Abstract

Using an analogy with quantum mechanics we employ a technique that enables us to calculate the efficiency of an incoherent pump in general-geometry double-clad fibers. This approach yields accurate estimates of the absorption rate of each mode of the pump in the first order of perturbation theory. Such estimates are compared with results of numerical simulations reported recently. The comparison confirms the high efficiency of a spiral-shaped cladding.

© 2002 Optical Society of America

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References

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  1. K. Ueda and A. Liu, “Future of high-power fiber lasers,” Laser Phys. 8, 774–781 (1998).
  2. V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
    [CrossRef]
  3. N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
    [CrossRef]
  4. C. K. Liu, F. S. Lai, and J. J. Jou, “Analysis of nonlinear response in erbium-doped fiber amplifiers,” Opt. Eng. 39, 1548–1555 (2000).
    [CrossRef]
  5. T. Ohtsuki, S. Honkanen, S. I. Najafi, and N. Peyghambarin, “Cooperative upconversion effects on the performance of the Er3+-doped phosphate glass waveguide amplifiers,” J. Opt. Soc. Am. B 14, 1838–1845 (1997).
    [CrossRef]
  6. A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Opt. Commun. 132, 511–518 (1996).
    [CrossRef]
  7. P. Leproux, S. Février, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6/7, 324–339 (2001).
    [CrossRef]
  8. C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
    [CrossRef]
  9. S. Bedö, W. Lüthy, and H. P. Weber, “The effective absorption coefficient in double-clad fibers,” Opt. Commun. 99, 331–335 (1993).
    [CrossRef]
  10. D. Kouznetsov, J. V. Moloney, and E. M. Wright, “Efficiency of pump absorption in double-clad fiber amplifiers. I. Fiber with circular symmetry,” J. Opt. Soc. Am. B 18, 743–749 (2001).
    [CrossRef]
  11. D. Kouznetsov and J. V. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers. II. Broken circular symmetry,” J. Opt. Soc. Am. B 19, 1259–1263 (2002).
    [CrossRef]
  12. V. Doya, O. Legrand, and F. Mortessagne, “Optimized absorption in a chaotic double-clad fiber amplifier,” Opt. Lett. 26, 872–874 (2001).
    [CrossRef]
  13. Y. C. Yan, A. J. Faber, H. de Waal, P. G. Kik, and A. Polman, “Erbium-doped phosphate glass waveguide on silicon with 4.1 dB/cm gain at 1.535 μm,” Appl. Phys. Lett. 71, 2922–2924 (1997).
    [CrossRef]
  14. Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
    [CrossRef]
  15. S. L. Lin, L. W. Li, T. S. Yeo, and M. S. Leong, “QZ factorization for generalized eigenvalues applied to waveguide analysis,” Microwave Opt. Technol. Lett. 28, 361–364 (2001).
    [CrossRef]
  16. A.-S. Bonnet-Bendhia and N. Gmati, “Spectral approximation of a boundary condition for an eigenvalue problem,” SIAM J. Numer. Anal. 32, 1263–1279 (1995).
    [CrossRef]

2002

2001

V. Doya, O. Legrand, and F. Mortessagne, “Optimized absorption in a chaotic double-clad fiber amplifier,” Opt. Lett. 26, 872–874 (2001).
[CrossRef]

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

S. L. Lin, L. W. Li, T. S. Yeo, and M. S. Leong, “QZ factorization for generalized eigenvalues applied to waveguide analysis,” Microwave Opt. Technol. Lett. 28, 361–364 (2001).
[CrossRef]

D. Kouznetsov, J. V. Moloney, and E. M. Wright, “Efficiency of pump absorption in double-clad fiber amplifiers. I. Fiber with circular symmetry,” J. Opt. Soc. Am. B 18, 743–749 (2001).
[CrossRef]

P. Leproux, S. Février, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6/7, 324–339 (2001).
[CrossRef]

2000

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
[CrossRef]

C. K. Liu, F. S. Lai, and J. J. Jou, “Analysis of nonlinear response in erbium-doped fiber amplifiers,” Opt. Eng. 39, 1548–1555 (2000).
[CrossRef]

