Abstract

We developed a three-dimensional numerical model of Large-Mode-Area chirped pulse fiber amplifiers which includes nonlinear beam propagation in nonuniform multimode waveguides as well as gain spectrum dynamics in quasi-three-level active ions. We used our model in tapered Yb-doped fiber amplifiers and showed that single-mode propagation is maintained along the taper even in the presence of strong Kerr nonlinearity and saturated gain, allowing extraction of up to 3 mJ of output energy in 1 ns pulse. Energy scaling and its limitation as well as the influence of fiber taper bending and core irregularities on the amplifier performance were studied. We also investigated numerically the capabilities for compression and coherent combining of up to 36 perturbed amplifying channels and showed more than 70% combining efficiency, even with up to 11% of high-order modes in individual channels.

© 2014 Optical Society of America

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References

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  1. G. Mourou, T. Tajima, M.N. Quinn, B. Brocklesby, and J. Limpert., “Are fiber-based lasers the future of accelerators?” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 740, 17–20 (2014).
    [Crossref]
  2. L. Dong, X. Peng, and J. Li, “Leakage channel optical fibers with large effective area,” J. Opt. Soc. Am. B 24, 1689–1697 (2007).
    [Crossref]
  3. J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tunnermann., “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science and Applications 1, e8 (2012).
    [Crossref]
  4. S. Fevrier, R. Jamier, J-M. Blondy, S.L. Semjonov, M.E. Likhachev, M.M. Bubnov, E.M. Dianov, V.F. Khopin, M.Y. Salganskii, and A.N. Guryanov, “Low-loss singlemode large mode area all-silica photonic bandgap fiber,” Opt. Express 14, 562–569 (2006).
    [Crossref] [PubMed]
  5. H. Chen, T. Sosnowski, C. Liu, L. Chen, J. Birge, A. Galvanauskas, F. Kartner, and G. Chang, “Chirally-coupled-core Yb-fiber laser delivering 80-fs pulses with diffraction-limited beam quality warranted by a high-dispersion mirror based compressor,” Opt. Express 18, 24699–24705 (2010).
    [Crossref] [PubMed]
  6. V. Filippov, Yu Chamorovskii, J. Kerttula, K. Golant, M. Pessa, and O. G. Okhotnikov., “Double clad tapered fiber for high power applications,” Opt. Express 16, 1929–1944 (2008).
    [Crossref] [PubMed]
  7. J. Kerttula, V. Filippov, Y. Chamorovskii, V. Ustimchik, K. Golant, and O.G. Okhotnikov., “Principles and performance of tapered fiber lasers: from uniform to flared geometry,” Appl. Opt. 51, 7025–7038 (2012).
    [Crossref] [PubMed]
  8. A.V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
    [Crossref] [PubMed]
  9. Ya. I. Khanin, Fundamentals of Laser Dynamics, ( Int Science Publishing, Cambridge2006)
  10. J.W. Arkwright, P. Elango, G.R. Atkins, T. Whitbread, and M.J. Digonnet, “Experimental and theoretical analysis of the resonant nonlinearity in ytterbium-doped fiber,” J. Lightwave Technol. 16, 798 (1998).
    [Crossref]
  11. M. Kuznetsov, O. Antipov, A. Fotiadi, and P. Megret, “Electronic and thermal refractive index changes in Ytterbium-doped fiber amplifiers,” Opt. Express 21, 22374–22388 (2013).
    [Crossref] [PubMed]
  12. C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schroter, H. Bartelt, and M. Duparre, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21, 3170–3181 (2013).
    [Crossref] [PubMed]
  13. N.V. Didenko, A.V. Konyashchenko, A.P. Lutsenko, and S. Yu Tenyakov., “Contrast degradation in a chirped-pulse amplifier due to generation of prepulses by postpulses,” Opt. Express 16, 3178–3190 (2008).
    [Crossref] [PubMed]
  14. D. Schimpf, E. Seise, J. Limpert, and A. Tunnermann, “The impact of spectral modulations on the contrast of pulses of nonlinearchirped-pulse amplification systems,” Opt. Express 16, 10664–10674 (2008).
    [Crossref] [PubMed]
  15. J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express 19, 17053–17058 (2011).
    [Crossref] [PubMed]
  16. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H. 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, 13218–13224 (2011).
    [Crossref] [PubMed]

