Abstract

A detrimental pulse distortion mechanism inherent to nonlinear chirped-pulse amplification systems is revealed and analyzed. When seeding the nonlinear amplification stage with pulses possessing weak side-pulses, the Kerr-nonlinearity causes a transfer of energy from the main pulse to side pulses. The resulting decrease in pulse contrast is determined by the accumulated nonlinear phase-shift (i.e., the B-integral) and the initial pulse-contrast. The energy transfer can be described by Bessel-functions. Thus, applications relying on a high pulse-contrast demand a low B-integral of the amplification system and a master-oscillator that exhibits an excellent pulse-contrast. In particular, nonlinear fiber CPA-systems operated at B-integrals far beyond π have to be revised in this context.

©2008 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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  23. C. Nielsen, B. Ortac, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tünnermann, “Self-starting self-similar all-polarization maintaining Yb-doped fiber laser,” Opt. Express 13, 9346–9351 (2005).
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2008 (4)

2007 (3)

2006 (1)

C. D. Brooks and F. Di Teodoro, “Multimegawatt peak-power, single-transverse-mode operation of a 100m core diameter, Yb-doped rodlike photonic crystal fiber amplifier,” Appl. Phys. Lett. 89, 111119 (2006).
[Crossref]

2005 (2)

2001 (2)

1999 (1)

1998 (1)

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[Crossref]

1997 (1)

1994 (3)

1985 (1)

D. M. Strickland and G. Mourou,”Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[Crossref]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” in Generating Function for the Bessel-function, formula 9.1.41 (Dover Publications, 1970).

Agrawal, G. P.

Akbulut, M.

T. Yilmaz, L. Vaissie, M. Akbulut, T. Booth, J. Jasapara, M. J. Andrejco, A. D. Yablon, C. Headley, and D. J. DiGovanni, “Large-mode-area Er-doped fiber chirped pulse amplification system for high-energy sub-picosecond pulses at 1.55 m,” Proc. SPIE 6873, 687354 (2008).

Akhmanov, S. A.

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

Andrejco, M. J.

T. Yilmaz, L. Vaissie, M. Akbulut, T. Booth, J. Jasapara, M. J. Andrejco, A. D. Yablon, C. Headley, and D. J. DiGovanni, “Large-mode-area Er-doped fiber chirped pulse amplification system for high-energy sub-picosecond pulses at 1.55 m,” Proc. SPIE 6873, 687354 (2008).

Booth, T.

T. Yilmaz, L. Vaissie, M. Akbulut, T. Booth, J. Jasapara, M. J. Andrejco, A. D. Yablon, C. Headley, and D. J. DiGovanni, “Large-mode-area Er-doped fiber chirped pulse amplification system for high-energy sub-picosecond pulses at 1.55 m,” Proc. SPIE 6873, 687354 (2008).

Braun, A.

Bromage, J.

Brooks, C. D.

C. D. Brooks and F. Di Teodoro, “Multimegawatt peak-power, single-transverse-mode operation of a 100m core diameter, Yb-doped rodlike photonic crystal fiber amplifier,” Appl. Phys. Lett. 89, 111119 (2006).
[Crossref]

Cao, X. D.

Chirkin, A. S.

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

Cho, G. C.

Di Teodoro, F.

C. D. Brooks and F. Di Teodoro, “Multimegawatt peak-power, single-transverse-mode operation of a 100m core diameter, Yb-doped rodlike photonic crystal fiber amplifier,” Appl. Phys. Lett. 89, 111119 (2006).
[Crossref]

Didenko, N. V.

DiGovanni, D. J.

T. Yilmaz, L. Vaissie, M. Akbulut, T. Booth, J. Jasapara, M. J. Andrejco, A. D. Yablon, C. Headley, and D. J. DiGovanni, “Large-mode-area Er-doped fiber chirped pulse amplification system for high-energy sub-picosecond pulses at 1.55 m,” Proc. SPIE 6873, 687354 (2008).

Ditmire, T.

Dorrer, C.

Eidam, T.

Fermann, M. E.

Fittinghoff, D.

Galvanauskas, A.

Guo, T.

Hariharan, A.

Harter, D.

Hartl, I.

Headley, C.

T. Yilmaz, L. Vaissie, M. Akbulut, T. Booth, J. Jasapara, M. J. Andrejco, A. D. Yablon, C. Headley, and D. J. DiGovanni, “Large-mode-area Er-doped fiber chirped pulse amplification system for high-energy sub-picosecond pulses at 1.55 m,” Proc. SPIE 6873, 687354 (2008).

Hohmuth, R.

Imeshev, G.

Jasapara, J.

T. Yilmaz, L. Vaissie, M. Akbulut, T. Booth, J. Jasapara, M. J. Andrejco, A. D. Yablon, C. Headley, and D. J. DiGovanni, “Large-mode-area Er-doped fiber chirped pulse amplification system for high-energy sub-picosecond pulses at 1.55 m,” Proc. SPIE 6873, 687354 (2008).

Kane, S.

