Abstract

Mode-interference along an active fiber in high-power operation gives rise to a longitudinally oscillating temperature profile which, in turn, is converted into a strong index grating via the thermo-optic effect. In the case of mode beating between the fundamental mode and a radially anti-symmetric mode such a grating exhibits two periodic features: a main one which is radially symmetric and has half the period of the modal beating, and a second one that closely follows the mode interference pattern and has its same period. In the case of modal beating between two radially symmetric modes the thermally induced grating only has radially symmetric features and exhibits the same period of the mode interference. The relevance of such gratings in the context of the recently observed mode instabilities of high-power fiber laser systems is discussed.

© 2011 OSA

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References

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2011 (5)

2010 (2)

2009 (2)

2007 (2)

2004 (1)

Y. Wang, C. Q. Xu, and H. Po, “Thermal effects in kilowatt fiber lasers,” IEEE Photon. Technol. Lett. 16(1), 63–65 (2004).
[CrossRef]

2000 (1)

1998 (2)

1993 (1)

L. Zenteno, “High-Power Double-Clad Fiber Lasers,” J. Lightwave Technol. 11(9), 1435–1446 (1993).
[CrossRef]

Andermahr, N.

Arkwright, J. W.

Atkins, G. R.

Carstens, H.

Clarkson, W. A.

Davis, M. K.

Digonnet, M. J. F.

Dong, L.

Eidam, T.

Elango, P.

Fallnich, C.

Goldberg, L.

Gong, M.

Hädrich, S.

Jansen, F.

Jauregui, C.

Kliner, D. A. V.

Koplow, J. P.

Li, C.

Li, J.

Liao, S.

Limpert, J.

Marciante, J. R.

J. R. Marciante, “Gain Filtering for Single-Spatial-Mode Operation of Large-Mode-Area Fiber Amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 30–36 (2009).
[CrossRef]

Nilsson, J.

Otto, H.-J.

Pantell, R. H.

Peng, X.

Po, H.

Y. Wang, C. Q. Xu, and H. Po, “Thermal effects in kilowatt fiber lasers,” IEEE Photon. Technol. Lett. 16(1), 63–65 (2004).
[CrossRef]

Richardson, D. J.

Rothhardt, J.

Schmidt, O.

Schreiber, T.

Smith, A. V.

Smith, J. J.

Steinmetz, A.

Stutzki, F.

Tünnermann, A.

Wang, Y.

Y. Wang, C. Q. Xu, and H. Po, “Thermal effects in kilowatt fiber lasers,” IEEE Photon. Technol. Lett. 16(1), 63–65 (2004).
[CrossRef]

Whitbread, T.

Wirth, C.

Xu, C. Q.

Y. Wang, C. Q. Xu, and H. Po, “Thermal effects in kilowatt fiber lasers,” IEEE Photon. Technol. Lett. 16(1), 63–65 (2004).
[CrossRef]

Yan, P.

Yuan, Y.

Zenteno, L.

L. Zenteno, “High-Power Double-Clad Fiber Lasers,” J. Lightwave Technol. 11(9), 1435–1446 (1993).
[CrossRef]

Zhang, H.

IEEE J. Sel. Top. Quantum Electron. (1)

J. R. Marciante, “Gain Filtering for Single-Spatial-Mode Operation of Large-Mode-Area Fiber Amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 30–36 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. Wang, C. Q. Xu, and H. Po, “Thermal effects in kilowatt fiber lasers,” IEEE Photon. Technol. Lett. 16(1), 63–65 (2004).
[CrossRef]

J. Lightwave Technol. (3)

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

Opt. Express (7)

N. Andermahr and C. Fallnich, “Optically induced long-period fiber gratings for guided mode conversion in few-mode fibers,” Opt. Express 18(5), 4411–4416 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-5-4411 .
[CrossRef] [PubMed]

A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10180 .
[CrossRef] [PubMed]

M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express 15(6), 3236–3246 (2007).
[CrossRef] [PubMed]

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(14), 13218–13224 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[CrossRef] [PubMed]

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 .
[CrossRef] [PubMed]

C. Jauregui, J. Limpert, and A. Tünnermann, “Derivation of Raman treshold formulas for CW double-clad fiber amplifiers,” Opt. Express 17(10), 8476–8490 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-10-8476 .
[CrossRef] [PubMed]

T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Fiber chirped-pulse amplification system emitting 3.8 GW peak power,” Opt. Express 19(1), 255–260 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-1-255 .
[CrossRef] [PubMed]

Opt. Lett. (2)

Other (2)

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

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,” in Frontiers in Guided Wave Optics and Optoelectronics, B. Pal, ed. (Intec, 2010), pp. 209–234.

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Figures (8)

Fig. 1
Fig. 1

a) Beam profile and b) inversion profile along the fiber amplifier in the x-z plane.

Fig. 2
Fig. 2

a) Evolution of the total number of excited ions along the fiber amplifier and b) amount of pump power absorbed at each position of the active fiber.

Fig. 3
Fig. 3

Temperature profile of the fiber amplifier in the x-z plane (left) and corresponding plot of the temperature evolution in the fiber axis (right) with (red line) and without (blue line) considering longitudinal heat flow.

Fig. 4
Fig. 4

Profile of the thermally induced index-grating in the x-z plane (left), together with the comparison of the evolution of the index change at three different positions in the fiber core (right): at the fiber axis (blue line), at a position of x = + 39µm and at a position of x = −39µm. The lines along which the evolutions of the index change have been plotted in the right graph are indicated by the white dashed lines in the left graph.

Fig. 5
Fig. 5

a) Transversal profiles of the thermally induced index change in the x-plane at two different positions along the fiber: the blue line corresponds to z = 0.96m and the red line corresponds to z = 0.98m. b) Periodic non-radially symmetric features of the thermally induced index change.

Fig. 6
Fig. 6

Comparison of the position of the maxima and minima of the interference pattern (red line) and of the secondary thermally induced grating (blue line) along the line x = + 39µm (upper dashed white line of Fig. 4). The blown-up plot on the right shows that there is no phase shift between the grating and the interference pattern.

Fig. 7
Fig. 7

a) Beam profile and b) inversion profile along the fiber amplifier in the x-z plane.

Fig. 8
Fig. 8

Profile of the thermally induced index-grating in the x-z plane (left), together with the comparison of the evolution of the index change (right).

Equations (4)

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1 r r ( r T(r,ϕ,z) r )+ 1 r 2 2 T(r,ϕ,z) ϕ 2 + 2 T(r,ϕ,z) z 2 = Q(r,ϕ,z) κ
Q(r,ϕ,z)=η P abs (r,ϕ,z) ΔV
P abs (r,ϕ,z)= Γ p (r,ϕ,z)[ σ ap N 1 (r,ϕ,z) σ ep N 2 (r,ϕ,z) ] P p (z)dz
mλ=( n eff FM n eff HOM )Λ

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