Abstract

Spatio-temporal instability of the fundamental mode in Yb3+-doped few-mode PM fiber amplifiers with a core diameter of 8.5 μm was registered at 2-30 Watts pump power. Both experimental and theoretical analysis revealed the nonlinear power transformation of the LP01 fundamental mode into high-order modes. Numerical simulation revealed self-consistent growth of the higher-order mode and traveling electronic index grating accompanying the population grating induced by the mode interference field (due to different polarizability of the excited and unexcited Yb3+ ions). Experimental results and numerical calculations showed the increase of the instability threshold along with an increase of the signal frequency bandwidth.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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  20. M. Melkumov, I. Bufetov, K. Kravtsov, A. Shubin, and E. Dianov, Cross Sections of Absorption and Stimulated Emission of Yb3+ Ions in Silica Fibers Doped with P2O5 and Al2O3 (FORC, Moscow, 2004).
  21. A. Fotiadi, O. Antipov, M. Kuznetsov, and P. Mégret, “Refractive index changes in rare earth-doped optical fibers and their applications in all-fiber coherent beam combinig,” in Coherent Laser Beam Combining, A. Brignon, ed. (John Wiley & Sons, 2013), chap. 7, pp. 193 – 230.
  22. M. Bass, E. Van Stryland, D. Williams, and W. Wolfe, Handbook for Optics, 2nd ed. (MGH, 1995).
  23. V. Privalko, Handbook for Physical Chemistry of Polymers (Naukova Dumka, 1984).
  24. H.-G. Unger, Planar Optical Waveguides and Fibres (Oxford University, 1977).
  25. O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Stimulated resonant scattering of optical waves in laser crystals with population inversion,” JETP Lett. 63(1), 13–18 (1996).
    [Crossref]
  26. O. L. Antipov, S. I. Belyaev, A. S. Kuzhelev, and D. V. Chausov, “Resonant two-wave mixing of optical beams by refractive index and gain gratings in inverted Nd:YAG,” J. Opt. Soc. Am. B 15(8), 2276–2281 (1998).
    [Crossref]
  27. M. Chi, J.-P. Huignard, and P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” JOSA B 26(8), 1578–1584 (2009).
    [Crossref]
  28. S. Stepanov, A. Fotiadi, and P. Mégret, “Effective recording of dynamic phase gratings in Yb-doped fibers with saturable absorption at 1064nm,” Opt. Express 15(14), 8832–8837 (2007).
    [Crossref] [PubMed]

2013 (3)

2012 (5)

2011 (4)

2009 (1)

M. Chi, J.-P. Huignard, and P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” JOSA B 26(8), 1578–1584 (2009).
[Crossref]

2007 (1)

1998 (2)

1996 (1)

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Stimulated resonant scattering of optical waves in laser crystals with population inversion,” JETP Lett. 63(1), 13–18 (1996).
[Crossref]

1966 (2)

V. I. Bespalov and V. I. Talanov, “About filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3(12), 307–310 (1966).

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated Four-Photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17(22), 1158–1161 (1966).
[Crossref]

Alkeskjold, T. T.

Antipov, O. L.

Arkwright, J. W.

Atkins, G. R.

Belyaev, S. I.

O. L. Antipov, S. I. Belyaev, A. S. Kuzhelev, and D. V. Chausov, “Resonant two-wave mixing of optical beams by refractive index and gain gratings in inverted Nd:YAG,” J. Opt. Soc. Am. B 15(8), 2276–2281 (1998).
[Crossref]

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Stimulated resonant scattering of optical waves in laser crystals with population inversion,” JETP Lett. 63(1), 13–18 (1996).
[Crossref]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, “About filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3(12), 307–310 (1966).

Broeng, J.

Chausov, D. V.

Chi, M.

M. Chi, J.-P. Huignard, and P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” JOSA B 26(8), 1578–1584 (2009).
[Crossref]

Chiao, R. Y.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated Four-Photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17(22), 1158–1161 (1966).
[Crossref]

Dajani, I.

de Vries, O.

Digonnet, M. J. F.

Dong, L.

Eberhardt, R.

Eidam, T.

Elango, P.

Fotiadi, A.

Fotiadi, A. A.

Gaida, C.

Garmire, E.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated Four-Photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17(22), 1158–1161 (1966).
[Crossref]

Haarlammert, N.

Hansen, K. R.

Huignard, J.-P.

M. Chi, J.-P. Huignard, and P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” JOSA B 26(8), 1578–1584 (2009).
[Crossref]

Jansen, F.

Jauregui, C.

Kelley, P. L.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated Four-Photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17(22), 1158–1161 (1966).
[Crossref]

Kliner, A.

