Abstract

We analyze the structure of space-time focusing of spatially-chirped pulses using a technique where each frequency component of the beam follows its own Gaussian beamlet that in turn travels as a ray through the system. The approach leads to analytic expressions for the axially-varying pulse duration, pulse-front tilt, and the longitudinal intensity profile. We find that an important contribution to the intensity localization obtained with spatial-chirp focusing arises from the evolution of the geometric phase of the beamlets.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, “Angular dispersion and temporal change of femtosecond pulses from misaligned pulse compressors,” IEEE J. Sel. Top. Quantum Electron.10, 213–220 (2004).
    [CrossRef]
  2. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt Express13, 1468–1476 (2005).
    [CrossRef] [PubMed]
  3. G. Zhu, J. van Howe, M. Durst, W. Zipfel, and C. Xu, “Simultaneous spatial and temporal focusing of femtosecond pulses,” Opt. Express13, 2153–2159 (2005).
    [CrossRef] [PubMed]
  4. M. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun.281, 1796–1805 (2008).
    [CrossRef] [PubMed]
  5. D. N. Vitek, D. E. Adams, A. Johnson, P. S. Tsai, S. Backus, C. G. Durfee, D. Kleinfeld, and J. A. Squier, “Temporally focused femtosecond laser pulses for low numerical aperture micromachining through optically transparent materials,” Opt. Express18, 18086–18094 (2010).
    [CrossRef] [PubMed]
  6. D. N. Vitek, E. Block, Y. Bellouard, D. E. Adams, S. Backus, D. Kleinfeld, C. G. Durfee, and J. A. Squier, “Spatio-temporally focused femtosecond laser pulses for nonreciprocal writing in optically transparent materials,” Opt. Express18, 24673–24678 (2010).
    [CrossRef] [PubMed]
  7. F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett.35, 1106–1108 (2010).
    [CrossRef] [PubMed]
  8. M. Coughlan, M. Plewicki, and R. Levis, “Parametric spatio-temporal control of focusing laser pulses,” Opt. Express17, 15808–15820 (2009).
    [CrossRef] [PubMed]
  9. P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
    [CrossRef]
  10. W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett.93, 171109 (2008).
    [CrossRef]
  11. M. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express14, 12243–12254 (2006).
    [CrossRef] [PubMed]
  12. D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
    [CrossRef]
  13. O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron.25, 2464–2468 (1989).
    [CrossRef]
  14. J. A. Fueloep, L. Palfalvi, M. C. Hoffmann, and J. Hebling, “Towards generation of mJ-level ultrashort THz pulses by optical rectification,” Opt. Express19, 15090–15097 (2011).
    [CrossRef]
  15. A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron.26, 1148–1157 (1990).
    [CrossRef]
  16. V. Chauhan, J. Cohen, and R. Trebino, “Simple dispersion law for arbitrary sequences of dispersive optics,” Appl. Opt.49, 6840–6844 (2010).
    [CrossRef] [PubMed]
  17. F. Druon, M. Hanna, G. Lucas-Leclin, Y. Zaouter, D. Papadopoulos, and P. Georges, “Simple and general method to calculate the dispersion properties of complex and aberrated stretchers-compressors,” J. Opt. Soc. Am. B25, 754–762 (2008).
    [CrossRef]
  18. C. G. Durfee, J. Squier, and S. Kane, “A modular approach to the analytic calculation of spectral phase for grisms and other refractive/diffractive structures,” Opt Express16, 18,004–18,016 (2008).
    [CrossRef]
  19. D. Oron and Y. Silberberg, “Harmonic generation with temporally focused ultrashort pulses,” J. Opt. Soc. Am. B22, 2660–2663 (2005).
    [CrossRef]
  20. J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, 2004).
  21. D. Oron and Y. Silberberg, “Spatiotemporal coherent control using shaped, temporally focused pulses,” Opt. Express13, 9903–9908 (2005).
    [CrossRef] [PubMed]
  22. M. Coughlan, M. Plewicki, and R. Levis, “Spatio-temporal and-spectral coupling of shaped laser pulses in a focusing geometry,” Opt. Express18, 23973–23986 (2010).
    [CrossRef] [PubMed]
  23. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon.4, 103–106 (2010).
    [CrossRef]
  24. A. E. Siegman, Lasers, 1st ed. (University Science Books, 1986).
  25. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008).
  26. F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13, 083014 (2011).
    [CrossRef]
  27. M. Durst, A. Straub, and C. Xu, “Enhanced axial confinement of sum-frequency generation in a temporal focusing setup,” Opt. Lett.34, 1786–1788 (2009).
    [CrossRef] [PubMed]

