Abstract

The exploitation of nonlinear phase shifts (ΦNL) in chirped-pulse fiber amplifiers has been demonstrated recently. Systematic optimization of the performance of a femtosecond-pulse fiber amplifier in the presence of substantial ΦNL is a challenging multivariable problem. We introduce an approximate theoretical model that is valid as long as the ΦNL is not so large that the spectrum changes substantially. The model allows an arbitrary chirped-pulse amplification system to be described by a set of four universal curves. These reveal the scaling of performance and allow determination of the optimal values of residual group-velocity dispersion and third-order dispersion for a given pulse duration and energy.

© 2007 Optical Society of America

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References

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  1. D. Strickland and G. Mourou, "Compression of amplified chirped optical pulses," Opt. Commun. 56, 219-221 (1985).
    [CrossRef]
  2. L. Shah, Z. Liu, I. Hart, G. Imeshev, G. Cho, and M. Fermann, "High energy femtosecond Yb cubicon fiber amplifier," Opt. Express 13, 4717-4722 (2005).
    [CrossRef] [PubMed]
  3. J. Limpert, A. Liem, T. Schreiber, M. Reich, H. Zellmer, and A. Tunnerman, "High-performance ultrafast fiber laser systems," Proc. SPIE 5335, 245-252 (2004).
    [CrossRef]
  4. S. Zhou, L. Kuznetsova, A. Chong, and F. W. Wise, "Compensation of nonlinear-phase shifts with third-order dispersion in short-pulse fiber amplifiers," Opt. Express 13, 4869-4877 (2005).
    [CrossRef] [PubMed]
  5. A. Galvanauskas, "Ultrashort pulse fiber lasers," in Ultrafast Lasers, Technology and Applications, M.E.Fermann, A.Galvanauskas, and G.Sucha, eds. (Marcel Dekker, 2003).
  6. A. Chong, L. Kuznetsova, S. Zhou, and F. W. Wise, "Exploiting nonlinearity in femtosecond fiber amplifiers," Proc. SPIE 6102, 61020Y (2006).
    [CrossRef]
  7. H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2μm region," IEEE J. Sel. Top. Quantum Electron. 1, 2-13 (1995).
    [CrossRef]
  8. R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped silica fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1995).
    [CrossRef]
  9. D. T. Walton, J. Nees, and G. Mouorou, "Broad-bandwidth pulse amplification to the 10-μJ level in an ytterbium-doped germanosilicate fiber," Opt. Lett. 21, 1061-1063 (1996).
    [CrossRef] [PubMed]
  10. L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, "Chirped-pulse amplification of femtosecond pulses in a Yb-doped fiber amplifier near the gain narrowing limit using a reflection grism compressor," in Advanced Solid-State Photonics, OSA Trends in Optics and Photonics Series (Optical Society of America, to be published), paper TuB3.
  11. S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.
  12. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  13. M. Miyagi and S. Nishida, "Pulse spreading in a single-mode fiber due to third-order dispersion," Appl. Opt. 18, 678-682 (1979).
    [CrossRef] [PubMed]
  14. K. C. Chan and H. F. Liu, "Short pulse generation by higher order soliton-effect compression: effects of optical fiber characteristics," IEEE J. Quantum Electron. 31, 2226-2235 (1979).
    [CrossRef]
  15. G. I. Barenblatt, Similarity, Self-Similarity, and Intermediate Asymptotics (Consultants Bureau, 1979).
    [CrossRef]
  16. L. Kuznetsova, A. Chong, and F. W. Wise, "Interplay of nonlinearity and gain shaping in femtosecond fiber amplifiers," Opt. Lett. 31, 2640-2642 (2006).
    [CrossRef] [PubMed]
  17. H. Hochstadt, The Function of Mathematical Physics (Dover, 1986).
  18. J. N. Elgin, T. Brabec, and S. M. J. Kelly, "A perturbation theory of soliton propagation in the presence of third order dispersion," Opt. Commun. 114, 321-328 (1995).
    [CrossRef]

2006 (2)

A. Chong, L. Kuznetsova, S. Zhou, and F. W. Wise, "Exploiting nonlinearity in femtosecond fiber amplifiers," Proc. SPIE 6102, 61020Y (2006).
[CrossRef]

