Abstract

We use numerical simulations with the beam propagation method (BPM) and rate equations to investigate the pump absorption and amplification characteristics in double-clad ytterbium-doped fibers with small cladding-to-core area ratios, in the range 1–3. The presence of modes with low overlap with the doped region (or alternatively, skew rays) hampers the pump absorption in a circular geometry, but we find that the effect is small for area ratios of ∼2.5 or less. We derive ray-based expressions for the small-signal absorption which show similar results. However, even when the small-signal absorption scales nearly ideally with the inverse of the area ratio, the absorption in an operating amplifier is much lower, and the dependence on the area ratio much weaker, when a large fraction of the Yb-ions is excited in a small-area-ratio fiber. We derive equations which show this, and that in contrast to conventional area ratios of, e.g., 100, the fiber length depends more strongly on the required gain than on the required pump absorption. However, fibers substantially shorter than 1 m still allow for adequate pump absorption and gain. The effective length for nonlinear interactions is less affected by this, since the Yb-excitation is low where the signal power is high. Although we treat single-mode cores, the BPM amplifier simulations show there are a few percent of the signal power in cladding-guided modes with high overlap with the Yb-doped core. Nevertheless, according to our simulations, it is possible to achieve high efficiency and mode purity with a small-area-ratio circularly symmetric double-clad fiber.

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References

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  1. S. Bedö, W. Lüthy, and H. Weber, “The effective absorption coefficient in double-clad fibres,” Opt. Commun. 99, 331–335 (1993).
    [Crossref]
  2. A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Opt. Commun. 132, 511–518 (1996).
    [Crossref]
  3. A. Liu and K. Ueda, “Propagation losses of pump light in rectangular double-clad fibers,” Opt. Eng. 35, 3130–3134 (1996).
    [Crossref]
  4. M. H. Muendel, “Optimal inner cladding shapes for double-clad fiber lasers,” in Conference on Lasers and Electro-Optics, vol. 9 of OSA Technical Digest (Optical Society of America, Anaheim, California, 1996), p. CTuU2.
  5. A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 2, 714–717 (1990).
    [Crossref]
  6. T. Yao, J. Ji, and J. Nilsson, “Ultra-low quantum-defect heating in ytterbium-doped aluminosilicate fibers,” J. Light. Technol. 32, 429–434 (2014).
    [Crossref]
  7. J. Nilsson, J. D. Minelly, R. Paschotta, A. C. Tropper, and D. C. Hanna, “Ring-doped cladding-pumped single-mode three-level fiber laser,” Opt. Lett. 23, 355–357 (1998).
    [Crossref]
  8. F. Roeser, C. Jauregui, J. Limpert, and A. Tünnermann, “94 W 980 nm high brightness Yb-doped fiber laser,” Opt. Express 16, 17310–17318 (2008).
    [Crossref]
  9. J. Boullet, Y. Zaouter, R. Desmarchelier, M. Cazaux, F. Salin, J. Saby, R. Bello-Doua, and E. Cormier, “High power ytterbium-doped rod-type three-level photonic crystal fiber laser,” Opt. Express 16, 17891–17902 (2008).
    [Crossref] [PubMed]
  10. C. A. Codemard, J. K. Sahu, and J. Nilsson, “Tandem cladding-pumping for control of excess gain in ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 46, 1860–1869 (2010).
    [Crossref]
  11. J. D. Minelly, R. I. Laming, J. E. Townsend, W. L. Barnes, E. R. Taylor, K. P. Jedrzejewski, and D. N. Payne, “High-gain fiber power amplifier tandem-pumped by a 3-W multistripe diode,” in Digest of Conference on Optical Fiber Communication, (Optical Society of America, 1992), p. TuG2.
    [Crossref]
  12. C. Unger and W. Stocklein, “Investigation of the microbending sensitivity of fibers,” J. Light. Technol. 12, 591–596 (1994).
    [Crossref]
  13. D. J. DiGiovanni and R. S. Windeler, “Article comprising an air-clad optical fiber,” U.S. patent 5,907,652, (May25, 1999).
  14. J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fibre laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
    [Crossref]
  15. J. Nilsson and D. N. Payne, “High-power fiber lasers,” Science 332, 921–922 (2011).
    [Crossref] [PubMed]
  16. P. E. Lagasse and R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems: A review,” Radio Sci. 22, 1225–1233 (1987).
    [Crossref]
  17. H. Zellmer, A. Tünnermann, H. Welling, and V. Reichel, “Double-clad fiber laser with 30 W output power,” in Optical Amplifiers and Their Applications, (Optical Society of America, 1997), p. FAW18.
    [Crossref]
  18. A. Ankiewicz and C. Pask, “Geometric optics approach to light acceptance and propagation in graded index fibres,” Opt. Quantum Electron. 9, 87–109 (1977).
    [Crossref]
  19. A. Ankiewicz and C. Pask, “Tunnelling rays in graded-index fibres,” Opt. Quantum Electron. 10, 83–93 (1978).
    [Crossref]
  20. Y. Feng, B. M. Zhang, J. Zhao, S. Zhu, J. H. V. Price, and J. Nilsson, “Absorption measurement errors in single-mode fibers resulting from re-emission of radiation,” IEEE J. Quantum Electron. 53, 1–11 (2017).
    [Crossref]
  21. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19, 13218–13224 (2011).
    [Crossref] [PubMed]
  22. M. N. Zervas and C. A. Codemard, “High power fiber lasers: A review,” IEEE J. Sel. Top. Quantum Electron. 20, 219–241 (2014).
    [Crossref]
  23. J. Ji, C. A. Codemard, and J. Nilsson, “Analysis of spectral bendloss filtering in a cladding-pumped W-type fiber Raman amplifier,” J. Light. Technol. 28, 2179–2186 (2010).
    [Crossref]
  24. A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, 1983), chap. 2.2.
  25. A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, 1983), chap. 2.7.

