Abstract

We present a theory of ultrashort-pulse difference-frequency generation (DFG) with quasi-phase-matching (QPM) gratings in the undepleted-pump, unamplified-signal approximation. In the special case of a cw (or quasi-cw) pump, the spectrum of the generated idler is related to the spectrum of the signal through a transfer-function relation that is valid for arbitrary dispersion in the medium. The engineerability of this QPM-DFG transfer function establishes the basis for arbitrary pulse shaping. Experimentally we demonstrate QPM-DFG devices operating in a frequency-degenerate type II configuration and producing pulse-shaped output at 1550 nm from 220-fs pulses at 1550 nm.

© 2001 Optical Society of America

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References

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    [CrossRef]
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  9. G. Imeshev, M. A. Arbore, S. Kasriel, and M. M. Fejer, “Pulse shaping and compression by second-harmonic generation with quasi-phase-matching gratings in the presence of arbitrary dispersion,” J. Opt. Soc. Am. B 17, 1420–1437 (2000).
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  10. S. K. Kurtz, in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975).
  11. J.-J. Zondy, “The effects of focusing in type-I and type-II difference-frequency generations,” Opt. Commun. 149, 181–206 (1998).
    [CrossRef]
  12. D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
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  15. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
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2000 (2)

1999 (4)

1998 (2)

1997 (3)

1995 (2)

1992 (1)

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

1984 (1)

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Arbore, M. A.

Bosenberg, W. R.

Byer, R. L.

Chou, M. H.

Ebrahimzadeh, M.

Eckardt, R. C.

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Faller, P.

Fejer, M. M.

Fermann, M.

Fermann, M. E.

M. Hofer, M. E. Fermann, A. Galvanauskas, D. Harter, and R. S. Windeler, “Low-noise amplification of high-power pulses in multimode fibers,” IEEE Photonics Technol. Lett. 11, 650–652 (1999).
[CrossRef]

Galvanauskas, A.

Harter, D.

Hellström, J.

Hofer, M.

M. Hofer, M. E. Fermann, A. Galvanauskas, D. Harter, and R. S. Windeler, “Low-noise amplification of high-power pulses in multimode fibers,” IEEE Photonics Technol. Lett. 11, 650–652 (1999).
[CrossRef]

Imeshev, G.

Jundt, D. H.

Karlsson, H.

Kasriel, S.

Laurell, F.

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Loza-Alvarez, P.

Marco, O.

Myers, L. E.

Pasiskevicius, V.

Pierce, J. W.

Proctor, M.

Reid, D. T.

Roberts, D. A.

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

Sibbett, W.

Wang, S.

Weiner, A. M.

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

Windeler, R. S.

M. Hofer, M. E. Fermann, A. Galvanauskas, D. Harter, and R. S. Windeler, “Low-noise amplification of high-power pulses in multimode fibers,” IEEE Photonics Technol. Lett. 11, 650–652 (1999).
[CrossRef]

Zondy, J.-J.

J.-J. Zondy, “The effects of focusing in type-I and type-II difference-frequency generations,” Opt. Commun. 149, 181–206 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

M. Hofer, M. E. Fermann, A. Galvanauskas, D. Harter, and R. S. Windeler, “Low-noise amplification of high-power pulses in multimode fibers,” IEEE Photonics Technol. Lett. 11, 650–652 (1999).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

J.-J. Zondy, “The effects of focusing in type-I and type-II difference-frequency generations,” Opt. Commun. 149, 181–206 (1998).
[CrossRef]

Opt. Lett. (6)

Opt. Quantum Electron. (1)

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Prog. Quantum Electron. (1)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[CrossRef]

Other (1)

S. K. Kurtz, in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. SPM is the self-phase-modulating fiber and GC is the grating compressor.

Fig. 2
Fig. 2

Autocorrelation traces of the shaped idler pulses: long top-hat picosecond pulse, trace (a); train of six pulses of length of approximately 200 fs, trace (b). Note that for clarity the traces are offset vertically with respect to each other.

Fig. 3
Fig. 3

Spectra of shaped idler pulses obtained with devices (a), (b), and (c).

Equations (24)

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2z2Eˆi(z, ω)+k2(ω)Eˆi(z, ω)=-μ0ω2PˆNL(z, ω),
2z2Eˆs(z, ω)+k2(ω)Eˆs(z, ω)=0,
2z2Eˆp(z, ω)+k2(ω)Eˆp(z, ω)=0,
PˆNL(z, ω)=2ε0d(z)-+Es*ˆ(z, ω-ω)Eˆp(z, ω)dω,
Eˆm(z, ω)=Aˆm(z, Ωm)exp[-ik(ωm+Ωm)z],
Eˆm(z, ω)=Bˆm(z, Ωm)exp[-ik(ωm)z],
zAˆi(z, Ωi)=-i μ0ωi22kiPˆNL(z, Ωi)exp[ik(ωi+Ωi)z],
zAˆs(z, Ωs)=0,
zAˆp(z, Ωp)=0,
PˆNL(z, Ω)=2ε0d(z)-+As*ˆ(z,-Ω+Ω)Aˆp(z, Ω)×exp{i[k(ωs-Ω+Ω)-k(ωp+Ω)]z}dΩ,
Aˆs(z, Ω)=Aˆs(Ω),
Aˆp(z, Ω)=Aˆp(Ω),
Aˆi(L, Ω)=-iγ0Ld(z)dz-+dΩAˆs*(Ω-Ω)×Aˆp(Ω)exp[-iΔk(Ω, Ω)z],
Δk(Ω, Ω)=k(ωp+Ω)-k(ωi+Ω)-k(ωs+Ω-Ω).
Aˆp(Ω)=Epδ(Ω=0),
Aˆi(L, Ω)=dˆ(Ω)Aˆs*(-Ω)Ep,
dˆ(Ω)=-iγ-+d(z)exp[-iΔk(Ω)z]dz,
Δk(Ω)=k(ωp)-k(ωi+Ω)-k(ωs-Ω).
Bˆi(L, Ω)=dˆ(Ω)Bˆs*(-Ω)Ep exp{-i[k(ωi+Ω)-k(ωi)]L}.
Δk(Ω)=Δk0+δνsiΩ-n=2 1n![(-1)nβsn+βin]Ωn,
dˆ(Ω)=-iγ-+d(z)exp[-i(Δk0+δνsiΩ)z]dz,
Aˆ2(L, Ω)=Dˆ(Ω)A12ˆ(Ω),
Dˆ(Ω)=-iγ-+d(z)exp[-iΔk(Ω)z]dz,
Ui=538cε0 |d|n2δνsi (λs-λp)3(λs+λp)2λs2λp2 τsτpfUsUp,

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