1999

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

1998

K. Ueda and A. Liu, “Future of high-power fiber lasers,” Laser Phys. 8, 774–781 (1998).

1997

T. Ohtsuki, S. Honkanen, S. I. Najafi, and N. Peyghambarin, “Cooperative upconversion effects on the performance of the Er3+-doped phosphate glass waveguide amplifiers,” J. Opt. Soc. Am. B 14, 1838–1845 (1997).
[CrossRef]

Y. C. Yan, A. J. Faber, H. de Waal, P. G. Kik, and A. Polman, “Erbium-doped phosphate glass waveguide on silicon with 4.1 dB/cm gain at 1.535 μm,” Appl. Phys. Lett. 71, 2922–2924 (1997).
[CrossRef]

1996

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

1995

A.-S. Bonnet-Bendhia and N. Gmati, “Spectral approximation of a boundary condition for an eigenvalue problem,” SIAM J. Numer. Anal. 32, 1263–1279 (1995).
[CrossRef]

1993

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

Bedö, S.

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

Bhutta, T.

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

Bicknese, S.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Bonner, C. L.

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

Bonnet-Bendhia, A.-S.

A.-S. Bonnet-Bendhia and N. Gmati, “Spectral approximation of a boundary condition for an eigenvalue problem,” SIAM J. Numer. Anal. 32, 1263–1279 (1995).
[CrossRef]

de Waal, H.

Y. C. Yan, A. J. Faber, H. de Waal, P. G. Kik, and A. Polman, “Erbium-doped phosphate glass waveguide on silicon with 4.1 dB/cm gain at 1.535 μm,” Appl. Phys. Lett. 71, 2922–2924 (1997).
[CrossRef]

Dohle, R.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Dominic, V.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Doya, V.

P. Leproux, S. Février, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6/7, 324–339 (2001).
[CrossRef]

V. Doya, O. Legrand, and F. Mortessagne, “Optimized absorption in a chaotic double-clad fiber amplifier,” Opt. Lett. 26, 872–874 (2001).
[CrossRef]

Faber, A. J.

Y. C. Yan, A. J. Faber, H. de Waal, P. G. Kik, and A. Polman, “Erbium-doped phosphate glass waveguide on silicon with 4.1 dB/cm gain at 1.535 μm,” Appl. Phys. Lett. 71, 2922–2924 (1997).
[CrossRef]

Février, S.

P. Leproux, S. Février, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6/7, 324–339 (2001).
[CrossRef]

Gmati, N.

A.-S. Bonnet-Bendhia and N. Gmati, “Spectral approximation of a boundary condition for an eigenvalue problem,” SIAM J. Numer. Anal. 32, 1263–1279 (1995).
[CrossRef]

Hamada, T.

N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
[CrossRef]

Honkanen, S.

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

T. Ohtsuki, S. Honkanen, S. I. Najafi, and N. Peyghambarin, “Cooperative upconversion effects on the performance of the Er3+-doped phosphate glass waveguide amplifiers,” J. Opt. Soc. Am. B 14, 1838–1845 (1997).
[CrossRef]

Hu, Y.

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

Jiang, S.

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

Jou, J. J.

C. K. Liu, F. S. Lai, and J. J. Jou, “Analysis of nonlinear response in erbium-doped fiber amplifiers,” Opt. Eng. 39, 1548–1555 (2000).
[CrossRef]

Kik, P. G.

Y. C. Yan, A. J. Faber, H. de Waal, P. G. Kik, and A. Polman, “Erbium-doped phosphate glass waveguide on silicon with 4.1 dB/cm gain at 1.535 μm,” Appl. Phys. Lett. 71, 2922–2924 (1997).
[CrossRef]

Kim, N. S.

N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
[CrossRef]

Kong, H. J.

N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
[CrossRef]

Kouznetsov, D.

Lai, F. S.

C. K. Liu, F. S. Lai, and J. J. Jou, “Analysis of nonlinear response in erbium-doped fiber amplifiers,” Opt. Eng. 39, 1548–1555 (2000).
[CrossRef]

Legrand, O.

Leong, M. S.

S. L. Lin, L. W. Li, T. S. Yeo, and M. S. Leong, “QZ factorization for generalized eigenvalues applied to waveguide analysis,” Microwave Opt. Technol. Lett. 28, 361–364 (2001).
[CrossRef]

Leproux, P.

P. Leproux, S. Février, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6/7, 324–339 (2001).
[CrossRef]

Li, C.

N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
[CrossRef]

Li, L. W.

