Abstract

We both theoretically and experimentally investigate the optimization of femtosecond Yb-doped fiber amplifiers (YDFAs) to achieve high-quality, high-power, compressed pulses. Ultrashort pulses amplified inside YDFAs are modeled by the generalized nonlinear Schrödinger equation coupled to the steady-state propagation-rate equations. We use this model to study the dependence of compressed-pulse quality on the YDFA parameters, such as the gain fiber’s doping concentration and length, and input pulse pre-chirp, duration, and power. The modeling results confirmed by experiments show that an optimum negative pre-chirp for the input pulse exists to achieve the best compression.

© 2012 OSA

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    [CrossRef] [PubMed]
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2012

2010

2009

2008

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1.,” Nature452(7187), 610–612 (2008).
[CrossRef] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D48(1), 57–66 (2008).
[CrossRef]

2007

2006

2004

2002

J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tünnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B74(2), 191–195 (2002).
[CrossRef]

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B19(3), 461–469 (2002).
[CrossRef]

2001

A. Galvanauskas, “Mode-scalable fiber-based chirped pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron.7(4), 504–517 (2001).
[CrossRef]

2000

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett.84(26), 6010–6013 (2000).
[CrossRef] [PubMed]

1997

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron.33(7), 1049–1056 (1997).
[CrossRef]

1993

M. Oberthaler and R. A. Höpfel, “Special narrowing of ultrashort laser pulses by self‐phase modulation in optical fibers,” Appl. Phys. Lett.63(8), 1017–1019 (1993).
[CrossRef]

T. J. Whitley and R. Wyatt, “Alternative Gaussian spot size polynomial for use with doped fiber amplifiers,” IEEE Photon. Technol. Lett.5(11), 1325–1327 (1993).
[CrossRef]

1991

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol.9(2), 271–283 (1991).
[CrossRef]

C. R. Giles and E. Desurvire, “Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers,” J. Lightwave Technol.9(2), 147–154 (1991).
[CrossRef]

1985

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun.55(6), 447–449 (1985).
[CrossRef]

Araujo-Hauck, C.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

Bender, C. F.

Benedick, A. J.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1.,” Nature452(7187), 610–612 (2008).
[CrossRef] [PubMed]

Birge, J. R.

Botzer, B.

Braje, D. A.

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D48(1), 57–66 (2008).
[CrossRef]

Chang, G.

Chen, H.-W.

Chen, L.-J.

Curto, G. L.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature485(7400), 611–614 (2012).
[CrossRef] [PubMed]

D’Odorico, S.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

Desurvire, E.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol.9(2), 271–283 (1991).
[CrossRef]

C. R. Giles and E. Desurvire, “Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers,” J. Lightwave Technol.9(2), 147–154 (1991).
[CrossRef]

Diddams, S. A.

Dudley, J. M.

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B19(3), 461–469 (2002).
[CrossRef]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett.84(26), 6010–6013 (2000).
[CrossRef] [PubMed]

Fendel, P.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1.,” Nature452(7187), 610–612 (2008).
[CrossRef] [PubMed]

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett.84(26), 6010–6013 (2000).
[CrossRef] [PubMed]

Fortier, T.

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D48(1), 57–66 (2008).
[CrossRef]

Gabler, T.

J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tünnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B74(2), 191–195 (2002).
[CrossRef]

Galvanauskas, A.

Giles, C. R.

C. R. Giles and E. Desurvire, “Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers,” J. Lightwave Technol.9(2), 147–154 (1991).
[CrossRef]

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol.9(2), 271–283 (1991).
[CrossRef]

Glenday, A. G.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1.,” Nature452(7187), 610–612 (2008).
[CrossRef] [PubMed]

González Hernández, J. I.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature485(7400), 611–614 (2012).
[CrossRef] [PubMed]

Grudinin, A. B.

Hanna, D. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron.33(7), 1049–1056 (1997).
[CrossRef]

Hänsch, T. W.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature485(7400), 611–614 (2012).
[CrossRef] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

Harvey, J. D.