2017 (1)

Y. Feng, B. M. Zhang, J. Zhao, S. Zhu, J. H. V. Price, and J. Nilsson, “Absorption measurement errors in single-mode fibers resulting from re-emission of radiation,” IEEE J. Quantum Electron. 53, 1–11 (2017).
[Crossref]

2014 (2)

M. N. Zervas and C. A. Codemard, “High power fiber lasers: A review,” IEEE J. Sel. Top. Quantum Electron. 20, 219–241 (2014).
[Crossref]

T. Yao, J. Ji, and J. Nilsson, “Ultra-low quantum-defect heating in ytterbium-doped aluminosilicate fibers,” J. Light. Technol. 32, 429–434 (2014).
[Crossref]

2011 (2)

2010 (2)

J. Ji, C. A. Codemard, and J. Nilsson, “Analysis of spectral bendloss filtering in a cladding-pumped W-type fiber Raman amplifier,” J. Light. Technol. 28, 2179–2186 (2010).
[Crossref]

C. A. Codemard, J. K. Sahu, and J. Nilsson, “Tandem cladding-pumping for control of excess gain in ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 46, 1860–1869 (2010).
[Crossref]

2008 (2)

2001 (1)

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fibre laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[Crossref]

1998 (1)

1996 (2)

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Opt. Commun. 132, 511–518 (1996).
[Crossref]

A. Liu and K. Ueda, “Propagation losses of pump light in rectangular double-clad fibers,” Opt. Eng. 35, 3130–3134 (1996).
[Crossref]

1994 (1)

C. Unger and W. Stocklein, “Investigation of the microbending sensitivity of fibers,” J. Light. Technol. 12, 591–596 (1994).
[Crossref]

1993 (1)

S. Bedö, W. Lüthy, and H. Weber, “The effective absorption coefficient in double-clad fibres,” Opt. Commun. 99, 331–335 (1993).
[Crossref]

