Abstract

We consider a programmable, phase, and amplitude femtosecond pulse shaper based on a two-dimensional (2D) reflective liquid-crystal (LC) spatial light modulator (SLM). A new zero-order pulse shaping scheme is introduced and compared to the first-order scheme, both theoretically and experimentally, using liquid crystal on silicon 2D SLM. While the spectral components of the pulse are spread across the horizontal dimension, we use the vertical direction for modulation of both spectral phases and amplitudes. It was found that while zero-order approach provided better light efficiency (67% versus 43%), the first-order scheme has superior dynamic range of amplitude modulation.

© 2007 Optical Society of America

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References

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  1. A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
    [CrossRef]
  2. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert II, "Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator," Opt. Lett. 15, 326-328 (1990).
    [CrossRef] [PubMed]
  3. A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
    [CrossRef] [PubMed]
  4. D. Meshulach and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239-242 (1998).
    [CrossRef]
  5. P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, "Femtosecond phase-coherent two-dimensional spectroscopy," Science 300, 1553-1555 (2003).
    [CrossRef] [PubMed]
  6. N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently-controlled nonlinear raman spectroscopy and microscopy," Nature 418, 512-514 (2002).
    [CrossRef] [PubMed]
  7. A. Efimov, A. J. Taylor, F. G. Omenetto, and E. Vanin, "Adaptive control of femtosecond soliton self-frequency shift in fibers," Opt. Lett. 29, 271-273 (2004).
    [CrossRef] [PubMed]
  8. R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays," Nature 406, 164-166 (2000).
    [CrossRef] [PubMed]
  9. E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, "Pulse compression by use of deformable mirrors," Opt. Lett. 24, 493-495 (1999).
    [CrossRef]
  10. C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, and W. S. Warren, "Femtosecond laser pulse shaping by use of microsecond radio-frequency pulses," Opt. Lett. 19, 737-739 (1994).
    [CrossRef] [PubMed]
  11. E. Frumker, D. Oron, D. Mandelik, and Y. Silberberg, "Femtosecond pulse-shape modulation at kilohertz rates," Opt. Lett. 29, 890-892 (2004).
    [CrossRef] [PubMed]
  12. E. Frumker, E. Tal, Y. Silberberg, and D. Majer, "Femtosecond pulse-shape modulation at nanosecond rates," Opt. Lett. 30, 2796-2798 (2005).
    [CrossRef] [PubMed]
  13. M. M. Wefers and K. A. Nelson, "Generation of high-fidelity programmable ultrafast optical waveforms," Opt. Lett. 20, 1047-1049 (1995).
    [CrossRef] [PubMed]
  14. M. C. Fischer, T. Ye, G. Yurtsever, A. Miller, M. Ciocca, W. Wagner, and W. S. Warren, "Two-photon absorption and self-phase modulation measurements with shaped femtosecond laser pulses," Opt. Lett. 30, 1551-1553 (2005).
    [CrossRef] [PubMed]
  15. M. M. Wefers and K. A. Nelson, "Programmable phase and amplitude femtosecond pulse shaping," Opt. Lett. 18, 2032-2034 (1993).
    [CrossRef] [PubMed]
  16. J. C. Vaughan, T. Hornung, T. Feurer, and K. A. Nelson, "Diffraction-based femtosecond pulse shaping with a 2D SLM," Opt. Lett. 30, 323-325 (2005).
    [CrossRef] [PubMed]
  17. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  18. K. Kwong, D. Yankelevich, K. Chu, J. Heritage, and A. Dienes, "400Hz mechanical scanning optical delay line," Opt. Lett. 18, 558-560 (1993).
    [CrossRef] [PubMed]
  19. G. J. Tearney, B. E. Bouma, and J. G. Fujimoto, "High-speed phase- and group-delay scanning with a grating-based phase control delay line," Opt. Lett. 22, 1811-1813 (1997).
    [CrossRef]
  20. E. Frumker and Y. Silberberg, "Femtosecond pulse shaping using a 2D liquid crystal spatial light modulator," Opt. Lett. 32, 1384-1386 (2007).
    [CrossRef] [PubMed]
  21. T. Feurer, J. C. Vaughan, R. M. Koehl, and K. A. Nelson, "Multidimensional control of femtosecond pulses by use of a programmable liquid-crystal matrix," Opt. Lett. 27, 652-654 (2002).
    [CrossRef]
  22. T. Feurer, J. C. Vaughan, and K. A. Nelson, "Spatiotemporal coherent control of lattice vibrational waves," Science 299, 374-377 (2003).
    [CrossRef] [PubMed]

2007 (1)

2005 (3)

2004 (2)

2003 (2)

T. Feurer, J. C. Vaughan, and K. A. Nelson, "Spatiotemporal coherent control of lattice vibrational waves," Science 299, 374-377 (2003).
[CrossRef] [PubMed]

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, "Femtosecond phase-coherent two-dimensional spectroscopy," Science 300, 1553-1555 (2003).
[CrossRef] [PubMed]

2002 (2)

N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently-controlled nonlinear raman spectroscopy and microscopy," Nature 418, 512-514 (2002).
[CrossRef] [PubMed]

T. Feurer, J. C. Vaughan, R. M. Koehl, and K. A. Nelson, "Multidimensional control of femtosecond pulses by use of a programmable liquid-crystal matrix," Opt. Lett. 27, 652-654 (2002).
[CrossRef]

2000 (2)

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

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

1999 (1)

1998 (2)

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239-242 (1998).
[CrossRef]

1997 (1)

1995 (1)

1994 (1)

1993 (2)

1990 (1)

Nature (3)

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays," Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239-242 (1998).
[CrossRef]

N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently-controlled nonlinear raman spectroscopy and microscopy," Nature 418, 512-514 (2002).
[CrossRef] [PubMed]

Opt. Lett. (14)

A. Efimov, A. J. Taylor, F. G. Omenetto, and E. Vanin, "Adaptive control of femtosecond soliton self-frequency shift in fibers," Opt. Lett. 29, 271-273 (2004).
[CrossRef] [PubMed]

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

K. Kwong, D. Yankelevich, K. Chu, J. Heritage, and A. Dienes, "400Hz mechanical scanning optical delay line," Opt. Lett. 18, 558-560 (1993).
[CrossRef] [PubMed]

G. J. Tearney, B. E. Bouma, and J. G. Fujimoto, "High-speed phase- and group-delay scanning with a grating-based phase control delay line," Opt. Lett. 22, 1811-1813 (1997).
[CrossRef]

E. Frumker and Y. Silberberg, "Femtosecond pulse shaping using a 2D liquid crystal spatial light modulator," Opt. Lett. 32, 1384-1386 (2007).
[CrossRef] [PubMed]

T. Feurer, J. C. Vaughan, R. M. Koehl, and K. A. Nelson, "Multidimensional control of femtosecond pulses by use of a programmable liquid-crystal matrix," Opt. Lett. 27, 652-654 (2002).
[CrossRef]

E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, "Pulse compression by use of deformable mirrors," Opt. Lett. 24, 493-495 (1999).
[CrossRef]

C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, and W. S. Warren, "Femtosecond laser pulse shaping by use of microsecond radio-frequency pulses," Opt. Lett. 19, 737-739 (1994).
[CrossRef] [PubMed]

E. Frumker, D. Oron, D. Mandelik, and Y. Silberberg, "Femtosecond pulse-shape modulation at kilohertz rates," Opt. Lett. 29, 890-892 (2004).
[CrossRef] [PubMed]

E. Frumker, E. Tal, Y. Silberberg, and D. Majer, "Femtosecond pulse-shape modulation at nanosecond rates," Opt. Lett. 30, 2796-2798 (2005).
[CrossRef] [PubMed]

M. M. Wefers and K. A. Nelson, "Generation of high-fidelity programmable ultrafast optical waveforms," Opt. Lett. 20, 1047-1049 (1995).
[CrossRef] [PubMed]

M. C. Fischer, T. Ye, G. Yurtsever, A. Miller, M. Ciocca, W. Wagner, and W. S. Warren, "Two-photon absorption and self-phase modulation measurements with shaped femtosecond laser pulses," Opt. Lett. 30, 1551-1553 (2005).
[CrossRef] [PubMed]

M. M. Wefers and K. A. Nelson, "Programmable phase and amplitude femtosecond pulse shaping," Opt. Lett. 18, 2032-2034 (1993).
[CrossRef] [PubMed]

J. C. Vaughan, T. Hornung, T. Feurer, and K. A. Nelson, "Diffraction-based femtosecond pulse shaping with a 2D SLM," Opt. Lett. 30, 323-325 (2005).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

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

Science (3)

T. Feurer, J. C. Vaughan, and K. A. Nelson, "Spatiotemporal coherent control of lattice vibrational waves," Science 299, 374-377 (2003).
[CrossRef] [PubMed]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

P. Tian, D. Keusters, Y. Suzaki, and W. S. Warren, "Femtosecond phase-coherent two-dimensional spectroscopy," Science 300, 1553-1555 (2003).
[CrossRef] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the 2D phase and amplitude SLM pulse shaper.

