Abstract

We experimentally demonstrate compensation of the impact of Kerr-nonlinearity with positive dispersion in chirped-pulse systems. The condition for the phase-compensation is derived and design guidelines are presented. The technique is shown with a fiber-based system employing conventional diffraction gratings as well in a system that is based on chirped volume Bragg-gratings. Practical requirements on the stretching unit are discussed.

© 2009 Optical Society of America

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References

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  1. D. Anderson, M. Desaix, M. Lisak, M. L. Quiroga-Teixeiro, "Wave breaking in nonlinear-optical fibers," J. Opt. Soc. Am. B 9,1358-1361 (1992).
    [CrossRef]
  2. K. Tamura, E. P. Ippen, H. A. Haus, L. E. Nelson, "77-fs generation from a stretched-pulse mode-locked all-fiber ring laser," Opt. Lett. 18,1080-1082 (1993).
    [CrossRef] [PubMed]
  3. F. ¨O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, "Self-similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92,2139021-4 (2004).
    [CrossRef]
  4. D. M. Strickland, G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56,219-221 (1985).
    [CrossRef]
  5. M. D. Perry, T. Ditmire, and B. C. Stuart, "Self-phase modulation in chirped-pulse amplification," Opt. Lett. 19,2149-2151 (1994).
    [CrossRef] [PubMed]
  6. G. P. Agrawal, Nonlinear Fiber Optics, 3rd edition (Academic Press, 2001).
  7. F. R¨oser, T. Eidam, J. Rothhardt, O. Schmidt, D. N. Schimpf, J. Limpert, and A. T¨unnermann, "Millijoule pulse energy high repetition rate femtosecond fiber chirped-pulse amplification system," Opt. Lett. 32,3495-3497 (2007).
    [CrossRef] [PubMed]
  8. O. M. Efimov, L. B. Glebov, and V. I. Smirnov, "High-frequency Bragg gratings in a photothermorefractive glass," Opt. Lett. 25,1693-1695 (2000).
    [CrossRef]
  9. K. Liao, M. Cheng, E. Flecher, V. I. Smirnov, L. B. Glebov, and A. Galvanauskas, "Large-aperture chirped volume Bragg grating based fiber CPA system," Opt. Express 15,4876-4882 (2007).
    [CrossRef] [PubMed]
  10. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, "Optics of Femtosecond Laser Pulses," p. 93-98 (American Institute of Physics, 1992).
  11. D. N. Schimpf, C. Ruchert, D. Nodop, J. Limpert, and A. T¨unnermann, "Compensation of pulse-distortion in saturated laser amplifiers," Opt. Express 16,17637-17646 (2008).
    [CrossRef] [PubMed]
  12. D. N. Schimpf, E. Seise, J. Limpert, and A. T¨unnermann, "The impact of spectral modulations on the contrast of pulses of nonlinear chirped-pulse amplification systems," Opt. Express 16,10664-10674 (2008).
    [CrossRef] [PubMed]
  13. D. N. Schimpf, E. Seise, J. Limpert, and A. T¨unnermann, "Decrease of pulse-contrast in nonlinear chirped-pulse amplification systems due to high-frequency spectral phase ripples," Opt. Express 16,8876-8886 (2008).
    [CrossRef] [PubMed]
  14. V. N. Mahajan, "Zernike annular polynomials for imaging systems with annular pupils," J. Opt. Soc. Am. 71,75-85 (1981).
    [CrossRef]
  15. L. Shah, Z. Liu, I. Hartl, G. Imeshev, G. C. Cho, and M. E. Fermann, "High energy femtosecond Yb cubicon fiber amplifier," Opt. Express 13,4717-4722 (2005).
    [CrossRef] [PubMed]
  16. S. Zhou, L. Kuznetsova, A. Chong, and F. Wise, "Compensation of nonlinear phase-shifts with third-order dispersion in short-pulse fiber amplifiers," Opt. Express 13,4869-4877 (2005).
    [CrossRef] [PubMed]
  17. D. N. Schimpf, J. Limpert, and A. T¨unnermann, "Controlling the influence of SPM in fiber-based chirped pulse amplification systems by using an actively shaped parabolic spectrum," Opt. Express 15,16945-16953 (2007).
    [CrossRef] [PubMed]
  18. F. He, H. S. S. Hung, J. H. V. Price, N. K. Daga, N. Naz, J. Prawiharjo, D. C. Hanna, D. P. Shepherd, D. J. Richardson, J. W. Dawson, C. W. Siders, and C. P. J. Barty "High energy femtosecond fiber chirped pulse amplification system with adaptive phase control," Opt. Express 16,5813-5821 (2008).
    [CrossRef] [PubMed]

2008 (4)

2007 (3)

2005 (2)

2004 (1)

F. ¨O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, "Self-similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92,2139021-4 (2004).
[CrossRef]

2000 (1)

1994 (1)

1993 (1)

1992 (1)

1985 (1)

D. M. Strickland, G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56,219-221 (1985).
[CrossRef]

1981 (1)

Anderson, D.

