Abstract

Femtosecond laser-induced alignment and periodic recurrences in hydrogen and deuterium are measured in a single shot for the first time, in a room temperature gas cell. Single-shot Supercontinuum Spectral Interferometry (SSSI) is employed, with measurements also performed in room temperature samples of nitrogen, oxygen, and nitrous oxide. Unlike previous optical techniques for probing molecular alignment in gases or liquids, SSSI quantitatively and directly measures the degree of molecular alignment without reliance on model fits, and it can do so with spatial resolution transverse to the pump beam. In addition, wavepacket collisional dephasing rates can be directly measured in gas samples at useful densities.

© 2007 Optical Society of America

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References

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  1. H. Stapelfeldt and T. Seideman, "Aligning molecules with strong laser pulses," Rev. Mod. Phys. 75, 543-557 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  25. I. Alexeev, A. Ting, D. F. Gordon, E. Briscoe, J. R. Penano, R. F. Hubbard, and P. Sprangle, "Longitudinal compression of short laser pulses in air," Appl. Phys. Lett. 84, 4080-4082 (2004).
    [CrossRef]
  26. C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13, 813-829 (1976).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  30. K. Kim, I. Alexeev, and H. Milchberg, "Single-shot measurement of laser-induced double step ionization of helium," Opt. Express 10, 1563-1572 (2002).
    [PubMed]

2007 (2)

2006 (3)

V. Loriot, E. Hertz, A. Rouzée, B. Sinardet, B. Lavorel, and O. Faucher, "Strong-field molecular ionization: determination of ionization probabilities calibrated with field-free alignment," Opt. Lett. 31, 2897-2899 (2006).
[CrossRef] [PubMed]

K. F. Lee, F. Legare, D. M. Villeneuve and P. B. Corkum, "Measured field-free alignment of deuterium by few-cycle pulses," J. Phys. B: At. Mol. Opt. Phys. 39, 4081-4086 (2006).
[CrossRef]

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirila, M. Lein, J. W. G. Tisch, and J. P. Marangos, "Probing Proton Dynamics in Molecules on an Attosecond Time Scale," Science 21, 424-427 (2006).
[CrossRef]

2005 (2)

C. Vozzi, F. Calegari, E. Benedetti, J.-P. Caumes, G. Sansone, S. Stagira, M. Nisoli, R. Torres, E. Heesel, N. Kajumba, J. P. Marangos, C. Altucci and R. Velotta, "Controlling Two-Center Interference in Molecular High Harmonic Generation," Phys. Rev. Lett. 95, 153902 (2005).
[CrossRef] [PubMed]

V. Renard, O. Faucher, and B. Lavorel, "Measurement of laser-induced alignment of molecules by cross defocusing," Opt. Lett. 30, 70-72 (2005).
[CrossRef] [PubMed]

2004 (2)

J. Itatani, J. Levesque, D. Zeidler, Hiromichi Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, D. M. Villeneuve, "Tomographic imaging of molecular orbitals," Nature 432, 867-871 (2004)
[CrossRef] [PubMed]

I. Alexeev, A. Ting, D. F. Gordon, E. Briscoe, J. R. Penano, R. F. Hubbard, and P. Sprangle, "Longitudinal compression of short laser pulses in air," Appl. Phys. Lett. 84, 4080-4082 (2004).
[CrossRef]

2003 (3)

H. Stapelfeldt and T. Seideman, "Aligning molecules with strong laser pulses," Rev. Mod. Phys. 75, 543-557 (2003).
[CrossRef]

J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, "Stimulated Raman scattering of intense laser pulses in air," Phys. Rev. E 68, 056502 (2003).
[CrossRef]

P. W. Dooley, I. V. Litvinyuk, KevinF. Lee, D. M. Rayner, M. Spanner, D. M. Villeneuve, and P. B. Corkum, "Direct imaging of rotational wave-packet dynamics of diatomic molecules," Phys. Rev. A 68, 023406 (2003).
[CrossRef]

2002 (3)

N. Hay, R. Velotta, M. Lein, R. de Nalda, E. Heesel, M. Castillejo, and J. P. Marangos, "High-order harmonic generation in laser-aligned molecules," Phys. Rev. A 65, 053805 (2002)
[CrossRef]

K. Kim, I. Alexeev, and H. Milchberg, "Single-shot measurement of laser-induced double step ionization of helium," Opt. Express 10, 1563-1572 (2002).
[PubMed]

K. Y. Kim, I. Alexeev, and H. M. Milchberg, "Single-shot supercontinuum spectral interferometry," Appl. Phys. Lett. 81, 4124-4126 (2002).
[CrossRef]

2001 (2)

R. Velotta, N. Hay, M. B. Mason, M. Castillejo, and J. P. Marangos, "High-Order Harmonic Generation in Aligned Molecules," Phys. Rev. Lett. 87, 183901 (2001);
[CrossRef]

F. Rosca-Pruna and M. J. J. Vrakking, "Experimental Observation of Revival Structures in Picosecond Laser-Induced Alignment of I2," Phys. Rev. Lett. 87, 153902 (2001).
[CrossRef] [PubMed]

1997 (2)

1993 (1)

R. Righini, "Ultrafast optical Kerr effect in liquids and solids," Science 262, 1386-1390 (1993).
[CrossRef] [PubMed]

1991 (1)

1990 (1)

L. L. Connell, T. C. Corcoran, P. W. Joireman, and P. M. Felker, "Observation and description of a new type of transient in rotational coherence spectroscopy," J. Phys. Chem. 94, 1229-1232 (1990).
[CrossRef]

1986 (1)

P. M. Felker, J. S. Baskin, and A. H. Zewail, "Rephasing of collisionless molecular coherence in large molecules," J. Phys. Chem. 90, 724-728 (1986)
[CrossRef]

1976 (1)

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13, 813-829 (1976).
[CrossRef]

1975 (2)

E. P. Ippen and C. V. Shank, "Picosecond response of a high-repetition-rate CS2 optical Kerr gate," Appl. Phys. Lett. 26, 92-93 (1975).
[CrossRef]

J. P. Heritage, T. K. Gustafson, and C. H. Lin, "Observation of coherent transient birefringence in CS2 vapor," Phys. Rev. Lett. 34, 1299-1302 (1975).
[CrossRef]

1969 (1)

M. A. Duguay and J. W. Hansen, "An ultrafast light gate," Appl. Phys. Lett. 15,192-194 (1969).
[CrossRef]

Appl. Phys. Lett. (4)

M. A. Duguay and J. W. Hansen, "An ultrafast light gate," Appl. Phys. Lett. 15,192-194 (1969).
[CrossRef]

E. P. Ippen and C. V. Shank, "Picosecond response of a high-repetition-rate CS2 optical Kerr gate," Appl. Phys. Lett. 26, 92-93 (1975).
[CrossRef]

K. Y. Kim, I. Alexeev, and H. M. Milchberg, "Single-shot supercontinuum spectral interferometry," Appl. Phys. Lett. 81, 4124-4126 (2002).
[CrossRef]

I. Alexeev, A. Ting, D. F. Gordon, E. Briscoe, J. R. Penano, R. F. Hubbard, and P. Sprangle, "Longitudinal compression of short laser pulses in air," Appl. Phys. Lett. 84, 4080-4082 (2004).
[CrossRef]

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

J. Phys. B: At. Mol. Opt. Phys. (1)

K. F. Lee, F. Legare, D. M. Villeneuve and P. B. Corkum, "Measured field-free alignment of deuterium by few-cycle pulses," J. Phys. B: At. Mol. Opt. Phys. 39, 4081-4086 (2006).
[CrossRef]

J. Phys. Chem. (2)

P. M. Felker, J. S. Baskin, and A. H. Zewail, "Rephasing of collisionless molecular coherence in large molecules," J. Phys. Chem. 90, 724-728 (1986)
[CrossRef]

L. L. Connell, T. C. Corcoran, P. W. Joireman, and P. M. Felker, "Observation and description of a new type of transient in rotational coherence spectroscopy," J. Phys. Chem. 94, 1229-1232 (1990).
[CrossRef]

Nature (1)

