Abstract

For powers exceeding a sharp threshold in the vicinity of several hundred watts the beam quality from some narrow bandwidth fiber amplifiers is severely degraded. We show that this can be caused by transverse thermal gradients induced by the amplification process.

© 2011 OSA

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References

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  1. 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, 3258–3271 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 .
    [CrossRef] [PubMed]
  2. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35, 94–96 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=ol-35-2-94 .
    [CrossRef] [PubMed]
  3. F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36, 689–691 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=ol-36-5-689 .
    [CrossRef] [PubMed]
  4. 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 Tech. 16, 798–806 (1998), http://www.opticsinfobase.org/abstract.cfm?URI=jlt-16-5-798 .
    [CrossRef]
  5. A. A. Fotiadi, O. L. Antipov, and P. Mégret, “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.
  6. N. Andermahr and C. Fallnich, “Optically induced long-period fiber gratings for guided mode conversion in few-mode fiber,” Opt. Express 18, 4411–4416 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-5-4411 .
    [CrossRef] [PubMed]
  7. M. Chi, J.-P. Huignard, and P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” J. Opt. Soc. Am. B 26, 1578–1584 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=josab-26-8-1578 .
    [CrossRef]
  8. R. Soulard, A. Brignon, J.-P. Huignard, and R. Moncorgé, “Non-degenerate near-resonant two-wave mixing in diode pumped Nd3+ and Yb3+ doped crystals in the presence of athermal refractive index grating,” J. Opt. Soc. Am. B 27, 2203–2210 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=josab-27-11-2203 .
    [CrossRef]
  9. M. D. Feit and J. A. Fleck “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978).
    [CrossRef] [PubMed]
  10. L. L. Zhang, P. Shi, and L. Li, “Semianalytical thermal analysis of rectangle Nd:GGG in heat capacity laser,” Appl. Phys. B 101, 137–142 (2010).
    [CrossRef]

2010

A. A. Fotiadi, O. L. Antipov, and P. Mégret, “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.

L. L. Zhang, P. Shi, and L. Li, “Semianalytical thermal analysis of rectangle Nd:GGG in heat capacity laser,” Appl. Phys. B 101, 137–142 (2010).
[CrossRef]

1978

Antipov, O. L.

A. A. Fotiadi, O. L. Antipov, and P. Mégret, “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.

Feit, M. D.

Fleck, J. A.

Fotiadi, A. A.

A. A. Fotiadi, O. L. Antipov, and P. Mégret, “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.

Li, L.

L. L. Zhang, P. Shi, and L. Li, “Semianalytical thermal analysis of rectangle Nd:GGG in heat capacity laser,” Appl. Phys. B 101, 137–142 (2010).
[CrossRef]

Mégret, P.

A. A. Fotiadi, O. L. Antipov, and P. Mégret, “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.

Shi, P.

L. L. Zhang, P. Shi, and L. Li, “Semianalytical thermal analysis of rectangle Nd:GGG in heat capacity laser,” Appl. Phys. B 101, 137–142 (2010).
[CrossRef]

Zhang, L. L.

L. L. Zhang, P. Shi, and L. Li, “Semianalytical thermal analysis of rectangle Nd:GGG in heat capacity laser,” Appl. Phys. B 101, 137–142 (2010).
[CrossRef]

Appl. Opt.

Appl. Phys. B

L. L. Zhang, P. Shi, and L. Li, “Semianalytical thermal analysis of rectangle Nd:GGG in heat capacity laser,” Appl. Phys. B 101, 137–142 (2010).
[CrossRef]

Other

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, 3258–3271 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 .
[CrossRef] [PubMed]

T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35, 94–96 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=ol-35-2-94 .
[CrossRef] [PubMed]

F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36, 689–691 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=ol-36-5-689 .
[CrossRef] [PubMed]

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 Tech. 16, 798–806 (1998), http://www.opticsinfobase.org/abstract.cfm?URI=jlt-16-5-798 .
[CrossRef]

A. A. Fotiadi, O. L. Antipov, and P. Mégret, “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.

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

M. Chi, J.-P. Huignard, and P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” J. Opt. Soc. Am. B 26, 1578–1584 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=josab-26-8-1578 .
[CrossRef]

R. Soulard, A. Brignon, J.-P. Huignard, and R. Moncorgé, “Non-degenerate near-resonant two-wave mixing in diode pumped Nd3+ and Yb3+ doped crystals in the presence of athermal refractive index grating,” J. Opt. Soc. Am. B 27, 2203–2210 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=josab-27-11-2203 .
[CrossRef]

Supplementary Material (1)

» Media 1: AVI (2132 KB)     

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Figures (12)

Fig. 1
Fig. 1

Light in mode one, traveling to the right encounters a wedge of higher refractive index. The wedge induces a phase tilt which causes the light to oscillate up and down with a period determined by the difference in propagation constants for modes one and two.