1990 (1)

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 2, 714–717 (1990).
[Crossref]

1987 (1)

P. E. Lagasse and R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems: A review,” Radio Sci. 22, 1225–1233 (1987).
[Crossref]

1978 (1)

A. Ankiewicz and C. Pask, “Tunnelling rays in graded-index fibres,” Opt. Quantum Electron. 10, 83–93 (1978).
[Crossref]

1977 (1)

A. Ankiewicz and C. Pask, “Geometric optics approach to light acceptance and propagation in graded index fibres,” Opt. Quantum Electron. 9, 87–109 (1977).
[Crossref]

Alvarez-Chavez, J. A.

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fibre laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[Crossref]

Ankiewicz, A.

A. Ankiewicz and C. Pask, “Tunnelling rays in graded-index fibres,” Opt. Quantum Electron. 10, 83–93 (1978).
[Crossref]

A. Ankiewicz and C. Pask, “Geometric optics approach to light acceptance and propagation in graded index fibres,” Opt. Quantum Electron. 9, 87–109 (1977).
[Crossref]

Aspell, J.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 2, 714–717 (1990).
[Crossref]

Baets, R.

P. E. Lagasse and R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems: A review,” Radio Sci. 22, 1225–1233 (1987).
[Crossref]

Barnes, W. L.

J. D. Minelly, R. I. Laming, J. E. Townsend, W. L. Barnes, E. R. Taylor, K. P. Jedrzejewski, and D. N. Payne, “High-gain fiber power amplifier tandem-pumped by a 3-W multistripe diode,” in Digest of Conference on Optical Fiber Communication, (Optical Society of America, 1992), p. TuG2.
[Crossref]

Bedö, S.

S. Bedö, W. Lüthy, and H. Weber, “The effective absorption coefficient in double-clad fibres,” Opt. Commun. 99, 331–335 (1993).
[Crossref]

Bello-Doua, R.

Boullet, J.

Cazaux, M.

Codemard, C. A.

M. N. Zervas and C. A. Codemard, “High power fiber lasers: A review,” IEEE J. Sel. Top. Quantum Electron. 20, 219–241 (2014).
[Crossref]

J. Ji, C. A. Codemard, and J. Nilsson, “Analysis of spectral bendloss filtering in a cladding-pumped W-type fiber Raman amplifier,” J. Light. Technol. 28, 2179–2186 (2010).
[Crossref]

C. A. Codemard, J. K. Sahu, and J. Nilsson, “Tandem cladding-pumping for control of excess gain in ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 46, 1860–1869 (2010).
[Crossref]

Cormier, E.

Desmarchelier, R.

DiGiovanni, D. J.

D. J. DiGiovanni and R. S. Windeler, “Article comprising an air-clad optical fiber,” U.S. patent 5,907,652, (May25, 1999).

Eidam, T.

Evankow, J. D.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 2, 714–717 (1990).
[Crossref]

Feng, Y.

Y. Feng, B. M. Zhang, J. Zhao, S. Zhu, J. H. V. Price, and J. Nilsson, “Absorption measurement errors in single-mode fibers resulting from re-emission of radiation,” IEEE J. Quantum Electron. 53, 1–11 (2017).
[Crossref]

Furusawa, K.

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fibre laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[Crossref]

Hanna, D. C.

Jansen, F.

Jauregui, C.

Jedrzejewski, K. P.

J. D. Minelly, R. I. Laming, J. E. Townsend, W. L. Barnes, E. R. Taylor, K. P. Jedrzejewski, and D. N. Payne, “High-gain fiber power amplifier tandem-pumped by a 3-W multistripe diode,” in Digest of Conference on Optical Fiber Communication, (Optical Society of America, 1992), p. TuG2.
[Crossref]

Ji, J.