2014 (1)

G. Mourou, T. Tajima, M.N. Quinn, B. Brocklesby, and J. Limpert., “Are fiber-based lasers the future of accelerators?” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 740, 17–20 (2014).
[Crossref]

2013 (2)

2012 (2)

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tunnermann., “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science and Applications 1, e8 (2012).
[Crossref]

J. Kerttula, V. Filippov, Y. Chamorovskii, V. Ustimchik, K. Golant, and O.G. Okhotnikov., “Principles and performance of tapered fiber lasers: from uniform to flared geometry,” Appl. Opt. 51, 7025–7038 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

2008 (3)

2007 (1)

2006 (1)

2001 (1)

A.V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

1998 (1)

Antipov, O.

Arkwright, J.W.

Atkins, G.R.

Bartelt, H.

Bellanger, C.

Birge, J.

Blondy, J-M.

Bourderionnet, J.

Brignon, A.

Brocklesby, B.

G. Mourou, T. Tajima, M.N. Quinn, B. Brocklesby, and J. Limpert., “Are fiber-based lasers the future of accelerators?” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 740, 17–20 (2014).
[Crossref]

Bubnov, M.M.

Chamorovskii, Y.

Chamorovskii, Yu

Chang, G.

Chen, H.

Chen, L.

Dianov, E.M.

Didenko, N.V.

Digonnet, M.J.

Dong, L.

Duparre, M.

Eidam, T.

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tunnermann., “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science and Applications 1, e8 (2012).
[Crossref]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H. 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, 13218–13224 (2011).
[Crossref] [PubMed]

Elango, P.

Fevrier, S.

Filippov, V.

Flamm, D.

Fotiadi, A.

Galvanauskas, A.

Golant, K.

Guryanov, A.N.

Hartung, A.

Herrmann, J.

A.V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Husakou, A.V.

A.V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Jamier, R.

Jansen, F.

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tunnermann., “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science and Applications 1, e8 (2012).
[Crossref]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H. 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, 13218–13224 (2011).
[Crossref] [PubMed]

Jauregui, C.

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tunnermann., “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science and Applications 1, e8 (2012).
[Crossref]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H. 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, 13218–13224 (2011).
[Crossref] [PubMed]

Kartner, F.

Kerttula, J.

Khanin, Ya. I.

Ya. I. Khanin, Fundamentals of Laser Dynamics, ( Int Science Publishing, Cambridge2006)

Khopin, V.F.

Konyashchenko, A.V.

Kuznetsov, M.

Li, J.

Likhachev, M.E.

Limpert, J.

Limpert., J.

G. Mourou, T. Tajima, M.N. Quinn, B. Brocklesby, and J. Limpert., “Are fiber-based lasers the future of accelerators?” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 740, 17–20 (2014).
[Crossref]

Liu, C.

Lorenz, A.

Lutsenko, A.P.

Megret, P.

Mourou, G.

G. Mourou, T. Tajima, M.N. Quinn, B. Brocklesby, and J. Limpert., “Are fiber-based lasers the future of accelerators?” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 740, 17–20 (2014).
[Crossref]

Okhotnikov., O. G.

Okhotnikov., O.G.

Otto, H.

Otto, H.-J.

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tunnermann., “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science and Applications 1, e8 (2012).
[Crossref]

Peng, X.

Pessa, M.

Primot, J.

Quinn, M.N.

G. Mourou, T. Tajima, M.N. Quinn, B. Brocklesby, and J. Limpert., “Are fiber-based lasers the future of accelerators?” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 740, 17–20 (2014).
[Crossref]

Salganskii, M.Y.

Schimpf, D.

Schmidt, O.

Schreiber, T.

Schroter, S.

Schulze, C.

Seise, E.

Semjonov, S.L.

Sosnowski, T.

Stutzki, F.

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tunnermann., “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science and Applications 1, e8 (2012).
[Crossref]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H. 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, 13218–13224 (2011).
[Crossref] [PubMed]

Tajima, T.

G. Mourou, T. Tajima, M.N. Quinn, B. Brocklesby, and J. Limpert., “Are fiber-based lasers the future of accelerators?” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 740, 17–20 (2014).
[Crossref]

Tenyakov., S. Yu

Tunnermann, A.

Tünnermann, A.

Tunnermann., A.