Kuzhelev, A. S.

O. L. Antipov, S. I. Belyaev, A. S. Kuzhelev, and D. V. Chausov, “Resonant two-wave mixing of optical beams by refractive index and gain gratings in inverted Nd:YAG,” J. Opt. Soc. Am. B 15(8), 2276–2281 (1998).
[Crossref]

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Stimulated resonant scattering of optical waves in laser crystals with population inversion,” JETP Lett. 63(1), 13–18 (1996).
[Crossref]

Kuznetsov, M. S.

Lægsgaard, J.

Liem, A.

Limpert, J.

Mégret, P.

Otto, H.-J.

Peschel, T.

Petersen, P. M.

M. Chi, J.-P. Huignard, and P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” JOSA B 26(8), 1578–1584 (2009).
[Crossref]

Robin, C.

Schmidt, O.

Schreiber, T.

Smith, A. V.

Smith, J. J.

Stepanov, S.

Stutzki, F.

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, “About filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3(12), 307–310 (1966).

Tünnermann, A.

Ward, B.

Whitbread, T.

Wirth, C.

J. Lightwave Technol. (1)

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

JETP Lett. (2)

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Stimulated resonant scattering of optical waves in laser crystals with population inversion,” JETP Lett. 63(1), 13–18 (1996).
[Crossref]

V. I. Bespalov and V. I. Talanov, “About filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3(12), 307–310 (1966).

JOSA B (1)

M. Chi, J.-P. Huignard, and P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” JOSA B 26(8), 1578–1584 (2009).
[Crossref]

Opt. Express (11)

S. Stepanov, A. Fotiadi, and P. Mégret, “Effective recording of dynamic phase gratings in Yb-doped fibers with saturable absorption at 1064nm,” Opt. Express 15(14), 8832–8837 (2007).
[Crossref] [PubMed]

A. V. Smith and J. J. Smith, “Increasing mode instability thresholds of fiber amplifiers by gain saturation,” Opt. Express 21(13), 15168–15182 (2013).
[Crossref] [PubMed]

L. Dong, “Stimulated thermal Rayleigh scattering in optical fibers,” Opt. Express 21(3), 2642–2656 (2013).
[Crossref] [PubMed]

M. S. Kuznetsov, O. L. Antipov, A. A. Fotiadi, and P. Mégret, “Electronic and thermal refractive index changes in ytterbium-doped fiber amplifiers,” Opt. Express 21(19), 22374–22388 (2013).
[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).
[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).
[Crossref] [PubMed]

N. Haarlammert, O. de Vries, A. Liem, A. Kliner, T. Peschel, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Build up and decay of mode instability in a high power fiber amplifier,” Opt. Express 20(12), 13274–13283 (2012).
[Crossref] [PubMed]

A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011).
[Crossref] [PubMed]

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440–451 (2012).
[Crossref] [PubMed]

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Physical origin of mode instabilities in high-power fiber laser systems,” Opt. Express 20(12), 12912–12925 (2012).
[Crossref] [PubMed]

B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20(10), 11407–11422 (2012).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated Four-Photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17(22), 1158–1161 (1966).
[Crossref]

Other (9)

S. N. Vlasov and V. I. Talanov, Wave Self-Focusing (IAP RAS, 1997).

C. Codemard, K. Yla-Jarkko, J. Singleton, P. W. Turner, I. Godfrey, S.-U. Alam, J. Nolssson, J. Sahu, and A. B. Grudinin, in Proceeding of European Conference on Optical Communication (ECOC'2002, Copenhagen, Denmark, 2002), PD1.6.

M. Melkumov, I. Bufetov, K. Kravtsov, A. Shubin, and E. Dianov, Cross Sections of Absorption and Stimulated Emission of Yb3+ Ions in Silica Fibers Doped with P2O5 and Al2O3 (FORC, Moscow, 2004).

A. Fotiadi, O. Antipov, M. Kuznetsov, and P. Mégret, “Refractive index changes in rare earth-doped optical fibers and their applications in all-fiber coherent beam combinig,” in Coherent Laser Beam Combining, A. Brignon, ed. (John Wiley & Sons, 2013), chap. 7, pp. 193 – 230.

M. Bass, E. Van Stryland, D. Williams, and W. Wolfe, Handbook for Optics, 2nd ed. (MGH, 1995).

V. Privalko, Handbook for Physical Chemistry of Polymers (Naukova Dumka, 1984).

H.-G. Unger, Planar Optical Waveguides and Fibres (Oxford University, 1977).

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 Opticsand Optoelectronics, B. Pal, ed. (Intec, 2010), pp. 209–234.