L. Kuznetsova, A. Chong, and F. W. Wise, "Interplay of nonlinearity and gain shaping in femtosecond fiber amplifiers," Opt. Lett. 31, 2640-2642 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (1)

J. Limpert, A. Liem, T. Schreiber, M. Reich, H. Zellmer, and A. Tunnerman, "High-performance ultrafast fiber laser systems," Proc. SPIE 5335, 245-252 (2004).
[CrossRef]

1996 (1)

1995 (3)

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2μm region," IEEE J. Sel. Top. Quantum Electron. 1, 2-13 (1995).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped silica fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1995).
[CrossRef]

J. N. Elgin, T. Brabec, and S. M. J. Kelly, "A perturbation theory of soliton propagation in the presence of third order dispersion," Opt. Commun. 114, 321-328 (1995).
[CrossRef]

1985 (1)

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

1979 (2)

M. Miyagi and S. Nishida, "Pulse spreading in a single-mode fiber due to third-order dispersion," Appl. Opt. 18, 678-682 (1979).
[CrossRef] [PubMed]

K. C. Chan and H. F. Liu, "Short pulse generation by higher order soliton-effect compression: effects of optical fiber characteristics," IEEE J. Quantum Electron. 31, 2226-2235 (1979).
[CrossRef]

Agrawal, G. P.

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

Barber, P. R.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2μm region," IEEE J. Sel. Top. Quantum Electron. 1, 2-13 (1995).
[CrossRef]

Barenblatt, G. I.

G. I. Barenblatt, Similarity, Self-Similarity, and Intermediate Asymptotics (Consultants Bureau, 1979).
[CrossRef]

Brabec, T.

J. N. Elgin, T. Brabec, and S. M. J. Kelly, "A perturbation theory of soliton propagation in the presence of third order dispersion," Opt. Commun. 114, 321-328 (1995).
[CrossRef]

Carman, R. J.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2μm region," IEEE J. Sel. Top. Quantum Electron. 1, 2-13 (1995).
[CrossRef]

Chan, K. C.

K. C. Chan and H. F. Liu, "Short pulse generation by higher order soliton-effect compression: effects of optical fiber characteristics," IEEE J. Quantum Electron. 31, 2226-2235 (1979).
[CrossRef]

Cho, G.

Chong, A.

Dawes, J. M.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2μm region," IEEE J. Sel. Top. Quantum Electron. 1, 2-13 (1995).
[CrossRef]

Dinger, H.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.

Durfee, Ch.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.

Elgin, J. N.

J. N. Elgin, T. Brabec, and S. M. J. Kelly, "A perturbation theory of soliton propagation in the presence of third order dispersion," Opt. Commun. 114, 321-328 (1995).
[CrossRef]

Fermann, M.

Galvanauskas, A.

A. Galvanauskas, "Ultrashort pulse fiber lasers," in Ultrafast Lasers, Technology and Applications, M.E.Fermann, A.Galvanauskas, and G.Sucha, eds. (Marcel Dekker, 2003).

Gibson, E.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.

Hanna, D. C.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2μm region," IEEE J. Sel. Top. Quantum Electron. 1, 2-13 (1995).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped silica fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1995).
[CrossRef]

Hart, I.

Hochstadt, H.

H. Hochstadt, The Function of Mathematical Physics (Dover, 1986).

Huff, R.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.

Imeshev, G.

Jimenez, R.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.

Kane, S.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, "Chirped-pulse amplification of femtosecond pulses in a Yb-doped fiber amplifier near the gain narrowing limit using a reflection grism compressor," in Advanced Solid-State Photonics, OSA Trends in Optics and Photonics Series (Optical Society of America, to be published), paper TuB3.

Kelly, S. M. J.

J. N. Elgin, T. Brabec, and S. M. J. Kelly, "A perturbation theory of soliton propagation in the presence of third order dispersion," Opt. Commun. 114, 321-328 (1995).
[CrossRef]

Kuznetsova, L.

