Abstract

Absorption of an incoherent pump in a double-clad fiber amplifier is analyzed in the paraxial wave approximation. Different inner cladding shapes are considered. A small spiral distortion of an otherwise circular inner cladding shape is shown to enhance the coupling efficiency significantly relative to other geometries.

© 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, “110W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
    [CrossRef]
  3. V. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, “High-power 1.48 μm phosphoro-silicate-fiber-based laser pumped by laser diodes,” Can. J. Phys. 78, 407–413 (2000).
    [CrossRef]
  4. 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]
  5. 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]
  6. M. A. Mahdi, S. Thirumeni, P. Poopalan, S. Selvakennedy, F. R. M. Adikan, W. Y. Chan, and H. Ahmad, “Effects of self-saturation in an erbium-doped fiber amplifier,” Opt. Fiber Technol. Mater., Devices Syst. 6, 265–274 (2000).
    [CrossRef]
  7. S. Bedö, W. Lüthy, and H. P. Weber, “The effective absorption coefficient in double-clad fibers,” Opt. Commun. 99, 331–335 (1993).
    [CrossRef]
  8. A. Liu and K. Ueda, “The absorption characteristics of circular, offset, and rectangular double-clad fibers,” Opt. Commun. 132, 511–518 (1996).
    [CrossRef]
  9. D. Kouznetsov, J. V. Moloney, and E. M. Wright, “Efficiency of pump absorption in double-clad amplifiers. I. Fiber with circular symmetry,” J. Opt. Soc. Am. B 18, 743–749 (2001).
    [CrossRef]
  10. V. Doya, O. Legrand, and F. Mortessagne, “Optimized absorption in a chaotic double-clad fiber amplifier,” Opt. Lett. 26, 872–874 (2001).
    [CrossRef]
  11. V. Doya, “Du SPECKLE au SCARS: une expérience de chaos ondulatoire dans une fibre optique,” Ph.D. Thesis (École Doctorale, Sciences et Technologies de l’Information et de la Communication, Université de Nice-Sophia Antipolis, France, December 12, 2000).
  12. A. Newell, J. V. Moloney, Nonlinear Optics (Addison-Wesley, New York, 1992).
  13. J. D. Jackson, “Boundary values problems in electrostatics,” in Classical Electrodynamics (Wiley, New York, 1999), p. 57.
  14. D. Kouznetsov and J. V. Moloney, “Efficiency of pump absorption in double-clad amplifiers. III. Calculation of modes,” J. Opt. Soc. Am. B 19, 1304–1309 (2002).
    [CrossRef]

2002 (1)

2001 (2)

2000 (4)

V. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, “High-power 1.48 μm phosphoro-silicate-fiber-based laser pumped by laser diodes,” Can. J. Phys. 78, 407–413 (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]

M. A. Mahdi, S. Thirumeni, P. Poopalan, S. Selvakennedy, F. R. M. Adikan, W. Y. Chan, and H. Ahmad, “Effects of self-saturation in an erbium-doped fiber amplifier,” Opt. Fiber Technol. Mater., Devices Syst. 6, 265–274 (2000).
[CrossRef]

1999 (1)

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

1998 (1)

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

1996 (1)

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

1993 (1)

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

Adikan, F. R. M.

M. A. Mahdi, S. Thirumeni, P. Poopalan, S. Selvakennedy, F. R. M. Adikan, W. Y. Chan, and H. Ahmad, “Effects of self-saturation in an erbium-doped fiber amplifier,” Opt. Fiber Technol. Mater., Devices Syst. 6, 265–274 (2000).
[CrossRef]

Ahmad, H.

M. A. Mahdi, S. Thirumeni, P. Poopalan, S. Selvakennedy, F. R. M. Adikan, W. Y. Chan, and H. Ahmad, “Effects of self-saturation in an erbium-doped fiber amplifier,” Opt. Fiber Technol. Mater., Devices Syst. 6, 265–274 (2000).
[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]

Bicknese, S.

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

Chan, W. Y.

M. A. Mahdi, S. Thirumeni, P. Poopalan, S. Selvakennedy, F. R. M. Adikan, W. Y. Chan, and H. Ahmad, “Effects of self-saturation in an erbium-doped fiber amplifier,” Opt. Fiber Technol. Mater., Devices Syst. 6, 265–274 (2000).
[CrossRef]

Clements, W. R. L.

V. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, “High-power 1.48 μm phosphoro-silicate-fiber-based laser pumped by laser diodes,” Can. J. Phys. 78, 407–413 (2000).
[CrossRef]

Dianov, E. M.

V. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, “High-power 1.48 μm phosphoro-silicate-fiber-based laser pumped by laser diodes,” Can. J. Phys. 78, 407–413 (2000).
[CrossRef]

Dohle, R.

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

Doya, V.

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]

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]

Karpov, V.

V. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, “High-power 1.48 μm phosphoro-silicate-fiber-based laser pumped by laser diodes,” Can. J. Phys. 78, 407–413 (2000).
[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.

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]

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]

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, “110W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Mahdi, M. A.

M. A. Mahdi, S. Thirumeni, P. Poopalan, S. Selvakennedy, F. R. M. Adikan, W. Y. Chan, and H. Ahmad, “Effects of self-saturation in an erbium-doped fiber amplifier,” Opt. Fiber Technol. Mater., Devices Syst. 6, 265–274 (2000).
[CrossRef]

Moloney, J. V.

Mortessagne, F.

Papernyi, S. B.

V. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, “High-power 1.48 μm phosphoro-silicate-fiber-based laser pumped by laser diodes,” Can. J. Phys. 78, 407–413 (2000).
[CrossRef]

Poopalan, P.

M. A. Mahdi, S. Thirumeni, P. Poopalan, S. Selvakennedy, F. R. M. Adikan, W. Y. Chan, and H. Ahmad, “Effects of self-saturation in an erbium-doped fiber amplifier,” Opt. Fiber Technol. Mater., Devices Syst. 6, 265–274 (2000).
[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]

Sanders, S.

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

Selvakennedy, S.

M. A. Mahdi, S. Thirumeni, P. Poopalan, S. Selvakennedy, F. R. M. Adikan, W. Y. Chan, and H. Ahmad, “Effects of self-saturation in an erbium-doped fiber amplifier,” Opt. Fiber Technol. Mater., Devices Syst. 6, 265–274 (2000).
[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]

Thirumeni, S.

M. A. Mahdi, S. Thirumeni, P. Poopalan, S. Selvakennedy, F. R. M. Adikan, W. Y. Chan, and H. Ahmad, “Effects of self-saturation in an erbium-doped fiber amplifier,” Opt. Fiber Technol. Mater., Devices Syst. 6, 265–274 (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, “110W 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, “110W fiber laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Wright, E. M.

Yeh, P. S.

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

Zuker, E.

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

Can. J. Phys. (1)

V. Karpov, W. R. L. Clements, E. M. Dianov, and S. B. Papernyi, “High-power 1.48 μm phosphoro-silicate-fiber-based laser pumped by laser diodes,” Can. J. Phys. 78, 407–413 (2000).
[CrossRef]

Electron. Lett. (1)

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

J. Opt. Soc. Am. B (2)

Laser Phys. (1)

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

Opt. Commun. (3)

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

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]

Opt. Eng. (1)

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. Mater., Devices Syst. (1)

M. A. Mahdi, S. Thirumeni, P. Poopalan, S. Selvakennedy, F. R. M. Adikan, W. Y. Chan, and H. Ahmad, “Effects of self-saturation in an erbium-doped fiber amplifier,” Opt. Fiber Technol. Mater., Devices Syst. 6, 265–274 (2000).
[CrossRef]

Opt. Lett. (1)

Other (3)

V. Doya, “Du SPECKLE au SCARS: une expérience de chaos ondulatoire dans une fibre optique,” Ph.D. Thesis (École Doctorale, Sciences et Technologies de l’Information et de la Communication, Université de Nice-Sophia Antipolis, France, December 12, 2000).

A. Newell, J. V. Moloney, Nonlinear Optics (Addison-Wesley, New York, 1992).

J. D. Jackson, “Boundary values problems in electrostatics,” in Classical Electrodynamics (Wiley, New York, 1999), p. 57.

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Figures (4)

Fig. 1
Fig. 1

Radial modes of a circular fiber in the absence of the core; (a) J1(3.831706ρ/R) and (b) J1(22.76008ρ/R). The solid curves depict the physically relevant inner cladding modes. Their extension (GI) outside of the cladding is depicted by the dotted curves and their AI [Eq. (5)] by the dashed curves.

Fig. 2
Fig. 2

Scheme of construction of the approximate image field EAI(X, Y) for a smooth boundary of a nonsymmetrical inner cladding.

Fig. 3
Fig. 3

(a) Efficiency η of absorption of the pump light in the core versus Z=K0z. Upper dashed curve, case of ideal mixing [estimate by Eq. (9)]; dotted curve, simulation of spiral cladding with displaced core; intermediate dashed curve, the analytical estimate by formula (10); upper solid curve, numerical simulation for the same case; vertical bars, simulation for the starlike cross section; circles, simulation for spiral cladding with centered core; lowest solid curve, simulation for circular-symmetric case; lowest dashed curve, analytical estimation for the same case according to Eq. (11). (b) Efficiency of absorption of the pump light in the core of the offset-spiral double-clad fiber at K0=0.005 µ-1, bars; 0.01 µ-1, dots; 0.02 µ-1 small circles; 0.04 µ-1, large circles; versus dimensionless Z.

Fig. 4
Fig. 4

Final distributions of amplitude of the field E after propagation of distance such that K0z=40. (a) Spiral cladding, offset core; (b) Circular cladding with offset core; (c) Cladding with the starlike cross section according to Eq. (7); (d) Spiral cladding, centered core; (e) Circular cladding, centered core; (f) Smoothed square cladding according to Eq. (8), centered core.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E˙=i2kΔE-ikνE-KE,
E(R(ϕ), ϕ)=0,
RR-(CX+SY)R+(SX-CY)R=0.
EAI=-E(X1, Y1)[1-(R-ρ)2/ρ02]θ(R+ρ0-ρ),
EAI=-E(X, Y)Wθ(W),
R(ϕ)=R0+α0ϕ,|ϕ|β0,R0+α0 sgn (ϕ)π+β0π-β0(π-|ϕ|)-π(π-β0)2(π-|ϕ|)2,|ϕ|β0;
starlikestructureR(ϕ)=R0+α0 cos 6ϕ;
squarelikestructureR(ϕ)=R0-α0 cos 4ϕ.
ηideal=1-exp-2K0r0R02z,
η=2πr0+|x0|R1-r0+|x0|R21/2+arcsinr0+|x0|R1-exp-2K0r0R02z
η=4r0πR01-exp-K0πr02R0z,

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