T. Yao, J. Ji, and J. Nilsson, “Ultra-low quantum-defect heating in ytterbium-doped aluminosilicate fibers,” J. Light. Technol. 32, 429–434 (2014).
[Crossref]

J. Ji, C. A. Codemard, and J. Nilsson, “Analysis of spectral bendloss filtering in a cladding-pumped W-type fiber Raman amplifier,” J. Light. Technol. 28, 2179–2186 (2010).
[Crossref]

Jopson, R. M.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 2, 714–717 (1990).
[Crossref]

Lagasse, P. E.

P. E. Lagasse and R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems: A review,” Radio Sci. 22, 1225–1233 (1987).
[Crossref]

Laming, R. I.

J. D. Minelly, R. I. Laming, J. E. Townsend, W. L. Barnes, E. R. Taylor, K. P. Jedrzejewski, and D. N. Payne, “High-gain fiber power amplifier tandem-pumped by a 3-W multistripe diode,” in Digest of Conference on Optical Fiber Communication, (Optical Society of America, 1992), p. TuG2.
[Crossref]

Limpert, J.

Liu, A.

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Opt. Commun. 132, 511–518 (1996).
[Crossref]

A. Liu and K. Ueda, “Propagation losses of pump light in rectangular double-clad fibers,” Opt. Eng. 35, 3130–3134 (1996).
[Crossref]

Love, J. D.

A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, 1983), chap. 2.2.

A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, 1983), chap. 2.7.

Lüthy, W.

S. Bedö, W. Lüthy, and H. Weber, “The effective absorption coefficient in double-clad fibres,” Opt. Commun. 99, 331–335 (1993).
[Crossref]

Minelly, J. D.

J. Nilsson, J. D. Minelly, R. Paschotta, A. C. Tropper, and D. C. Hanna, “Ring-doped cladding-pumped single-mode three-level fiber laser,” Opt. Lett. 23, 355–357 (1998).
[Crossref]

J. D. Minelly, R. I. Laming, J. E. Townsend, W. L. Barnes, E. R. Taylor, K. P. Jedrzejewski, and D. N. Payne, “High-gain fiber power amplifier tandem-pumped by a 3-W multistripe diode,” in Digest of Conference on Optical Fiber Communication, (Optical Society of America, 1992), p. TuG2.
[Crossref]

Muendel, M. H.

M. H. Muendel, “Optimal inner cladding shapes for double-clad fiber lasers,” in Conference on Lasers and Electro-Optics, vol. 9 of OSA Technical Digest (Optical Society of America, Anaheim, California, 1996), p. CTuU2.

Nilsson, J.

Y. Feng, B. M. Zhang, J. Zhao, S. Zhu, J. H. V. Price, and J. Nilsson, “Absorption measurement errors in single-mode fibers resulting from re-emission of radiation,” IEEE J. Quantum Electron. 53, 1–11 (2017).
[Crossref]

T. Yao, J. Ji, and J. Nilsson, “Ultra-low quantum-defect heating in ytterbium-doped aluminosilicate fibers,” J. Light. Technol. 32, 429–434 (2014).
[Crossref]

J. Nilsson and D. N. Payne, “High-power fiber lasers,” Science 332, 921–922 (2011).
[Crossref] [PubMed]

J. Ji, C. A. Codemard, and J. Nilsson, “Analysis of spectral bendloss filtering in a cladding-pumped W-type fiber Raman amplifier,” J. Light. Technol. 28, 2179–2186 (2010).
[Crossref]

C. A. Codemard, J. K. Sahu, and J. Nilsson, “Tandem cladding-pumping for control of excess gain in ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 46, 1860–1869 (2010).
[Crossref]

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fibre laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[Crossref]

J. Nilsson, J. D. Minelly, R. Paschotta, A. C. Tropper, and D. C. Hanna, “Ring-doped cladding-pumped single-mode three-level fiber laser,” Opt. Lett. 23, 355–357 (1998).
[Crossref]

Otto, H.-J.

Paschotta, R.

Pask, C.

