Abstract

A model based on propagation-rate equations with consideration of transverse gain distribution is built up to describe the transverse mode competition in strongly pumped multimode fiber lasers and amplifiers. An approximate practical numerical algorithm by multilayer method is presented. Based on the model and the numerical algorithm, the behaviors of multitransverse mode competition are demonstrated and individual transverse modes power distributions of output are simulated numerically for both fiber lasers and amplifiers under various conditions.

© 2007 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 kWcontinuous-wave output power," Opt. Express 12,6088-6092 (2004).
    [CrossRef] [PubMed]
  2. G.  Bonati, H.  Voelckel, T.  Gabler, U.  Krause, A.  Tünnermann, J.  Limpert, A.  Liem, T.  Schreiber, S.  Nolte, and H.  Zellmer, "1.53 kW from a single Yb-doped photonic crystal fiber laser," Photonics West, San Jose, Late Breaking Developments, Session 5709-2a (2005).
  3. J. Limpert, S. Höfer, A. Liem, H. Zellmer, A. Tünnermann, S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier," Appl. Phys. B: Lasers & Optics 75, 477-479 (2002).
    [CrossRef]
  4. J. P.  Koplow, D. A. V.  Kliner, and L. Goldberg, "Single-mode operation of a coiled multimode fiber amplifier," Opt. Lett.  25, 442-444 (2000).
    [CrossRef]
  5. M. D. Nielsen, N. A. Mortensen, M. Albersen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibers," Opt. Express 12, 1775 (2004)
    [CrossRef] [PubMed]
  6. A. Hardy and R. Oron, "Signal amplification in strongly pumped fiber amplifiers," IEEE J. Quantum Electron. 33, 307-313 (1997).
    [CrossRef]
  7. I. Kelson and A. A. Hardy, "Strongly pumped fiber lasers," IEEE J. Quantum Electron. 34, 1570-1577(1998).
    [CrossRef]
  8. J. Limpert, H. Zellmer, and A.  Tünnermann, "Suppression of high order modes in a multimode fiber amplifier using efficient gain-loss-management (GLM)," in Advanced Solid-State Lasers, Québec City, Canada, paper MB20, 112-114, 2002.
  9. M. Hotoleanu, M. Söderlund, D. Kliner, J. Koplow, S. Tammela, and V. Philipov, "High order modes suppression in large mode area active fibers by controlling the radial distribution of the rare earth dopant," In Fiber Lasers III, A.J.W. Brow, J. Nilsson, D. J. Harter, A. Tünnermann, eds., Proc. SPIE 6102, 61021T1-61021T8 (2006).
  10. T. Bhutta, J. I. Mackenzie, D. P. Shepherd, and R. J. Beach, "Spatial dopant profiles for transverse-mode selection in multimode waveguides," J. Opt. Soc. Am. B,  19, 1539-1543 (2002).
    [CrossRef]
  11. A. Galvanauskas, "Mode-Scalable Fiber-Based Chirped Pulse Amplification Systems," IEEE J. Sel. Top. Quantum Electron. 7,504-517 (2001).
    [CrossRef]
  12. R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
    [CrossRef]
  13. D. Marcuse, "Curvature loss formula for optical fibers," J. Opt. Soc. Am. 66,216-220 (1976).
    [CrossRef]

2004

2002

J. Limpert, S. Höfer, A. Liem, H. Zellmer, A. Tünnermann, S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier," Appl. Phys. B: Lasers & Optics 75, 477-479 (2002).
[CrossRef]

T. Bhutta, J. I. Mackenzie, D. P. Shepherd, and R. J. Beach, "Spatial dopant profiles for transverse-mode selection in multimode waveguides," J. Opt. Soc. Am. B,  19, 1539-1543 (2002).
[CrossRef]

2001

A. Galvanauskas, "Mode-Scalable Fiber-Based Chirped Pulse Amplification Systems," IEEE J. Sel. Top. Quantum Electron. 7,504-517 (2001).
[CrossRef]

2000

1998

I. Kelson and A. A. Hardy, "Strongly pumped fiber lasers," IEEE J. Quantum Electron. 34, 1570-1577(1998).
[CrossRef]

1997

A. Hardy and R. Oron, "Signal amplification in strongly pumped fiber amplifiers," IEEE J. Quantum Electron. 33, 307-313 (1997).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

1976

Albersen, M.

Beach, R. J.

Bhutta, T.

Bjarklev, A.

Bonacinni, D.

Folkenberg, J. R.

Galvanauskas, A.