Kawanishi, S.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[Crossref]

Kolner, B. H.

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[Crossref]

Konyashchenko, A. V.

Kuznetsova, L.

Limpert, J.

Liu, Z.

Lutsenko, A. P.

Mandel, L.

L. Mandel and E Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

Meyerhofer, D. D.

Mori, K.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[Crossref]

Mourou, G.

D. M. Strickland and G. Mourou,”Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[Crossref]

Nielsen, C.

Norris, T.

Ortac, B.

Perry, M. D.

Richter, W.

Röser, F.

Rothhardt, J.

Schimpf, D. N.

Schmidt, O.

Schreiber, T.

Seise, E.

Shah, L.

Shake, I.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[Crossref]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” in Generating Function for the Bessel-function, formula 9.1.41 (Dover Publications, 1970).

Strickland, D. M.

D. M. Strickland and G. Mourou,”Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[Crossref]

Stuart, B. C.

Takara, H.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[Crossref]

Tenyakov, S. Yu.

Toth, C.

Tünnermann, A.

Vaissie, L.

T. Yilmaz, L. Vaissie, M. Akbulut, T. Booth, J. Jasapara, M. J. Andrejco, A. D. Yablon, C. Headley, and D. J. DiGovanni, “Large-mode-area Er-doped fiber chirped pulse amplification system for high-energy sub-picosecond pulses at 1.55 m,” Proc. SPIE 6873, 687354 (2008).

Vysloukh, V. A.

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

Walker, B. C

Wise, F. W.

Wolf, E

L. Mandel and E Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

Yablon, A. D.

T. Yilmaz, L. Vaissie, M. Akbulut, T. Booth, J. Jasapara, M. J. Andrejco, A. D. Yablon, C. Headley, and D. J. DiGovanni, “Large-mode-area Er-doped fiber chirped pulse amplification system for high-energy sub-picosecond pulses at 1.55 m,” Proc. SPIE 6873, 687354 (2008).

Yamabayashi, Y.

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[Crossref]

Yilmaz, T.

T. Yilmaz, L. Vaissie, M. Akbulut, T. Booth, J. Jasapara, M. J. Andrejco, A. D. Yablon, C. Headley, and D. J. DiGovanni, “Large-mode-area Er-doped fiber chirped pulse amplification system for high-energy sub-picosecond pulses at 1.55 m,” Proc. SPIE 6873, 687354 (2008).

Appl. Phys. Lett. (1)

C. D. Brooks and F. Di Teodoro, “Multimegawatt peak-power, single-transverse-mode operation of a 100m core diameter, Yb-doped rodlike photonic crystal fiber amplifier,” Appl. Phys. Lett. 89, 111119 (2006).
[Crossref]

Electron. Lett. (1)

I. Shake, H. Takara, K. Mori, S. Kawanishi, and Y. Yamabayashi, “Influence of inter-bit four-wave mixing in optical TDM transmission,” Electron. Lett. 34, 1600–1601 (1998).
[Crossref]

IEEE J. Quantum Electron. (1)

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[Crossref]

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

A. Galvanauskas, “Mode-scalable Fiber-Based Chirped Pulse Amplification Systems,” IEEE J. Sel. Top. Quantum Electron. 7, 504–517 (2001).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

D. M. Strickland and G. Mourou,”Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[Crossref]

Opt. Express (6)

Opt. Lett. (5)

Proc. SPIE (1)

T. Yilmaz, L. Vaissie, M. Akbulut, T. Booth, J. Jasapara, M. J. Andrejco, A. D. Yablon, C. Headley, and D. J. DiGovanni, “Large-mode-area Er-doped fiber chirped pulse amplification system for high-energy sub-picosecond pulses at 1.55 m,” Proc. SPIE 6873, 687354 (2008).

Other (4)

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

L. Mandel and E Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

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

M. Abramowitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” in Generating Function for the Bessel-function, formula 9.1.41 (Dover Publications, 1970).

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Figures (6)

Fig. 1.
Fig. 1. (a) Experimental and simulated spectrum of a main pulse and with a post pulse, (b) corresponding spectra after nonlinear amplification. The B-integral is about 3 rad.

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Fig. 2.
Fig. 2. Stretched state prior to nonlinear amplification: (a) the temporal pulse-profile is determined by the spectrum. The temporal FWHM of the stretched pulse is 500ps. (b) the linear stretching chirp maps the spectrum into time-domain, (c) the spectrum remains unchanged during the stretching. The spectral modulations have a frequency of Δt=10ps. (d) parabolic spectral phase, and (e) parabolic spectral phase corresponding to the linear chirp. The corresponding state after nonlinear amplification is shown in Fig. 3.

