Abstract

Recent work on high-power fiber amplifiers report on a degradation of the output beam quality or even on the appearance of mode instabilities. By combining the transversally resolved rate equations with a 3D Beam propagation method we have managed to create a model able to provide an explanation of what we believe is at the root of this effect. Even though this beam quality degradation is conventionally linked to transversal hole burning, our simulations show that this alone cannot explain the effect in very large mode area fibers. According to the model presented in this paper, the most likely cause for the beam quality degradation is an inversion-induced grating created by the interplay between modal interference along the fiber and transversal hole burning.

©2011 Optical Society of America

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References

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    [Crossref]

2010 (3)

2009 (1)

2008 (1)

2007 (1)

2005 (1)

2002 (1)

1998 (1)

1997 (2)

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low-power all-optical switching: a review,” Opt. Fiber Technol. 3(1), 44–64 (1997).
[Crossref]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997).
[Crossref]

1995 (1)

C. Xu and W. Huang, “Finite-difference beam propagation method for guide-wave optics,” Prog. Electromagn. Res. 11, 1–49 (1995) (PIER).

1994 (1)

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, “Modal fields calculation using the finite difference beam propagation method,” J. Lightwave Technol. 12(12), 2066–2072 (1994).
[Crossref]

1993 (1)

L. Zenteno, “High-power double-clad fiber lasers,” J. Lightwave Technol. 11(9), 1435–1446 (1993).
[Crossref]

1992 (1)

H. A. van der Vorst, “BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13(2), 631–644 (1992).
[Crossref]

1991 (1)

Andermahr, N.

Andersen, T. V.

Arkwright, J. W.

Atkins, G. R.

Beach, R. J.

Bhutta, T.

Broeng, J.

de Ridder, R. M.

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, “Modal fields calculation using the finite difference beam propagation method,” J. Lightwave Technol. 12(12), 2066–2072 (1994).
[Crossref]

Deguil-Robin, N.

Digonnet, M. J. F.

J. W. Arkwright, P. Elango, G. R. Atkins, T. Whitbread, and M. J. F. Digonnet, “Experimental and theoretical analysis of the resonant nonlinearity in Ytterbium-doped fiber,” J. Lightwave Technol. 16(5), 798–806 (1998).
[Crossref]

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low-power all-optical switching: a review,” Opt. Fiber Technol. 3(1), 44–64 (1997).
[Crossref]

Eidam, T.

Elango, P.

Fallnich, C.

Gabler, T.

Gong, M.

Hadley, G. R.

Hanf, S.

Hanna, D. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997).
[Crossref]

Hoekstra, H. J. W. M.

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, “Modal fields calculation using the finite difference beam propagation method,” J. Lightwave Technol. 12(12), 2066–2072 (1994).
[Crossref]

Huang, W.

C. Xu and W. Huang, “Finite-difference beam propagation method for guide-wave optics,” Prog. Electromagn. Res. 11, 1–49 (1995) (PIER).

Jakobsen, C.

Jauregui, C.

Krijnen, G. J. M.

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, “Modal fields calculation using the finite difference beam propagation method,” J. Lightwave Technol. 12(12), 2066–2072 (1994).
[Crossref]

Li, C.

Liao, S.

Liem, A.

Limpert, J.

Mackenzie, J. I.

Manek-Hönninger, I.

Nilsson, J.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997).
[Crossref]

Nolte, S.

Pantell, R. H.

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low-power all-optical switching: a review,” Opt. Fiber Technol. 3(1), 44–64 (1997).
[Crossref]

Paschotta, R.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997).
[Crossref]

Petersson, A.

Röser, F.

Sadowski, R. W.

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low-power all-optical switching: a review,” Opt. Fiber Technol. 3(1), 44–64 (1997).
[Crossref]

Salin, F.

Schreiber, T.

Seise, E.

Shaw, H. J.

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low-power all-optical switching: a review,” Opt. Fiber Technol. 3(1), 44–64 (1997).
[Crossref]

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(7), 1049–1056 (1997).
[Crossref]

Tünnermann, A.

van der Vorst, H. A.

H. A. van der Vorst, “BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13(2), 631–644 (1992).
[Crossref]

Whitbread, T.

Wijnands, F.

