Abstract

The effects of aberrations on coherent beam combination (CBC) of nanosecond fiber lasers are analyzed in this paper. These effects include imperfect overlap of the pulses, spectral phase shift, and nonlinear phase shift, which are induced by optical path difference and self-phase modulation. A typical system of CBC of two lasers is calculated in detail and design guidelines are given.

© 2013 Optical Society of America

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  1. J. Geng, Q. Wang, Z. Jiang, T. Luo, S. Jiang, and G. Czarnecki, “Kilowatt-peak-power, single-frequency, pulsed fiber laser near 2 μm,” Opt. Lett. 36, 2293–2295 (2011).
    [CrossRef]
  2. W. Shi, M. A. Leigh, J. Zong, Z. Yao, D. T. Nguyen, A. Chavez-Pirson, and N. Peyghambarian, “High-power all-fiber-based narrow-linewidth single-mode fiber laser pulses in the C-band and frequency conversion to THz generation,” IEEE J. Sel. Top. Quantum Electron. 15, 377–384 (2009).
    [CrossRef]
  3. A. Liu, M. A. Norsen, and R. D. Mead, “60 W green output by frequency doubling of a polarized Yb-doped fiber laser,” Opt. Lett. 30, 67–69 (2005).
    [CrossRef]
  4. P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
    [CrossRef]
  5. B. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34, 863–865 (2009).
    [CrossRef]
  6. M. A. Vorontsov, S. L. Lachinova, L. A. Beresnev, and T. Weyrauch, “Obscuration-free pupil-plane phase locking of a coherent array of fiber collimators,” J. Opt. Soc. Am. A 27, A106–A121 (2010).
    [CrossRef]
  7. T. M. Shay, V. Benham, J. T. Baker, C. B. Ward, A. D. Sanchez, M. A. Culpepper, S. D. Pilkington, L. J. Spring, L. D. J. Nelson, and L. C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14, 12015–12021 (2006).
    [CrossRef]
  8. G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. S. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4 kW fiber amplifier,” Opt. Lett. 35, 1542–1544 (2010).
    [CrossRef]
  9. B. He, Q. Lou, J. Zhou, J. Dong, Y. Wei, D. Xue, Y. Qi, Z. Su, L. Li, and F. Zhang, “High power coherent beam combination from two fiber lasers,” Opt. Express 14, 2721–2726(2006).
    [CrossRef]
  10. E. Seise, A. Klenke, S. Breitkopf, J. Limpert, and A. Tünermann, “88 W 0.5 mJ femtosecond laser pulses from two coherently combined fiber amplifiers,” Opt. Lett. 36, 3858–3860 (2011).
    [CrossRef]
  11. S. Palese, E. Cheung, G. Goodno, C. Shih, F. Di Teodoro, T. McComb, and M. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime with intra-pulse phase control,” Opt. Express 20, 7422–7435 (2012).
    [CrossRef]
  12. A. Klenke, E. Seise, S. Demmler, J. Rothhardt, S. Breitkopf, J. Limpert, and A. Tünnermann, “Coherently-combined two channel femtosecond fiber CPA system producing 3 mJ pulse energy,” Opt. Express 19, 24280–24285 (2011).
    [CrossRef]
  13. L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett. 36, 621–623 (2011).
    [CrossRef]
  14. R. Su, P. Zhou, X. Wang, H. Zhang, and X. Xu, “Active coherent beam combining of a five-element, 800 watt nanosecond fiber amplifier array,” Opt. Lett. 37, 3978–3980 (2012).
    [CrossRef]
  15. H. Liu, B. He, J. Zhou, J. Dong, Y. Wei, and Q. Lou, “Coherent beam combination of two nanosecond fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 37, 3885–3887 (2012).
    [CrossRef]
  16. G. D. Goodno, C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18, 25403–25414 (2010).
    [CrossRef]
  17. P. Zhou, Z. Liu, X. Xu, and Z. Chen, “Numerical analysis of the effects of aberrations on coherently combined fiber laser beams,” Appl. Opt. 47, 3350–3359 (2008).
    [CrossRef]
  18. A. Klenke, E. Seise, J. Limpert, and A. Tünnermann, “Basic considerations on coherent combining of ultrashort laser pulses,” Opt. Express 19, 25379–25387 (2011).
    [CrossRef]
  19. S. Jiang, M. Hanna, F. Druon, and P. Georges, “Impact of self-phase modulation on coherently combined fiber chirped-pulse amplifiers,” Opt. Lett. 35, 1293–1295 (2010).
    [CrossRef]
  20. L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Impact of spectral phase mismatch on femtosecond coherent beam combining systems,” Opt. Lett. 37, 650–652 (2012).
    [CrossRef]
  21. M. D. Perry, T. Ditmire, and B. C. Stuart, “Self-phase modulation in chirped-pulse amplification,” Opt. Lett. 19, 2149–2151 (1994).
    [CrossRef]
  22. D. Schimpf, E. Seise, J. Limpert, and A. Tünnermann, “Self-phase modulation compensated by positive dispersion in chirped-pulse systems,” Opt. Express 17, 4997–5007 (2009).
    [CrossRef]

