Abstract

A detailed analytical investigation is made of the effect of nonlinear self-phase modulation in chirped-pulse-amplification-like schemes. It is demonstrated that self-phase modulation in the amplifier between the stretcher and the compressor breaks the dispersive sign symmetry of the configuration. This implies that, although self-phase modulation is usually considered a deleterious effect, different situations are possible, depending on the parameter regimes considered. In particular, the influence of self-phase modulation on the low-intensity wings of the compressed pulse may be more or less deleterious, depending on the dispersive sign combination of the stretcher and the compressor; in certain parameter regimes, it may in fact even enhance the pulse compression.

© 1999 Optical Society of America

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References

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  1. G. Mourou, C. Barty, and M. D. Perry, “Ultra-high intensity lasers: physics of the extreme on a tabletop,” Phys. Today 51, 22–28 (1998).
    [CrossRef]
  2. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
    [CrossRef]
  3. Y.-H. Chuang, D. D. Meyerhofer, S. Augst, H. Chen, J. Peatross, and S. Uchida, “Suppression of the pedestal in a chirped-pulse-amplification laser,” J. Opt. Soc. Am. B 8, 1226–1235 (1991).
    [CrossRef]
  4. M. D. Perry, T. Ditmire, and B. C. Stuart, “Self-phase modulation in chirped-pulse amplification,” Opt. Lett. 19, 2149–2151 (1994).
    [CrossRef] [PubMed]
  5. J.-L. Tapié and G. Mourou, “Shaping of clean, femtosecond pulses at 1.053 μm for chirped-pulse amplification,” Opt. Lett. 17, 136–138 (1992).
    [CrossRef]
  6. A. Braun, S. Kane, and T. Norris, “Compensation of self-phase modulation in chirped-pulse amplification of laser systems,” Opt. Lett. 22, 615–617 (1997).
    [CrossRef] [PubMed]
  7. J. A. Hermann, “Self-focusing effects using thin nonlinear media,” Int. J. Nonlinear Opt. Phys. 1, 541–561 (1992).
    [CrossRef]
  8. A. Berntson, D. Anderson, M. Lisak, M. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fiber transmission systems,” Opt. Commun. 130, 153–162 (1996).
    [CrossRef]
  9. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
    [CrossRef]
  10. S. C. Pinault and M. J. Potasek, “Frequency broadening by self-phase modulation in optical fibers,” J. Opt. Soc. Am. B 2, 1318–1319 (1985).
    [CrossRef]
  11. D. Anderson and M. Lisak, “Analytic study of pulse broadening in dispersive optical fibers,” Phys. Rev. A 35, 184–187 (1987).
    [CrossRef] [PubMed]

1998 (2)

G. Mourou, C. Barty, and M. D. Perry, “Ultra-high intensity lasers: physics of the extreme on a tabletop,” Phys. Today 51, 22–28 (1998).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

1997 (1)

1996 (1)

A. Berntson, D. Anderson, M. Lisak, M. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fiber transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

1994 (1)

1992 (2)

J. A. Hermann, “Self-focusing effects using thin nonlinear media,” Int. J. Nonlinear Opt. Phys. 1, 541–561 (1992).
[CrossRef]

J.-L. Tapié and G. Mourou, “Shaping of clean, femtosecond pulses at 1.053 μm for chirped-pulse amplification,” Opt. Lett. 17, 136–138 (1992).
[CrossRef]

1991 (1)

1987 (1)

D. Anderson and M. Lisak, “Analytic study of pulse broadening in dispersive optical fibers,” Phys. Rev. A 35, 184–187 (1987).
[CrossRef] [PubMed]

1985 (2)

S. C. Pinault and M. J. Potasek, “Frequency broadening by self-phase modulation in optical fibers,” J. Opt. Soc. Am. B 2, 1318–1319 (1985).
[CrossRef]

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

Anderson, D.