L. Kuznetsova, A. Chong, and F. W. Wise, "Interplay of nonlinearity and gain shaping in femtosecond fiber amplifiers," Opt. Lett. 31, 2640-2642 (2006).
[CrossRef] [PubMed]

A. Chong, L. Kuznetsova, S. Zhou, and F. W. Wise, "Exploiting nonlinearity in femtosecond fiber amplifiers," Proc. SPIE 6102, 61020Y (2006).
[CrossRef]

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

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, "Chirped-pulse amplification of femtosecond pulses in a Yb-doped fiber amplifier near the gain narrowing limit using a reflection grism compressor," in Advanced Solid-State Photonics, OSA Trends in Optics and Photonics Series (Optical Society of America, to be published), paper TuB3.

Liem, A.

J. Limpert, A. Liem, T. Schreiber, M. Reich, H. Zellmer, and A. Tunnerman, "High-performance ultrafast fiber laser systems," Proc. SPIE 5335, 245-252 (2004).
[CrossRef]

Limpert, J.

J. Limpert, A. Liem, T. Schreiber, M. Reich, H. Zellmer, and A. Tunnerman, "High-performance ultrafast fiber laser systems," Proc. SPIE 5335, 245-252 (2004).
[CrossRef]

Liu, H. F.

K. C. Chan and H. F. Liu, "Short pulse generation by higher order soliton-effect compression: effects of optical fiber characteristics," IEEE J. Quantum Electron. 31, 2226-2235 (1979).
[CrossRef]

Liu, Z.

Mackechnie, C. J.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2μm region," IEEE J. Sel. Top. Quantum Electron. 1, 2-13 (1995).
[CrossRef]

Miyagi, M.

Mouorou, G.

Mourou, G.

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

Nees, J.

Nilsson, J.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped silica fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1995).
[CrossRef]

Nishida, S.

Paschotta, R.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped silica fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1995).
[CrossRef]

Pask, H. M.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2μm region," IEEE J. Sel. Top. Quantum Electron. 1, 2-13 (1995).
[CrossRef]

Reich, M.

J. Limpert, A. Liem, T. Schreiber, M. Reich, H. Zellmer, and A. Tunnerman, "High-performance ultrafast fiber laser systems," Proc. SPIE 5335, 245-252 (2004).
[CrossRef]

Schreiber, T.

J. Limpert, A. Liem, T. Schreiber, M. Reich, H. Zellmer, and A. Tunnerman, "High-performance ultrafast fiber laser systems," Proc. SPIE 5335, 245-252 (2004).
[CrossRef]

Shah, L.

Squier, J.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, "Chirped-pulse amplification of femtosecond pulses in a Yb-doped fiber amplifier near the gain narrowing limit using a reflection grism compressor," in Advanced Solid-State Photonics, OSA Trends in Optics and Photonics Series (Optical Society of America, to be published), paper TuB3.

Strickland, D.

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

Tortajada, F.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.

Touzet, B.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.

Tropper, A. C.

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2μm region," IEEE J. Sel. Top. Quantum Electron. 1, 2-13 (1995).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped silica fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1995).
[CrossRef]

Tunnerman, A.

J. Limpert, A. Liem, T. Schreiber, M. Reich, H. Zellmer, and A. Tunnerman, "High-performance ultrafast fiber laser systems," Proc. SPIE 5335, 245-252 (2004).
[CrossRef]

Walton, D. T.

Wise, F. W.

A. Chong, L. Kuznetsova, S. Zhou, and F. W. Wise, "Exploiting nonlinearity in femtosecond fiber amplifiers," Proc. SPIE 6102, 61020Y (2006).
[CrossRef]

L. Kuznetsova, A. Chong, and F. W. Wise, "Interplay of nonlinearity and gain shaping in femtosecond fiber amplifiers," Opt. Lett. 31, 2640-2642 (2006).
[CrossRef] [PubMed]

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

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, "Chirped-pulse amplification of femtosecond pulses in a Yb-doped fiber amplifier near the gain narrowing limit using a reflection grism compressor," in Advanced Solid-State Photonics, OSA Trends in Optics and Photonics Series (Optical Society of America, to be published), paper TuB3.

Zellmer, H.

