Abstract

A compact multicore ytterbium doped fiber amplifier has been implemented according to the spectral division scheme. It was shown that it allows amplification of pulses with about 40 nm wide spectrum. Compensation of the different spectral bands delay through bending and twist of the multicore ribbon fiber followed by appropriate setting of their phase permitted the synthesis of pulses close to 100 fs duration.

© 2015 Optical Society of America

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References

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  1. 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(2), 94–96 (2010).
    [Crossref] [PubMed]
  2. S. Zhou, F. W. Wise, and D. G. Ouzounov, “Divided-pulse amplification of ultrashort pulses,” Opt. Lett. 32(7), 871–873 (2007).
    [Crossref] [PubMed]
  3. Y. Zaouter, F. Guichard, L. Daniault, M. Hanna, F. Morin, C. Hönninger, E. Mottay, F. Druon, and P. Georges, “Femtosecond fiber chirped- and divided-pulse amplification system,” Opt. Lett. 38(2), 106–108 (2013).
    [Crossref] [PubMed]
  4. M. Kienel, A. Klenke, T. Eidam, S. Hädrich, J. Limpert, and A. Tünnermann, “Energy scaling of femtosecond amplifiers using actively controlled divided-pulse amplification,” Opt. Lett. 39(4), 1049–1052 (2014).
    [Crossref] [PubMed]
  5. A. Klenke, S. Hädrich, T. Eidam, J. Rothhardt, M. Kienel, S. Demmler, T. Gottschall, J. Limpert, and A. Tünnermann, “22 GW peak-power fiber chirped-pulse-amplification system,” Opt. Lett. 39(24), 6875–6878 (2014).
    [Crossref] [PubMed]
  6. 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(5), 621–623 (2011).
    [Crossref] [PubMed]
  7. L. A. Siiman, W.-Z. Chang, T. Zhou, and A. Galvanauskas, “Coherent femtosecond pulse combining of multiple parallel chirped pulse fiber amplifiers,” Opt. Express 20(16), 18097–18116 (2012).
    [Crossref] [PubMed]
  8. L. P. Ramirez, M. Hanna, G. Bouwmans, H. El Hamzaoui, M. Bouazaoui, D. Labat, K. Delplace, J. Pouysegur, F. Guichard, P. Rigaud, V. Kermène, A. Desfarges-Berthelemot, A. Barthélémy, F. Prévost, L. Lombard, Y. Zaouter, F. Druon, and P. Georges, “Coherent beam combining with an ultrafast multicore Yb-doped fiber amplifier,” Opt. Express 23(5), 5406–5416 (2015).
    [Crossref] [PubMed]
  9. Y. Zaouter, L. Daniault, M. Hanna, D. N. Papadopoulos, F. Morin, C. Hönninger, F. Druon, E. Mottay, and P. Georges, “Passive coherent combination of two ultrafast rod type fiber chirped pulse amplifiers,” Opt. Lett. 37(9), 1460–1462 (2012).
    [Crossref] [PubMed]
  10. F. Guichard, Y. Zaouter, M. Hanna, K. L. Mai, F. Morin, C. Hönninger, E. Mottay, and P. Georges, “High-energy chirped- and divided-pulse Sagnac femtosecond fiber amplifier,” Opt. Lett. 40(1), 89–92 (2015).
    [Crossref] [PubMed]
  11. D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
    [Crossref]
  12. C. P. Hauri, M. Bruck, W. Kornelis, J. Biegert, and U. Keller, “Generation of 14.8-fs pulses in a spatially dispersed amplifier,” Opt. Lett. 29(2), 201–203 (2004).
    [Crossref] [PubMed]
  13. Method and device for amplifying an optical signal, patent FR20100057107 20100907; WO2011FR52027 20110905.
  14. W-Z. Chang, T. Zhou, L. A. Siiman, and A. Galvanauskas, “Femtosecond pulse coherent combining and spectral synthesis using four parallel chirped pulse fiber amplifiers,” in Advanced Solid-States Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2012), paper AM4A.25.
    [Crossref]
  15. W.-Z. Chang, T. Zhou, L. A. Siiman, and A. Galvanauskas, “Femtosecond pulse spectral synthesis in coherently-spectrally combined multi-channel fiber chirped pulse amplifiers,” Opt. Express 21(3), 3897–3910 (2013).
    [Crossref] [PubMed]
  16. P. Rigaud, V. Kermene, G. Bouwmans, L. Bigot, A. Desfarges-Berthelemot, D. Labat, A. Le Rouge, T. Mansuryan, and A. Barthélémy, “Spatially dispersive amplification in a 12-core fiber and femtosecond pulse synthesis by coherent spectral combining,” Opt. Express 21(11), 13555–13563 (2013).
    [Crossref] [PubMed]
  17. F. Guichard, M. Hanna, L. Lombard, Y. Zaouter, C. Hönninger, F. Morin, F. Druon, E. Mottay, and P. Georges, “Two-channel pulse synthesis to overcome gain narrowing in femtosecond fiber amplifiers,” Opt. Lett. 38(24), 5430–5433 (2013).
    [Crossref] [PubMed]
  18. A. Klenke, M. Wojdyr, M. Müller, M. Kienel, T. Eidam, H. J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Large pitch Multicore Fiber for Coherent Combination of Ultrashort Pulses,” in 2015 European Conference on Lasers and Electro-Optics - European Quantum Electronics Conference, (Optical Society of America, 2015), paper CJ 1.2.
  19. I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
    [Crossref]
  20. H.-J. Otto, A. Klenke, C. Jauregui, F. Stutzki, J. Limpert, and A. Tünnermann, “Scaling the mode instability threshold with multicore fibers,” Opt. Lett. 39(9), 2680–2683 (2014).
    [Crossref] [PubMed]