A. Ankiewicz and C. Pask, “Tunnelling rays in graded-index fibres,” Opt. Quantum Electron. 10, 83–93 (1978).
[Crossref]

A. Ankiewicz and C. Pask, “Geometric optics approach to light acceptance and propagation in graded index fibres,” Opt. Quantum Electron. 9, 87–109 (1977).
[Crossref]

Payne, D. N.

J. Nilsson and D. N. Payne, “High-power fiber lasers,” Science 332, 921–922 (2011).
[Crossref] [PubMed]

J. D. Minelly, R. I. Laming, J. E. Townsend, W. L. Barnes, E. R. Taylor, K. P. Jedrzejewski, and D. N. Payne, “High-gain fiber power amplifier tandem-pumped by a 3-W multistripe diode,” in Digest of Conference on Optical Fiber Communication, (Optical Society of America, 1992), p. TuG2.
[Crossref]

Price, J. H. V.

Y. Feng, B. M. Zhang, J. Zhao, S. Zhu, J. H. V. Price, and J. Nilsson, “Absorption measurement errors in single-mode fibers resulting from re-emission of radiation,” IEEE J. Quantum Electron. 53, 1–11 (2017).
[Crossref]

Reichel, V.

H. Zellmer, A. Tünnermann, H. Welling, and V. Reichel, “Double-clad fiber laser with 30 W output power,” in Optical Amplifiers and Their Applications, (Optical Society of America, 1997), p. FAW18.
[Crossref]

Renaud, C. C.

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fibre laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[Crossref]

Richardson, D. J.

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fibre laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[Crossref]

Roeser, F.

Saby, J.

Sahu, J. K.

C. A. Codemard, J. K. Sahu, and J. Nilsson, “Tandem cladding-pumping for control of excess gain in ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 46, 1860–1869 (2010).
[Crossref]

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fibre laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[Crossref]

Saleh, A. A. M.

A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell, “Modeling of gain in erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 2, 714–717 (1990).
[Crossref]

Salin, F.

Schmidt, O.

Schreiber, T.

Selvas, R.

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fibre laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[Crossref]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, 1983), chap. 2.7.

A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, 1983), chap. 2.2.

Stocklein, W.

C. Unger and W. Stocklein, “Investigation of the microbending sensitivity of fibers,” J. Light. Technol. 12, 591–596 (1994).
[Crossref]

Stutzki, F.

Taylor, E. R.

J. D. Minelly, R. I. Laming, J. E. Townsend, W. L. Barnes, E. R. Taylor, K. P. Jedrzejewski, and D. N. Payne, “High-gain fiber power amplifier tandem-pumped by a 3-W multistripe diode,” in Digest of Conference on Optical Fiber Communication, (Optical Society of America, 1992), p. TuG2.
[Crossref]

Townsend, J. E.

J. D. Minelly, R. I. Laming, J. E. Townsend, W. L. Barnes, E. R. Taylor, K. P. Jedrzejewski, and D. N. Payne, “High-gain fiber power amplifier tandem-pumped by a 3-W multistripe diode,” in Digest of Conference on Optical Fiber Communication, (Optical Society of America, 1992), p. TuG2.
[Crossref]

Tropper, A. C.

Tünnermann, A.

Ueda, K.

A. Liu and K. Ueda, “Propagation losses of pump light in rectangular double-clad fibers,” Opt. Eng. 35, 3130–3134 (1996).
[Crossref]

A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Opt. Commun. 132, 511–518 (1996).
[Crossref]

Unger, C.

C. Unger and W. Stocklein, “Investigation of the microbending sensitivity of fibers,” J. Light. Technol. 12, 591–596 (1994).
[Crossref]

Weber, H.

S. Bedö, W. Lüthy, and H. Weber, “The effective absorption coefficient in double-clad fibres,” Opt. Commun. 99, 331–335 (1993).
[Crossref]

Welling, H.