2011

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13, 083014 (2011).
[CrossRef]

J. A. Fueloep, L. Palfalvi, M. C. Hoffmann, and J. Hebling, “Towards generation of mJ-level ultrashort THz pulses by optical rectification,” Opt. Express19, 15090–15097 (2011).
[CrossRef]

2010

F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett.35, 1106–1108 (2010).
[CrossRef] [PubMed]

D. N. Vitek, D. E. Adams, A. Johnson, P. S. Tsai, S. Backus, C. G. Durfee, D. Kleinfeld, and J. A. Squier, “Temporally focused femtosecond laser pulses for low numerical aperture micromachining through optically transparent materials,” Opt. Express18, 18086–18094 (2010).
[CrossRef] [PubMed]

M. Coughlan, M. Plewicki, and R. Levis, “Spatio-temporal and-spectral coupling of shaped laser pulses in a focusing geometry,” Opt. Express18, 23973–23986 (2010).
[CrossRef] [PubMed]

D. N. Vitek, E. Block, Y. Bellouard, D. E. Adams, S. Backus, D. Kleinfeld, C. G. Durfee, and J. A. Squier, “Spatio-temporally focused femtosecond laser pulses for nonreciprocal writing in optically transparent materials,” Opt. Express18, 24673–24678 (2010).
[CrossRef] [PubMed]

V. Chauhan, J. Cohen, and R. Trebino, “Simple dispersion law for arbitrary sequences of dispersive optics,” Appl. Opt.49, 6840–6844 (2010).
[CrossRef] [PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon.4, 103–106 (2010).
[CrossRef]

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

2009

2008

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett.93, 171109 (2008).
[CrossRef]

M. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun.281, 1796–1805 (2008).
[CrossRef] [PubMed]

C. G. Durfee, J. Squier, and S. Kane, “A modular approach to the analytic calculation of spectral phase for grisms and other refractive/diffractive structures,” Opt Express16, 18,004–18,016 (2008).
[CrossRef]

F. Druon, M. Hanna, G. Lucas-Leclin, Y. Zaouter, D. Papadopoulos, and P. Georges, “Simple and general method to calculate the dispersion properties of complex and aberrated stretchers-compressors,” J. Opt. Soc. Am. B25, 754–762 (2008).
[CrossRef]

2007

P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
[CrossRef]

2006

2005

2004

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, “Angular dispersion and temporal change of femtosecond pulses from misaligned pulse compressors,” IEEE J. Sel. Top. Quantum Electron.10, 213–220 (2004).
[CrossRef]

1990

A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron.26, 1148–1157 (1990).
[CrossRef]

1989

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron.25, 2464–2468 (1989).
[CrossRef]

Adams, D. E.

Arai, A.

P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
[CrossRef]

Aurand, B.

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Backus, S.

Bagnoud, V.

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Bellouard, Y.

Block, E.

Bovatsek, J.

P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008).

Bricchi, E.

P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
[CrossRef]

Chauhan, V.

Cheng, Y.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13, 083014 (2011).
[CrossRef]

F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett.35, 1106–1108 (2010).
[CrossRef] [PubMed]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon.4, 103–106 (2010).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon.4, 103–106 (2010).
[CrossRef]

Cohen, J.

Coughlan, M.