2015 (2)

2014 (3)

2013 (4)

2012 (3)

2011 (1)

2010 (1)

2008 (1)

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
[Crossref]

2007 (1)

2004 (1)

Andersen, T. V.

Barthélémy, A.

Biegert, J.

Bigot, L.

Bouazaoui, M.

Bourdon, P.

Bouwmans, G.

Bruck, M.

Chang, W.-Z.

Daniault, L.

Delplace, K.

Demmler, S.

Desfarges-Berthelemot, A.

Druon, F.

Eidam, T.

El Hamzaoui, H.

Gabler, T.

Galvanauskas, A.

Georges, P.

F. Guichard, Y. Zaouter, M. Hanna, K. L. Mai, F. Morin, C. Hönninger, E. Mottay, and P. Georges, “High-energy chirped- and divided-pulse Sagnac femtosecond fiber amplifier,” Opt. Lett. 40(1), 89–92 (2015).
[Crossref] [PubMed]

L. P. Ramirez, M. Hanna, G. Bouwmans, H. El Hamzaoui, M. Bouazaoui, D. Labat, K. Delplace, J. Pouysegur, F. Guichard, P. Rigaud, V. Kermène, A. Desfarges-Berthelemot, A. Barthélémy, F. Prévost, L. Lombard, Y. Zaouter, F. Druon, and P. Georges, “Coherent beam combining with an ultrafast multicore Yb-doped fiber amplifier,” Opt. Express 23(5), 5406–5416 (2015).
[Crossref] [PubMed]

F. Guichard, M. Hanna, L. Lombard, Y. Zaouter, C. Hönninger, F. Morin, F. Druon, E. Mottay, and P. Georges, “Two-channel pulse synthesis to overcome gain narrowing in femtosecond fiber amplifiers,” Opt. Lett. 38(24), 5430–5433 (2013).
[Crossref] [PubMed]

