Abstract

The finite-difference time-domain technique is employed to examine the evolution of the amplitude, duration, waveform, and phase of ultrashort light pulses propagating in a medium of two-level atoms or molecules. The results of these numerical simulations agree reasonably well with predictions of the McCall-Hahn analysis for the evolution of the amplitude and the phase of short pulses in a two-level medium until the pulse duration becomes less than the duration of a single optical cycle. Noticeable deviations from the McCall-Hahn scenario were observed for pulses with durations shorter than the duration of a single field cycle.

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References

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  1. M. Nisoli, S. De Silvestri, O. Svelto, R. Szipocs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, "Compression of high-energylaser pulses below 5 fs," Opt. Lett. 22, 522-524 (1997).
    [CrossRef] [PubMed]
  2. A. Baltuska, Z. Wei, M.S. Pshenichnikov, and D.A. Wiersma, "Optical pulse compression 5fs at a 1-MHz repetition rate," Opt. Lett. 22, 102-104 (1997).
    [CrossRef] [PubMed]
  3. M.F. Emde, A. Baltuska, A. Kummrow, M.S. Pshenichnikov, D.A. Wiersma, "Ultrafast Librational Dynamics of the Hydrated Electron," Phys. Rev. Lett. 80, 4645-4648 (1998).
    [CrossRef]
  4. P. Villoresi, P. Ceccherini, L. Poletto, G. Tondello, C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, G. Cerullo, S. Stagira, S. De Silvestri, O. Svelto, and A. Boscolo, "Spectral Features and Modeling of High-Order Harmonics Generated by Sub-10-fs Pulses," Phys. Rev. Lett. 85, 2494-2497(2000).
    [CrossRef] [PubMed]
  5. P. Antoine, D.B. Miloševic , A. L'Huillier, M.B. Gaarde, P. Salières, and M. Lewenstein, "Generation of attosecond pulses in macroscopic media," Phys. Rev. A 56, 4960-4969 (1997).
    [CrossRef]
  6. K. J. Schafer and K. C. Kulander, "High Harmonic Generation from Ultrafast Pump Lasers," Phys. Rev. Lett. 78, 638-641 (1997).
    [CrossRef]
  7. I.P. Christov, M.M. Murnane, and H.C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the 'Single-Cycle' Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
    [CrossRef]
  8. S. E. Harris and A. V. Sokolov, "Subfemtosecond Pulse Generation by Molecular Modulation," Phys. Rev. Lett. 81, 2894-2897 (1998).
    [CrossRef]
  9. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, "Raman Generation by Phased and Antiphased Molecular States," Phys. Rev. Lett. 85, 562-565 (2000).
    [CrossRef] [PubMed]
  10. M. Wittmann, A. Nazarkin, and G. Korn, "fs-Pulse Synthesis Using Phase Modulation by Impulsively Excited Molecular Vibrations," Phys. Rev. Lett. 84, 5508-5511 (2000).
    [CrossRef] [PubMed]
  11. S. L. McCall and E. L. Hahn, "Self-induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908-911 (1967).
    [CrossRef]
  12. S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
    [CrossRef]
  13. J.H. Eberly, "Area Theorem rederived," Opt. Express 2, 173-176 (1998), http://www.opticsexpress.org/oearchive/source/4295.htm .
    [CrossRef] [PubMed]
  14. R.W. Ziolkowski, J.M. Arnold, and D.M. Gogny, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3094 (1995).
    [CrossRef] [PubMed]
  15. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 1995).
  16. S. Hughes, "Subfemtosecond soft-x-ray generation from a two-level atom: Extreme carrier-wave Rabi flopping," Phys. Rev. A 62, 055401-055405 (2000).
    [CrossRef]
  17. S. Hughes, "Breakdown of the Area Theorem: Carrier-Wave Rabi Flopping of Femtosecond Optical Pulses," Phys. Rev. Lett 81, 3363-3366 (1998).
    [CrossRef]

Other

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipocs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, "Compression of high-energylaser pulses below 5 fs," Opt. Lett. 22, 522-524 (1997).
[CrossRef] [PubMed]

A. Baltuska, Z. Wei, M.S. Pshenichnikov, and D.A. Wiersma, "Optical pulse compression 5fs at a 1-MHz repetition rate," Opt. Lett. 22, 102-104 (1997).
[CrossRef] [PubMed]

M.F. Emde, A. Baltuska, A. Kummrow, M.S. Pshenichnikov, D.A. Wiersma, "Ultrafast Librational Dynamics of the Hydrated Electron," Phys. Rev. Lett. 80, 4645-4648 (1998).
[CrossRef]

P. Villoresi, P. Ceccherini, L. Poletto, G. Tondello, C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, G. Cerullo, S. Stagira, S. De Silvestri, O. Svelto, and A. Boscolo, "Spectral Features and Modeling of High-Order Harmonics Generated by Sub-10-fs Pulses," Phys. Rev. Lett. 85, 2494-2497(2000).
[CrossRef] [PubMed]

P. Antoine, D.B. Miloševic , A. L'Huillier, M.B. Gaarde, P. Salières, and M. Lewenstein, "Generation of attosecond pulses in macroscopic media," Phys. Rev. A 56, 4960-4969 (1997).
[CrossRef]

K. J. Schafer and K. C. Kulander, "High Harmonic Generation from Ultrafast Pump Lasers," Phys. Rev. Lett. 78, 638-641 (1997).
[CrossRef]

I.P. Christov, M.M. Murnane, and H.C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the 'Single-Cycle' Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

S. E. Harris and A. V. Sokolov, "Subfemtosecond Pulse Generation by Molecular Modulation," Phys. Rev. Lett. 81, 2894-2897 (1998).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, "Raman Generation by Phased and Antiphased Molecular States," Phys. Rev. Lett. 85, 562-565 (2000).
[CrossRef] [PubMed]

M. Wittmann, A. Nazarkin, and G. Korn, "fs-Pulse Synthesis Using Phase Modulation by Impulsively Excited Molecular Vibrations," Phys. Rev. Lett. 84, 5508-5511 (2000).
[CrossRef] [PubMed]

S. L. McCall and E. L. Hahn, "Self-induced transparency by pulsed coherent light," Phys. Rev. Lett. 18, 908-911 (1967).
[CrossRef]

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

J.H. Eberly, "Area Theorem rederived," Opt. Express 2, 173-176 (1998), http://www.opticsexpress.org/oearchive/source/4295.htm .
[CrossRef] [PubMed]

R.W. Ziolkowski, J.M. Arnold, and D.M. Gogny, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3094 (1995).
[CrossRef] [PubMed]

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 1995).

S. Hughes, "Subfemtosecond soft-x-ray generation from a two-level atom: Extreme carrier-wave Rabi flopping," Phys. Rev. A 62, 055401-055405 (2000).
[CrossRef]

S. Hughes, "Breakdown of the Area Theorem: Carrier-Wave Rabi Flopping of Femtosecond Optical Pulses," Phys. Rev. Lett 81, 3363-3366 (1998).
[CrossRef]

Supplementary Material (4)

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Figures (3)

Fig. 1.
Fig. 1.

Evolution of single-cycle (a) π (0.98 MB), (b) 2π (1.81 MB), (c) 2.9π (1.88 MB), and (d) 4π (2.14 MB) pulses in a two-level medium.

Fig. 2.
Fig. 2.

(a) Evolution of a half-cycle 2π pulse in a two-level medium: τ=0.5 T, 2µ/ħE0πτ=2π, and µN/E0 =0.0016, (b) Evolution of a quarter-cycle 2π pulse in a two-level medium: τ=0.25 T, 2µ/ħE0πτ=2π, and µN/E0 =0.0032

Fig. 3.
Fig. 3.

Evolution of the excited- and ground-state populations in a two-level medium under the action of (a) a half-cycle 2π pulse and (b) a quarter-cycle 2π pulse: (dashed line) ground-state population r1 and (solid line) excited-state population r2.

Equations (10)

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D z ( x , t ) t = H y ( x , t ) x , H y ( x , t ) t = E z ( x , t ) x ,
ψ ( t ) = a ( x , t ) ψ 1 + b ( x , t ) ψ 2 ,
i d a ( x , t ) d t = E 1 a ( x , t ) μ E z ( x , t ) b ( x , t ) , i d b ( x , t ) d t = E 2 b ( x , t ) μ E z ( x , t ) a ( x , t ) ,
D z , i n + 1 = D z , i n + Δ t Δ x ( H y , i + 1 2 n + 1 2 H y , i 1 2 n + 1 2 ) , H y , i + 1 2 n + 3 2 = H y , i + 1 2 n + 1 2 + Δ t Δ x ( E z , i + 1 n + 1 E z , i n + 1 ) ,
E ( x , t ) = A ( x , t ) e i ϕ + i k z i ω t + c . c . ,
A ( x , t ) x + n c A ( x , t ) t = 2 π ω μ N n c sin ( θ ( x , t ) ) ,
A ( x , t ) = μ τ sec h ( t x V τ ) ,
V = [ 4 π μ 2 τ 2 ω N n c + n c ] 1 = [ 4 π ω N E 0 2 n c + n c ] 1 .
φ = k X ω X V = ω X ( 1 v 1 V ) = 4 π ω 2 μ 2 τ 2 N X ( n c ) .
L = ( n c ) ( 4 ω 2 μ 2 τ 2 N ) = ( E 0 2 n c ) ( 4 ω 2 N ) .

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