Csatari, M.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, “Angular dispersion and temporal change of femtosecond pulses from misaligned pulse compressors,” IEEE J. Sel. Top. Quantum Electron.10, 213–220 (2004).
[CrossRef]

Druon, F.

Durfee, C. G.

Durst, M.

Ecker, B.

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Fueloep, J. A.

Georges, P.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, 2004).

Guilbaud, O.

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Habib, J.

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Hanna, M.

He, F.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13, 083014 (2011).
[CrossRef]

F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett.35, 1106–1108 (2010).
[CrossRef] [PubMed]

Hebling, J.

Heiner, Z.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, “Angular dispersion and temporal change of femtosecond pulses from misaligned pulse compressors,” IEEE J. Sel. Top. Quantum Electron.10, 213–220 (2004).
[CrossRef]

Hirao, K.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett.93, 171109 (2008).
[CrossRef]

P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
[CrossRef]

Hochhaus, D.

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Hoffmann, M. C.

Johnson, A.

Kane, S.

C. G. Durfee, J. Squier, and S. Kane, “A modular approach to the analytic calculation of spectral phase for grisms and other refractive/diffractive structures,” Opt Express16, 18,004–18,016 (2008).
[CrossRef]

Kazamias, S.

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Kazansky, P. G.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett.93, 171109 (2008).
[CrossRef]

P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
[CrossRef]

Klebniczki, J.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, “Angular dispersion and temporal change of femtosecond pulses from misaligned pulse compressors,” IEEE J. Sel. Top. Quantum Electron.10, 213–220 (2004).
[CrossRef]

Kleinfeld, D.

Kostenbauder, A. G.

A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron.26, 1148–1157 (1990).
[CrossRef]

Kovacs, A. P.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, “Angular dispersion and temporal change of femtosecond pulses from misaligned pulse compressors,” IEEE J. Sel. Top. Quantum Electron.10, 213–220 (2004).
[CrossRef]

Kurdi, G.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, “Angular dispersion and temporal change of femtosecond pulses from misaligned pulse compressors,” IEEE J. Sel. Top. Quantum Electron.10, 213–220 (2004).
[CrossRef]

Levis, R.

Lin, J.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13, 083014 (2011).
[CrossRef]

Lucas-Leclin, G.

Martinez, O. E.

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron.25, 2464–2468 (1989).
[CrossRef]

Midorikawa, K.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13, 083014 (2011).
[CrossRef]

F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett.35, 1106–1108 (2010).
[CrossRef] [PubMed]

Miura, K.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett.93, 171109 (2008).
[CrossRef]

P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
[CrossRef]

Ni, J.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13, 083014 (2011).
[CrossRef]

F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett.35, 1106–1108 (2010).
[CrossRef] [PubMed]

Oron, D.

Osvay, K.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, “Angular dispersion and temporal change of femtosecond pulses from misaligned pulse compressors,” IEEE J. Sel. Top. Quantum Electron.10, 213–220 (2004).
[CrossRef]

Palfalvi, L.

Papadopoulos, D.

Plewicki, M.

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon.4, 103–106 (2010).
[CrossRef]

Ros, D.

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Sakakura, M.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett.93, 171109 (2008).
[CrossRef]

Shimotsuma, Y.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett.93, 171109 (2008).
[CrossRef]

P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers, 1st ed. (University Science Books, 1986).

Silberberg, Y.

Squier, J.

C. G. Durfee, J. Squier, and S. Kane, “A modular approach to the analytic calculation of spectral phase for grisms and other refractive/diffractive structures,” Opt Express16, 18,004–18,016 (2008).
[CrossRef]

Squier, J. A.

Straub, A.

Sugioka, K.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13, 083014 (2011).
[CrossRef]

F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett.35, 1106–1108 (2010).
[CrossRef] [PubMed]

Tal, E.

D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt Express13, 1468–1476 (2005).
[CrossRef] [PubMed]

Trebino, R.

Tsai, P. S.

van Howe, J.

Vitek, D. N.