A. Galvanauskas, "Mode-Scalable Fiber-Based Chirped Pulse Amplification Systems," IEEE J. Sel. Top. Quantum Electron. 7,504-517 (2001).
[CrossRef]

Goldberg, L.

Hanna, D. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Hardy, A.

A. Hardy and R. Oron, "Signal amplification in strongly pumped fiber amplifiers," IEEE J. Quantum Electron. 33, 307-313 (1997).
[CrossRef]

Hardy, A. A.

I. Kelson and A. A. Hardy, "Strongly pumped fiber lasers," IEEE J. Quantum Electron. 34, 1570-1577(1998).
[CrossRef]

Höfer, S.

J. Limpert, S. Höfer, A. Liem, H. Zellmer, A. Tünnermann, S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier," Appl. Phys. B: Lasers & Optics 75, 477-479 (2002).
[CrossRef]

Jeong, Y.

Kelson, I.

I. Kelson and A. A. Hardy, "Strongly pumped fiber lasers," IEEE J. Quantum Electron. 34, 1570-1577(1998).
[CrossRef]

Kliner, D. A. V.

Knoke, S.

J. Limpert, S. Höfer, A. Liem, H. Zellmer, A. Tünnermann, S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier," Appl. Phys. B: Lasers & Optics 75, 477-479 (2002).
[CrossRef]

Koplow, J. P.

Liem, A.

J. Limpert, S. Höfer, A. Liem, H. Zellmer, A. Tünnermann, S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier," Appl. Phys. B: Lasers & Optics 75, 477-479 (2002).
[CrossRef]

Limpert, J.

J. Limpert, S. Höfer, A. Liem, H. Zellmer, A. Tünnermann, S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier," Appl. Phys. B: Lasers & Optics 75, 477-479 (2002).
[CrossRef]

Mackenzie, J. I.

Marcuse, D.

Mortensen, N. A.

Nielsen, M. D.

Nilsson, J.

Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, "Ytterbium-doped large-core fiber laser with 1.36 kWcontinuous-wave output power," Opt. Express 12,6088-6092 (2004).
[CrossRef] [PubMed]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Oron, R.

A. Hardy and R. Oron, "Signal amplification in strongly pumped fiber amplifiers," IEEE J. Quantum Electron. 33, 307-313 (1997).
[CrossRef]

Paschotta, R.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Payne, D. N.

Sahu, J. K.

Shepherd, D. P.

Tropper, A. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Tünnermann, A.

J. Limpert, S. Höfer, A. Liem, H. Zellmer, A. Tünnermann, S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier," Appl. Phys. B: Lasers & Optics 75, 477-479 (2002).
[CrossRef]

Voelckel, H.

J. Limpert, S. Höfer, A. Liem, H. Zellmer, A. Tünnermann, S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier," Appl. Phys. B: Lasers & Optics 75, 477-479 (2002).
[CrossRef]

Zellmer, H.

J. Limpert, S. Höfer, A. Liem, H. Zellmer, A. Tünnermann, S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier," Appl. Phys. B: Lasers & Optics 75, 477-479 (2002).
[CrossRef]

Appl. Phys. B: Lasers & Optics

J. Limpert, S. Höfer, A. Liem, H. Zellmer, A. Tünnermann, S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier," Appl. Phys. B: Lasers & Optics 75, 477-479 (2002).
[CrossRef]

IEEE J. Quantum Electron.

A. Hardy and R. Oron, "Signal amplification in strongly pumped fiber amplifiers," IEEE J. Quantum Electron. 33, 307-313 (1997).
[CrossRef]

I. Kelson and A. A. Hardy, "Strongly pumped fiber lasers," IEEE J. Quantum Electron. 34, 1570-1577(1998).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

A. Galvanauskas, "Mode-Scalable Fiber-Based Chirped Pulse Amplification Systems," IEEE J. Sel. Top. Quantum Electron. 7,504-517 (2001).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Other

G.  Bonati, H.  Voelckel, T.  Gabler, U.  Krause, A.  Tünnermann, J.  Limpert, A.  Liem, T.  Schreiber, S.  Nolte, and H.  Zellmer, "1.53 kW from a single Yb-doped photonic crystal fiber laser," Photonics West, San Jose, Late Breaking Developments, Session 5709-2a (2005).

J. Limpert, H. Zellmer, and A.  Tünnermann, "Suppression of high order modes in a multimode fiber amplifier using efficient gain-loss-management (GLM)," in Advanced Solid-State Lasers, Québec City, Canada, paper MB20, 112-114, 2002.