A. Berntson, D. Anderson, M. Lisak, M. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fiber transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

D. Anderson and M. Lisak, “Analytic study of pulse broadening in dispersive optical fibers,” Phys. Rev. A 35, 184–187 (1987).
[CrossRef] [PubMed]

Augst, S.

Barty, C.

G. Mourou, C. Barty, and M. D. Perry, “Ultra-high intensity lasers: physics of the extreme on a tabletop,” Phys. Today 51, 22–28 (1998).
[CrossRef]

Berntson, A.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

A. Berntson, D. Anderson, M. Lisak, M. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fiber transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

Braun, A.

Chen, H.

Chuang, Y.-H.

Ditmire, T.

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

Hermann, J. A.

J. A. Hermann, “Self-focusing effects using thin nonlinear media,” Int. J. Nonlinear Opt. Phys. 1, 541–561 (1992).
[CrossRef]

Kane, S.

Karlsson, M.

A. Berntson, D. Anderson, M. Lisak, M. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fiber transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

Lisak, M.

A. Berntson, D. Anderson, M. Lisak, M. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fiber transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

D. Anderson and M. Lisak, “Analytic study of pulse broadening in dispersive optical fibers,” Phys. Rev. A 35, 184–187 (1987).
[CrossRef] [PubMed]

Meyerhofer, D. D.

Mourou, G.

G. Mourou, C. Barty, and M. D. Perry, “Ultra-high intensity lasers: physics of the extreme on a tabletop,” Phys. Today 51, 22–28 (1998).
[CrossRef]

J.-L. Tapié and G. Mourou, “Shaping of clean, femtosecond pulses at 1.053 μm for chirped-pulse amplification,” Opt. Lett. 17, 136–138 (1992).
[CrossRef]

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

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

Norris, T.

Peatross, J.

Perry, M. D.

G. Mourou, C. Barty, and M. D. Perry, “Ultra-high intensity lasers: physics of the extreme on a tabletop,” Phys. Today 51, 22–28 (1998).
[CrossRef]

M. D. Perry, T. Ditmire, and B. C. Stuart, “Self-phase modulation in chirped-pulse amplification,” Opt. Lett. 19, 2149–2151 (1994).
[CrossRef] [PubMed]

Pinault, S. C.

Potasek, M. J.

Quiroga-Teixeiro, M.

A. Berntson, D. Anderson, M. Lisak, M. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fiber transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

Strickland, D.

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

Stuart, B. C.

Tapié, J.-L.

Uchida, S.

Electron. Lett. (1)

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion managed solitons and WDM,” Electron. Lett. 34, 481–482 (1998).
[CrossRef]

Int. J. Nonlinear Opt. Phys. (1)

J. A. Hermann, “Self-focusing effects using thin nonlinear media,” Int. J. Nonlinear Opt. Phys. 1, 541–561 (1992).
[CrossRef]

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

Opt. Commun. (2)

A. Berntson, D. Anderson, M. Lisak, M. Quiroga-Teixeiro, and M. Karlsson, “Self-phase modulation in dispersion compensated optical fiber transmission systems,” Opt. Commun. 130, 153–162 (1996).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. A (1)

D. Anderson and M. Lisak, “Analytic study of pulse broadening in dispersive optical fibers,” Phys. Rev. A 35, 184–187 (1987).
[CrossRef] [PubMed]

Phys. Today (1)

G. Mourou, C. Barty, and M. D. Perry, “Ultra-high intensity lasers: physics of the extreme on a tabletop,” Phys. Today 51, 22–28 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Exact rms width for different values of the Kerr parameter as a function of the normalized length of the stretcher x¯1. Dashed curve, B=0.5; continuous curve, B=3.

Fig. 2
Fig. 2

Recompressed pulse shape for an initially Gaussian pulse (continuous curve) amplified to a level of B=0.5 with a stretcher with normal dispersion (short-dashed curve) and anomalous dispersion (long-dashed curve), calculated with the parabolic approximation. For comparison, the numerical result for B=0.5 with a stretcher with normal dispersion is also shown. I is the relative intensity (with respect to the initial intensity), and time is measured in units of the initial pulse width.