H. Zellmer, A. Tünnermann, H. Welling, and V. Reichel, “Double-clad fiber laser with 30 W output power,” in Optical Amplifiers and Their Applications, (Optical Society of America, 1997), p. FAW18.
[Crossref]

Windeler, R. S.

D. J. DiGiovanni and R. S. Windeler, “Article comprising an air-clad optical fiber,” U.S. patent 5,907,652, (May25, 1999).

Wirth, C.

Yao, T.

T. Yao, J. Ji, and J. Nilsson, “Ultra-low quantum-defect heating in ytterbium-doped aluminosilicate fibers,” J. Light. Technol. 32, 429–434 (2014).
[Crossref]

Zaouter, Y.

Zellmer, H.

H. Zellmer, A. Tünnermann, H. Welling, and V. Reichel, “Double-clad fiber laser with 30 W output power,” in Optical Amplifiers and Their Applications, (Optical Society of America, 1997), p. FAW18.
[Crossref]

Zervas, M. N.

M. N. Zervas and C. A. Codemard, “High power fiber lasers: A review,” IEEE J. Sel. Top. Quantum Electron. 20, 219–241 (2014).
[Crossref]

Zhang, B. M.

Y. Feng, B. M. Zhang, J. Zhao, S. Zhu, J. H. V. Price, and J. Nilsson, “Absorption measurement errors in single-mode fibers resulting from re-emission of radiation,” IEEE J. Quantum Electron. 53, 1–11 (2017).
[Crossref]

Zhao, J.

Y. Feng, B. M. Zhang, J. Zhao, S. Zhu, J. H. V. Price, and J. Nilsson, “Absorption measurement errors in single-mode fibers resulting from re-emission of radiation,” IEEE J. Quantum Electron. 53, 1–11 (2017).
[Crossref]

Zhu, S.

Y. Feng, B. M. Zhang, J. Zhao, S. Zhu, J. H. V. Price, and J. Nilsson, “Absorption measurement errors in single-mode fibers resulting from re-emission of radiation,” IEEE J. Quantum Electron. 53, 1–11 (2017).
[Crossref]

Electron. Lett. (1)

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fibre laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[Crossref]

IEEE J. Quantum Electron. (2)

C. A. Codemard, J. K. Sahu, and J. Nilsson, “Tandem cladding-pumping for control of excess gain in ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 46, 1860–1869 (2010).
[Crossref]

Y. Feng, B. M. Zhang, J. Zhao, S. Zhu, J. H. V. Price, and J. Nilsson, “Absorption measurement errors in single-mode fibers resulting from re-emission of radiation,” IEEE J. Quantum Electron. 53, 1–11 (2017).
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Figures (13)

