Abstract

The strong chromatic behavior associated with a conventional diffractive lens is fully exploited to propose a novel optical device for pulse shaping in the femtosecond regime. This device consists of two optical elements: a spatially patterned circularly symmetric mask and a kinoform diffractive lens, which are facing each other. The system performs a mapping between the spatial position of the masking function expressed in the squared radial coordinate and the temporal position in the output waveform. This space-to-time conversion occurs at the chromatic focus of the diffractive lens, and makes it possible to tailor the output central wavelength along the axial location of the output point. Inspection of the validity of our device is performed by means of computer simulations involving the generation of femtosecond optical packets.

© 2008 Optical Society of America

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  1. J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nat. Photonics 1, 319-330 (2007).
    [CrossRef]
  2. A. M. Weiner, "Femtosecond pulse shaping with spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
    [CrossRef]
  3. A. Assion, T. Baurmert, M. Bergt, 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. C. Nuss and R. L. Morrison, "Time-domain images," Opt. Lett. 20, 740-742, (1995).
    [CrossRef] [PubMed]
  5. D. M. Marom, D. Panasenko, P.-C. Sun, and Y. Fainman, "Spatial-temporal wave mixing for space-to-time conversion," Opt. Lett. 24, 563-565 (1999).
    [CrossRef]
  6. C. Froehly, B. Colombeau, and M. Vampouille, "Shaping and analysis of picosecond light pulses," in Prog. Opt. XX, E. Wolf, ed., 65-153 (North-Holland, Amsterdam, 1983).
  7. D. E. Leaird and A. M. Weiner, "Femtosecond optical packet generation by a direct space-to-time pulse shaper," Opt. Lett. 24, 853-855 (1999).
    [CrossRef]
  8. J. D. McKinney, D. E. Leaird, and A. M. Weiner, "Millimiter-wave arbitrary waveform generation with a direct space-to-time pulse shaper," Opt. Lett. 27, 1345-1347 (2002).
    [CrossRef]
  9. S. Xiao, J. D. McKinney, and A. M. Weiner, "Photonic microwave arbitrary waveform generation using a virtual imaged phased-array direct space-to-time pulse shaper," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
    [CrossRef]
  10. V. Moreno, J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: Deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
    [CrossRef]
  11. Y. X. Wang, W. B. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
    [CrossRef] [PubMed]
  12. M. Hacker, G. Stobrawa, R. Sauerbrey, T. Buckup, M. Motzkus, M. Wildenhain, and A. Gehner, "Micromirror SLM for femtosecond pulse shaping in the ultraviolet," Appl. Phys. B 76, 711-714 (2003).
    [CrossRef]
  13. B. J. Pearson and T. C. Weinacht "Shaped ultrafast laser pulses in the deep ultraviolet," Opt. Express 15, 4385-4388 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-7-4385.
    [CrossRef] [PubMed]
  14. See, for instance, about Linac Coherent Light Source at http://lcls.slac.stanford.edu/.
  15. A. G. Michette, Optical Systems for Soft X-Rays (Plenum, 1986).
    [CrossRef]
  16. Z. Bor, "Distortion of femtosecond laser pulses in lenses," Opt. Lett. 14, 119-121 (1989).
    [CrossRef] [PubMed]
  17. G. Mínguez-Vega, O. Mendoza-Yero, J. Lancis, and V. Climent, "Proposal for the generation of THz bursts and codes of shaped femtosecond pulses using binary mask," IEEE Photon. Technol. Lett. 19, 1732-1734 (2007).
    [CrossRef]
  18. C. G. Leburn, A. A. Lagatsky, C. T. A. Brown and W. Sibbett, "Femtosecond Cr4+:YAG laser with 4 GHz pulse repetition rate," Electron. Lett. 40, 805-807 (2004).
    [CrossRef]

2007

J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nat. Photonics 1, 319-330 (2007).
[CrossRef]

B. J. Pearson and T. C. Weinacht "Shaped ultrafast laser pulses in the deep ultraviolet," Opt. Express 15, 4385-4388 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-7-4385.
[CrossRef] [PubMed]