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon.4, 103–106 (2010).
[CrossRef]

Xiong, H.

Xu, C.

Xu, H.

Xu, Z.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13, 083014 (2011).
[CrossRef]

F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett.35, 1106–1108 (2010).
[CrossRef] [PubMed]

Yang, W.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett.93, 171109 (2008).
[CrossRef]

P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
[CrossRef]

Zaouter, Y.

Zhu, G.

Zielbauer, B.

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Zimmer, D.

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Zipfel, W.

Appl. Opt.

Appl. Phys. Lett.

P. G. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90, 151120 (2007).
[CrossRef]

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett.93, 171109 (2008).
[CrossRef]

IEEE J. Quantum Electron.

O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron.25, 2464–2468 (1989).
[CrossRef]

A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron.26, 1148–1157 (1990).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. Osvay, A. P. Kovacs, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatari, “Angular dispersion and temporal change of femtosecond pulses from misaligned pulse compressors,” IEEE J. Sel. Top. Quantum Electron.10, 213–220 (2004).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photon.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon.4, 103–106 (2010).
[CrossRef]

New J. Phys.

F. He, Y. Cheng, J. Lin, J. Ni, Z. Xu, K. Sugioka, and K. Midorikawa, “Independent control of aspect ratios in the axial and lateral cross sections of a focal spot for three-dimensional femtosecond laser micromachining,” New J. Phys.13, 083014 (2011).
[CrossRef]

Opt Express

D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt Express13, 1468–1476 (2005).
[CrossRef] [PubMed]

C. G. Durfee, J. Squier, and S. Kane, “A modular approach to the analytic calculation of spectral phase for grisms and other refractive/diffractive structures,” Opt Express16, 18,004–18,016 (2008).
[CrossRef]

Opt. Commun.

M. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing in nonlinear microscopy,” Opt. Commun.281, 1796–1805 (2008).
[CrossRef] [PubMed]

Opt. Express

G. Zhu, J. van Howe, M. Durst, W. Zipfel, and C. Xu, “Simultaneous spatial and temporal focusing of femtosecond pulses,” Opt. Express13, 2153–2159 (2005).
[CrossRef] [PubMed]

D. Oron and Y. Silberberg, “Spatiotemporal coherent control using shaped, temporally focused pulses,” Opt. Express13, 9903–9908 (2005).
[CrossRef] [PubMed]

M. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express14, 12243–12254 (2006).
[CrossRef] [PubMed]

J. A. Fueloep, L. Palfalvi, M. C. Hoffmann, and J. Hebling, “Towards generation of mJ-level ultrashort THz pulses by optical rectification,” Opt. Express19, 15090–15097 (2011).
[CrossRef]

M. Coughlan, M. Plewicki, and R. Levis, “Parametric spatio-temporal control of focusing laser pulses,” Opt. Express17, 15808–15820 (2009).
[CrossRef] [PubMed]

D. N. Vitek, D. E. Adams, A. Johnson, P. S. Tsai, S. Backus, C. G. Durfee, D. Kleinfeld, and J. A. Squier, “Temporally focused femtosecond laser pulses for low numerical aperture micromachining through optically transparent materials,” Opt. Express18, 18086–18094 (2010).
[CrossRef] [PubMed]

M. Coughlan, M. Plewicki, and R. Levis, “Spatio-temporal and-spectral coupling of shaped laser pulses in a focusing geometry,” Opt. Express18, 23973–23986 (2010).
[CrossRef] [PubMed]

D. N. Vitek, E. Block, Y. Bellouard, D. E. Adams, S. Backus, D. Kleinfeld, C. G. Durfee, and J. A. Squier, “Spatio-temporally focused femtosecond laser pulses for nonreciprocal writing in optically transparent materials,” Opt. Express18, 24673–24678 (2010).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

D. Zimmer, D. Ros, O. Guilbaud, J. Habib, S. Kazamias, B. Zielbauer, V. Bagnoud, B. Ecker, D. Hochhaus, and B. Aurand, “Short-wavelength soft-x-ray laser pumped in double-pulse single-beam non-normal incidence,” Phys. Rev. A82, 013803 (2010).
[CrossRef]

Other

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, 2004).