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Fig. 3.
Fig. 3. State of the pulse after nonlinear amplification when starting with the state shown in Fig. 2: (a) temporal pulse. The temporal FWHM is 500 ps. In the numerical calculation of the nonlinear amplification, the dispersion is neglected. The SPM does not affect the intensity distribution. (b) chirp. Modulations are superimposed on the linear stretching chirp because of SPM, (c) spectrum of the pulse, which is modified due to the influence of SPM. The spectrum was obtained by numerical calculation. (d) residual non-parabolic spectral phase at the output of the CPA-system due to the nonlinear action. (e) temporal self-phase modulation (blue curve), this phase adds onto the existing stretching phase shown in Fig. 2(e), and its non-parabolic part (magenta curve).

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Fig. 4.
Fig. 4. Comparision between the numerical calculation of the pulse after the nonlinear CPA-system (B=20 rad) and the analytical result (B=20 rad) according to Eq. (14). The input pulse is also shown (B=0 rad).

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Fig. 5.
Fig. 5. (a) Relative intensities of the pulses contained within the multi-pulse as a function of the parameter a=0.7B2√r, (b) total intensity that is in the side pulses relative to the intensity in the main pulse as a function of the value of the B-integral and for different initial pulse-contrasts r [dB].

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Fig. 6.
Fig. 6. (a) Spectral modulation superimposed on the envelope of the spectrum at the output of the nonlinear amplification stage (B=20 rad) the intial contrast relative to the post-pulse is r=40dB, the horizontal line corresponds to the state shown in Fig. 3(c), (b) corresponding residual spectral phase at the output of the nonlinear CPA-system, the horizontal line corresponds to the state shown in Fig. 3(d), (c) pulse-contrast at the output of the nonlinear CPA-system

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Equations (16)

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∣ A ~ 0 ( Ω ) + r A ~ 0 ( Ω ) exp ⁡ ( i Ω Δ t ) ∣ 2 = F 2 s ( Ω ) [ 1 + r + 2 r cos ⁡ ( Ω Δ t ) ] .
A st ( T ) = 1 2 π ∫ dΩ exp ⁡ ( − i Ω T ) exp ( i ϕ ( 2 ) 2 Ω 2 ) [ A ~ 0 ( Ω ) + r A ~ 0 ( Ω ) exp ( i Ω Δ t ) ] .
A st ( T ) = F − i 2 πϕ ( 2 ) [ exp ( − i T 2 2 ϕ ( 2 ) ) s ( T ϕ ( 2 ) ) + r exp ( − i ( T − Δ t ) 2 2 ϕ ( 2 ) ) s ( T − Δ t ϕ ( 2 ) ) ] .
∣ A st ( T ) ∣ 2 = F 2 2 π ϕ ( 2 ) [ s ( T ϕ ( 2 ) ) + rs ( T − Δ t ϕ ( 2 ) ) + 2 rs ( T ϕ ( 2 ) ) s ( T − Δ t ϕ ( 2 ) ) cos ( T Δ t ϕ ( 2 ) − ( Δ t ) 2 2 ϕ ( 2 ) ) ] .
A amp ( T ) = A st ( T ) exp ( gL 2 ) exp ( i γ L eff ∣ A st ( T ) ∣ 2 ) .
A amp ( T ) ≈ exp ( g L 2 ) − i 2 πϕ ( 2 ) A ~ 0 ( T ϕ ( 2 ) ) exp ( − i T 2 2 ϕ ( 2 ) ) exp ( ia cos ( T Δ t ϕ ( 2 ) − ( Δ t ) 2 2 ϕ ( 2 ) ) ) .
exp ( ia cos ( x − b ) ) = ∑ m = − ∞ ∞ J m ( a ) i m exp ( − imx ) exp ( + imb ) ,
A amp ( T ) = exp ( g L 2 ) − i 2 πϕ ( 2 ) ∑ m = − ∞ ∞ i m J m ( a ) A ~ 0 ( T ϕ ( 2 ) ) exp ( i φ m ( T ) ) ,
φ m ( T ) = − T 2 2 ϕ ( 2 ) − m T Δ t ϕ ( 2 ) + m ( Δ t ) 2 2 ϕ ( 2 ) .
T s = ϕ ( 2 ) Ω − m Δ t .
A ~ amp ( Ω ) = ∫ d T exp ( i Ω T ) A amp ( T )
= exp ( gL 2 ) ∑ m = − ∞ ∞ i m J m ( a ) A ~ 0 ( Ω − m Δ t ϕ ( 2 ) ) exp [ i ( Ω T s + φ m ( T s ) ) ] ,
Ω T s + φ m ( T s ) = ϕ ( 2 ) 2 Ω 2 − m Δ t Ω + m ( 1 + m ) ( Δ t ) 2 2 ϕ ( 2 ) .
1 2 π ∫ d Ω exp ( − i Ω T ) exp ( − i m Δ t Ω ) A ~ 0 ( Ω − m Δ t ϕ ( 2 ) )
A out ( T ) = exp ( gL 2 ) ∑ m = − ∞ ∞ i m J m ( a ) A 0 ( T + m Δ t ) exp ⁡ ( i φ m out ( T ) )
φ in out ( T ) = − m Δ t T ϕ ( 2 ) + m ( 1 − m ) ( Δ t ) 2 2 ϕ ( 2 ) .

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