Abstract

The analytical solution for a monochromatic focused laser beam was recently published [Opt. Lett. 31, 1447 (2006) ]. The effect of introducing bandwidth by including a finite-length temporal pulse envelope is included exactly. This is done formally first in the frequency domain for an arbitrary pulse shape, and the specific case of a cosine-squared envelope is then solved analytically for all pulse lengths, thereby decreasing the computation time by 2 orders of magnitude. The inclusion of longer wavelengths reduces the fraction of laser energy in the focus from 86.5% to 83.5% for a 5fs Ti:sapphire laser and 72.7% in a single-cycle pulse.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Nisoli, S. D. Silvestri, O. Svelto, R. Szipcs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997).
    [CrossRef] [PubMed]
  2. N. L. Wagner, E. A. Gibson, T. Popmintchev, and I. P. Christov, Phys. Rev. Lett. 93, 173902 (2004).
    [CrossRef] [PubMed]
  3. A. A. Balakin, G. M. Fraiman, N. J. Fisch, and S. Suckewer, Phys. Rev. E 72, 036401 (2005).
    [CrossRef]
  4. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, Opt. Lett. 30, 2657 (2005).
    [CrossRef] [PubMed]
  5. A. J. Waddie, M. J. Thomson, and M. R. Taghizadeh, Opt. Lett. 30, 991 (2005).
    [CrossRef] [PubMed]
  6. M. Spanner, M. Y. Ivanov, V. Kalosha, J. Hermann, D. A. Wiersma, and M. Pshenichnikov, Opt. Lett. 28, 749 (2003).
    [CrossRef] [PubMed]
  7. E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, Opt. Lett. 24, 493 (1999).
    [CrossRef]
  8. B. Rau, T. Tajima, and H. Hojo, Phys. Rev. Lett. 78, 3310 (1997).
    [CrossRef]
  9. J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
    [CrossRef] [PubMed]
  10. N. M. Naumova, J. A. Nees, I. V. Sokolov, B. Houl, and G. A. Mourou, Phys. Rev. Lett. 92, 063902 (2004).
    [CrossRef] [PubMed]
  11. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
    [CrossRef] [PubMed]
  12. S. Sepke and D. Umstadter, Opt. Lett. 31, 1447 (2006).
    [CrossRef] [PubMed]
  13. S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, Phys. Rev. Lett. 95, 035004 (2005).
    [CrossRef] [PubMed]
  14. B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998).
    [CrossRef]
  15. A. Maltsev and T. Ditmire, Phys. Rev. Lett. 90, 053002 (2003).
    [CrossRef] [PubMed]
  16. H. Hora, Laser Plasma Physics (SPIE, 2000), and references therein.
  17. H. Hora, M. Hoelss, W. Scheid, J. X. Wang, Y. K. Ho, F. Osman, and R. Castillo, Laser Part. Beams 18, 135 (2000).
    [CrossRef]
  18. S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
    [CrossRef]
  19. J. A. Stratton and L. J. Chu, Phys. Rev. 56, 99 (1939).
    [CrossRef]
  20. P. Varga and P. Török, J. Opt. Soc. Am. A 17, 2081 (2000).
    [CrossRef]
  21. A. Ludu and R. F. O'Connell, Phys. Scr. 65, 369 (2002).
    [CrossRef]

2006 (1)

2005 (5)

S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, Phys. Rev. Lett. 95, 035004 (2005).
[CrossRef] [PubMed]

A. A. Balakin, G. M. Fraiman, N. J. Fisch, and S. Suckewer, Phys. Rev. E 72, 036401 (2005).
[CrossRef]

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, Opt. Lett. 30, 2657 (2005).
[CrossRef] [PubMed]

A. J. Waddie, M. J. Thomson, and M. R. Taghizadeh, Opt. Lett. 30, 991 (2005).
[CrossRef] [PubMed]

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

2004 (3)

N. M. Naumova, J. A. Nees, I. V. Sokolov, B. Houl, and G. A. Mourou, Phys. Rev. Lett. 92, 063902 (2004).
[CrossRef] [PubMed]

N. L. Wagner, E. A. Gibson, T. Popmintchev, and I. P. Christov, Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

2003 (2)