A. E. Siegman, Lasers, 1st ed. (University Science Books, 1986).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Configurations for space-time focusing. a) Single-pass, parallel grating compressor. b) Double-pass compressor, but with retroreflection mirror tilted in the horizontal plane. c) Collimation of spectral components from single grating, refocus with second lens. d) Imaging of single grating to target.

Fig. 2
Fig. 2

Dependence of geometric second-order chirp (ϕ2) on axial position.

Fig. 3
Fig. 3

Evolution of beam wavefronts from a point relatively close to the lens (left side) toward the focal plane at z = 0. Each colored wavefront corresponds to a particular frequency beamlet.

Fig. 4
Fig. 4

Contributions to axial intensity localization. The outer dashed line corresponds to the axial intensity for the non-spatially-chirped beamlet. The next line in (blue) accounts only for the change in beam fluence that arises from spreading the beam at the lens in the x-direction. When the on-axis spectral width is calculated, the minimum possible pulse duration is increased away from the focus, resulting in the third curve (black, solid). The full Fresnel calculation shows further localization resulting from the geometric chirp (red).

Fig. 5
Fig. 5

Variation of the axial intensity with input spectral chirp (ϕ2) for a beam focused with a beam aspect ratio of βBA = 4 and a transform-limited pulse duration of 40 fs. In both graphs, the second-order phases are ϕ2 = 0 (red), ϕ2 = 2000 fs2 (blue), ϕ2 = 4000 fs2 (green). (a) No input third-order phase. (b) Positive input ϕ3 = 2 × 105 fs3

Fig. 6
Fig. 6

Depth of focus (DOF) and B-integral through focus as a function of the beam aspect ratio, for linear (a) and log (b). Dashed curve in (a) indicates the effective decrease in the DOF for a conventional Gaussian beam focus for a beam that uses the full aperture of the lens.

Fig. 7
Fig. 7

Calculation of the spatial chirp dependence of aspect ratio of the focal volume as the ratio of the longitudinal intensity FWHM to the transverse intensity FWHM for two different focal spot sizes. Dashed line indicates the point where the focal volume is approximately spherical.

Equations (33)