G. Mínguez-Vega, O. Mendoza-Yero, J. Lancis, and V. Climent, "Proposal for the generation of THz bursts and codes of shaped femtosecond pulses using binary mask," IEEE Photon. Technol. Lett. 19, 1732-1734 (2007).
[CrossRef]

2004

C. G. Leburn, A. A. Lagatsky, C. T. A. Brown and W. Sibbett, "Femtosecond Cr4+:YAG laser with 4 GHz pulse repetition rate," Electron. Lett. 40, 805-807 (2004).
[CrossRef]

S. Xiao, J. D. McKinney, and A. M. Weiner, "Photonic microwave arbitrary waveform generation using a virtual imaged phased-array direct space-to-time pulse shaper," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
[CrossRef]

2003

Y. X. Wang, W. B. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

M. Hacker, G. Stobrawa, R. Sauerbrey, T. Buckup, M. Motzkus, M. Wildenhain, and A. Gehner, "Micromirror SLM for femtosecond pulse shaping in the ultraviolet," Appl. Phys. B 76, 711-714 (2003).
[CrossRef]

2002

2000

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

1999

1998

A. Assion, T. Baurmert, M. Bergt, 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]

1997

V. Moreno, J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: Deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
[CrossRef]

1995

1989

Assion, A.

A. Assion, T. Baurmert, M. Bergt, 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]

Baurmert, T.

A. Assion, T. Baurmert, M. Bergt, 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]

Bergt, M.

A. Assion, T. Baurmert, M. Bergt, 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]

Bor, Z.

Brown, C. T. A.

C. G. Leburn, A. A. Lagatsky, C. T. A. Brown and W. Sibbett, "Femtosecond Cr4+:YAG laser with 4 GHz pulse repetition rate," Electron. Lett. 40, 805-807 (2004).
[CrossRef]

Buckup, T.

M. Hacker, G. Stobrawa, R. Sauerbrey, T. Buckup, M. Motzkus, M. Wildenhain, and A. Gehner, "Micromirror SLM for femtosecond pulse shaping in the ultraviolet," Appl. Phys. B 76, 711-714 (2003).
[CrossRef]

Capmany, J.

J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nat. Photonics 1, 319-330 (2007).
[CrossRef]

Climent, V.

G. Mínguez-Vega, O. Mendoza-Yero, J. Lancis, and V. Climent, "Proposal for the generation of THz bursts and codes of shaped femtosecond pulses using binary mask," IEEE Photon. Technol. Lett. 19, 1732-1734 (2007).
[CrossRef]

Fainman, Y.

Gehner, A.

M. Hacker, G. Stobrawa, R. Sauerbrey, T. Buckup, M. Motzkus, M. Wildenhain, and A. Gehner, "Micromirror SLM for femtosecond pulse shaping in the ultraviolet," Appl. Phys. B 76, 711-714 (2003).
[CrossRef]

Gerber, G.

A. Assion, T. Baurmert, M. Bergt, 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]

Hacker, M.

M. Hacker, G. Stobrawa, R. Sauerbrey, T. Buckup, M. Motzkus, M. Wildenhain, and A. Gehner, "Micromirror SLM for femtosecond pulse shaping in the ultraviolet," Appl. Phys. B 76, 711-714 (2003).
[CrossRef]

Jacobsen, C.

Y. X. Wang, W. B. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Kiefer, B.

A. Assion, T. Baurmert, M. Bergt, 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]

Lagatsky, A. A.

C. G. Leburn, A. A. Lagatsky, C. T. A. Brown and W. Sibbett, "Femtosecond Cr4+:YAG laser with 4 GHz pulse repetition rate," Electron. Lett. 40, 805-807 (2004).
[CrossRef]

Lancis, J.

G. Mínguez-Vega, O. Mendoza-Yero, J. Lancis, and V. Climent, "Proposal for the generation of THz bursts and codes of shaped femtosecond pulses using binary mask," IEEE Photon. Technol. Lett. 19, 1732-1734 (2007).
[CrossRef]

Leaird, D. E.

Leburn, C. G.