Barty, C. P. J.

Buckley, J. R.

F. ¨O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, "Self-similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92,2139021-4 (2004).
[CrossRef]

Cheng, M.

Cho, G. C.

Chong, A.

Clark, W. G.

F. ¨O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, "Self-similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92,2139021-4 (2004).
[CrossRef]

Daga, N. K.

Dawson, J. W.

Desaix, M.

Ditmire, T.

Efimov, O. M.

Eidam, T.

Fermann, M. E.

Flecher, E.

Galvanauskas, A.

Glebov, L. B.

Hanna, D. C.

Hartl, I.

Haus, H. A.

He, F.

Hung, H. S. S.

Ilday, F. ¨O.

F. ¨O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, "Self-similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92,2139021-4 (2004).
[CrossRef]

Imeshev, G.

Ippen, E. P.

Kuznetsova, L.

Liao, K.

Limpert, J.

Lisak, M.

Liu, Z.

Mahajan, V. N.

Mourou, G.

D. M. Strickland, G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56,219-221 (1985).
[CrossRef]

Naz, N.

Nelson, L. E.

Nodop, D.

Perry, M. D.

Prawiharjo, J.

Price, J. H. V.

Quiroga-Teixeiro, M. L.

R¨oser, F.

Richardson, D. J.

Rothhardt, J.

Ruchert, C.

Schimpf, D. N.

Schmidt, O.

Seise, E.

Shah, L.

Shepherd, D. P.

Siders, C. W.

Smirnov, V. I.

Strickland, D. M.

D. M. Strickland, G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56,219-221 (1985).
[CrossRef]

Stuart, B. C.

T¨unnermann, A.

Tamura, K.

Wise, F.

Wise, F. W.

F. ¨O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, "Self-similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92,2139021-4 (2004).
[CrossRef]

Zhou, S.

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

D. M. Strickland, G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56,219-221 (1985).
[CrossRef]

Opt. Express (8)

L. Shah, Z. Liu, I. Hartl, G. Imeshev, G. C. Cho, and M. E. Fermann, "High energy femtosecond Yb cubicon fiber amplifier," Opt. Express 13,4717-4722 (2005).
[CrossRef] [PubMed]

S. Zhou, L. Kuznetsova, A. Chong, and F. Wise, "Compensation of nonlinear phase-shifts with third-order dispersion in short-pulse fiber amplifiers," Opt. Express 13,4869-4877 (2005).
[CrossRef] [PubMed]

K. Liao, M. Cheng, E. Flecher, V. I. Smirnov, L. B. Glebov, and A. Galvanauskas, "Large-aperture chirped volume Bragg grating based fiber CPA system," Opt. Express 15,4876-4882 (2007).
[CrossRef] [PubMed]

D. N. Schimpf, J. Limpert, and A. T¨unnermann, "Controlling the influence of SPM in fiber-based chirped pulse amplification systems by using an actively shaped parabolic spectrum," Opt. Express 15,16945-16953 (2007).
[CrossRef] [PubMed]

F. He, H. S. S. Hung, J. H. V. Price, N. K. Daga, N. Naz, J. Prawiharjo, D. C. Hanna, D. P. Shepherd, D. J. Richardson, J. W. Dawson, C. W. Siders, and C. P. J. Barty "High energy femtosecond fiber chirped pulse amplification system with adaptive phase control," Opt. Express 16,5813-5821 (2008).
[CrossRef] [PubMed]

D. N. Schimpf, E. Seise, J. Limpert, and A. T¨unnermann, "Decrease of pulse-contrast in nonlinear chirped-pulse amplification systems due to high-frequency spectral phase ripples," Opt. Express 16,8876-8886 (2008).
[CrossRef] [PubMed]

D. N. Schimpf, E. Seise, J. Limpert, and A. T¨unnermann, "The impact of spectral modulations on the contrast of pulses of nonlinear chirped-pulse amplification systems," Opt. Express 16,10664-10674 (2008).
[CrossRef] [PubMed]

D. N. Schimpf, C. Ruchert, D. Nodop, J. Limpert, and A. T¨unnermann, "Compensation of pulse-distortion in saturated laser amplifiers," Opt. Express 16,17637-17646 (2008).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

F. ¨O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, "Self-similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92,2139021-4 (2004).
[CrossRef]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd edition (Academic Press, 2001).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, "Optics of Femtosecond Laser Pulses," p. 93-98 (American Institute of Physics, 1992).