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tunnermann., “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science and Applications 1, e8 (2012).
[Crossref]

Ustimchik, V.

Whitbread, T.

Wirth, C.

Appl. Opt. (1)

J. Lightwave Technol. (1)

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

Light: Science and Applications (1)

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tunnermann., “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science and Applications 1, e8 (2012).
[Crossref]

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment (1)

G. Mourou, T. Tajima, M.N. Quinn, B. Brocklesby, and J. Limpert., “Are fiber-based lasers the future of accelerators?” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 740, 17–20 (2014).
[Crossref]

Opt. Express (9)

S. Fevrier, R. Jamier, J-M. Blondy, S.L. Semjonov, M.E. Likhachev, M.M. Bubnov, E.M. Dianov, V.F. Khopin, M.Y. Salganskii, and A.N. Guryanov, “Low-loss singlemode large mode area all-silica photonic bandgap fiber,” Opt. Express 14, 562–569 (2006).
[Crossref] [PubMed]

H. Chen, T. Sosnowski, C. Liu, L. Chen, J. Birge, A. Galvanauskas, F. Kartner, and G. Chang, “Chirally-coupled-core Yb-fiber laser delivering 80-fs pulses with diffraction-limited beam quality warranted by a high-dispersion mirror based compressor,” Opt. Express 18, 24699–24705 (2010).
[Crossref] [PubMed]

V. Filippov, Yu Chamorovskii, J. Kerttula, K. Golant, M. Pessa, and O. G. Okhotnikov., “Double clad tapered fiber for high power applications,” Opt. Express 16, 1929–1944 (2008).
[Crossref] [PubMed]

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

C. Schulze, A. Lorenz, D. Flamm, A. Hartung, S. Schroter, H. Bartelt, and M. Duparre, “Mode resolved bend loss in few-mode optical fibers,” Opt. Express 21, 3170–3181 (2013).
[Crossref] [PubMed]

N.V. Didenko, A.V. Konyashchenko, A.P. Lutsenko, and S. Yu Tenyakov., “Contrast degradation in a chirped-pulse amplifier due to generation of prepulses by postpulses,” Opt. Express 16, 3178–3190 (2008).
[Crossref] [PubMed]

D. Schimpf, E. Seise, J. Limpert, and A. Tunnermann, “The impact of spectral modulations on the contrast of pulses of nonlinearchirped-pulse amplification systems,” Opt. Express 16, 10664–10674 (2008).
[Crossref] [PubMed]

J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express 19, 17053–17058 (2011).
[Crossref] [PubMed]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H. 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, 13218–13224 (2011).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

A.V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Other (1)

Ya. I. Khanin, Fundamentals of Laser Dynamics, ( Int Science Publishing, Cambridge2006)

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Figures (8)