2002 (1)

A. Ludu and R. F. O'Connell, Phys. Scr. 65, 369 (2002).
[CrossRef]

2001 (1)

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

2000 (2)

P. Varga and P. Török, J. Opt. Soc. Am. A 17, 2081 (2000).
[CrossRef]

H. Hora, M. Hoelss, W. Scheid, J. X. Wang, Y. K. Ho, F. Osman, and R. Castillo, Laser Part. Beams 18, 135 (2000).
[CrossRef]

1999 (1)

1998 (1)

B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998).
[CrossRef]

1997 (2)

1939 (1)

J. A. Stratton and L. J. Chu, Phys. Rev. 56, 99 (1939).
[CrossRef]

Backus, S.

Balakin, A. A.

A. A. Balakin, G. M. Fraiman, N. J. Fisch, and S. Suckewer, Phys. Rev. E 72, 036401 (2005).
[CrossRef]

Banerjee, S.

S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, Phys. Rev. Lett. 95, 035004 (2005).
[CrossRef] [PubMed]

Biegert, J.

Bonnaud, G.

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

Castillo, R.

H. Hora, M. Hoelss, W. Scheid, J. X. Wang, Y. K. Ho, F. Osman, and R. Castillo, Laser Part. Beams 18, 135 (2000).
[CrossRef]

Christov, I. P.

N. L. Wagner, E. A. Gibson, T. Popmintchev, and I. P. Christov, Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

Chu, L. J.

J. A. Stratton and L. J. Chu, Phys. Rev. 56, 99 (1939).
[CrossRef]

Couairon, A.

Ditmire, T.

A. Maltsev and T. Ditmire, Phys. Rev. Lett. 90, 053002 (2003).
[CrossRef] [PubMed]

Ewald, F.

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

Faure, J.

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

Ferencz, K.

Fisch, N. J.

A. A. Balakin, G. M. Fraiman, N. J. Fisch, and S. Suckewer, Phys. Rev. E 72, 036401 (2005).
[CrossRef]

Fraiman, G. M.

A. A. Balakin, G. M. Fraiman, N. J. Fisch, and S. Suckewer, Phys. Rev. E 72, 036401 (2005).
[CrossRef]

Franco, M.

Gibson, E. A.

N. L. Wagner, E. A. Gibson, T. Popmintchev, and I. P. Christov, Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

Glinec, Y.

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

Grasbon, F.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Hermann, J.

Ho, Y. K.

H. Hora, M. Hoelss, W. Scheid, J. X. Wang, Y. K. Ho, F. Osman, and R. Castillo, Laser Part. Beams 18, 135 (2000).
[CrossRef]

Hoelss, M.

H. Hora, M. Hoelss, W. Scheid, J. X. Wang, Y. K. Ho, F. Osman, and R. Castillo, Laser Part. Beams 18, 135 (2000).
[CrossRef]

Hojo, H.

B. Rau, T. Tajima, and H. Hojo, Phys. Rev. Lett. 78, 3310 (1997).
[CrossRef]

Hora, H.

H. Hora, M. Hoelss, W. Scheid, J. X. Wang, Y. K. Ho, F. Osman, and R. Castillo, Laser Part. Beams 18, 135 (2000).
[CrossRef]

H. Hora, Laser Plasma Physics (SPIE, 2000), and references therein.

Hosokai, T.

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

Houl, B.

N. M. Naumova, J. A. Nees, I. V. Sokolov, B. Houl, and G. A. Mourou, Phys. Rev. Lett. 92, 063902 (2004).
[CrossRef] [PubMed]

Ivanov, M. Y.

Kalosha, V.

Kapteyn, H.

Keller, U.

Kiselev, S.

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

Krausz, F.

Loubere, R.

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

Ludu, A.

A. Ludu and R. F. O'Connell, Phys. Scr. 65, 369 (2002).
[CrossRef]

Maginnis, K.

Maksimchuk, A.

S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, Phys. Rev. Lett. 95, 035004 (2005).
[CrossRef] [PubMed]

Malka, V.

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

Maltsev, A.

A. Maltsev and T. Ditmire, Phys. Rev. Lett. 90, 053002 (2003).
[CrossRef] [PubMed]

Michel, P.