J. Limpert, A. Liem, T. Schreiber, M. Reich, H. Zellmer, and A. Tunnerman, "High-performance ultrafast fiber laser systems," Proc. SPIE 5335, 245-252 (2004).
[CrossRef]

Zhou, S.

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

K. C. Chan and H. F. Liu, "Short pulse generation by higher order soliton-effect compression: effects of optical fiber characteristics," IEEE J. Quantum Electron. 31, 2226-2235 (1979).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped silica fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1995).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, "Ytterbium-doped silica fiber lasers: versatile sources for the 1-1.2μm region," IEEE J. Sel. Top. Quantum Electron. 1, 2-13 (1995).
[CrossRef]

Opt. Commun. (2)

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

J. N. Elgin, T. Brabec, and S. M. J. Kelly, "A perturbation theory of soliton propagation in the presence of third order dispersion," Opt. Commun. 114, 321-328 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (2)

J. Limpert, A. Liem, T. Schreiber, M. Reich, H. Zellmer, and A. Tunnerman, "High-performance ultrafast fiber laser systems," Proc. SPIE 5335, 245-252 (2004).
[CrossRef]

A. Chong, L. Kuznetsova, S. Zhou, and F. W. Wise, "Exploiting nonlinearity in femtosecond fiber amplifiers," Proc. SPIE 6102, 61020Y (2006).
[CrossRef]

Other (6)

A. Galvanauskas, "Ultrashort pulse fiber lasers," in Ultrafast Lasers, Technology and Applications, M.E.Fermann, A.Galvanauskas, and G.Sucha, eds. (Marcel Dekker, 2003).

L. Kuznetsova, F. W. Wise, S. Kane, and J. Squier, "Chirped-pulse amplification of femtosecond pulses in a Yb-doped fiber amplifier near the gain narrowing limit using a reflection grism compressor," in Advanced Solid-State Photonics, OSA Trends in Optics and Photonics Series (Optical Society of America, to be published), paper TuB3.

S. Kane, R. Huff, J. Squier, E. Gibson, R. Jimenez, Ch. Durfee, F. Tortajada, H. Dinger, and B. Touzet, "Design and fabrication of efficient reflection grisms for pulse compression and dispersion compensation," in Conference on Lasers and Electro-Optics (CLEO), OSA Trends in Optics and Photonics Series (Optical Society of America, 2006), paper CThA5.

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

G. I. Barenblatt, Similarity, Self-Similarity, and Intermediate Asymptotics (Consultants Bureau, 1979).
[CrossRef]

H. Hochstadt, The Function of Mathematical Physics (Dover, 1986).

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Figures (9)

Fig. 1
Fig. 1

Comparison of the CPA model and the numerical simulation for 150 fs Gaussian input. The CPA system consists of a 2 m gain fiber ( 60 nm gain bandwidth) and a 600/mm grating pair compressor: (a) 100 m SMF stretcher with Φ N L = 2 π , (b) 400 m SMF stretcher with Φ N L = 10 π .

Fig. 2
Fig. 2

CPA output RPP improvement achived by adding TOD for 150 fs Gaussian input with Φ N L = 2 π . (a) Relative intensity; (b) phase in wavelength domain. Dotted curve, GVD = 55,290 fs 2 , TOD = 0 ; solid curve), GVD = 55,290 fs 2 , TOD = 5.09 × 10 7 fs 3 .

Fig. 3
Fig. 3

Linearly chirped peak power improvement by adding TOD for 150 fs Gaussian pulse: (a) relative, (b) T R M S versus TOD. Dotted curve, GVD = 20,000 fs 2 , TOD = 0 ; solid curve, GVD = 20,000 fs 2 , TOD = 2.4 × 10 6 fs 3 .

Fig. 4
Fig. 4

Relationship between G V D T F W H M 2 and ( T O D G V D ) T F W H M that maximizes Gaussian pulse peak power.

Fig. 5
Fig. 5

RPP with TOD and GVD as independent variables at Φ N L = 6 π for a Gaussian pulse.

Fig. 6
Fig. 6

Relationship among dimensionless parameters with RPP optimized.

Fig. 7
Fig. 7

RPP improvement with appropriate design parameters for indicated pulse shapes. Dotted curve, RPP optimized with GVD only ( TOD = 0 ) ; solid curve, RPP optimized with GVD and TOD.