Y. Zaouter, F. Guichard, L. Daniault, M. Hanna, F. Morin, C. Hönninger, E. Mottay, F. Druon, and P. Georges, “Femtosecond fiber chirped- and divided-pulse amplification system,” Opt. Lett. 38(2), 106–108 (2013).
[Crossref] [PubMed]

Y. Zaouter, L. Daniault, M. Hanna, D. N. Papadopoulos, F. Morin, C. Hönninger, F. Druon, E. Mottay, and P. Georges, “Passive coherent combination of two ultrafast rod type fiber chirped pulse amplifiers,” Opt. Lett. 37(9), 1460–1462 (2012).
[Crossref] [PubMed]

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(5), 621–623 (2011).
[Crossref] [PubMed]

Gottschall, T.

Goular, D.

Grüner-Nielsen, L.

D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
[Crossref]

Guichard, F.

Hädrich, S.

Hanf, S.

Hanna, M.

F. Guichard, Y. Zaouter, M. Hanna, K. L. Mai, F. Morin, C. Hönninger, E. Mottay, and P. Georges, “High-energy chirped- and divided-pulse Sagnac femtosecond fiber amplifier,” Opt. Lett. 40(1), 89–92 (2015).
[Crossref] [PubMed]

L. P. Ramirez, M. Hanna, G. Bouwmans, H. El Hamzaoui, M. Bouazaoui, D. Labat, K. Delplace, J. Pouysegur, F. Guichard, P. Rigaud, V. Kermène, A. Desfarges-Berthelemot, A. Barthélémy, F. Prévost, L. Lombard, Y. Zaouter, F. Druon, and P. Georges, “Coherent beam combining with an ultrafast multicore Yb-doped fiber amplifier,” Opt. Express 23(5), 5406–5416 (2015).
[Crossref] [PubMed]

F. Guichard, M. Hanna, L. Lombard, Y. Zaouter, C. Hönninger, F. Morin, F. Druon, E. Mottay, and P. Georges, “Two-channel pulse synthesis to overcome gain narrowing in femtosecond fiber amplifiers,” Opt. Lett. 38(24), 5430–5433 (2013).
[Crossref] [PubMed]

Y. Zaouter, F. Guichard, L. Daniault, M. Hanna, F. Morin, C. Hönninger, E. Mottay, F. Druon, and P. Georges, “Femtosecond fiber chirped- and divided-pulse amplification system,” Opt. Lett. 38(2), 106–108 (2013).
[Crossref] [PubMed]

Y. Zaouter, L. Daniault, M. Hanna, D. N. Papadopoulos, F. Morin, C. Hönninger, F. Druon, E. Mottay, and P. Georges, “Passive coherent combination of two ultrafast rod type fiber chirped pulse amplifiers,” Opt. Lett. 37(9), 1460–1462 (2012).
[Crossref] [PubMed]

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(5), 621–623 (2011).
[Crossref] [PubMed]

Hauri, C. P.

Hausmann, K.

D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
[Crossref]

Hönninger, C.

Jauregui, C.

Jespersen, K. G.

D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
[Crossref]

Keller, U.

Kermene, V.

Kermène, V.

Kienel, M.

Klenke, A.

Kornelis, W.

Kracht, D.

D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
[Crossref]

Labat, D.

Le Rouge, A.

Limpert, J.

Lombard, L.

Mai, K. L.

Mansuryan, T.

Morgner, U.

D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
[Crossref]

Morin, F.

Mortag, D.

D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
[Crossref]

Mosk, A. P.

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
[Crossref]

Mottay, E.

Neumann, J.

D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
[Crossref]

Otto, H.-J.

Ouzounov, D. G.

Papadopoulos, D. N.

Pouysegur, J.

Prévost, F.

Ramirez, L. P.

Rigaud, P.

Rothhardt, J.

Schreiber, T.

Seise, E.

Siiman, L. A.

Stutzki, F.

Theeg, T.

D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
[Crossref]

Tünnermann, A.