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, “Modal fields calculation using the finite difference beam propagation method,” J. Lightwave Technol. 12(12), 2066–2072 (1994).
[Crossref]

Wirth, C.

Xu, C.

C. Xu and W. Huang, “Finite-difference beam propagation method for guide-wave optics,” Prog. Electromagn. Res. 11, 1–49 (1995) (PIER).

Yan, P.

Yuan, Y.

Zellmer, H.

Zenteno, L.

L. Zenteno, “High-power double-clad fiber lasers,” J. Lightwave Technol. 11(9), 1435–1446 (1993).
[Crossref]

Zhang, H.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997).
[Crossref]

J. Lightwave Technol. (3)

J. W. Arkwright, P. Elango, G. R. Atkins, T. Whitbread, and M. J. F. Digonnet, “Experimental and theoretical analysis of the resonant nonlinearity in Ytterbium-doped fiber,” J. Lightwave Technol. 16(5), 798–806 (1998).
[Crossref]

L. Zenteno, “High-power double-clad fiber lasers,” J. Lightwave Technol. 11(9), 1435–1446 (1993).
[Crossref]

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, “Modal fields calculation using the finite difference beam propagation method,” J. Lightwave Technol. 12(12), 2066–2072 (1994).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Express (5)

Opt. Fiber Technol. (1)

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, “Resonantly enhanced nonlinearity in doped fibers for low-power all-optical switching: a review,” Opt. Fiber Technol. 3(1), 44–64 (1997).
[Crossref]

Opt. Lett. (2)

Prog. Electromagn. Res. (1)

C. Xu and W. Huang, “Finite-difference beam propagation method for guide-wave optics,” Prog. Electromagn. Res. 11, 1–49 (1995) (PIER).

SIAM J. Sci. Stat. Comput. (1)

H. A. van der Vorst, “BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13(2), 631–644 (1992).
[Crossref]

Other (4)

A. A. Fotiadi, O. L. Antipov and P. Megret, “Resonantly induced refractive index changes in Yb-doped fibers: the origin, properties and application for all-fiber coherent beam combining,” Frontiers in Guided Wave Optics and Optoelectronics, 209–234 (2010).

J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. Barty, “Ultimate power limits of optical fibers, ” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMO6, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OMO6 .

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).

D. Gapontsev and I. P. G. Photonics, “6kW CW single mode ytterbium fiber laser in all-fiber format,” in Solid State and Diode Laser Technology Review (Albuquerque, 2008).

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Figures (9)
Fig. 1
Fig. 1 Picture of the cooperative up-conversion as seen in a ~15cm long piece of 100μm core diameter Rod-type fiber (the photo has been processed to enhance the interference contrast).

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Fig. 2
Fig. 2 (a) Evolution of the beam intensity along a 1m long active fiber with an initial excitation of 95% LP01 and 5% LP11 modes (only fiber core shown). (b) Corresponding inversion profile showing the areas with non-depleted inversion (only fiber core shown).

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Fig. 3
Fig. 3 (a) Power evolution in a 2 m long 80/280 fiber seeded with 30 W signal power at 1064 nm and co-propagating pumped with 300 W. (b) Corresponding evolution of the relative modal content when no inversion-grating is considered.

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Fig. 4
Fig. 4 Inversion map (in the x-z plane) along the 2 m long 80/280 fiber (only core region shown) (right), and corresponding inversion profiles near the center (left up) and near the edge of the core (left down).

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Fig. 5
Fig. 5 Evolution of the modal content along the 2 m long 80/280 fiber.

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Fig. 6
Fig. 6 Inversion map (in the x-z plane) along the 2 m long 80/400 fiber (only core region shown) (right), and corresponding inversion profiles near the center (left up) and near the edge of the core (left down).

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Fig. 7
Fig. 7 Evolution of the modal content along the 2m long 80/400 fiber.

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Fig. 8
Fig. 8 Inversion map (in the x-z plane) along the 1 m long 80/200 fiber (only core region shown) (right), and corresponding inversion profiles near the center (left up) and near the edge of the core (left down).

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Fig. 9
Fig. 9 Evolution of the modal content along the 1m long 80/200 fiber.