Fig. 8
Fig. 8

Behavior of other merit functions for a Gaussian pulse at the RPP optimization condition: (a) pulse quality merit function versus Φ N L and (b) intensity autocorrelation at Φ N L = 6 π . Dotted curve, RPP optimized with GVD only ( TOD = 0 ) ; solid curve, RPP optimized with GVD and TOD.

Fig. 9
Fig. 9

Input Gaussian pulse with Airy function envelope of Eq. (A6) t o = 50 fs , TOD = 1 × 10 7 fs 3 .

Tables (2)

Tables Icon

Table 1 Asymptotic k of Eq. (4) for Various Input Pulse Shapes in Linear Dispersive Propagation

Tables Icon

Table 2 Asymptotic k of Eq. (4) for Various Input Pulse Shapes in an Ideal CPA System

Equations (23)

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

Φ N L I ( t ) I ( ω ) ,
Φ N L ( ω ) = Φ N L I ¯ ( ω ) ,
h ( t ) = G 2 π H i ( ω ) exp ( i ( D 2 ω 2 + D 3 ω 3 ) ) × exp ( i Φ N L I ¯ ( ω ) ) exp ( i w t ) d w .
h r e l ( t ) = h ( t ) P A i G ,
T O D G V D T F W H M = k .
h ( t ) = 1 2 π H i ( ω ) e ( i ( D 2 ω 2 + D 3 ω 3 ) ) e ( i ω t ) d ω ,
h ( t ) = 1 2 π h i ( t ) g ( t ) ,
g ( t ) = 1 2 π e ( i ( D 2 ω 2 + D 3 ω 3 ) ) e ( i ω t ) d ω .
g ( t ) = 2 π b e i ( A + B t ) A i ( a b t ) ,
A = 2 D 2 3 27 D 3 2 , B = D 2 3 D 3 , a = D 2 2 ( 3 D 3 ) 4 3 , b = 1 ( 3 D 3 ) 1 3 .
h ( t ) = b h i ( t t ) e i ( A + B t ) A i ( a b t ) d t .
h ( t ) = b e ( t t ) 2 2 t o 2 e i ( A + B t ) A i ( a b t ) d t .
t t m = s a b = ( s D 2 2 ( 3 D 3 ) 4 3 ) ( 3 D 3 ) 1 3 .
M a x ( h ( t ) 2 ) h ( t m ) 2 = b e ( t t ) 2 2 t o 2 e i ( A + B t ) A i ( a b t ) d t 2 .
h ( t m ) = b n = 0 C n e ( ( s a ) b t ) 2 2 t o 2 e i ( A + B t ) ( t s a b ) n d t .
e ( ( s a ) b t ) 2 2 t o 2 A i ( a b t ) e ( ( s a ) b t ) 2 2 t o 2 A i ( s ) .
h ( t m ) b A i ( s ) e ( ( s a ) b t ) 2 2 t o 2 e i ( A + B t ) d t = 2 π b t o A i ( s ) e i ( a + ( B b ) ( s a ) ) e B 2 t 0 2 2 .
M a x ( h ( t ) 2 ) 2 π b 2 A i 2 ( s ) t o 2 e B 2 t o 2 = 2 π b 2 A i 2 ( s ) t o 2 e D 2 2 t o 2 ( 9 D 3 2 ) ( 3 D 3 ) 2 3 .
D 3 = t o 3 D 2 .
T O D G V D T F W H M = k , k = 1.040 .
h ( t ) = 1 2 π H i ( ω ) e ( i ( D 2 ω 2 ) ) e ( i Φ N L I ¯ ( ω ) ) e ( i ω t ) d ω .
h ( t ) = 1 2 π e ω 2 t o 2 2 e ( i ( D 2 ω 2 ) ) e ( i Φ N L ( 1 ω 2 t o 2 ) ) e ( i ω t ) d ω .
T O D G V D T F W H M = k ( 1 Φ N L 2 ( 1.665 ) 2 T F W H M 2 G V D ) = k ( 1 1 2 ( 1.665 ) 2 1 u ) = k ,

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