S. L. Lin, L. W. Li, T. S. Yeo, and M. S. Leong, “QZ factorization for generalized eigenvalues applied to waveguide analysis,” Microwave Opt. Technol. Lett. 28, 361–364 (2001).
[CrossRef]

Lin, S. L.

S. L. Lin, L. W. Li, T. S. Yeo, and M. S. Leong, “QZ factorization for generalized eigenvalues applied to waveguide analysis,” Microwave Opt. Technol. Lett. 28, 361–364 (2001).
[CrossRef]

Liu, A.

K. Ueda and A. Liu, “Future of high-power fiber lasers,” Laser Phys. 8, 774–781 (1998).

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

Liu, A. P.

N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
[CrossRef]

Liu, C. K.

C. K. Liu, F. S. Lai, and J. J. Jou, “Analysis of nonlinear response in erbium-doped fiber amplifiers,” Opt. Eng. 39, 1548–1555 (2000).
[CrossRef]

Lucas, J.

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

Luo, T.

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

Lüthy, W.

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

MacCormack, S.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Moloney, J. V.

Morell, M.

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

Mortessagne, F.

Najafi, S. I.

Ohtsuki, T.

Pagnoux, D.

P. Leproux, S. Février, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6/7, 324–339 (2001).
[CrossRef]

Peyghambarian, N.

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

Peyghambarin, N.

Polman, A.

Y. C. Yan, A. J. Faber, H. de Waal, P. G. Kik, and A. Polman, “Erbium-doped phosphate glass waveguide on silicon with 4.1 dB/cm gain at 1.535 μm,” Appl. Phys. Lett. 71, 2922–2924 (1997).
[CrossRef]

Prabhu, M.

N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
[CrossRef]

Roy, P.

P. Leproux, S. Février, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6/7, 324–339 (2001).
[CrossRef]

Sanders, S.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Seneshal, K.

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

Shepherd, D. P.

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

Smektala, F.

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

Song, J.

N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
[CrossRef]

Tropper, A. C.

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

Ueda, K.

N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
[CrossRef]

K. Ueda and A. Liu, “Future of high-power fiber lasers,” Laser Phys. 8, 774–781 (1998).

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

Waarts, R.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Weber, H. P.

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

Wolak, E.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Wright, E. M.

Yan, Y. C.

Y. C. Yan, A. J. Faber, H. de Waal, P. G. Kik, and A. Polman, “Erbium-doped phosphate glass waveguide on silicon with 4.1 dB/cm gain at 1.535 μm,” Appl. Phys. Lett. 71, 2922–2924 (1997).
[CrossRef]

Yeh, P. S.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Yeo, T. S.

S. L. Lin, L. W. Li, T. S. Yeo, and M. S. Leong, “QZ factorization for generalized eigenvalues applied to waveguide analysis,” Microwave Opt. Technol. Lett. 28, 361–364 (2001).
[CrossRef]

Zuker, E.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Appl. Phys. Lett.

Y. C. Yan, A. J. Faber, H. de Waal, P. G. Kik, and A. Polman, “Erbium-doped phosphate glass waveguide on silicon with 4.1 dB/cm gain at 1.535 μm,” Appl. Phys. Lett. 71, 2922–2924 (1997).
[CrossRef]

Electron. Lett.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zuker, “110 W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

IEEE J. Quantum Electron.

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

IEEE Photonics Technol. Lett.

Y. Hu, S. Jiang, T. Luo, K. Seneshal, M. Morell, F. Smektala, S. Honkanen, J. Lucas, and N. Peyghambarian, “Performance of high-concentration Er3+-Yb3+-codoped phosphate fiber amplifiers,” IEEE Photonics Technol. Lett. 13, 657–659 (2001).
[CrossRef]

J. Opt. Soc. Am. B

Laser Phys.

K. Ueda and A. Liu, “Future of high-power fiber lasers,” Laser Phys. 8, 774–781 (1998).

Microwave Opt. Technol. Lett.

S. L. Lin, L. W. Li, T. S. Yeo, and M. S. Leong, “QZ factorization for generalized eigenvalues applied to waveguide analysis,” Microwave Opt. Technol. Lett. 28, 361–364 (2001).
[CrossRef]

Opt. Commun.