V. Tyrtyshnyy, O. Vershnin, and S. Larin, “Influence of the radiation spectral parameters on the nonlinear interaction of modes in active fiber,” in Technical digests of International Symposium “High-Power Fiber Lasers and Their Applications,” (S-Petersburg, Russia, 2010), paper TuSy, p. 04.M.

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Figures (11)

Fig. 1
Fig. 1 Experimental setup.
Fig. 2
Fig. 2 Oscillograms of the fundamental mode (bright blue, from PD 1), and the higher-order mode (dark blue, from PD 2) below (a), slightly above (b), and far above (c) MI threshold.
Fig. 3
Fig. 3 Output power dependence on pump power (a), and dependence of the mode instability threshold (for output power of the signal) on input power (b). Input signal bandwidth was less than 0.05 nm, active fiber length was 6 m.
Fig. 4
Fig. 4 Mode instability threshold dependence on the input signal bandwidth (the signal input power is 50 mW).
Fig. 5
Fig. 5 Oscillogram of the fundamental mode above MI threshold.
Fig. 6
Fig. 6 Beam at the output of the active fiber below (a) and above (b) the MI threshold, and the red-light fiber images (c) at the same space scale.
Fig. 7
Fig. 7 Powers of the fundamental mode LP01 (red), anti-Stokes (blue) and Stokes (green) shifted LP11 mode and the pump inside the active fiber (violet) and the auxiliary fiber (black) on the fiber length at the time t = 2 ms after switch on of the pump with power 5 mW (the signal with power mW was switched on in 20 μs before the pump) (a), and on the time in the fiber output (b). The input ratio of the LP01 and LP11 mode power was 40, the frequency detuning Ω = 4 kHz.
Fig. 8
Fig. 8 The relative gain of the anti-Stokes shifted LP11 mode (with respect to the fundamental mode) on the frequency detuning Ω for different pump and signal powers (Pp and PS) in the fiber input, numerical aperture (NA) and the time.
Fig. 9
Fig. 9 Amplitudes of the RIGs caused by the temperature change (red) and polarizability difference (brown, violet, green) on the fiber length at the time 2 ms after signal switch on (left) and the time in the fiber output (right). The input power of the LP01 mode is 5 mW (the LP01 and LP11 mode power ratio on the input is 40), the input pump power (in the auxiliary fiber) is Pax(0) = 2.5 W and the frequency shift is Ω = 6 kHz (green and red), Pax(0) = 1.5 W and Ω = 4.25 kHz (brown), Pax(0) = 0.75 W and Ω = 4.25 kHz (violet).
Fig. 10
Fig. 10 Output power of the LP01 mode (solid lines) and the optimal-shifted LP11 mode (dashed lines) on the pump power for the input LP01-mode power 5 mW (blue and green) or 60 mW (red), and the input power ratio of the LP01 and LP11 modes 40 (for blue and red) or 200 (for green).
Fig. 11
Fig. 11 Output power of the LP01 mode (solid curves) and the optimal-shifted LP11 mode (dushed curves) on the pump power for the different longitudinal mode numbers M (a); the threshold LP mode power on the signal bandwidth (b) (the input LP01-mode power is 5 mW; the ratio of the input mode-power is 350 (a), and is varied from 40 to 103 (b).

Tables (2)

Tables Icon

Table 1 Experimental Parameters of Active Fiber, Pump and Input Signal

Tables Icon

Table 2 Fiber Parameters Used for Calculation

Equations (19)