Vellekoop, I. M.

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
[Crossref]

Wandt, D.

D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
[Crossref]

Wirth, C.

Wise, F. W.

Zaouter, Y.

F. Guichard, Y. Zaouter, M. Hanna, K. L. Mai, F. Morin, C. Hönninger, E. Mottay, and P. Georges, “High-energy chirped- and divided-pulse Sagnac femtosecond fiber amplifier,” Opt. Lett. 40(1), 89–92 (2015).
[Crossref] [PubMed]

L. P. Ramirez, M. Hanna, G. Bouwmans, H. El Hamzaoui, M. Bouazaoui, D. Labat, K. Delplace, J. Pouysegur, F. Guichard, P. Rigaud, V. Kermène, A. Desfarges-Berthelemot, A. Barthélémy, F. Prévost, L. Lombard, Y. Zaouter, F. Druon, and P. Georges, “Coherent beam combining with an ultrafast multicore Yb-doped fiber amplifier,” Opt. Express 23(5), 5406–5416 (2015).
[Crossref] [PubMed]

F. Guichard, M. Hanna, L. Lombard, Y. Zaouter, C. Hönninger, F. Morin, F. Druon, E. Mottay, and P. Georges, “Two-channel pulse synthesis to overcome gain narrowing in femtosecond fiber amplifiers,” Opt. Lett. 38(24), 5430–5433 (2013).
[Crossref] [PubMed]

Y. Zaouter, F. Guichard, L. Daniault, M. Hanna, F. Morin, C. Hönninger, E. Mottay, F. Druon, and P. Georges, “Femtosecond fiber chirped- and divided-pulse amplification system,” Opt. Lett. 38(2), 106–108 (2013).
[Crossref] [PubMed]

Y. Zaouter, L. Daniault, M. Hanna, D. N. Papadopoulos, F. Morin, C. Hönninger, F. Druon, E. Mottay, and P. Georges, “Passive coherent combination of two ultrafast rod type fiber chirped pulse amplifiers,” Opt. Lett. 37(9), 1460–1462 (2012).
[Crossref] [PubMed]

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(5), 621–623 (2011).
[Crossref] [PubMed]

Zhou, S.

Zhou, T.

Opt. Commun. (2)

D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012).
[Crossref]

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
[Crossref]

Opt. Express (4)

Opt. Lett. (11)

Y. Zaouter, L. Daniault, M. Hanna, D. N. Papadopoulos, F. Morin, C. Hönninger, F. Druon, E. Mottay, and P. Georges, “Passive coherent combination of two ultrafast rod type fiber chirped pulse amplifiers,” Opt. Lett. 37(9), 1460–1462 (2012).
[Crossref] [PubMed]

F. Guichard, Y. Zaouter, M. Hanna, K. L. Mai, F. Morin, C. Hönninger, E. Mottay, and P. Georges, “High-energy chirped- and divided-pulse Sagnac femtosecond fiber amplifier,” Opt. Lett. 40(1), 89–92 (2015).
[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(2), 94–96 (2010).
[Crossref] [PubMed]

S. Zhou, F. W. Wise, and D. G. Ouzounov, “Divided-pulse amplification of ultrashort pulses,” Opt. Lett. 32(7), 871–873 (2007).
[Crossref] [PubMed]

Y. Zaouter, F. Guichard, L. Daniault, M. Hanna, F. Morin, C. Hönninger, E. Mottay, F. Druon, and P. Georges, “Femtosecond fiber chirped- and divided-pulse amplification system,” Opt. Lett. 38(2), 106–108 (2013).
[Crossref] [PubMed]

M. Kienel, A. Klenke, T. Eidam, S. Hädrich, J. Limpert, and A. Tünnermann, “Energy scaling of femtosecond amplifiers using actively controlled divided-pulse amplification,” Opt. Lett. 39(4), 1049–1052 (2014).
[Crossref] [PubMed]