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

Mora, P.

B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998).
[CrossRef]

Mourou, G.

Mourou, G. A.

N. M. Naumova, J. A. Nees, I. V. Sokolov, B. Houl, and G. A. Mourou, Phys. Rev. Lett. 92, 063902 (2004).
[CrossRef] [PubMed]

Murnane, M.

Mysyrowicz, A.

Naumova, N. M.

N. M. Naumova, J. A. Nees, I. V. Sokolov, B. Houl, and G. A. Mourou, Phys. Rev. Lett. 92, 063902 (2004).
[CrossRef] [PubMed]

Nees, J. A.

N. M. Naumova, J. A. Nees, I. V. Sokolov, B. Houl, and G. A. Mourou, Phys. Rev. Lett. 92, 063902 (2004).
[CrossRef] [PubMed]

Nisoli, M.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

M. Nisoli, S. D. Silvestri, O. Svelto, R. Szipcs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997).
[CrossRef] [PubMed]

O'Connell, R. F.

A. Ludu and R. F. O'Connell, Phys. Scr. 65, 369 (2002).
[CrossRef]

Osman, F.

H. Hora, M. Hoelss, W. Scheid, J. X. Wang, Y. K. Ho, F. Osman, and R. Castillo, Laser Part. Beams 18, 135 (2000).
[CrossRef]

Ovadia, J.

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

Paulus, G. G.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Popmintchev, T.

N. L. Wagner, E. A. Gibson, T. Popmintchev, and I. P. Christov, Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

Priori, E.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Pshenichnikov, M.

Pukhov, A.

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

Quesnel, B.

B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998).
[CrossRef]

Rau, B.

B. Rau, T. Tajima, and H. Hojo, Phys. Rev. Lett. 78, 3310 (1997).
[CrossRef]

Riazuelo, G.

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

Rousseau, J.-P.

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

Russek, U.

Santos, J. J.

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

Sartania, S.

Scheid, W.

H. Hora, M. Hoelss, W. Scheid, J. X. Wang, Y. K. Ho, F. Osman, and R. Castillo, Laser Part. Beams 18, 135 (2000).
[CrossRef]

Sepke, S.

S. Sepke and D. Umstadter, Opt. Lett. 31, 1447 (2006).
[CrossRef] [PubMed]

S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, Phys. Rev. Lett. 95, 035004 (2005).
[CrossRef] [PubMed]

Shah, R.

S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, Phys. Rev. Lett. 95, 035004 (2005).
[CrossRef] [PubMed]

Silvestri, S. D.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

M. Nisoli, S. D. Silvestri, O. Svelto, R. Szipcs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997).
[CrossRef] [PubMed]

Sokolov, I. V.

N. M. Naumova, J. A. Nees, I. V. Sokolov, B. Houl, and G. A. Mourou, Phys. Rev. Lett. 92, 063902 (2004).
[CrossRef] [PubMed]

Spanner, M.

Spielmann, C.

Stagira, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Stratton, J. A.

J. A. Stratton and L. J. Chu, Phys. Rev. 56, 99 (1939).
[CrossRef]

Suckewer, S.

A. A. Balakin, G. M. Fraiman, N. J. Fisch, and S. Suckewer, Phys. Rev. E 72, 036401 (2005).
[CrossRef]

Svelto, O.

Szipcs, R.

Taghizadeh, M. R.

Tajima, T.

B. Rau, T. Tajima, and H. Hojo, Phys. Rev. Lett. 78, 3310 (1997).
[CrossRef]

Thomson, M. J.

Tikhonchuk, V. T.

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

Török, P.

Umstadter, D.

S. Sepke and D. Umstadter, Opt. Lett. 31, 1447 (2006).
[CrossRef] [PubMed]

S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, Phys. Rev. Lett. 95, 035004 (2005).
[CrossRef] [PubMed]

Valenzuela, A.

S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, Phys. Rev. Lett. 95, 035004 (2005).
[CrossRef] [PubMed]

Varga, P.

Vdovin, G.

Villoresi, P.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Waddie, A. J.

Wagner, N. L.

N. L. Wagner, E. A. Gibson, T. Popmintchev, and I. P. