Abstract

It is well-known that the process of optical parametric amplification (OPA) can be sensitive to the phases of the incident waves. In OPA realized by three-wave mixing, injection of all three waves into the same mode with appropriate phase relationship results in amplification of the signal phase, with an associated deamplification of the signal energy. Prospects for the use of this technique in the temporal domain for shaping ultrashort laser pulses are analyzed using a numerical model. Several representative pulse shaping capabilities of this technique are identified, which can significantly augment the performance of common passive pulse shaping methods operating in the Fourier domain. It is found that the use of phase-sensitive OPA shows a potential for significant compression of ~ 100 fs pulses, steepening of the rise time of ultrashort pulses, and production of pulse doublets and pulse trains. It is also shown that the group velocity mismatch can assist the shaping process. Such pulse shaping capabilities are found to be within reach of this technique in common nonlinear optical crystals pumped by pulses available from compact femtosecond chirped-pulse amplification laser systems.

© 2010 Optical Society of America

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    [CrossRef]
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2009 (1)

2008 (1)

2007 (4)

C. J. McKinstrie, R. O. Moore, S. Radic, and R. Jiang, "Phase-sensitive amplification of chirped optical pulses in fibers," Opt. Express 15, 3737-3758 (2007).
[CrossRef] [PubMed]

J. Moses, E. Alhammali, J. M. Eichenholz, and F. W. Wise, "Efficient high-energy femtosecond pulse compression in quadratic media with flattop beams," Opt. Lett. 32, 2469-2471 (2007).
[CrossRef] [PubMed]

J. Moses, B. A. Malomed, and F. W. Wise, "Self-steepening of ultrashort optical pulses without self-phase modulation," Phys. Rev. A 76, 021802 (2007).
[CrossRef]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi-phase matching and quantum-path control of high-harmonic generation using counterpropagating light," Nat. Photonics 3, 270-275 (2007).

2006 (3)

2005 (1)

R. Yano, and H. Gotoh, "Tunable terahertz electromagnetic wave generation using birefringent crystal and grating pair," Jpn. J. Appl. Phys. 44, 8470-8473 (2005).
[CrossRef]

2004 (1)

2000 (5)

1999 (3)

X. Liu, L. J. Qian, and F. W. Wise, "Generation of Optical Spatiotemporal Solitons," Phys. Rev. Lett. 82, 4631-4634 (1999).
[CrossRef]

D. Meshulach, and Y. Silberberg, "Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses," Phys. Rev. A 60, 1287-1292 (1999).
[CrossRef]

X. Liu, L. Qian, and F. Wise, "High-energy pulse compression by use of negative phase shifts produced by the cascade χ(2):χ(2) nonlinearity," Opt. Lett. 24, 1777-1779 (1999).
[CrossRef]

1998 (2)

C. Laconis, and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Opt. Lett. 23, 792-794 (1998).
[CrossRef]

D. Meshulach, and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239 (1998).
[CrossRef]

1997 (2)

P. Tournois, "Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems," Opt. Commun. 140, 245-249 (1997).
[CrossRef]

M. A. Dugan, J. X. Tull, and W. S. Warren, "High-resolution acousto-optic shaping of unamplified and amplified femtosecond laser pulses," J. Opt. Soc. Am. B 14, 2348-2358 (1997).
[CrossRef]

1996 (1)

G. M. D’Ariano, C. Macchiavello, N. Sterpi, and H. P. Yuen, "Quantum phase amplification," Phys. Rev. A 54, 4712-4718 (1996).
[CrossRef] [PubMed]

1993 (1)

1990 (1)

1986 (1)

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

1984 (1)

1982 (1)

C. M. Caves, "Quantum limits on noise in linear amplifiers," Phys. Rev. D Part. Fields 26, 1817-1839 (1982).
[CrossRef]

1980 (1)

1978 (1)

R. H. Stolen, and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448-1453 (1978).
[CrossRef]

Alhammali, E.

Beckwitt, K.

Caves, C. M.

C. M. Caves, "Quantum limits on noise in linear amplifiers," Phys. Rev. D Part. Fields 26, 1817-1839 (1982).
[CrossRef]

Cerullo, G.

Cheng, Z.

Cohen, O.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi-phase matching and quantum-path control of high-harmonic generation using counterpropagating light," Nat. Photonics 3, 270-275 (2007).

D’Ariano, G. M.

G. M. D’Ariano, C. Macchiavello, N. Sterpi, and H. P. Yuen, "Quantum phase amplification," Phys. Rev. A 54, 4712-4718 (1996).
[CrossRef] [PubMed]

da Silva, V.

Dugan, M. A.

Eichenholz, J. M.

Feit, M. D.

Fermann, M. E.

Fleck, J. A.

Fraucher, O.

French, D.

Gotoh, H.

R. Yano, and H. Gotoh, "Tunable terahertz electromagnetic wave generation using birefringent crystal and grating pair," Jpn. J. Appl. Phys. 44, 8470-8473 (2005).
[CrossRef]

Hall, J. L.

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

Hamm, P.

Hornung, T.

T. Hornung, R. Meier, and M. Motzkus, "Optimal control of molecular states in a learning loop with a parameterization in frequency and time domain," Chem. Phys. Lett. 326, 445-453 (2000).
[CrossRef]

Ilday, F. O.

Jiang, R.

Jovanovic, I.

Kaindl, R. A.

Kapteyn, H. C.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi-phase matching and quantum-path control of high-harmonic generation using counterpropagating light," Nat. Photonics 3, 270-275 (2007).

Kimble, H. J.

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

Klemz, G.

Laconis, C.

Laude, V.

Lavorel, R.

Leaird, D. E.

Lin, C.

R. H. Stolen, and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448-1453 (1978).
[CrossRef]

Liu, X.

Lytle, A. L.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi-phase matching and quantum-path control of high-harmonic generation using counterpropagating light," Nat. Photonics 3, 270-275 (2007).

Macchiavello, C.

G. M. D’Ariano, C. Macchiavello, N. Sterpi, and H. P. Yuen, "Quantum phase amplification," Phys. Rev. A 54, 4712-4718 (1996).
[CrossRef] [PubMed]

Malomed, B. A.

J. Moses, B. A. Malomed, and F. W. Wise, "Self-steepening of ultrashort optical pulses without self-phase modulation," Phys. Rev. A 76, 021802 (2007).
[CrossRef]

Manzoni, C.

Marangoni, M.

McKinstrie, C. J.

Meier, R.

T. Hornung, R. Meier, and M. Motzkus, "Optimal control of molecular states in a learning loop with a parameterization in frequency and time domain," Chem. Phys. Lett. 326, 445-453 (2000).
[CrossRef]

Meshulach, D.

D. Meshulach, and Y. Silberberg, "Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses," Phys. Rev. A 60, 1287-1292 (1999).
[CrossRef]

D. Meshulach, and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239 (1998).
[CrossRef]

Moore, R. O.

Moses, J.

J. Moses, B. A. Malomed, and F. W. Wise, "Self-steepening of ultrashort optical pulses without self-phase modulation," Phys. Rev. A 76, 021802 (2007).
[CrossRef]

J. Moses, E. Alhammali, J. M. Eichenholz, and F. W. Wise, "Efficient high-energy femtosecond pulse compression in quadratic media with flattop beams," Opt. Lett. 32, 2469-2471 (2007).
[CrossRef] [PubMed]

J. Moses, and F. W. Wise, "Controllable Self-Steepening of Ultrashort Pulses in Quadratic Nonlinear Media," Phys. Rev. Lett. 97, 073903 (2006).
[CrossRef] [PubMed]

J. Moses, and F. W. Wise, "Soliton compression in quadratic media: high-energy few-cycle pulses with a frequency-doubling crystal," Opt. Lett. 31, 1881-1883 (2006).
[CrossRef] [PubMed]

Motzkus, M.