M. Hotoleanu, M. Söderlund, D. Kliner, J. Koplow, S. Tammela, and V. Philipov, "High order modes suppression in large mode area active fibers by controlling the radial distribution of the rare earth dopant," In Fiber Lasers III, A.J.W. Brow, J. Nilsson, D. J. Harter, A. Tünnermann, eds., Proc. SPIE 6102, 61021T1-61021T8 (2006).

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Figures (9)

Fig. 1.
Fig. 1.

Schematic illustration of the model: (a) fiber lasers (b) fiber amplifiers.

Fig. 2.
Fig. 2.

Illustration of multilayered method (M layers divided).

Fig. 3.
Fig. 3.

Power propagation of each mode in fiber amplifiers with various dopant profiles.

Fig. 4.
Fig. 4.

Power faction of LP01 mode versus doping confinement factor in flat doping fibers with different core diameters (28, 50 and 100 um).

Fig. 5.
Fig. 5.

Power propagation of each mode in fiber amplifiers with discriminative loss factors.

Fig. 6.
Fig. 6.

Power distribution of each mode in fiber lasers varied with pump powers in flat-doping fiber lasers with Γ =1.

Fig. 7.
Fig. 7.

Transverse gain distributions at the output end with different pump powers.

Fig. 8.
Fig. 8.

Output power distributions of each mode in fiber lasers with various dopant profiles and discriminative loss factors.

Fig. 9.
Fig. 9.

Power faction of LP01 mode varies fiber length with different mode coupling coefficients in a two mode fiber lasers.

Tables (1)

Tables Icon

Table 1. Parameters used for simulations of Yb-doped fiber lasers and amplifiers

Equations (13)

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N 2 ( r , φ , z ) N 1 ( r , φ , z ) = [ P p + ( z ) + P p ( z ) ] σ ap Γ p ( r , φ ) hv p + i [ P si + ( z ) + P si ( z ) ] σ as Γ si ( r , φ ) hv s [ P p + ( z ) + P p ( z ) ] σ ep Γ p ( r , φ ) hv p + 1 τ + i [ P si + ( z ) + P si ( z ) ] σ es Γ si ( r , φ ) hv s
± dp p ± ( z ) dz = { 0 2 π 0 a [ σ ep N 2 ( r , φ , z ) σ ap N 1 ( r , φ , z ) ] Γ p ( r , φ ) rdrdφ } P p ± ( z ) α p P p ± ( z )
± dp si ± ( z ) dz = { 0 2 π 0 a [ σ es N 2 ( r , φ , z ) σ as N 1 ( r , φ , z ) ] Γ si ( r , φ ) rdrdφ } P si ± ( z ) α si P si ± ( z )
j d ij [ P si ± ( z ) P sj ± ( z ) ]
Γ p ( r , φ ) = 1 A clad , 0 0 a Γ p ( r , φ ) rd rdφ = Γ p = A core A clad
Γ si ( r , φ ) = ψ i ( r , φ ) 0 2 π 0 i ( r , ψ ) drdφ , 0 0 a Γ si ( r , φ ) rd rdφ = Γ si = P i core P i core + P i clad
N 2 k ( z ) N 1 k ( z ) = [ P p + ( z ) + P p ( z ) ] σ ap Γ pk hv p A k + i [ P si + ( z ) + P si ( z ) ] σ as Γ sik hv s A k [ P p + ( z ) + P p ( z ) ] σ ep Γ pk hv p A k + 1 τ + i [ P si + ( z ) + P si ( z ) ] σ es Γ sik hv s A k ( k = 1,2 , , M )
± dP p ± ( z ) dz = k Γ pk [ σ ep N 2 k ( z ) σ ap N 1 k ] P p ± ( z ) α p P p ± ( z )
± dP si ± ( z ) dz = k Γ sik [ σ es N 2 k ( z ) σ as N 1 k ] P si ± ( z ) α si P si ± ( z ) j d ij [ P si ± ( z ) P sj ± ( z ) ]
Γ pk = A k A clad , Γ sik = r k 1 r k 0 2 π r ψ i ( r , ϕ ) drdφ 0 0 2 π r ψ i ( r , ϕ ) drdφ
Γ sik = ( r k 1 a ) 2 [ J m ( U r k 1 a ) 2 J m 1 ( U r k 1 a ) J m + 1 ( U r k 1 a ) ] ( r k a ) 2 [ J m ( U r k a ) 2 J m 1 ( U r k a ) J m + 1 ( U r k a ) ] V 2 V 2 U 2 J m 1 ( U ) J m + 1 ( U )
P si + ( 0 ) = R 1 P si ( 0 )
P si ( L ) = R 2 P si + ( L )

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