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B19(3), 461–469 (2002).
[CrossRef]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett.84(26), 6010–6013 (2000).
[CrossRef] [PubMed]

He, F.

Heidt, A.

Holzwarth, R.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature485(7400), 611–614 (2012).
[CrossRef] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

Höpfel, R. A.

M. Oberthaler and R. A. Höpfel, “Special narrowing of ultrashort laser pulses by self‐phase modulation in optical fibers,” Appl. Phys. Lett.63(8), 1017–1019 (1993).
[CrossRef]

Hult, J.

Kärtner, F. X.

Kentischer, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

Kirchner, M. S.

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” Eur. Phys. J. D48(1), 57–66 (2008).
[CrossRef]

Kruglov, V. I.

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B19(3), 461–469 (2002).
[CrossRef]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett.84(26), 6010–6013 (2000).
[CrossRef] [PubMed]

Li, C.-H.

G. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kärtner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express18(12), 12736–12747 (2010).
[CrossRef] [PubMed]

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1.,” Nature452(7187), 610–612 (2008).
[CrossRef] [PubMed]

Liem, A.

J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tünnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B74(2), 191–195 (2002).
[CrossRef]

Limpert, J.

B. Ortaç, J. Limpert, and A. Tünnermann, “High-energy femtosecond Yb-doped fiber laser operating in the anomalous dispersion regime,” Opt. Lett.32(15), 2149–2151 (2007).
[CrossRef] [PubMed]

J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tünnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B74(2), 191–195 (2002).
[CrossRef]

Liu, C.-H.

Mahadevan, S.

Malinowski, A.

Manescau, A.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature485(7400), 611–614 (2012).
[CrossRef] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun.55(6), 447–449 (1985).
[CrossRef]

Murphy, M. T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

Nilsson, J.

Norris, T. B.

Oberthaler, M.

M. Oberthaler and R. A. Höpfel, “Special narrowing of ultrashort laser pulses by self‐phase modulation in optical fibers,” Appl. Phys. Lett.63(8), 1017–1019 (1993).
[CrossRef]

Ortaç, B.

Osterman, S.

Paschotta, R.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron.33(7), 1049–1056 (1997).
[CrossRef]

Pasquini, L.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature485(7400), 611–614 (2012).
[CrossRef] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

Peacock, A. C.

Phillips, D. F.

G. Chang, C.-H. Li, D. F. Phillips, R. L. Walsworth, and F. X. Kärtner, “Toward a broadband astro-comb: effects of nonlinear spectral broadening in optical fibers,” Opt. Express18(12), 12736–12747 (2010).
[CrossRef] [PubMed]

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1.,” Nature452(7187), 610–612 (2008).
[CrossRef] [PubMed]

Price, J. H.

Probst, R. A.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature485(7400), 611–614 (2012).
[CrossRef] [PubMed]

Quinlan, F.

Ramsey, L.

Rebolo, R.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature485(7400), 611–614 (2012).
[CrossRef] [PubMed]

Redman, S.

Richardson, D. J.

Sahu, J. K.

Sasselov, D.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1.,” Nature452(7187), 610–612 (2008).
[CrossRef] [PubMed]

Schmidt, W.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

Sigurdsson, S.

Soh, D. B.

Sosnowski, T.

Steinmetz, T.

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T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
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J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tünnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B74(2), 191–195 (2002).
[CrossRef]

Udem, T.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature485(7400), 611–614 (2012).
[CrossRef] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

Appl. Phys. B

J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tünnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B74(2), 191–195 (2002).
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[CrossRef]

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Nature

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1.,” Nature452(7187), 610–612 (2008).
[CrossRef] [PubMed]

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature485(7400), 611–614 (2012).
[CrossRef] [PubMed]

Opt. Commun.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun.55(6), 447–449 (1985).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett.84(26), 6010–6013 (2000).
[CrossRef] [PubMed]

Science

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008).
[CrossRef] [PubMed]

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2006).