J. Itatani, J. Levesque, D. Zeidler, Hiromichi Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, D. M. Villeneuve, "Tomographic imaging of molecular orbitals," Nature 432, 867-871 (2004)
[CrossRef] [PubMed]

Opt. Commun. (1)

J.-F. Ripoche, G. Grillon, B. Prade, M. France, E. Nibbering, R. Lange, A. Mysyrowicz, "Determination of the time dependence of n2 in air," Opt. Commun. 135, 310-314 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (3)

P. W. Dooley, I. V. Litvinyuk, KevinF. Lee, D. M. Rayner, M. Spanner, D. M. Villeneuve, and P. B. Corkum, "Direct imaging of rotational wave-packet dynamics of diatomic molecules," Phys. Rev. A 68, 023406 (2003).
[CrossRef]

N. Hay, R. Velotta, M. Lein, R. de Nalda, E. Heesel, M. Castillejo, and J. P. Marangos, "High-order harmonic generation in laser-aligned molecules," Phys. Rev. A 65, 053805 (2002)
[CrossRef]

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, "Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases," Phys. Rev. A 13, 813-829 (1976).
[CrossRef]

Phys. Rev. E (1)

J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, "Stimulated Raman scattering of intense laser pulses in air," Phys. Rev. E 68, 056502 (2003).
[CrossRef]

Phys. Rev. Lett. (4)

C. Vozzi, F. Calegari, E. Benedetti, J.-P. Caumes, G. Sansone, S. Stagira, M. Nisoli, R. Torres, E. Heesel, N. Kajumba, J. P. Marangos, C. Altucci and R. Velotta, "Controlling Two-Center Interference in Molecular High Harmonic Generation," Phys. Rev. Lett. 95, 153902 (2005).
[CrossRef] [PubMed]

R. Velotta, N. Hay, M. B. Mason, M. Castillejo, and J. P. Marangos, "High-Order Harmonic Generation in Aligned Molecules," Phys. Rev. Lett. 87, 183901 (2001);
[CrossRef]

F. Rosca-Pruna and M. J. J. Vrakking, "Experimental Observation of Revival Structures in Picosecond Laser-Induced Alignment of I2," Phys. Rev. Lett. 87, 153902 (2001).
[CrossRef] [PubMed]

J. P. Heritage, T. K. Gustafson, and C. H. Lin, "Observation of coherent transient birefringence in CS2 vapor," Phys. Rev. Lett. 34, 1299-1302 (1975).
[CrossRef]

Rev. Mod. Phys. (1)

H. Stapelfeldt and T. Seideman, "Aligning molecules with strong laser pulses," Rev. Mod. Phys. 75, 543-557 (2003).
[CrossRef]

Science (2)

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirila, M. Lein, J. W. G. Tisch, and J. P. Marangos, "Probing Proton Dynamics in Molecules on an Attosecond Time Scale," Science 21, 424-427 (2006).
[CrossRef]

R. Righini, "Ultrafast optical Kerr effect in liquids and solids," Science 262, 1386-1390 (1993).
[CrossRef] [PubMed]

Other (3)

W. Demtroder, Molecular Physics, Wiley-VCH (Weinheim, 2005).
[CrossRef]

S. Varma, Y.-H. Chen, H. M. Milchberg, and I. Alexeev, "Single-Shot Time Resolved Measurement of Molecular Alignment in Laser-Irradiated Gases," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JFC3

S. Varma, Y.-H. Chen, I. Alexeev, R. Moon, and H. M. Milchberg, "Single-shot time resolved measurement of molecular alignment in laser-irradiated gases: application to ‘self-channeled’ plasma columns," presented at 48th Annual Meeting of the Division of Plasma Physics, American Physical Society, Philadelphia, 30 Oct.-3 Nov. 2006, abstract #NO3.015.

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Figures (9)

Fig. 1.
Fig. 1.

Experimental setup. HWP: half waveplate, BS: beamsplitter for combining pump and SC pulses, M: zero degree Ti:Sapphire dielectric mirror. The inset shows interferograms in 3 temporal windows, corresponding to laser field alignment (0 ps), quarter revival (~3 ps), and half revival (~6 ps) of the rotational wave packet in 5.1 atm O2.

Fig. 2.
Fig. 2.