Fig. 3
Fig. 3

Numerically calculated recompressed pulse shapes for an initially Gaussian pulse (continuous curve) amplified to a level of (a) B=0.5 and (b) B=3; dotted and dashed curves, a stretcher having normal dispersion and a stretcher having anomalous dispersion, respectively. The best recompressed pulse is obtained with a stretcher with normal dispersion (x¯1=1), whereas anomalous dispersion (x¯1=-1) leads to degradation of the final pulse shape. I is the relative intensity (with respect to the initial intensity), and time is measured in units of the initial pulse width.

Fig. 4
Fig. 4

Normalized energy content of the recompressed pulse ET as a function of T, the width of the central part of the pulse (measured in units of initial pulse width), for the initial pulse (continuous curve), the final pulse in the case of a stretcher with normal dispersion (dotted curve) and a stretcher with anomalous dispersion (dashed curve); B=3.

Equations (34)

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i Ψjx=iγj2Ψj+α2(j)22Ψjτ2-Kj|Ψj|2Ψj=0,
Ψ1,out(τ)=Ψ1(x1, τ)=A1,out exp-τ22a1,out2+iϕ1,out,
A1,out=A(1+x12/LD12)1/4,
a1,out2=a2(1+x12/LD12),
ϕ1,out=12-x1LD1τ2a1,out2+arctan x1LD1.
Ψ2,out=A2,out exp-τ22a2,out2+iϕ2,out,
A2,out=GA1,out=AG(1+x12/LD12)1/4,
a2,out=a1,out,
ϕ2,out=ϕ1,out+K|Ψ1,out|2=ϕ1,out+B exp-τ2a1,out2,
B=K exp(γ x2)-1γA1,out2=K exp(γ x2)-1γA2(1+x12/LD12)1/2.
(Δω)2=-+dAd t+i dϕd tA2dt-+|A|2d t,
(Δω)2=12a021+2x¯1B+(43/9)B21+x¯12,
σout2σin2=(1+x¯12)1+2x¯3x¯1+B2+1+x¯12+2Bx¯1+4B233x¯32,
x¯=x¯m=-x¯11+x¯12,
minσout2σin2=σout2(x¯m)σin2=1.
σout2(x¯m)σin2=1-2Bx¯1-(4B2x¯12/33)1+x¯12.
σout2(x¯m)σin2=1-2Bx¯11+x¯12.
x¯=x¯m*=-x¯1+B/21+x¯12+2Bx¯1+4B2/33,
minσout2σin2=(1+x¯12) 1+(4/33-1/2)B21+x¯12+2Bx¯1+4B2/33.
exp-τ22a1,out21-τ2a1,out2.
ϕ2,outϕ1,out+B1-τ2a1,out2,
Iout(τ)=|Ψ3,out|2=GA[F(x¯3)(1+x¯12)]1/2exp-τ22a1,out2F(x¯3),
F(x¯3)=[1+x¯3(x¯1+2B)]2+x¯32.
F(x¯m)=11+x¯12-4Bx¯1-4B2x¯12(1+x¯12)2,
aout2ain2=1-4Bx¯1-4B2x¯121+x¯12,
max Ioutmin Iin=G ainaout=G1-4Bx¯1-4B2x¯121+x¯12-1/2,
aout2ain2=1-4Bx¯11+x¯12,
max Ioutmin Iin=G1+2Bx¯11+x¯12.
x¯=x¯m=-x¯1+2B1+(x¯1+2B)2,
min F(x)=F(x¯m)=11+(x¯1+2B)2.
minaout2ain2=1+x¯121+(x¯1+2B)2,
aout2ain21+4B2-4Bx¯1.
Ioutexp-τ2aout2exp-τ2ain2(1+4B2)-4τ2ain2Bx¯1.
E(t)=-tt|Ψ3,out(τ)|2dτ

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