Fig. 1
Fig. 1 Amplification of 0.5 ns pulses in 0.5 meter long tapered fiber: (a) distribution of field amplitude at y = 0, t = 0 along the fiber, (b) transverse output field distribution at the time corresponding to absolute pulse maximum, (c) distribution of output field amplitude at y = 0 as a function of x and t, (d) evolution of pulse temporal profile at the core center, (e) evolution of spectral amplitude at the core center, (f) evolution of nonlinear frequency modulation at the core center, (g) fiber diameter (solid line) and effective area of fundamental mode Aeff (dashed line), (h) total pulse energy (solid line) and peak intensity (dashed line). Note that color maps represent amplitude (square root of intensity) distributions.
Fig. 2
Fig. 2 The influence of different perturbations on the mode structure and spatiotemporal distortions during amplification of 0.5 ns pulse in tapered fiber: (a) distribution of field amplitude at y = 0 along the fiber, (b) transverse output field distribution at the time corresponding to the absolute pulse maximum, (c) distribution of output field amplitude at y = 0 as a function of x and t; (d,e,f) - the same as (a,b,c) but for the fiber bent with the radius increasing from 10 cm to 60 cm; (g,h,i) - the same as (a,b,c), but for the fiber with regular core shift from the centerline with amplitude of 4 μm; (g,h,i) - the same as (a,b,c) but for the fiber with random core shift from the centerline (peak-to peak amplitude of variations is 1 μm); (i,k,l) - the same as (a,b,c) but for the fiber with complicated refractive index profile fitted to the one measured in the preform.
Fig. 3
Fig. 3 Distortions of the spectrum and the chirp of the pulse with postpulse (50 dB lower intensity at the input) due to nonlinear phase resulting from SPM: (a) Distribution of output field amplitude at y = 0 as a function of x and t, (b) output spectrum at y = 0, (c) spectrum evolution at the core center, (d) frequency modulation evolution at the core center.
Fig. 4
Fig. 4 Energy scaling of 1 ns pulses: (a) output energy from 10–60 μm taper versus small signal gain at 1030 nm for input pulse energy 10 μJ (crosses) and 20 μJ (rhombs), (b) maximum peak intensity at the output of 10–60 μm taper as a function of output energy, (c) and (d) - the same as in (a) and (b) but for 10–110μm taper.
Fig. 5
Fig. 5 Amplification of 10μJ 1 ns pulses in 10–110 μm taper: (a) distribution of field amplitude at y = 0,t = 0 along the fiber, (b) transverse output field distribution at the time corresponding to the absolute pulse maximum, (c) distribution of output field amplitude at y = 0 as a function of x and t, (g) the pulse energy (solid line) and peak intensity (dashed line). The same for 20μJ input pulse (d,e,f,h).
Fig. 6
Fig. 6 Compression of pulses amplified in 10–60 μm tapers: (a) temporal profile of ideally compressed pulse after unperturbed amplifier (blue curve), compressed pulse after irregular taper at the core center (black curve) and in 10 μm off-center position (red curve). Compression of the pulse amplified in 10–110 μm taper (b). Insets show spatiotemporal intensity distributions and compressed pulse profiles on linear scale.
Fig. 7
Fig. 7 Far field pattern of 36 combined channels: (a) temporal intensity distributions of combined and compressed pulses, (b) combined and compressed pulse (red curve), compressed pulse in one individual perturbed channel (black curve), compressed pulse from unperturbed amplifier (blue rhombs). Inset shows compressed pulse profiles on linear scale.
Fig. 8
Fig. 8 Combining efficiency as a function of the number of combined channels. Insets show beam arrangement patterns.

Equations (12)

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n ( x , y , ω ) = n 0 ( ω ) + Δ n ( x , y , z , ω ) ,
E ( x , y , z , t ) = Re ( A ( x , y , z , t ) exp ( i k 0 z i ω 0 t ) ) ,
A ω ( x , y , z , ω ) = F ^ ω [ A ( x , y , z , t ) ] ,
F ^ ω [ A ] = 1 2 π + A ( x , y , z , t ) exp ( i ω t ) d t ,
A k ( k x , k y , z , t ) = F ^ k [ A ( x , y , z , t ) ] ,
F ^ k [ A ] = 1 2 π + A ( x , y , z , t ) exp ( i k x x i k y y ) d x d y
A ω k ( k x , k y , z , ω ˜ ) z = i ( ω 2 n 0 ( ω ) 2 / c 2 k x 2 k y 2 k 0 k 1 ω ˜ ) A ω k + + i F ^ k [ ω A ω ( x , y , z , ω ˜ ) Δ n ( x , y , z , ω ) / c ] + i F ^ ω k [ ω 0 n 2 A ( x , y , z , t ) | A ( x , y , z , t ) | 2 / c ] + F ^ k [ G ( A ) ]
P ( t ) t + [ 1 T 2 i ( ω 0 ω 21 ) ] P ( t ) = i d 2 N h ¯ A ( t ) Δ ρ ( t )
P ω ( ω ˜ ) = i N ( x , y , z ) L ( ω ˜ ) F ^ ω [ A ( t ) Δ ρ ( t ) ] ,
A ω k ( x , y , z , ω ˜ ) z = σ L + i β 2 N ( x , y , z ) F ^ ω [ A ( t ) Δ N ( t ) ] ,
A ω ( x , y , z , ω ˜ ) z = G = N ( x , y , z ) 2 ( ( σ e ( ω ) + i β 1 ) F ^ ω [ A ( t ) ρ 2 ( t ) ] ( σ a ( ω ) + i β 2 ) F ^ ω [ A ( t ) ρ 1 ( t ) ] ) .
N ( x , y , z ) h ¯ ω 0 2 π n 0 c ρ 2 ( x , y , z , t ) t = ( | A ( x , y , z , t ) | 2 z ) Due to gain .

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