Transient shift of refractive index induced by a 110-fs laser pulse in 4.4 atm Ar, N2, and N2O, with 95 µJ (6.7×1013 W/cm2), 60 µJ (4.2×1013 W/cm2), and 20 µJ (1.4×1013 W/cm2) pulse energy (peak intensity), respectively.

Fig. 3.
Fig. 3.

Normalized Δn profiles comparing experimental results from Fig. 2 (open circles) and calculations (solid red line) for (a) N2 and (b) N2O. The pump pulse envelope, with its peak centered at t=0, is shown in solid blue circles.

Fig. 4.
Fig. 4.

Measured N2 alignment <cos2 θ> t -1/3 up to t=1.25T for 6.4 atm gas pressure and 4.1×1013 W/cm2 pump peak intensity: (a) probe beam central lineout, and (b) corresponding 2-D space- and time-resolved image across the probe beam. Simulated <cos2 θ> t -1/3 is shown in (c), assuming two different excitation pulse shapes: δ-function (blue line) and cos2 function with 110 fs FWHM (red line). Dephasing is not included in this calculation.

Fig. 5.
Fig. 5.

Measured O2 alignment <cos2 θ> t -1/3 up to t=1.25T for 5.1 atm gas pressure and 2.7×1013 W/cm2 pump peak intensity: (a) probe beam central lineout, and (b) corresponding 2-D space- and time-resolved image across the probe beam. The dephasing time constant 1/γ=23.2 ps was obtained by fitting the peak amplitudes of (a) to an exponential. Simulated <cos2 θ> t -1/3 is shown in (c), including dephasing by using the extracted value of γ, and assuming two different excitation pulse shapes: δ-function (blue line) and cos2 function with 110 fs FWHM (red line).

Fig. 6.
Fig. 6.

Measured N2O alignment <cos2 θ> t -1/3 up to t=T for 2.4 atm gas pressure and 1.4×1013 W/cm2 pump peak intensity: (a) probe beam central lineout, and (b) corresponding 2-D spaceand time-resolved image across the probe beam. Note that the 1/4 and 3/4 revivals are not present due to the axial asymmetry of the N2O molecule. The dephasing time constant 1/γ=23.8 ps was obtained by fitting the peak amplitudes of (a) to an exponential. Simulated <cos2 θ> t -1/3 is shown in (c), using the extracted dephasing rate γ and assuming two different excitation pulse shapes: δ-function (blue line) and cos2 function with 110 fs FWHM (red line).

Fig. 7.
Fig. 7.

Measured D2 molecule alignment <cos2 θ> t -1/3 up to t=2.5T for 7.8 atm gas pressure, 110 fs pump pulse duration, and 4.4×1013 W/cm2 pump peak intensity: (a) probe beam central lineout, and (b) corresponding 2-D space- and time-resolved image across the probe beam. Simulated <cos2 θ> t -1/3 is shown in (c), assuming two different excitation pulse shapes: δ-function (blue line) and cos2 function with 110 fs FWHM (red line). (d) Fourier transform of measured D2 alignment response of (a), with the first peak in (a) (partly contributed by instantaneous n2 I) excluded. The peak in (d) is identified as the beat frequency between j=0 and j=2.

Fig. 8.
Fig. 8.

Measured H2 alignment <cos2 θ> t -1/3 up to t=3T, for 7.8 atm gas pressure, 110 fs pump pulse duration, and 4.4×1013 W/cm2 pump peak intensity: (a) probe beam central lineout, and (b) corresponding 2-D space- and time-resolved image across the probe beam. Simulated <cos2 θ> t -1/3 is shown in (c), assuming δ-function (blue line) and 110 fs FWHM cos2 (red line) excitation pulses. Experiment and simulation show that the revival amplitude is much smaller than for D2. (d) Fourier transform of measured H2 alignment response in (a) (neglecting the first peak) shows that the dominant contribution is beating between the j=0 and j=2 states.

Fig. 9.
Fig. 9.