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

E ( x , y , z = 0 , ω ) = E 0 exp [ ( ω ω 0 ) 2 Δ ω 2 + i ϕ in ( ω ) ] exp [ ( x α ( ω ω 0 ) ) 2 + y 2 w in 2 ]
E ( x , z , ω ) = FT x 1 { e i k 0 z ( 1 1 2 ( 2 π k 0 f x ) 2 ) FT x { E ( x , z = 0 , ω ) e i k 0 x 2 2 f } } .
β = α Δ ω w in .
β B A = 1 + β 2 .
I ( x , z = 0 , ω ) exp { 2 [ β B A 2 ( ω ω 0 Δ ω x w in β β B A 2 ) 2 ] } .
ϕ ( x , ω ) = ω c sin [ θ , ( ω ) ] x ω c α ( ω ω 0 ) f x .
ϕ 1 ( x ) = ϕ ( x , ω ) | ω 0 = ω 0 α x c f .
ϕ 1 ( x ) = x w 0 β τ 0 .
ϕ 2 ( x ) = ϕ ( x , ω ) | ω 0 = 2 α x f c , ϕ 2 ( w 0 ) Δ ω = 4 β ω 0 .
E ˜ ( f x f x 0 , z ) = E ˜ ( f x f x 0 , 0 ) exp [ i k 0 ( 1 ( 2 π f x k 0 ) 2 ) 1 / 2 z ] .
E ˜ ( f x f x 0 , z ) = E ˜ ( f x , 0 ) exp [ i k z z i 2 π 2 z k z ( f x ) 2 i 2 π z tan θ x f x ] .
E ( x , z ) = exp [ i ( k x x + k z z ) ] × FT f x 1 { E ˜ ( f x , 0 ) exp [ i 2 π 2 z k z ( f x ) 2 ] exp [ i 2 π z tan θ x f x ] } .
k 0 k z = ω c cos θ x and x x z tan θ x ,
E ( x , z ) = exp [ i ( k x x + k z z ) ] FT 1 { E ˜ [ f x ] e i 2 π 2 z k 0 ( f x ) 2 e i 2 π z sin θ x f x } ,
x x z sin θ x .
A ( x , y , z , ω ) = E 0 ( ω ) w 0 w ( z ) exp [ x 2 + y 2 w 2 ( z ) ] and ϕ ( x , y , z , ω ) = k 0 z η ( z ) + k 0 x 2 + y 2 2 R ( z ) ,
w ( z ) = w 0 1 + z 2 / z R 2 , R ( z ) = z ( 1 + z R 2 / z 2 ) and η ( z ) = arctan ( z / z R ) .
A ( x , y , z , ω ) = E 0 ( ω ) w 0 w ( z ) exp [ ( x z sin θ x ) 2 + y 2 w 2 ( z ) ] .
ϕ ( x , y , z , ω ) = k 0 x sin θ x + k 0 z ( 1 1 2 sin 2 θ x ) η ( z ) + k 0 ( x z sin θ x ) 2 + y 2 2 R ( z ) .
ϕ 1 ( x , z ) = z c + x α ω 0 c f ( 1 z R ( z ) ) + x 2 2 c R ( z ) .
ϕ 1 ( x , z ) = z c + x w 0 β τ 0 ( 1 1 + z 2 / z R 2 ) + x 2 2 c R ( z ) .
ϕ 2 ( x , z ) = ( x w 0 τ 0 β ω 0 z z R τ 0 2 β 2 4 ) ( 1 1 + z 2 / z R 2 ) .
A ( x , y , z , ω ) = A 0 w 0 w ( z ) exp [ ( x 2 w x ( z ) 2 + y 2 w ( z ) 2 ) ] exp [ ( ω ω L ( x , z ) ) 2 Δ ω L 2 ( z ) ] .
w x ( ζ ) 2 = w 0 2 ( 1 + β B A 2 ζ 2 ) ,
ω L ( x , ζ ) = ω 0 + β Δ ω x w 0 ζ 1 + β B A 2 ζ 2 .
Δ ω L 2 ( ζ ) = Δ ω 2 ζ 2 1 + β B A 2 ζ 2 .
τ b w ( ζ ) = 2 Δ ω L ( ζ ) = τ 0 1 + β B A 2 ζ 2 1 + ζ 2 .
E ( x , y , z , t ) = A 0 w 0 w ( z ) exp [ ( x 2 w x ( z ) 2 + y 2 w ( z ) 2 ) + i ϕ 0 ] × FT 1 { exp [ ( ω ω L ( x , z ) ) 2 Δ ω L 2 ( z ) + i ϕ 2 ( ω ω 0 ) 2 ] exp [ i ϕ 1 ( ω ω 0 ) ] } .
τ L ( ζ ) = τ b w ( ζ ) 1 + β 4 ( ζ 1 + β B A 2 ζ 2 ) 2 = τ 0 1 + β B A 4 ζ 2 1 + β B A 2 ζ 2 .
τ L ( ζ , ϕ 2 in ) = τ b w ( ζ ) 1 + ( Δ ω 2 1 + ζ 2 1 + β B A 2 ζ 2 ) 2 ( ϕ 2 in β 2 Δ ω 2 ζ 1 + ζ 2 ) 2 .
I ( ζ ) = I 0 1 ( 1 + ζ 2 ) ( 1 + β B A 4 ζ 2 ) ,
ζ D O F = 2 1 β B A 4 + 1 + 14 β B A 4 + β B A 8 2 β B A 4 .
ρ G = π w 0 ln ( 2 ) / 2 λ ,

Metrics