Fig. 1
Fig. 1 Double-clad fiber structure under consideration. (a) outer cladding; (b) inner cladding; (c) core, which coincides with the Yb-doped region.
Fig. 2
Fig. 2 Small signal absorption of pump vs. scaled fiber length for circular and non-circular inner cladding at different area ratios. Solid lines: circular inner cladding. Dashed lines: 10%-D-shaped inner cladding. Dotted lines: octagonal inner cladding.
Fig. 3
Fig. 3 Small signal pump absorption vs. scaled fiber length at different area ratios with circular inner claddings. Solid lines: analytical expressions in ray model. Dashed lines: beam propagation method. For area ratio of 3, fibers that are scaled up in core and cladding diameter by 2 and 4 times are included, in addition to the default case with parameters as given in Table 1.
Fig. 4
Fig. 4 Evolution of pump power (in dBm) and signal power (in W) in the high-power regime for circular inner claddings with different area ratios.
Fig. 5
Fig. 5 Effective length of signal for circular inner claddings with different area ratios as a function of (a) actual length and (b) signal output power. Signal output powers of 5, 15, and 20 W are also marked in (a), where lower output powers have shorter effective length.
Fig. 6
Fig. 6 Pump and signal power along the fiber for circular (solid, blue), 10%-D-shaped (dashed, red) and octagonal (dotted, black) inner cladding at (a) area ratio 2 and (b) area ratio 3.
Fig. 7
Fig. 7 Effective length vs. signal output power for circular (solid, blue), 10%-D-shaped (dashed, red) and octagonal (dotted, black) inner cladding at area ratio 2 and 3.
Fig. 8
Fig. 8 Power evolution for fibers with area ratio of 2 selected from Fig. 4 (solid, black); with core and cladding diameters which are twice as large (dashed, red). The pump and signal powers for the larger-diameter case are scaled to yield the same power density as for the smaller default diameters.
Fig. 9
Fig. 9 Power fraction of fundamental mode for different signal seed profiles, but with same total seed power. Solid line: mixture of modes LP01 and LP11 where the phase difference of LP01 and LP11 is zero and where 5% of the power is in LP11; Dashed line: mixture of modes LP01 and all other guided modes where the phases of LP01 and high-order-mode are random and where a total of 10% of the power is in all HOMs with equal power.
Fig. 10
Fig. 10 Fiber cross-section and symbol definitions.
Fig. 11
Fig. 11 (a) Fiber cross-section where shaded area represents fraction of power with non-zero overlap with core. (b) Fraction of power with zero overlap with core p0 vs. relative core radius a.
Fig. 12
Fig. 12 Distribution of power f(b) (a, left) and cumulative distribution of power F(b) (b, right) vs. overlap b for relative core radius a = 0.2, 0.4, 0.6, and 0.8.
Fig. 13
Fig. 13 Power evolution for a = 0.2, 0.4, 0.6, 0.8, and 1, in log scale.

Tables (3)

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Table 1 Fiber and Simulation Parameters used in this paper unless otherwise stated

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Table 2 Summary of Key Results.

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Table 3 Overlap, Effective Index, and Output Power in Different Modes for Different Area Ratios for Circularly Symmetric Fibers.

Equations (15)

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G dB = 4.343 Γ N 0 L [ ( σ e + σ a ) n 2 σ a ] ,
L = G dB s ( σ a p + σ e p ) + r A Γ α dB op ( σ a s + σ e s ) 4.343 N 0 ( σ a p σ e s σ e p σ a s ) ,
L L 1 = r A Γ 1 1 + G dB s / ( σ a s + σ e s ) α dB op ( σ a p + σ e p ) + 1 ,
L L 1 = r A Γ 1 20.51 + 1 ,
L eff = 0 L P ( z ) d z P ( L ) ,
L = 2 ( 1 x 2 ) 1 / 2 .
b = ( a 2 x 2 ) 1 / 2 / ( 1 x 2 ) 1 / 2 x < a b = 0 x > a .
p 0 = 1 ( 2 / π ) [ a ( 1 a 2 ) 1 / 2 + arcsin a ] ,
x = ( a 2 b 2 ) 1 / 2 / ( 1 b 2 ) 1 / 2 b < a .
f 1 ( b ) = h ( b ) d x / d b = [ ( 1 a 2 ) / ( 1 b 2 ) ] 1 / 2 b ( 1 a 2 ) ( 1 b 2 ) 3 / 2 ( a 2 b 2 ) 1 / 2 = b ( 1 a 2 ) 3 / 2 ( 1 b 2 ) 2 ( a 2 b 2 ) 1 / 2 b < a ,
f ( b ) = ( 1 p 0 ) f 1 ( b ) / I 1 ,
I 1 = [ a ( 1 a 2 ) 1 / 2 + arcsin a ] / 2 .
f ( b ) = [ 1 ( 2 / π ) ( a ( 1 a 2 ) 1 / 2 + arcsin a ) ] δ ( b ) + ( 4 b / π ) ( 1 a 2 ) 3 / 2 ( 1 b 2 ) 2 ( a 2 b 2 ) 1 / 2 b < a ,
F ( b ) = 0 1 f ( b ) d b .
p ( z ) = 0 1 f ( b ) e b z db .