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Figures (8)

Fig. 1
Fig. 1

Iteration flow chart of the modelling.

Fig. 2
Fig. 2

(a) Pump and signal power as a function of Yb-fiber length. (b) RMS duration of the optimum compressed- pulse and the transform-limited pulse as a function of Yb-fiber length.

Fig. 3
Fig. 3

The typical experimental scheme for further optimization.

Fig. 4
Fig. 4

(a) Optimum RMS duration of the compressed-pulse and the corresponding transform-limited RMS duration as a function of pre-chirping GDD for the input pulse. Insets: compressed pulses and transform-limited pulses for three different pre-chirp. (b) bandwith evolution inside the Yb-fiber amplifier. (c) output sepctra for three different pre-chirp.

Fig. 5
Fig. 5

Calculated RMS duration for optimum compressed-pulse as a function of input signal power for five different spectral bandwidth corresponding to transform-limited pulse FWHM duration of 200 fs, 300 fs, 400 fs, 500 fs, and 600fs.

Fig. 6
Fig. 6

Calculated RMS duration of the optimum compressed pulse as a function of the FWHM pulse duration of the transform-limited Gaussian input pulse for three doping levels: blue-triangle curve for high doping at 1025/3 m−3; red-circle curve for medium doping at 1025 m−3; and black-square curve for low doping at 3 × 1025 m−3. The purple-diamond curve shows the compressed-pulse RMS duration obtained with a low-doping Yb-fiber amplifer seeded with transform-limited pulses.

Fig. 7
Fig. 7

Experimental set-up, OSC: oscillator, HP: half waveplate. M: mirror, G: Grating, LS: lens, FBS: fiber beam splitter, LD: laser diode, PBC: polarization beam combiner, WDM: wavelength division multiplexer, YDF: Yb doped fiber, QP: quarter waveplate, OSA: optical spectrum analyzer, AC: autocorrelator, P.M.: power meter.

Fig. 8
Fig. 8

(a) Calculated RMS pulse duration of optimum compressed pulses from the measured spectrum (black scattered) and simulated curve (green line). The shortest autocorrelation (AC) trace is achieved at the lowest RMS pulse duration. τAC (FWHM) = 134 fs for a pre-chirping GDD of −6.3 × 104 fs2, τAC (FWHM) = 149 fs for −1.8 × 104 fs2, and τAC (FWHM) = 169 fs for 1 × 104 fs2 respectively. (b) The spectra corresponding to three AC traces in (a). The pulse has the largest spectral bandwidth and smoothest edge for the pre-chirping GDD of −6.3 × 104 fs2.

Tables (1)

Tables Icon

Table 1 Amplifier Parameters Used in the Simulation

Equations (3)

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N 2 ( t,z ) t =[ R 12 ( λ,z )+ W 12 ( λ,z )] N 1 ( t,z )[ R 21 ( λ,z )+ W 21 ( λ,z )+1/ τ 21 ] N 2 ( t,z ) N 1 ( t,z ) t =[ R 21 ( λ,z )+ W 21 ( λ,z )+1/ τ 21 ] N 2 ( t,z )[ R 12 ( λ,z )+ W 12 ( λ,z )] N 1 ( t,z ) P p ( λ,z ) z = Γ p ( λ )[ σ e ( λ ) N 2 ( z ) σ a ( λ ) N 1 ( z )]ρ P p ( λ,z ) P s ( λ,z ) z = Γ s ( λ )[ σ e ( λ ) N 2 ( z ) σ a ( λ ) N 1 ( z )]ρ P s ( λ,z ).
A z = 0 g(ω) A ˜ (ω) e iωT dω β 2 2 i 2 A T 2 + β 3 6 3 A T 3 +iγ(1+ i ω 0 T )(A(z,T) 0 R(t') | A(z,Tt') | 2 dt').
N 2 ( z )=[ R 12 ( λ,z )+ W 12 ( λ,z )] / [ R 12 ( λ,z )+ R 21 ( λ,z )+ W 12 ( λ,z )+ W 21 ( λ,z )+1/ τ 21 ].

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