C. G. Leburn, A. A. Lagatsky, C. T. A. Brown and W. Sibbett, "Femtosecond Cr4+:YAG laser with 4 GHz pulse repetition rate," Electron. Lett. 40, 805-807 (2004).
[CrossRef]

Marom, D. M.

McKinney, J. D.

S. Xiao, J. D. McKinney, and A. M. Weiner, "Photonic microwave arbitrary waveform generation using a virtual imaged phased-array direct space-to-time pulse shaper," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
[CrossRef]

J. D. McKinney, D. E. Leaird, and A. M. Weiner, "Millimiter-wave arbitrary waveform generation with a direct space-to-time pulse shaper," Opt. Lett. 27, 1345-1347 (2002).
[CrossRef]

Mendoza-Yero, O.

G. Mínguez-Vega, O. Mendoza-Yero, J. Lancis, and V. Climent, "Proposal for the generation of THz bursts and codes of shaped femtosecond pulses using binary mask," IEEE Photon. Technol. Lett. 19, 1732-1734 (2007).
[CrossRef]

Mínguez-Vega, G.

G. Mínguez-Vega, O. Mendoza-Yero, J. Lancis, and V. Climent, "Proposal for the generation of THz bursts and codes of shaped femtosecond pulses using binary mask," IEEE Photon. Technol. Lett. 19, 1732-1734 (2007).
[CrossRef]

Moreno, V.

V. Moreno, J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: Deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
[CrossRef]

Morrison, R. L.

Motzkus, M.

M. Hacker, G. Stobrawa, R. Sauerbrey, T. Buckup, M. Motzkus, M. Wildenhain, and A. Gehner, "Micromirror SLM for femtosecond pulse shaping in the ultraviolet," Appl. Phys. B 76, 711-714 (2003).
[CrossRef]

Novak, D.

J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nat. Photonics 1, 319-330 (2007).
[CrossRef]

Nuss, C.

Panasenko, D.

Pearson, B. J.

Roman, J. F.

V. Moreno, J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: Deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
[CrossRef]

Salgueiro, J. R.

V. Moreno, J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: Deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
[CrossRef]

Sauerbrey, R.

M. Hacker, G. Stobrawa, R. Sauerbrey, T. Buckup, M. Motzkus, M. Wildenhain, and A. Gehner, "Micromirror SLM for femtosecond pulse shaping in the ultraviolet," Appl. Phys. B 76, 711-714 (2003).
[CrossRef]

Seyfried, V.

A. Assion, T. Baurmert, M. Bergt, 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]

Sibbett, W.

C. G. Leburn, A. A. Lagatsky, C. T. A. Brown and W. Sibbett, "Femtosecond Cr4+:YAG laser with 4 GHz pulse repetition rate," Electron. Lett. 40, 805-807 (2004).
[CrossRef]

Stobrawa, G.

M. Hacker, G. Stobrawa, R. Sauerbrey, T. Buckup, M. Motzkus, M. Wildenhain, and A. Gehner, "Micromirror SLM for femtosecond pulse shaping in the ultraviolet," Appl. Phys. B 76, 711-714 (2003).
[CrossRef]

Strehle, M.

A. Assion, T. Baurmert, M. Bergt, 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]

Sun, P.-C.

Wang, Y. X.

Y. X. Wang, W. B. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Weinacht, T. C.

Weiner, A. M.

S. Xiao, J. D. McKinney, and A. M. Weiner, "Photonic microwave arbitrary waveform generation using a virtual imaged phased-array direct space-to-time pulse shaper," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
[CrossRef]

J. D. McKinney, D. E. Leaird, and A. M. Weiner, "Millimiter-wave arbitrary waveform generation with a direct space-to-time pulse shaper," Opt. Lett. 27, 1345-1347 (2002).
[CrossRef]

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

D. E. Leaird and A. M. Weiner, "Femtosecond optical packet generation by a direct space-to-time pulse shaper," Opt. Lett. 24, 853-855 (1999).
[CrossRef]

Wildenhain, M.