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

N. S. Kim, T. Hamada, M. Prabhu, C. Li, J. Song, K. Ueda, A. P. Liu, and H. J. Kong, “Numerical analysis and experimental results of output performance for Nd-doped double-clad fiber lasers,” Opt. Commun. 180, 329–337 (2000).
[CrossRef]

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

Opt. Eng.

C. K. Liu, F. S. Lai, and J. J. Jou, “Analysis of nonlinear response in erbium-doped fiber amplifiers,” Opt. Eng. 39, 1548–1555 (2000).
[CrossRef]

Opt. Fiber Technol.

P. Leproux, S. Février, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of pump,” Opt. Fiber Technol. 6/7, 324–339 (2001).
[CrossRef]

Opt. Lett.

SIAM J. Numer. Anal.

A.-S. Bonnet-Bendhia and N. Gmati, “Spectral approximation of a boundary condition for an eigenvalue problem,” SIAM J. Numer. Anal. 32, 1263–1279 (1995).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Eigenvalues versus number of eigenfunctions for the circular double-clad fiber, estimated with kmax=1 µm-1, 195 basis functions, large circles; kmax=1.5 µm-1, 447 basis functions, medium circles; kmax=2 µm-1, 803 basis functions, small circles; kmax=3 µm-1, 1830 basis functions, dots. The solid line represents the estimate En=(kR0)2n.

Fig. 2
Fig. 2

Efficiency η versus dimensionless length of propagation Z=K0z. The lower group of curves corresponds to the fiber with circular symmetry; dashed curve, estimate on basis of geometric optics10,11; vertical bars, AI simulation11; solid curves, calculations based on first order perturbation theory with respect to K0 by Eq. (11) with J=300 (lowest), J=200 (intermediate), J=100 (highest). The same conditions as in Fig. 1, i.e., 1830 basis functions, were used to diagonalize the Hamiltonian. The upper group of curves corresponds to the fiber with spiral cladding by Eq. (22) and offset core; dashed curve, case of ideal mixing of pump,10,11 η=1-exp[-2K0(r0/R0)2z]; vertical bars, AI simulation.11 Two solid curves represent the first order perturbation theory calculations showing the first 150 modes (upper) and first 300 modes (lower).

Fig. 3
Fig. 3

Distribution of amplitude of modes of spiral fiber with offset core. Modes 1–5, 51–55, 101–105, 151–155 are shown top row to bottom row. Dashed outlines indicate the core and the cladding.

Equations (26)

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curl E=-1c H˙,
curl H=c E˙+4πσE,
-2E=-c2 E¨+4πσc E˙.
-2E=μc2ω2E+4πcσ(-iω)E,
f=12ik[-Δ+(k2-k02)]f-2πσk0kf,
Δ=2x2+2y2,f=(x, y, z)/z.
H=-Δ+U,
f=12ikHf-Kf.
f=nCnψn exp12ik Enz,
Cm(z)=-nKm,n expi2k(Em-En)zCn,
Km,n=dxdyKψmψn.
Cm=-Km,mCm.
Cm(z)=exp(-Km,mz)Cm(0).
η=1-1Lm=1L exp(-2Km,mz).
Fj(x, y)=2(AB)1/2sinπmxAsinπnyB,
Fj1|-Δ|Fj2=δj1,j2πAm2+πBn2.
Uj1,j2=Fj1|U|Fj2=1MNdμdνcosπ(m1-m2)μM-cosπ(m1+m2)μM×cosπ(n1-n2)νN-cosπ(n1+n2)νMUAμM,BνN.
Uj1,j21MN(Um1-m2,n1-n2-Um1-m2,n1+n2-Um1+m2,n1-n2+Um1+m2,n1+n2),
Um,n=μ,ν cosπmμMcosπnνNUAμM,BνN.
Ha,b=Fa|H|Fb.
(SHS)a,b=Ebδa,b,SS=1.
m2,n2Hjm1,n1,jm2,n2Sjm2,n2,b=EbSjm1,n1,b.
ψbAμM,BνN=m,n sinπmμMsinπnνNSjm,n,b.
U=U11+exp[(ρ-r0)/dx]+U31+exp[(R0-ρ)/dx].
Ej=4j/(kR0)2,
R(ϕ)=R0+α0ϕ,|ϕ|β0R0+α0 sin ϕπ+β0π-β0(π-|ϕ|)-π(π-β0)2(π-|ϕ|)2,|ϕ|β0,

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