T. Hornung, R. Meier, and M. Motzkus, "Optimal control of molecular states in a learning loop with a parameterization in frequency and time domain," Chem. Phys. Lett. 326, 445-453 (2000).
[CrossRef]

Murnane, M. M.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi-phase matching and quantum-path control of high-harmonic generation using counterpropagating light," Nat. Photonics 3, 270-275 (2007).

Patel, J. S.

Popmintchev, T.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi-phase matching and quantum-path control of high-harmonic generation using counterpropagating light," Nat. Photonics 3, 270-275 (2007).

Qian, L.

Qian, L. J.

X. Liu, L. J. Qian, and F. W. Wise, "Generation of Optical Spatiotemporal Solitons," Phys. Rev. Lett. 82, 4631-4634 (1999).
[CrossRef]

Radic, S.

Ramponi, R.

Ratowsky, R. P.

Reimann, K.

Renard, M.

Shank, C. V.

Silberberg, Y.

D. Meshulach, and Y. Silberberg, "Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses," Phys. Rev. A 60, 1287-1292 (1999).
[CrossRef]

D. Meshulach, and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239 (1998).
[CrossRef]

M. E. Fermann, V. da Silva, D. A. Smith, Y. Silberberg, and A. M. Weiner, "Shaping of ultrashort optical pulses by using an integrated acousto-optic tunable filter," Opt. Lett. 18, 1505-1507 (1993).
[CrossRef] [PubMed]

Smith, D. A.

Spielmann, Ch.

Sterpi, N.

G. M. D’Ariano, C. Macchiavello, N. Sterpi, and H. P. Yuen, "Quantum phase amplification," Phys. Rev. A 54, 4712-4718 (1996).
[CrossRef] [PubMed]

Stolen, R. H.

R. H. Stolen, and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448-1453 (1978).
[CrossRef]

Stolenn, R. H.

Tomlinson, W. J.

Tournois, P.

Tull, J. X.

Verluise, F.

Walmsley, I. A.

Walter, J. C.

Warren, W. S.

Weiner, A. M.

Will, I.

Wise, F.

Wise, F. W.

J. Moses, E. Alhammali, J. M. Eichenholz, and F. W. Wise, "Efficient high-energy femtosecond pulse compression in quadratic media with flattop beams," Opt. Lett. 32, 2469-2471 (2007).
[CrossRef] [PubMed]

J. Moses, B. A. Malomed, and F. W. Wise, "Self-steepening of ultrashort optical pulses without self-phase modulation," Phys. Rev. A 76, 021802 (2007).
[CrossRef]

J. Moses, and F. W. Wise, "Controllable Self-Steepening of Ultrashort Pulses in Quadratic Nonlinear Media," Phys. Rev. Lett. 97, 073903 (2006).
[CrossRef] [PubMed]

J. Moses, and F. W. Wise, "Soliton compression in quadratic media: high-energy few-cycle pulses with a frequency-doubling crystal," Opt. Lett. 31, 1881-1883 (2006).
[CrossRef] [PubMed]

X. Liu, F. O. Ilday, K. Beckwitt, and F. W. Wise, "Femtosecond nonlinear polarization evolution based on cascade quadratic nonlinearities," Opt. Lett. 25, 1394-1396 (2000).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, "Generation of Optical Spatiotemporal Solitons," Phys. Rev. Lett. 82, 4631-4634 (1999).
[CrossRef]

Woerner, M.

Wu, H.

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

Wu, L. A.

L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

Wullert, J. R.

Wurm, M.

Yano, R.

R. Yano, and H. Gotoh, "Tunable terahertz electromagnetic wave generation using birefringent crystal and grating pair," Jpn. J. Appl. Phys. 44, 8470-8473 (2005).
[CrossRef]

Yuen, H. P.

G. M. D’Ariano, C. Macchiavello, N. Sterpi, and H. P. Yuen, "Quantum phase amplification," Phys. Rev. A 54, 4712-4718 (1996).
[CrossRef] [PubMed]

Zhang, X.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi-phase matching and quantum-path control of high-harmonic generation using counterpropagating light," Nat. Photonics 3, 270-275 (2007).

