Abstract

We propose the use of birefringent materials to attain pulse separations suitable for pump–probe spectroscopy and spectral interferometry. By choice of material thickness and cut angle, it is possible to balance second-order dispersion while allowing for variable delays. The generated pulse pair is used to calibrate the phase response of an ultrafast liquid-crystal pulse shaper, and in the measurement of a rotational wave packet in impulsively aligned CO2 molecules.

© 2007 Optical Society of America

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References

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  1. P. Hannaford, Femtosecond Laser Spectroscopy (Springer, 2006).
  2. J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, "Nouvelle méthode de mesure de la réponse impulsionnelle des fibres optiques," Appl. Opt. 19, 3749-3755 (1980).
    [CrossRef] [PubMed]
  3. D. Meshulach, D. Yelin, and Y. Silberberg, "White light dispersion measurements by one- and two-dimensional spectral interference," IEEE J. Quantum Electron. 33, 1969-1974 (1997).
    [CrossRef]
  4. P. Hlubina, D. Ciprian, J. Lunacek, and M. Lesnak, "Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film," Opt. Express 14, 7678-7685 (2006).
    [CrossRef] [PubMed]
  5. A. B. Vakhtin, K. A. Peterson, W. R. Wood, and D. J. Kane, "Differential spectral interferometry: an imaging technique for biomedical applications," Opt. Lett. 28, 1332-1334 (2003).
    [CrossRef] [PubMed]
  6. K. Y. Kim, I. Alexeev, and H. M. Milchberg, "Single-shot supercontinuum spectral interferometry," Appl. Phys. Lett. 81, 4124 (2002).
    [CrossRef]
  7. A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000), and references therein.
    [CrossRef]
  8. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer-Verlag, 2006).
  9. B. D. Guenther, Modern Optics (Wiley, 1990).
  10. G. Ghosh and G. Bhar, "Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices," IEEE J. Quantum Electron. QE-18, 143-145 (1982).
    [CrossRef]
  11. Parasitic nonlinear frequency conversion from phase-matched processes is readily suppressed in the large crystal lengths necessary for macroscopic pulse separations due to narrow acceptance bandwidths. A small detuning of the crystal angle is sufficient to suppress the undesired interactions. For example, a 12 mm KDP cut such that θ = 45° introduces a 1 ps delay and is simultaneously phase matched for type-I second-harmonic generation (SHG) at 800 nm. The acceptance angle is 1.8 mrad cm . The detuning of 1.5 mrad required to suppress SHG changes the pulse separation by 30 fs or 0.3%. The phase-matching angle for, in this case the more efficient, type-II SHG is 71° and is thus not phase matched.
  12. W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, "High-efficiency and narrow-linewidth operation of a 2-crystal β-BaB2O4 optical parametric oscillator," Appl. Phys. Lett. 55, 1952-1954 (1989).
    [CrossRef]
  13. K. Kato, "Second-harmonic generation to 2048 Å in β-Ba2O4," IEEE J. Quantum Electron QE-22, 1013-1014 (1986).
    [CrossRef]
  14. G. Ghosh, "Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals," Opt. Commun. 163, 95-102 (1999).
    [CrossRef]
  15. K. Kato and E. Takaoka, "Sellmeier and thermo-optic dispersion formulas for KTP," Appl. Opt. 41, 5040-5044 (2002).
    [CrossRef] [PubMed]
  16. G. J. Edwards and M. Lawrence, "A temperature-dependent dispersion-equation for congruently grown lithium-niobate," Opt. Quantum Electron. 16, 373-375 (1984).
    [CrossRef]
  17. A. C. DeFranzo and B. G. Pazol, "Index of refraction measurement on sapphire at low temperatures and visible wavelengths," Appl. Opt. 32, 2224-2234 (1993).
    [CrossRef] [PubMed]
  18. C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Opt. Lett. 23, 792-794 (1998).
    [CrossRef]
  19. M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. B 72, 156-160 (1982).
    [CrossRef]
  20. H. Stapelfeldt and T. Seideman, "Colloquium: Aligning molecules with strong laser pulses," Rev. Mod. Phys. 75, 543-557 (2003), and references therein.
    [CrossRef]
  21. R. A. Bartels, T. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, "Phase modulation of ultrashort light pulses using molecular rotational wave packets," Phys. Rev. Lett. 88, 013909 (2002).
    [CrossRef]
  22. R. A. Bartels and K. Hartinger, "Pulse polarization splitting in a transient wave plate," Opt. Lett. 31, 3526-3528 (2006).
    [CrossRef] [PubMed]
  23. SNLO nonlinear optics code available from A. V. Smith, Sandia National Laboratories, Albuquerque, New Mexico 87185-1423.