Fig. 2
Fig. 2

A properly spaced array of index wedges coherently transfers light from mode one to mode two, leading to large amplitude oscillations, or equivalently to large power transfer from mode one to mode two.

Fig. 3
Fig. 3

The sinusoid represents the oscillation in the irradiance profile, the wedges show the symmetry of the thermally-induced refractive index changes.

Fig. 4
Fig. 4

Like Fig. 3 except there is a frequency offset of the light in modes one and two. Because (ω 2 < ω 1) the irradiance grating moves downstream, and the time lag of the induced temperature profile caused by thermal diffusion makes the refractive index pattern lag the irradiance profile.

Fig. 5
Fig. 5

Pump and signal powers versus z for the modeled fiber amplifier in the absence of mode coupling. The input powers are [1200, 30, 0] W for [pump, mode one, mode two].

Fig. 6
Fig. 6

Irradiance profile (left) and temperature profile (right) at the input end of the amplifier. The powers are 1200 W pump, 30 W mode one, 10 W mode two, and the frequency offset between modes is 2 kHz. In this illustration we use an exagerated mode two power to dramatize the oscillations of the irradiance and temperature profiles. The phase delay of the temperature relative to the irradiance is readily apparent in the movie ( Media 1).

Fig. 7
Fig. 7

Small signal gain of mode two versus frequency offset (ν 2ν 1) for different z positions along the fiber. The laser gains are included and can be found from the left axis intercepts.

Fig. 8
Fig. 8

Small signal gain of mode two at 200 kHz for the test amplifier. The solid curve is total gain of mode two; the dashed curve shows the contribution of laser gain.

Fig. 9
Fig. 9

KK coupling at 200 kHz with inputs of [1200, 30, 1E-6] W for [pump, mode one, mode two]. The dashed curve shows mode one power without mode coupling.

Fig. 10
Fig. 10

Small signal gain of mode two versus frequency offset (ν 1ν 2) for different z positions along the fiber. The laser gain is included but it is a small fraction of the small signal gain.

Fig. 11
Fig. 11

Small signal gain of mode two at 2 kHz versus z for the test amplifier. The solid curve is total gain of mode two and the dashed line is the contribution of laser gain. The mode coupling gain is the difference between the two curves.

Fig. 12
Fig. 12

Net gain of thermal mode coupling versus pump power. The symbols are the integrated small signal gains of mode two for three pump powers. The dashed line is for comparison with a linear dependence on pump power.

Tables (1)

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Table 1 Parameters of Test Amplifier

Equations (17)

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v grating = c ω ω 2 ω 1 n ¯ 2 n ¯ 1
dU dt = R U τ
R = R [ 1 + α sin ( ω t ) ] .
U = R τ [ 1 + α 1 + ω 2 τ 2 sin ( ω t δ ) ] ,
sin δ = ω τ 1 + ω 2 τ 2 .
S ω τ 1 + ω 2 τ 2 ,
dn u dt = ( P p σ p a / Ah ν p + I s σ s a / h ν s ) n l ( P p σ p e / Ah ν p + I s σ s e / h ν s + 1 / τ ) n u ,
1 / τ eff = P p σ p e / Ah ν p + I s σ s e / h ν s = 1 / τ .
Δ n = N Y b n u Δ KK
τ = C ρ K r 2 = 1.12 × 10 6 r 2 .
n u = P p σ p a / h ν p A + I s σ s a / h ν s P p ( σ p a + σ p e ) / h ν p A + I s ( σ s a + σ s e ) / h ν s + 1 / τ .
Q = N Yb [ ν p ν s ν p ] [ σ p a ( σ p a + σ p e ) n u ] P p A ,
ρ C dT dt = Q + K ( 2 T x 2 + 2 T y 2 )
Δ n = 1.2 × 10 5 Δ T .
dP s 2 dz = g ( z , Δ ν ) P s 2
P s 2 ( z ) = P s 2 ( 0 ) e G ( z )
G ( z ) = 0 z g ( z ) d z .

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