for a PCF with a NA of 0.03 (a) and NA of 0.04 (b). The dashed line is the single-mode condition described in the text.

Fig. 5.
Fig. 5.

Thermal load at cut-off condition for a SIF (a) and PCF (b) as a function of numerical aperture for different V parameters.

Fig. 6.
Fig. 6.

Simulated average slope of the MFD change for a SIF (a) and PCF (b) versus NA for different V-parameters.

Equations (5)

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T core ( r r core ) = T cool + Q r core 2 4 K [ 2 ln ( r clad r core ) + 2 K r clad h ] + Q r core 2 4 K ( 1 ( r r core ) 2 )
T core ( r core < r r clad ) = T cool + Q r core 2 2 r clad h Q r core 2 2 K ln ( r r clad ) ,
( 2 x 2 + 2 y 2 + ( x , y ) k 2 ) Ψ ( x , y ) = β 2 Ψ ( x , y )
V SIF = 2 π λ r core n core 2 n clad 2
V PCF = 2 π λ a eff n core 2 n FSM 2

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