M. Hacker, G. Stobrawa, R. Sauerbrey, T. Buckup, M. Motzkus, M. Wildenhain, and A. Gehner, "Micromirror SLM for femtosecond pulse shaping in the ultraviolet," Appl. Phys. B 76, 711-714 (2003).
[CrossRef]

Xiao, S.

S. Xiao, J. D. McKinney, and A. M. Weiner, "Photonic microwave arbitrary waveform generation using a virtual imaged phased-array direct space-to-time pulse shaper," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
[CrossRef]

Yun, W. B.

Y. X. Wang, W. B. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Am. J. Phys.

V. Moreno, J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: Deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
[CrossRef]

Appl. Phys. B

M. Hacker, G. Stobrawa, R. Sauerbrey, T. Buckup, M. Motzkus, M. Wildenhain, and A. Gehner, "Micromirror SLM for femtosecond pulse shaping in the ultraviolet," Appl. Phys. B 76, 711-714 (2003).
[CrossRef]

Electron. Lett.

C. G. Leburn, A. A. Lagatsky, C. T. A. Brown and W. Sibbett, "Femtosecond Cr4+:YAG laser with 4 GHz pulse repetition rate," Electron. Lett. 40, 805-807 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

G. Mínguez-Vega, O. Mendoza-Yero, J. Lancis, and V. Climent, "Proposal for the generation of THz bursts and codes of shaped femtosecond pulses using binary mask," IEEE Photon. Technol. Lett. 19, 1732-1734 (2007).
[CrossRef]

S. Xiao, J. D. McKinney, and A. M. Weiner, "Photonic microwave arbitrary waveform generation using a virtual imaged phased-array direct space-to-time pulse shaper," IEEE Photon. Technol. Lett. 16, 1936-1938 (2004).
[CrossRef]

Nat. Photonics

J. Capmany and D. Novak, "Microwave photonics combines two worlds," Nat. Photonics 1, 319-330 (2007).
[CrossRef]

Nature

Y. X. Wang, W. B. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Rev. Sci. Instrum.

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

Science

A. Assion, T. Baurmert, M. Bergt, 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]

Other

C. Froehly, B. Colombeau, and M. Vampouille, "Shaping and analysis of picosecond light pulses," in Prog. Opt. XX, E. Wolf, ed., 65-153 (North-Holland, Amsterdam, 1983).

See, for instance, about Linac Coherent Light Source at http://lcls.slac.stanford.edu/.

A. G. Michette, Optical Systems for Soft X-Rays (Plenum, 1986).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram of the all-diffractive pulse shaper.

Fig. 2.
Fig. 2.

Temporal and spectral response of the system plotted in Fig. 1. (a) Normalized instantaneous intensity, and (b) Normalized power spectrum. In both cases, three different z distances were considered: z=98 mm (short-dashed curve), z=100 mm (solid curve) and z=102 mm (long-dashed curve). For z=100 mm, the power spectrum in logarithmic scale is shown as an inset.

Fig. 3.
Fig. 3.

(a). Mask N used for the generation of the binary code 01001101011101; (b) Normalized spatiotemporal intensity distribution for system in Fig. 1 by placing Mask N calculated for z=100 mm; (c) Normalized output instantaneous intensity distribution for a punctual pinhole locate 2 µm off-axis (solid line) and for two on-axis pinholes of radii r=0.5 µm (long-dashed line) and r=40 µm (short-dashed line); (d) Monochromatic efficiency of the system as a function of the pinhole radius for masks M and N.

Equations (4)

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U ˜ out ( ω ) = ω iBc S ˜ ( ω ˜ ) exp [ i ω c L ] o t ( r ) exp [ i ω c A 2 B r 2 ] rdr .
( A B C D ) = ( 1 Z 0 ω 1 ω 0 0 1 ) ( 1 0 ω 0 Z 0 ω 1 ) .
U ˜ out ( ω ) = ω i 2 Z ( ω 1 ) c exp [ i ω c Z ( ω 1 ) ] S ˜ ( ω ˜ ) Q ˜ [ ω ω 1 2 c Z ( ω 1 ) ] ,
u out ( τ ) = i ω 0 u in ( τ ) [ q ( τ β ) exp ( i ω 1 τ ) ] ,

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