A. Klenke, S. Hädrich, T. Eidam, J. Rothhardt, M. Kienel, S. Demmler, T. Gottschall, J. Limpert, and A. Tünnermann, “22 GW peak-power fiber chirped-pulse-amplification system,” Opt. Lett. 39(24), 6875–6878 (2014).
[Crossref] [PubMed]

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(5), 621–623 (2011).
[Crossref] [PubMed]

F. Guichard, M. Hanna, L. Lombard, Y. Zaouter, C. Hönninger, F. Morin, F. Druon, E. Mottay, and P. Georges, “Two-channel pulse synthesis to overcome gain narrowing in femtosecond fiber amplifiers,” Opt. Lett. 38(24), 5430–5433 (2013).
[Crossref] [PubMed]

C. P. Hauri, M. Bruck, W. Kornelis, J. Biegert, and U. Keller, “Generation of 14.8-fs pulses in a spatially dispersed amplifier,” Opt. Lett. 29(2), 201–203 (2004).
[Crossref] [PubMed]

H.-J. Otto, A. Klenke, C. Jauregui, F. Stutzki, J. Limpert, and A. Tünnermann, “Scaling the mode instability threshold with multicore fibers,” Opt. Lett. 39(9), 2680–2683 (2014).
[Crossref] [PubMed]

Other (3)

Method and device for amplifying an optical signal, patent FR20100057107 20100907; WO2011FR52027 20110905.

W-Z. Chang, T. Zhou, L. A. Siiman, and A. Galvanauskas, “Femtosecond pulse coherent combining and spectral synthesis using four parallel chirped pulse fiber amplifiers,” in Advanced Solid-States Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2012), paper AM4A.25.
[Crossref]

A. Klenke, M. Wojdyr, M. Müller, M. Kienel, T. Eidam, H. J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Large pitch Multicore Fiber for Coherent Combination of Ultrashort Pulses,” in 2015 European Conference on Lasers and Electro-Optics - European Quantum Electronics Conference, (Optical Society of America, 2015), paper CJ 1.2.

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Figures (7)

Fig. 1
Fig. 1 Oscillator pulse spectrum (black line) and broadened spectrum at the output of the polarization maintaining single mode fiber (red line).
Fig. 2
Fig. 2 Schematic drawing of the setup. The broad spectrum obtained after propagation of the oscillator pulses in a piece of single mode fiber is dispersed by a grating (G1) and then displayed on the deformable mirror (DM) for phase profiling. A microlens array (MLA) is used to couple the spectral bands into the multicore fiber amplifier (Yb MCF). On the fiber opposite side, the exit fields are collimated by a microlens array (MLA) and then combined in a common direction by a spectroscope (lens L4 + grating G2) to form the output beam. Pump radiations are combined with the laser field through the dichroic mirror DiM.
Fig. 3
Fig. 3 Picture of the multicore fiber arrangement for group delay adjustment by tilt (θ) of the loop (for better clarity, two channels only have been illustrated).
Fig. 4
Fig. 4 Measured differential group delay in the array at 1050 nm central wavelength, for different tilt angle of the multicore fiber loop.
Fig. 5
Fig. 5 Normalized spectra exiting from the different cores of the multicore fiber amplifier (individual recording at the exit of the set-up before spectral combining).
Fig. 6
Fig. 6 SHG-FROG traces of the synthesized pulses derived from simulation of the whole amplification scheme for illustration of the different steps to get the shortest output pulses.
Fig. 7
Fig. 7 Spectrum (a) and autocorrelation traces (b) of the synthesized pulses at the exit of the spectral division fiber amplifier before (in purple line) and after (in blue line) adjustment of the group delay and zero order phase of the different spectral channels. The autocorrelation trace of the pulse computed from the recorded spectrum and assuming a flat spectral phase is plot for comparison (red dotted line).

Equations (1)

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ΔL=2πnδsin(θ)

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