2006 (2)

2003 (2)

A. B. Vakhtin, K. A. Peterson, W. R. Wood, and D. J. Kane, "Differential spectral interferometry: an imaging technique for biomedical applications," Opt. Lett. 28, 1332-1334 (2003).
[CrossRef] [PubMed]

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

2002 (3)

R. A. Bartels, T. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, "Phase modulation of ultrashort light pulses using molecular rotational wave packets," Phys. Rev. Lett. 88, 013909 (2002).
[CrossRef]

K. Kato and E. Takaoka, "Sellmeier and thermo-optic dispersion formulas for KTP," Appl. Opt. 41, 5040-5044 (2002).
[CrossRef] [PubMed]

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

2000 (1)

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000), and references therein.
[CrossRef]

1999 (1)

G. Ghosh, "Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals," Opt. Commun. 163, 95-102 (1999).
[CrossRef]

1998 (1)

1997 (1)

D. Meshulach, D. Yelin, and Y. Silberberg, "White light dispersion measurements by one- and two-dimensional spectral interference," IEEE J. Quantum Electron. 33, 1969-1974 (1997).
[CrossRef]

1993 (1)

1989 (1)

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, "High-efficiency and narrow-linewidth operation of a 2-crystal β-BaB2O4 optical parametric oscillator," Appl. Phys. Lett. 55, 1952-1954 (1989).
[CrossRef]

1986 (1)

K. Kato, "Second-harmonic generation to 2048 Å in β-Ba2O4," IEEE J. Quantum Electron QE-22, 1013-1014 (1986).
[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]

1982 (2)

M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. B 72, 156-160 (1982).
[CrossRef]

G. Ghosh and G. Bhar, "Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices," IEEE J. Quantum Electron. QE-18, 143-145 (1982).
[CrossRef]

1980 (1)

Appl. Opt. (3)

Appl. Phys. Lett. (2)

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, "High-efficiency and narrow-linewidth operation of a 2-crystal β-BaB2O4 optical parametric oscillator," Appl. Phys. Lett. 55, 1952-1954 (1989).
[CrossRef]

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

IEEE J. Quantum Electron (1)

K. Kato, "Second-harmonic generation to 2048 Å in β-Ba2O4," IEEE J. Quantum Electron QE-22, 1013-1014 (1986).
[CrossRef]

IEEE J. Quantum Electron. (2)

G. Ghosh and G. Bhar, "Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices," IEEE J. Quantum Electron. QE-18, 143-145 (1982).
[CrossRef]

D. Meshulach, D. Yelin, and Y. Silberberg, "White light dispersion measurements by one- and two-dimensional spectral interference," IEEE J. Quantum Electron. 33, 1969-1974 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. B 72, 156-160 (1982).
[CrossRef]

Opt. Commun. (1)

G. Ghosh, "Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals," Opt. Commun. 163, 95-102 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

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]

Phys. Rev. Lett. (1)

R. A. Bartels, T. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, "Phase modulation of ultrashort light pulses using molecular rotational wave packets," Phys. Rev. Lett. 88, 013909 (2002).
[CrossRef]

Rev. Mod. Phys. (1)

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

Rev. Sci. Instrum. (1)

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000), and references therein.
[CrossRef]

Other (5)

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer-Verlag, 2006).

B. D. Guenther, Modern Optics (Wiley, 1990).

Parasitic nonlinear frequency conversion from phase-matched processes is readily suppressed in the large crystal lengths necessary for macroscopic pulse separations due to narrow acceptance bandwidths. A small detuning of the crystal angle is sufficient to suppress the undesired interactions. For example, a 12 mm KDP cut such that θ = 45° introduces a 1 ps delay and is simultaneously phase matched for type-I second-harmonic generation (SHG) at 800 nm. The acceptance angle is 1.8 mrad cm . The detuning of 1.5 mrad required to suppress SHG changes the pulse separation by 30 fs or 0.3%. The phase-matching angle for, in this case the more efficient, type-II SHG is 71° and is thus not phase matched.

