Abstract

An optimal control approach is used to extend to the regime of pump depletion the idea of using spatially nonuniform nonlinear coefficients to tailor the shapes of optical pulses in a process of transient second-harmonic generation.

© 2002 Optical Society of America

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References

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    [CrossRef]
  6. G. Imeshev, M. S. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, J. Opt. Soc. Am. B 17, 304 (2000).
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    [CrossRef]
  9. N. Wang and H. Rabitz, J. Chem. Phys. 104, 1173 (1996).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. R. Buffa, “Optimal control of transient sum frequency mixing processes,” J. Opt. Soc. Am. B (to be published).

2001 (1)

2000 (2)

1998 (2)

1997 (1)

R. L. Bayer, J. Nonlin. Opt. Phys. Mater. 6, 549 (1997).
[CrossRef]

1996 (2)

N. Wang and H. Rabitz, J. Chem. Phys. 104, 1173 (1996).

N. Wang and H. Rabitz, Phys. Rev. A 53, 1879 (1996).
[CrossRef] [PubMed]

1995 (4)

Arbore, M. A.

Arbore, M. S.

Bayer, R. L.

R. L. Bayer, J. Nonlin. Opt. Phys. Mater. 6, 549 (1997).
[CrossRef]

Buffa, R.

R. Buffa, Opt. Lett. 26, 722 (2001).
[CrossRef]

R. Buffa and S. Cavalieri, J. Opt. Soc. Am. B 17, 1901 (2000).
[CrossRef]

R. Buffa, “Optimal control of transient sum frequency mixing processes,” J. Opt. Soc. Am. B (to be published).

Cavalieri, S.

Dienes, A.

Fejer, M. M.

Fermann, M.

Galvanauskas, A.

Harter, D.

Huang, J. Y.

Imeshev, G.

Kalintsev, A. G.

Knoesen, A.

Krylov, V.

Proctor, M.

Rabitz, H.

N. Wang and H. Rabitz, J. Chem. Phys. 104, 1173 (1996).

N. Wang and H. Rabitz, Phys. Rev. A 53, 1879 (1996).
[CrossRef] [PubMed]

N. Wang and H. Rabitz, Phys. Rev. A 52, R17 (1995).
[CrossRef]

Rebane, A.

Schwoerer, H.

Sidick, E.

Wang, H.

Wang, N.

N. Wang and H. Rabitz, Phys. Rev. A 53, 1879 (1996).
[CrossRef] [PubMed]

N. Wang and H. Rabitz, J. Chem. Phys. 104, 1173 (1996).

N. Wang and H. Rabitz, Phys. Rev. A 52, R17 (1995).
[CrossRef]

Wild, U. P.

Wong, G. K.

Wong, K. S.

Zhang, J.

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Figures (3)

Fig. 1
Fig. 1

(a) Flat-topped, (b) Gaussian, and (c) triangular pulse shapes used as target pulses Xrτ in Eq. (9) (solid curves) and SH output pulses X2Lτ produced, with a conversion efficiency of 90%, by the spatially nonuniform nonlinear coefficients Γη shown in Fig. 2 when a Gaussian FF laser pulse X102τ, with a temporal FWHM of 1 and a peak value X1020=1, is used as input (open circles).

Fig. 2
Fig. 2

Spatial distributions of the nonlinear coefficients Γη that produce the output SH pulses X2Lτ shown in Fig. 1 when a Gaussian FF laser pulse X102τ, with a temporal FWHM of 1 and a peak value X1020=1, is used as input.

Fig. 3
Fig. 3

SH output pulses X2Lτ produced, with a conversion efficiency of 90%, when a Gaussian FF laser pulse X102τ, with a temporal FWHM of 1 and a peak value X1020=1, is used as input and the nonlinear coefficients are designed by use of transfer function relation (1). For easy comparison, the target pulses Xrτ of Fig. 1 are also shown (dashed curves).

Equations (11)

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S2Ω=GΩS1Ω,
LˆX+fX=0,
Xη,τ=X1η,τX2η,τ,
Lˆ=η+L0T01u1-1u2τ00η,
fX=ΓX1X2-X12,
Xη=0,τ=X10τ0,
X2η,τ=0ηΓηX12η,τdη.
X2Lτ=-+ΓηX102τ-δνηdη.
Φ=-+X2Lτ-Xrτ2 dτ-+Xrτ2 dτ.
λη,τ=λ1η,τλ2η,τ,
J=Φ+0L/L0dη-+dτλTLˆX+fX

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