Zhou, X.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi-phase matching and quantum-path control of high-harmonic generation using counterpropagating light," Nat. Photonics 3, 270-275 (2007).

Appl. Opt. (1)

Chem. Phys. Lett. (1)

T. Hornung, R. Meier, and M. Motzkus, "Optimal control of molecular states in a learning loop with a parameterization in frequency and time domain," Chem. Phys. Lett. 326, 445-453 (2000).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

R. Yano, and H. Gotoh, "Tunable terahertz electromagnetic wave generation using birefringent crystal and grating pair," Jpn. J. Appl. Phys. 44, 8470-8473 (2005).
[CrossRef]

Nat. Photonics (1)

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi-phase matching and quantum-path control of high-harmonic generation using counterpropagating light," Nat. Photonics 3, 270-275 (2007).

Nature (1)

D. Meshulach, and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239 (1998).
[CrossRef]

Opt. Commun. (1)

P. Tournois, "Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems," Opt. Commun. 140, 245-249 (1997).
[CrossRef]

Opt. Express (3)

Opt. Lett. (9)

M. Marangoni, C. Manzoni, R. Ramponi, and G. Cerullo, "Group-velocity control by quadratic nonlinear interactions," Opt. Lett. 31, 534-536 (2006).
[CrossRef] [PubMed]

J. Moses, and F. W. Wise, "Soliton compression in quadratic media: high-energy few-cycle pulses with a frequency-doubling crystal," Opt. Lett. 31, 1881-1883 (2006).
[CrossRef] [PubMed]

C. Laconis, and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Opt. Lett. 23, 792-794 (1998).
[CrossRef]

X. Liu, L. Qian, and F. Wise, "High-energy pulse compression by use of negative phase shifts produced by the cascade χ(2):χ(2) nonlinearity," Opt. Lett. 24, 1777-1779 (1999).
[CrossRef]

X. Liu, F. O. Ilday, K. Beckwitt, and F. W. Wise, "Femtosecond nonlinear polarization evolution based on cascade quadratic nonlinearities," Opt. Lett. 25, 1394-1396 (2000).
[CrossRef]

F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, and P. Tournois, "Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping," Opt. Lett. 25, 575-577 (2000).
[CrossRef]

J. Moses, E. Alhammali, J. M. Eichenholz, and F. W. Wise, "Efficient high-energy femtosecond pulse compression in quadratic media with flattop beams," Opt. Lett. 32, 2469-2471 (2007).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, "Programmable femtosecond pulse shaping by use of a multi-element liquid-crystal phase modulator," Opt. Lett. 15, 326-328 (1990).
[CrossRef] [PubMed]

M. E. Fermann, V. da Silva, D. A. Smith, Y. Silberberg, and A. M. Weiner, "Shaping of ultrashort optical pulses by using an integrated acousto-optic tunable filter," Opt. Lett. 18, 1505-1507 (1993).
[CrossRef] [PubMed]

Phys. Rev. A (4)

D. Meshulach, and Y. Silberberg, "Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses," Phys. Rev. A 60, 1287-1292 (1999).
[CrossRef]

R. H. Stolen, and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448-1453 (1978).
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Supplementary Material (6)

» Media 1: AVI (575 KB)     
» Media 2: AVI (520 KB)     
» Media 3: AVI (625 KB)     
» Media 4: AVI (840 KB)     
» Media 5: AVI (659 KB)     
» Media 6: AVI (854 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Qualitative representation of the effect of temporal phase amplification on the phase of the signal/idler wave (red), shown in degenerate OPA with temporally varying pump (blue). The amplified quantity is the departure (Δϕ) of the phase difference between the signal/idler and the pump wave from the ideal power deamplification condition. The phase of the signal/idler wave is advanced or retarded at a rate dependent on the pump intensity and the original departure from the ideal power deamplification condition, with effective gain factor g 0.