2012

2011

2010

2009

W. Shi, M. A. Leigh, J. Zong, Z. Yao, D. T. Nguyen, A. Chavez-Pirson, and N. Peyghambarian, “High-power all-fiber-based narrow-linewidth single-mode fiber laser pulses in the C-band and frequency conversion to THz generation,” IEEE J. Sel. Top. Quantum Electron. 15, 377–384 (2009).
[CrossRef]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

B. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34, 863–865 (2009).
[CrossRef]

D. Schimpf, E. Seise, J. Limpert, and A. Tünnermann, “Self-phase modulation compensated by positive dispersion in chirped-pulse systems,” Opt. Express 17, 4997–5007 (2009).
[CrossRef]

2008

2006

2005

1994

Baker, J. T.

Benham, V.

Beresnev, L. A.

Bourdon, P.

Breitkopf, S.

Chavez-Pirson, A.

W. Shi, M. A. Leigh, J. Zong, Z. Yao, D. T. Nguyen, A. Chavez-Pirson, and N. Peyghambarian, “High-power all-fiber-based narrow-linewidth single-mode fiber laser pulses in the C-band and frequency conversion to THz generation,” IEEE J. Sel. Top. Quantum Electron. 15, 377–384 (2009).
[CrossRef]

Chen, Z.

Cheung, E.

Culpepper, M. A.

Czarnecki, G.

Daniault, L.

Demmler, S.

Di Teodoro, F.

Ditmire, T.

Dong, J.

Druon, F.

Geng, J.

Georges, P.

Goodno, G.

Goodno, G. D.

Goular, D.

Guo, S.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Hanna, M.

He, B.

Jiang, S.

Jiang, Z.

Klenke, A.

Lachinova, S. L.

Leigh, M. A.

W. Shi, M. A. Leigh, J. Zong, Z. Yao, D. T. Nguyen, A. Chavez-Pirson, and N. Peyghambarian, “High-power all-fiber-based narrow-linewidth single-mode fiber laser pulses in the C-band and frequency conversion to THz generation,” IEEE J. Sel. Top. Quantum Electron. 15, 377–384 (2009).
[CrossRef]

Li, L.

Limpert, J.

Liu, A.

Liu, H.

Liu, Z.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

P. Zhou, Z. Liu, X. Xu, and Z. Chen, “Numerical analysis of the effects of aberrations on coherently combined fiber laser beams,” Appl. Opt. 47, 3350–3359 (2008).
[CrossRef]

Lombard, L.

Lou, Q.

Lu, L. C. A.

Luo, T.

Ma, H.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Ma, Y.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

McComb, T.

McComb, T. S.

McNaught, S. J.

Mead, R. D.

Mies, E.

Minden, M.

Mottay, E.

Nelson, L. D. J.

Nguyen, D. T.

W. Shi, M. A. Leigh, J. Zong, Z. Yao, D. T. Nguyen, A. Chavez-Pirson, and N. Peyghambarian, “High-power all-fiber-based narrow-linewidth single-mode fiber laser pulses in the C-band and frequency conversion to THz generation,” IEEE J. Sel. Top. Quantum Electron. 15, 377–384 (2009).
[CrossRef]

Norsen, M. A.

Palese, S.

Perry, M. D.

Peyghambarian, N.

W. Shi, M. A. Leigh, J. Zong, Z. Yao, D. T. Nguyen, A. Chavez-Pirson, and N. Peyghambarian, “High-power all-fiber-based narrow-linewidth single-mode fiber laser pulses in the C-band and frequency conversion to THz generation,” IEEE J. Sel. Top. Quantum Electron. 15, 377–384 (2009).
[CrossRef]

Pilkington, S. D.

Qi, Y.

Rothenberg, J. E.

Rothhardt, J.

Sanchez, A.

Sanchez, A. D.

Schimpf, D.

Seise, E.

Shay, T. M.

Shi, W.

W. Shi, M. A. Leigh, J. Zong, Z. Yao, D. T. Nguyen, A. Chavez-Pirson, and N. Peyghambarian, “High-power all-fiber-based narrow-linewidth single-mode fiber laser pulses in the C-band and frequency conversion to THz generation,” IEEE J. Sel. Top. Quantum Electron. 15, 377–384 (2009).
[CrossRef]

Shih, C.