P. Hannaford, Femtosecond Laser Spectroscopy (Springer, 2006).

SNLO nonlinear optics code available from A. V. Smith, Sandia National Laboratories, Albuquerque, New Mexico 87185-1423.

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Figures (10)

Fig. 1
Fig. 1

Pulse delays, measured by spectral interferometry and normalized to crystal length, for different single- and double-passed KDP crystals cut at 44.9°, as a function of external incidence angle.

Fig. 2
Fig. 2

Double-pass geometries of angular delay tuning. The backreflected beam is displaced in the plane (a) perpendicular to the rotation or (b) within the rotation plane.

Fig. 3
Fig. 3

Configuration for dispersion-matched delay tuning. The two materials of length L 1 and L 2 , cut at angles Θ 1 and Θ 2 to the respective optic axes, are simultaneously rotated through angle α ext .

Fig. 4
Fig. 4

Numerically predicted (a) pulse delay and (b) dispersion for a dispersion-matched, angle-tuned KDP + BBO crystal pair.

Fig. 5
Fig. 5

Tuning about time-zero from the combination of a double-passed, tilted 4 mm , and a fixed 12 mm bias KDP crystal.

Fig. 6
Fig. 6

(a) Measured spectral interferometry fringes and (b) retrieved phase response for a liquid-crystal mask SLM pulse shaper. The fringes were generated by passing through a single 12 mm KDP crystal cut at 44.9°.

Fig. 7
Fig. 7

Retrieved phase response of a rotational wave packet in CO 2 , measured with a probe pulse pair with a 2.2 ps separation.

Fig. 8
Fig. 8

Construction for angle-tuned pulse separation calculation. See text for details.

Fig. 9
Fig. 9

Geometrical construction for the beam displacement of a double-passed tilted refractive element. See text for details.

Fig. 10
Fig. 10

Beam displacement measured for an in-plane, near-retro-reflected double-pass of a 1 mm thick fused silica plate, and the deviations predicted by Eq. (B3).

Tables (1)

Tables Icon

Table 1 Crystal Lengths (mm), Second-Order Dispersions (fs2∕rad), and Third-Order Dispersions (fs3∕rad) Evaluated at 800 nm for a Number of Crystal Combinations, Each With Θ 1 = Θ 2 = 90°, Chosen Such That the Pulse Separation is 1 ps a

Equations (14)

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T = L c [ n g o n g e ( θ ) ] ,
[ n g 1 o n g 1 e ( Θ 1 ) n g 2 o n g 2 e ( Θ 2 ) β 1 o β 1 e ( Θ 1 ) β 2 o β 2 e ( Θ 2 ) ] [ d 1 d 2 ] = [ c T 0 ] .
κ d 1 d 2 = Δ β 2 Δ β 1 ,
d c T = Δ β 2 Δ β 1 Δ n g 1 Δ β 2 Δ n g 2 Δ β 1 .
Δ n g 1 Δ β 2 = Δ n g 2 Δ β 1 .
L o = d cos θ o = n o d n o 2 sin 2 α ext .
n e ( θ ) = n o n e n e 2 cos 2 θ + n o 2 sin 2 θ ,
tan ρ = sin θ cos θ ( n o 2 n e 2 ) n e 2 cos 2 θ + n o 2 sin 2 θ ,
L e = d cos ( θ e + ρ ) .
L ext = [ tan ( θ e + ρ ) tan θ o ] d sin α ext .
T = 1 c [ L o ( α ext ) n g o + L ext ( α ext ) L e ( α ext ) n g e ( α ext ) ] .
y = sin [ α ext ( α int + ρ ) ] cos ( α int + ρ ) d .
y = sin [ α ext ( α int + ρ ) ] cos θ m cos ( α int + ρ ) d .
Δ y = { sin [ α ext ( α int + ρ ) ] cos ( α int + ρ ) [ 1 + tan θ m 2 tan θ m ] sin [ α ext ( α int + ρ ) ] cos θ m cos ( α int + ρ ) } d .

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