Fig. 2
Fig. 2

Example of actual 2D phase encoding into the SLM. (a) Periodic amplitude-only modulation. (b) Periodic phase-only modulation. (c) and (d) Zero-order mask encoded for amplitude only (c) and phase only (d). (e) and (f) First-order mask encoded for amplitude only (e) and phase only (f).

Fig. 3
Fig. 3

Experimental results of amplitude modulation in the zero-order approach. (a) and (b) Periodic binary spectral amplitude modulation with a period of 6.2 THz and 3.1 THz , respectively. Solid line—spectral amplitude modulation applied. Dotted line—no modulation applied. (c) Amplitude modulation versus A ( ω ) encoded. Solid line—experimental result. Dashed-dotted line—theoretical expectation.

Fig. 4
Fig. 4

Experimentally observed flicker. (a) No phase is applied. (b) A ( ω ) = π 2 applied for all ω. (c) A ( ω ) = π applied for all ω.

Fig. 5
Fig. 5

Experimental results for cross correlation for zero-order approach. (a) No phase is applied. (b) Periodic phase-only modulation with binary modulation depth of π 2 and period 3.1 THz . (c) Periodic phase-only modulation with modulation depth of π. (d) Periodic amplitude-only modulation.

Fig. 6
Fig. 6

Experimental results of amplitude modulation in the first-order approach. (a) and (b) Periodic binary spectral amplitude modulation with period of 6.2 THz and 3.1 THz , respectively. Solid line—spectral amplitude modulation applied. Dotted line—no modulation applied. (c) Amplitude modulation versus blazing multiplier factor— α ( ω ) encoded. Solid line—experimental result. Dashed-dotted line—theoretical expectation.

Fig. 7
Fig. 7

Experimental results of “two spectral slit” experiment in the first-order approach. (a) Dotted line—nonmodulated spectra. Solid line—two spectral slit was applied. Slit full width— 1.5 nm , distance between the centers of the slits— 5 nm . (b) Cross correlation with no phase was applied. (c) Cross correlation with π phase step applied between the slits.

Fig. 8
Fig. 8

Experimental results for cross correlation for first-order approach. (a) No phase is applied. (b) Periodic phase-only modulation with binary modulation depth of π 2 and period 3.1 THz . (c) Periodic phase-only modulation with modulation depth of π. (d) Periodic amplitude-only modulation.

Equations (12)

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T ( z , ω ) = [ rect ( z 2 z 0 ) e i ( A ( ω ) rect ( z z 0 ) + B ( ω ) ) ] * n = + δ ( z 2 z 0 n ) .
T ( z , ω ) = n = + C n e i 2 π n P z .
C 0 ( ω ) = 1 2 z 0 z 0 z 0 T ( z , ω ) d z = 1 2 ( 1 + e i A ( ω ) ) e i B ( ω ) .
I 0 C 0 ( ω ) 2 = cos 2 ( A ( ω ) 2 ) .
A ( ω ) = 2 arccos [ τ ( ω ) ] ,
B ( ω ) = φ ( ω ) arg ( 1 + e i A ( ω ) ) = φ ( ω ) A ( ω ) 2 .
T ( z , ω ) = [ e i ( 2 π α ( ω ) P z + π ) rect ( z P ) ] * n = + δ ( z n P ) * δ ( z s ( ω ) ) ,
E form ( k z , ω ) sinc ( k z 1 P ) * δ ( k z α ( ω ) P ) .
E ( k z , ω ) { sinc ( k z α ( ω ) P 1 P ) e i 2 π s ( ω ) k z n = + δ ( k z n P ) } * A ̃ ( k z 1 D ) .
E + 1 ( k z , ω ) sinc [ 1 α ( ω ) ] e i 2 π s ( ω ) P A ̃ ( k z 1 P 1 D ) ,
Φ max ( ω ) 2 π 2 π N ω .
η q = sinc 2 ( q 2 N ) sinc 2 ( q Φ 0 2 π ) sinc 2 ( q Φ 0 2 π 2 N ) ,

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