Spring, L. J.

Stuart, B. C.

Su, R.

Su, Z.

Thielen, P. A.

Tünermann, A.

Tünnermann, A.

Vorontsov, M. A.

Wang, B.

Wang, Q.

Wang, X.

R. Su, P. Zhou, X. Wang, H. Zhang, and X. Xu, “Active coherent beam combining of a five-element, 800 watt nanosecond fiber amplifier array,” Opt. Lett. 37, 3978–3980 (2012).
[CrossRef]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Ward, C. B.

Weber, M.

Weber, M. E.

Wei, Y.

Weyrauch, T.

Wickham, M. G.

Xu, X.

Xue, D.

Yao, Z.

W. Shi, M. A. Leigh, J. Zong, Z. Yao, D. T. Nguyen, A. Chavez-Pirson, and N. Peyghambarian, “High-power all-fiber-based narrow-linewidth single-mode fiber laser pulses in the C-band and frequency conversion to THz generation,” IEEE J. Sel. Top. Quantum Electron. 15, 377–384 (2009).
[CrossRef]

Zaouter, Y.

Zhang, F.

Zhang, H.

Zhou, J.

Zhou, P.

Zong, J.

W. Shi, M. A. Leigh, J. Zong, Z. Yao, D. T. Nguyen, A. Chavez-Pirson, and N. Peyghambarian, “High-power all-fiber-based narrow-linewidth single-mode fiber laser pulses in the C-band and frequency conversion to THz generation,” IEEE J. Sel. Top. Quantum Electron. 15, 377–384 (2009).
[CrossRef]

Appl. Opt.

IEEE J. Sel. Top. Quantum Electron.

W. Shi, M. A. Leigh, J. Zong, Z. Yao, D. T. Nguyen, A. Chavez-Pirson, and N. Peyghambarian, “High-power all-fiber-based narrow-linewidth single-mode fiber laser pulses in the C-band and frequency conversion to THz generation,” IEEE J. Sel. Top. Quantum Electron. 15, 377–384 (2009).
[CrossRef]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

T. M. Shay, V. Benham, J. T. Baker, C. B. Ward, A. D. Sanchez, M. A. Culpepper, S. D. Pilkington, L. J. Spring, L. D. J. Nelson, and L. C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14, 12015–12021 (2006).
[CrossRef]

B. He, Q. Lou, J. Zhou, J. Dong, Y. Wei, D. Xue, Y. Qi, Z. Su, L. Li, and F. Zhang, “High power coherent beam combination from two fiber lasers,” Opt. Express 14, 2721–2726(2006).
[CrossRef]

A. Klenke, E. Seise, J. Limpert, and A. Tünnermann, “Basic considerations on coherent combining of ultrashort laser pulses,” Opt. Express 19, 25379–25387 (2011).
[CrossRef]

S. Palese, E. Cheung, G. Goodno, C. Shih, F. Di Teodoro, T. McComb, and M. Weber, “Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime with intra-pulse phase control,” Opt. Express 20, 7422–7435 (2012).
[CrossRef]

A. Klenke, E. Seise, S. Demmler, J. Rothhardt, S. Breitkopf, J. Limpert, and A. Tünnermann, “Coherently-combined two channel femtosecond fiber CPA system producing 3 mJ pulse energy,” Opt. Express 19, 24280–24285 (2011).
[CrossRef]

G. D. Goodno, C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18, 25403–25414 (2010).
[CrossRef]

D. Schimpf, E. Seise, J. Limpert, and A. Tünnermann, “Self-phase modulation compensated by positive dispersion in chirped-pulse systems,” Opt. Express 17, 4997–5007 (2009).
[CrossRef]

Opt. Lett.

J. Geng, Q. Wang, Z. Jiang, T. Luo, S. Jiang, and G. Czarnecki, “Kilowatt-peak-power, single-frequency, pulsed fiber laser near 2 μm,” Opt. Lett. 36, 2293–2295 (2011).
[CrossRef]

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett. 36, 621–623 (2011).
[CrossRef]

R. Su, P. Zhou, X. Wang, H. Zhang, and X. Xu, “Active coherent beam combining of a five-element, 800 watt nanosecond fiber amplifier array,” Opt. Lett. 37, 3978–3980 (2012).
[CrossRef]

H. Liu, B. He, J. Zhou, J. Dong, Y. Wei, and Q. Lou, “Coherent beam combination of two nanosecond fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 37, 3885–3887 (2012).
[CrossRef]