Fig. 2.
Fig. 2.

Conceptual schematic of temporal phase amplification and its effect on pulse bandwidth: ϕin and ϕout are the incident and the amplified phase, and Δωin and Δωout are the incident and amplified width of the frequency spectrum, respectively. Phase amplification steepens the change of temporal phase, effectively adding spectral bandwidth to the pulse.

Fig. 3.
Fig. 3.

Examples of temporal phase amplification with dispersion and SPM excluded from the model (input pump pulse duration: 100 fs). Shown are the temporal and spectral intensity and phase of signal/idler before (dashed) and after (solid) PSTWM. Quadratic case: (a) (Media 1) and (b); Linear case: (c) (Media 2) and (d).

Fig. 4.
Fig. 4.

Pulse compression without SPM in the quadratic case with input pump pulse duration of 100 fs: (a) Temporal intensity and phase of signal before (dashed, ~ 100 fs) and after (solid, 6 fs) PSTWM; (b) Spectral intensity and phase of signal before (dashed) and after (solid) PSTWM; (c) Temporal intensity of signal before (blue) and after (red, 6 fs) PSTWM and output with an ideal phase compensation (green, 6 fs); (d) Pulse compression process as signal (red) and pump (blue) traverse the nonlinear medium (Media 3).

Fig. 5.
Fig. 5.

Signal pulse profiles variations due to (a) input signal phase variations (input signal intensity: 1.6 TW/cm2; input pump intensity: 0.8 TW/cm2; input pump phase: flat); (b) input signal intensity variations (input pump intensity: 0.8 TW/cm2; input signal GDD: ϕ (2) = −401 fs2); input pump phase: flat); (c) input pump intensity variations (input signal intensity: 1.6 TW/cm2; input signal GDD: ϕ (2) = −401 fs2); input pump phase: flat).

Fig. 6.
Fig. 6.

Pulse compression with SPM in the quadratic case (a) Temporal intensity and phase of signal before (dashed, ~ 100 fs) and after (solid, 6 fs) PSTWM; (b) Spectral intensity and phase of signal before (dashed) and after (solid) PSTWM; (c) Temporal intensity of signal before (blue) and after (red, 6 fs) PSTWM and output with an ideal phase compensation (green, 6 fs); (d) Pulse compression process as signal (red) and pump (blue) traverse BBO (Media 4).

Fig. 7.
Fig. 7.

Production of a steep pulse edge by PSTWM in a 315 µm-long BBO crystal with the signal intensity of 0.4 TW/cm2 and the pump intensity of 0.2 TW/cm2: (a) temporal profiles of signal before (dashed) and after (solid) PSTWM; (b) spectrums of signal before (dashed) and after (solid) PSTWM. Peak signal intensities in (b) have been normalized to the initial peak signal intensity.

Fig. 8.
Fig. 8.

Generation of pulse doublets and pulse trains at the pump frequency. Production of pulse doublets: (a)temporal profile of pump before (blue) and after PSTWM (red); (b) Pulse doublets shaping process as pump (blue) and signal (red) go through BBO (Media 5). Production of pulse trains: (c) temporal profile of pump before (blue) and after PSTWM (red); (d) Pulse trains shaping process as pump (blue) and signal (red) go through BBO (Media 6).

Equations (6)

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φ = ϕ 3 ( 0 ) ϕ 2 ( 0 ) ϕ 1 ( 0 ) π 2 ,
d A 1 d z = i 2 d eff ω 1 2 k 1 c 2 A 2 * A 1 exp ( i Δ k z )
d A 2 d z = i d eff ω 2 2 k 2 c 2 A 1 2 exp ( i Δ k z ) ,
A i ( ω ) A i ( ω ) exp ( in i ( ω ) ω c ) ,
A i ( t ) A i ( t ) exp ( in 2 NL ω i I i ( t ) dz c ) ,
A i ( ω ) A i ( ω ) exp ( in 1 ( ω 1 ) ω 1 c ) ,

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