(a) Measured N2O revivals at t=1/2 T at pressures of 2.4, 3.7, 5.1, and 6.4 atm, normalized to the peak alignment amplitude near t=0. (b) Dephasing rate γ versus pressure (open circles) showing linear fit (solid line). The dephasing rate per unit pressure is 1.46×1010 s-1 atm-1. The other measurement conditions are the same as for Fig. 6.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

n 2 ( t ) = 1 + 4 π N ( Δ α < cos 2 θ > t + α ) ,
Δ n ( t ) = 2 π N n 0 1 Δ α ( < cos 2 θ > t 1 3 ) ,
n 2 ( t ) 1 4 π N = Δ α < cos 2 θ > t + α
+ E ( t ) 2 ( < sin 4 θ > t α xxxx ( 3 ) + 1 2 < sin 2 2 θ > t α xxzz ( 3 ) + < cos 4 θ > t α zzzz ( 3 ) ) ,
[ ρ 1 ( t ) ] kl = i t d τ [ 𝓱 ( τ ) , ρ ( 0 ) ] kl e ( i ω kl + γ kl ) ( τ t ) ,
ρ j , j 2 , m ( 1 ) ( t ) = i 2 ( ρ j , m ( 0 ) ρ j 2 , m ( 0 ) ) Δ α Q j , j 2 m e ( i ω i , j 2 + γ i , j 2 ) t t d τ ε 2 ( τ ) e ( i ω j , j 2 + γ j , j 2 ) τ ,
< cos 2 θ > t = 1 3 1 ( ρ j , m ( 0 ) ρ j 2 , m ( 0 ) ) Δ α ( Q j , j 2 m ) 2
× Im ( e ( i ω j , j 2 γ j , j 2 ) t t d τ ε 2 ( τ ) e ( i ω j , j 2 + γ j , j 2 ) τ ) ,
< cos 2 θ > t = 1 3 2 15 j ( j 1 ) 2 j 1 ( ρ j ( 0 ) ρ j 2 ( 0 ) ) Δ α
× Im ( e ( i ω j , j 2 γ j , j 2 ) t t d τ ε 2 ( τ ) e ( i ω j , j 2 + γ j , j 2 ) τ ) ,
< cos 2 θ > t = 1 3 1 15 j ( j 1 ) 2 j 1 16 π F c ( ρ j ( 0 ) ρ j 2 ( 0 ) ) Δ α e γ j , j 2 t sin ( ω j , j 2 t ) .
< cos 2 θ > t = 1 3 2 15 j ( j 1 ) 2 j 1 ( ρ j ( 0 ) ρ j 2 ( 0 ) ) Δ α E 0 2 ( π ln 2 ) 1 2 τ p
× e ( ω j , j 2 2 γ j , j 2 2 ) τ p 2 16 ln 2 e γ j , j 2 t sin ( ω j , j 2 t γ j , j 2 ω j , j 2 τ p 2 8 ln 2 ) .
< cos 2 θ > t = 1 3 2 15 j ( j 1 ) 2 j 1 ( ρ j ( 0 ) ρ j 2 ( 0 ) ) Δ α E 0 2 [ a 1 + ( a 2 + a 3 ) cos ( π t τ 0 )
+ ( a 4 a 5 ) sin ( π t τ 0 ) + ( a 4 + a 5 a 6 ) e γ j , j 2 ( t + τ 0 ) sin ω j , j 2 ( t + τ 0 )
+ ( a 1 + a 2 + a 3 ) e γ j , j 2 ( t + τ 0 ) cos ω j , j 2 ( t + τ 0 ) ] ,
< cos 2 θ > t = 1 3 + 2 15 j ( j 1 ) 2 j 1 ( ρ j ( 0 ) ρ j 2 ( 0 ) ) Δ α E 0 2
× [ ( a 6 a 4 a 5 ) e γ j , j 2 ( t τ 0 ) sin ω j , j 2 ( t τ 0 ) + ( a 6 + a 4 + a 5 ) e γ j , j 2 ( t + τ 0 ) sin ω j , j 2 ( t + τ 0 )
+ ( a 1 a 2 a 3 ) e γ j , j 2 ( t τ 0 ) cos ω j , j 2 ( t τ 0 ) + ( a 1 + a 2 + a 3 ) e γ j , j 2 ( t + τ 0 ) cos ω j , j 2 ( t + τ 0 ) ] ,

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