S. Jiang, M. Hanna, F. Druon, and P. Georges, “Impact of self-phase modulation on coherently combined fiber chirped-pulse amplifiers,” Opt. Lett. 35, 1293–1295 (2010).
[CrossRef]

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Impact of spectral phase mismatch on femtosecond coherent beam combining systems,” Opt. Lett. 37, 650–652 (2012).
[CrossRef]

M. D. Perry, T. Ditmire, and B. C. Stuart, “Self-phase modulation in chirped-pulse amplification,” Opt. Lett. 19, 2149–2151 (1994).
[CrossRef]

E. Seise, A. Klenke, S. Breitkopf, J. Limpert, and A. Tünermann, “88 W 0.5 mJ femtosecond laser pulses from two coherently combined fiber amplifiers,” Opt. Lett. 36, 3858–3860 (2011).
[CrossRef]

G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. S. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4 kW fiber amplifier,” Opt. Lett. 35, 1542–1544 (2010).
[CrossRef]

B. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34, 863–865 (2009).
[CrossRef]

A. Liu, M. A. Norsen, and R. D. Mead, “60 W green output by frequency doubling of a polarized Yb-doped fiber laser,” Opt. Lett. 30, 67–69 (2005).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Schematic of OPD-induced imperfect overlap between pulses and spectral phase shift.

Fig. 2.
Fig. 2.

Typical shapes of the combined pulses when CBC of two pulsed lasers with νFWHM of (a) 0.15 GHz, (b) 1 GHz, (c) 5 GHz, and (d) 10 GHz.

Fig. 3.
Fig. 3.

Dependencies of the normalized (a) pulse energy and (b) peak power of combined pulses on the OPD and of the spectral bandwidth, and (c) the maximum acceptable OPD when the pulse energy is more than 95%.

Fig. 4.
Fig. 4.

(a) Nonlinear phase shift and (b) spectral phase shift when OPD is not zero.

Fig. 5.
Fig. 5.

Typical shapes of the combined pulses when CBC of pulsed lasers with the same B-integral and with νFWHM of (a) 0.15 GHz, (b) 1 GHz, and (c) 3 GHz.

Fig. 6.
Fig. 6.

Dependencies of the normalized pulse energy (up) and peak power (down) of combined pulses on the OPD and of B-integral when νFWHM is (a) and (d) 0.15 GHz, (b) and (e) 1 GHz and (c) and (f) 3 GHz.

Fig. 7.
Fig. 7.

Dependencies of the (a) normalized pulse energy and (b) peak power of combined pulses on the Δφother and of B-integral difference.

Fig. 8.
Fig. 8.

Dependencies of the optimum Δφother for (a) CBC and (b) maximal pulse energy of combined pulses on B-integral difference.

Fig. 9.
Fig. 9.

Typical shapes of the combined pulses when maximal pulse energy (left) and peak power (right) are obtained: (a) and (b) E01=E0, and (c) and (d) E01=0.5E02.

Equations (18)

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

En(r⃑,ν,t)=E0n(r⃑)An(t)Sn(ν)exp[i(2πνt+ϕn(ν,t))].
ϕn(ν,t)=φchirp(ν)+φdelay-n(ν)+φNL-n(t)+φother-n(t),
I(r⃑,ν,t)=(n=1n=NEn(r⃑,ν,t))(n=1n=NEn(r⃑,ν,t))*,
I(r⃑,t)=I(r⃑,ν,t)dν.
En(ν,t)=E0nAn(t)Sn(ν)exp[i(2πνtϕ(ν,t))],
I(ν,t)=(n=1,2En(ν,t))(n=1,2En(ν,t))*=I1(ν,t)+I2(ν,t)+2I1(ν,t)I2(ν,t)cos(Δϕ(ν,t))
Δϕ(ν,t)=Δφchirp(ν)+Δφdelay(ν)+ΔφNL(t)+Δφother(t),
I(t)=I(ν,t))dν,
J=I(t)dt,
Δϕ(ν,t)=Δϕdelay(ν)+ΔϕNL(t)+Δϕother(t),
I(t)=I1(t)+I2(t)+2E01E02S(ν)1S(ν)2A1(t)A2(tΔt)cos(Δϕ(ν,t))dν
J=J1+J2+2E01E02S1(ν)S2(ν)A1(t)A2(tΔt)cos(Δϕ(ν,t))dνdt
An(t)=exp[2ln2(tt0tFWHM)2],
Sn(ω)=exp[2ln2(νν0νFWHM)2],
ϕNL(t)=BA2(t).
Leff=[exp(gLg)1]/g+exp(gLg)Ld,
ΔφNL(t)=B1A12(t)B2A22(t).
ΔϕNL(t)=B1A12(t)B2A22(t)=ΔBA2(t),

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