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

E 01 = A 0 (z,t) e i(2π ν s t k 0 z) ψ 0 (r),
E 11 =( A 1 s (z,t) e iΩt+iϕ + A 1 as (z,t) e iΩtiϕ ) e i(2π ν s t k 1 z) ψ 1 (r),
A 0 z + 1 υ 0 A 0 t =i 2π n 0 λ s k 0 ( A 0 ψ 0 2 δH+ A 1 s e iΩt+iqz ψ 1 ψ 0 δH e iϕ + A 1 as e iΩt+iqz ψ 1 ψ 0 δH e iϕ ),
A 1 s z + 1 υ 1 A 1 s t =i 2π n 0 λ s k 1 ( A 1 s ψ 1 2 δH+ A 0 e iΩtiqz ψ 0 ψ 1 δH e iϕ ),
A 1 as z + 1 υ 1 A 1 as t =i 2π n 0 λ s k 1 ( A 1 as ψ 1 2 δH+ A 0 e iΩtiqz ψ 0 ψ 1 δH e iϕ ),
δH= 2π λ s ( n T )δT+ i 2 (( σ em s + σ ab s )(1+iβ)δ N ex σ ab s N d ),
N ex t + N ex τ + N ex ( σ ab p + σ em p ) P p h ν p S cl = σ ab p N d P p h ν p S cl ( σ em s + σ ab s ) I s h ν s ( N ex σ ab s N d σ em s + σ ab s ),
T t Κ 1 ρ 1 C 1p 2 T= h ν T ρ 1 C 1p N ex τ + ν p ν s ν s ( σ em s + σ ab s ) I s ρ 1 C 1p ( N ex σ ab s N d σ em s + σ ab s ),
( δT δ N ex )=( T 0 (z,r,t) δ N ex 0 (z,r,t) )+( δ T s (z,r,t) δ N ex s (z,r,t) ) e iΩt+iϕ+iqz +( δ T as (z,r,t) δ N ex as (z,r,t) ) e iΩtiϕ+iqz .
( T 00 N 00 T 11 N 11 T 01 s N 01 s T 01 as N 01 as )( T 0 (z,r,t) ψ 0 2 δ N ex 0 (z,r,t) ψ 0 2 T 0 (z,r,t) ψ 1 2 δ N ex 0 (z,r,t) ψ 1 2 δ T s (z,r,t) ψ 0 ψ 1 e iϕ δ N ex s (z,r,t) ψ 0 ψ 1 e iϕ δ T as (z,r,t) ψ 1 ψ 0 e iϕ δ N ex as (z,r,t) ψ 1 ψ 0 e iϕ ).
δ N ex 0 ψ 0,1 4 N 00,11 ψ 0,1 4 (r) ψ 0,1 2 (r) , δ N ex 0 ψ 0 2 ψ 1 2 N 00 ψ 0 2 (r) ψ 1 2 (r) ψ 0 2 (r) , δ N ex s,as ψ 0,1 3 ψ 1,0 N 01 s,as ψ 0,1 4 (r) ψ 1,0 2 (r) ψ 0 2 (r) ψ 1 2 (r) .
b 2 = u 0 2 + u 1 2 r 0 2 + 2 u 0 u 1 0 r 0 J 1 ( u 1 r/ r 0 ) J 0 ( u 0 r/ r 0 ) ( J 1 ( u 0 r/ r 0 ) J 0 ( u 1 r/ r 0 ) r J 1 ( u 1 r/ r 0 ) J 1 ( u 0 r/ r 0 ) r 0 / u 1 )dr r 0 2 0 r 0 J 1 2 ( u 1 r/ r 0 ) J 0 2 ( u 0 r/ r 0 ) rdr 13 r 0 2 .
T 01 s,as t iΩ T 01 s,as Κ 1 ρ 1 C 1p ( b 2 + q 2 ) T 01 s = ( σ em s + σ ab s )( ν p ν s ) ρ 1 C 1p ν s [ N 01 s,as ψ 0 4 ψ 1 2 | A 0 | 2 +( | A 1 s | 2 + | A 1 as | 2 ) ψ 1 4 ψ 0 2 ψ 0 2 ψ 1 2 + +( N 00 ψ 0 2 σ ab s N d σ em s + σ ab s ) ψ 0 2 ψ 1 2 ( A 0 * A 1 ,s,as + A 1 as,s* A 0 e 2iqz ) ] с n 0 8π + h ν T ρ 1 C 1p τ N 01 s,as ,
N 01 s,as t iΩ N 01 s,as + N 01 s,as τ + N 01 s,as ( σ em p + σ ab p ) P p π r 1 2 h ν p = σ em s + σ ab s h ν s c n 0 8π [ N 01 s,as ψ 0 4 ψ 1 2 | A 0 | 2 +( | A 1 s | 2 + | A 1 as | 2 ) ψ 1 4 ψ 0 2 ψ 1 2 ψ 0 2 + +( N 00 ψ 0 2 σ ab s N d σ em s + σ ab s ) ψ 1 2 ψ 0 2 ( A 0 * A 1 s,as + A 1 as,s* A 0 e 2iqz ) ],
P p z =( N d ( σ em p + σ ab p ab )+ σ em p δ N ex ) r 0 2 r 1 2 P p +γ( P ax P p ),
P ax z =γ( P ax P p ),
A 0,1 s,as (z,t)= m=M M B 0,1m s,as (z,t) e imΔt+i φ m ,
B 0m z + imΔ υ 0 B 0m = σ em s + σ ab s 2 (1+iβ)( N 00 B 0m + N 01 B 1m as ) σ ab s 2 N d B 0m i 2π λ s ( n T )( T 00 B 0m + T 01 B 1m as ),
B 1m as z + imΔ υ 1 B 1m as = σ em s + σ ab s 2 (1+iβ)( N 00 B 1m as + N 01 * B 0m ) σ ab s 2 N d B 1m as i 2π λ s ( n T )( T 00 B 1m as + T 01 * B 0m ),

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