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Equations (14)

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

∇ 2 E → s + n ( x , y , z ) 2 k 2 E → s = ∇ ( ∇ ⋅ E → s )
∇ 2 E → s , t + n 2 k 2 E → s , t = ∇ t [ ∇ t ⋅ E → s , t − 1 n 2 ∇ t ⋅ ( n 2 E → s , t ) ]
E → s , t ( x , y , z ) = A → s , t ( x , y , z ) e − j n o k z
∂ ∂ z ( j 2 n o k − ∂ ∂ z ) A → s , t ( x , y , z ) = P A → s , t ( x , y , z )
P A → s , t = ∇ t 2 A → s , t ( x , y , z ) + ( n 2 − n o 2 ) k 2 A → s , t ( x , y , z ) − ∇ t [ ∇ t ⋅ A → s , t ( x , y , z ) − 1 n 2 ∇ t ⋅ ( n 2 A → s , t ( x , y , z ) ) ]
j 2 n o k ∂ A → s , t ( x , y , z ) ∂ z = P A → s , t ( x , y , z )
A → s , t ( x , y , z + Δ z ) = 2 n o k − j Δ z ( 1 − α ) P 2 n o k + j Δ z α P A → s , t ( x , y , z )
A [ A → s , t ] l + 1 = B [ A → s , t ] l
N 2 ( x , y , z ) N 1 ( x , y , z ) = [ P p + ( z ) + P p − ( z ) ] σ a p Γ p ( x , y ) h υ p + P s + ( z ) σ a s Γ s ( x , y ) h υ s [ P p + ( z ) + P p − ( z ) ] σ e p Γ p ( x , y ) h υ p + 1 τ + P s + ( z ) σ e s Γ s ( x , y ) h υ s d P p ± ( z ) d z = { ∫ x 1 x 2 ∫ y 1 y 2 [ σ e p N 2 ( x , y , z ) − σ a p N 1 ( x , y , z ) ] Γ p ( x , y ) d x d y } P p ± ( z ) − α p P p ± ( z ) d P s + ( z ) d z = { ∫ x 1 x 2 ∫ y 1 y 2 [ σ e s N 2 ( x , y , z ) − σ a s N 1 ( x , y , z ) ] Γ s ( x , y ) d x d y } P s + ( z ) − α s P s + ( z )
Γ p ( x , y ) = 1 A c l a d and Γ s ( x , y ) = ψ ( x , y ) ∫ − ∞ ∞ ∫ − ∞ ∞ ψ ( x , y ) d x d y
N 2 ( m , k ) ( z ) N 1 ( m , k ) ( z ) = [ P p + ( z ) + P p − ( z ) ] σ a p Γ p ( m , k ) h υ p A ( m , k ) + P s + ( z ) σ a s Γ s ( m , k ) h υ s A ( m , k ) [ P p + ( z ) + P p − ( z ) ] σ e p Γ p ( m , k ) h υ p A ( m , k ) + 1 τ + P s + ( z ) σ e s Γ s ( m , k ) h υ s A ( m , k ) d P p ± ( z ) d z = ∑ m ∑ k [ σ e p N 2 ( m , k ) ( z ) − σ a p N 1 ( m , k ) ( z ) ] Γ p ( m , k ) P p ± ( z ) − α p P p ± ( z ) d P s + ( z ) d z = ∑ m ∑ k [ σ e s N 2 ( m , k ) ( z ) − σ a s N 1 ( m , k ) ( z ) ] Γ s ( m , k ) P s + ( z ) − α s P s + ( z )
A ( m , k ) = Δ x ⋅ Δ y Γ p ( m , k ) = A ( m , k ) A c l a d Γ s ( m , k ) = ψ ( m Δ x , k Δ y ) ∑ m ∑ k ψ ( m Δ x , k Δ y ) N ( m , k ) = N 1 ( m , k ) + N 2 ( m , k )
n ( m , k ) = n ( m Δ x , k Δ y ) = Δ n ⋅ N 2 ( m , k ) N ( m , k ) + j λ 4 π ( σ e s N 2 ( m , k ) − σ a s N 1 ( m , k ) )
c i ( z ) = ∫ − ∞ ∞ ∫ − ∞ ∞ A ^ s , t ( x , y , z ) ⋅ ϕ ^ * i ( x , y ) d x d y

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