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Figures (8)

Fig. 1.
Fig. 1.

(a) The condition for phase-compensation: length of the amplifier as a function of the FWHM bandwidth of the sech 2 spectrum for B-integral values 5rad, 10rad and 20rad. The center-wavelength is 1030nm and β (2) is 25ps 2/km. (b) For the case of a FWHM bandwidth of 2.8nm and a 50m length of fiber, the autocorrelation trace at the optimum B-integral of 10rad is plotted (red cross in (a) ). To illustrate the effect of the phase-compensation, autocorrelation traces for B-integrals above and below the optimum are also shown. The traces are normalized to the peak.

Fig. 2.
Fig. 2.

(a) The residual spectral phase at point of optimum phase-compensation at different B-integral values (top) and the corresponding spectrum of sech 2-shape (bottom), (b) corresponding spread of the temporal intensity with increasing B-integral values.

Fig. 3.
Fig. 3.

(a) The condition for phase-compensation: length of the amplifier as a function of the FWHM bandwidth of the parabolic spectrum for different B-integral values. The center-wavelength is 1030nm and β (2) is 25ps 2/km. (b) For the case of a FWHM-bandwidth of 5nm and a fiber of 15.4 m, the autocorrelation trace at the optimum B-integral of 10 rad is plotted. Autocorrelation traces for B-integrals above and below the optimum are also plotted.

Fig. 4.
Fig. 4.

Schematic of the experimental setup of the ultra-compact fiber CPA-system with intrinsic phase-compensation. One chirped volume Bragg-grating is used for stretching and compression of the pulses.

Fig. 5.
Fig. 5.

(a) Spectrum of the pulse before and after passage of the CVBG, and numerically calculated (i.e. ‘simulated’) ideal spectrum (b) Simulated (normalized) Peak-power at the output of the experimental configurations as a function of the B-integral and the fiber-length.

Fig. 6.
Fig. 6.

(a) Measured temporal widths (FWHM) of the autocorrelation traces as function of the B-integral of the nonlinear pulse propagation for different fiber-lengths, (b) Autocorrelation traces for characteristic B-integral values for 40m length of fiber. (c) Spectrum at the output at low and high B-integral value.

Fig. 7.
Fig. 7.

Simulation of performance with the real experimental spectrum: Peak-power (normalized to the energy) at the output of the CPA-system as a function of the B-integral and the fiber-length.

Fig. 8.
Fig. 8.

(a) Measured temporal widths (FWHM) of the autocorrelation traces as function of the B-integral of the nonlinear pulse propagation for the 50m fiber-length. (b) Autocorrelation traces at different B-integral values for 50m length of fiber. (c) Spectrum at the output at low and high B-integral value.

Equations (10)

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A st ( T ) = 1 2 π exp ( i Ω T ) exp ( i ϕ st ( 2 ) 2 Ω 2 ) A ̃ 0 ( Ω ) .
A st ( T ) 1 i 2 π ϕ st ( 2 ) exp ( i T 2 2 ϕ st ( 2 ) ) A ̃ 0 ( T ϕ st ( 2 ) ) .
A amp ( T ) = A st ( T ) exp ( gL 2 ) exp ( i γ L eff A st ( T ) 2 ) .
A amp ( T ) exp ( gL 2 ) i 2 π ϕ st ( 2 ) A ̃ 0 ( T ϕ st ( 2 ) ) exp ( i φ ( T ) ) ,
φ ( T ) = T 2 2 ϕ st ( 2 ) + B s ( T ϕ st ( 2 ) ) .
A ̃ amp ( Ω ) exp ( gL 2 ) i 2 π ϕ st ( 2 ) d T exp ( i Ω T ) exp ( i φ ( T ) ) A ̃ 0 ( T ϕ st ( 2 ) ) .
A ̃ amp ( Ω ) = exp ( gL 2 ) A ̃ 0 ( Ω ) exp ( i ϕ st ( 2 ) 2 Ω 2 ) exp ( i B s ( Ω ) ) .
S = max exp ( i Ω T ) s ( Ω ) exp ( i [ φ D + B s ( Ω ) ] ) 2 max exp ( i Ω T ) s ( Ω ) 2 .
φ SPM = B [ s ( 0 ) + s ( 1 ) Ω + s ( 2 ) Ω ( 2 ) / 2 ]
B 2 Δ Ω fwhm 2 = β (2) L / 2 .

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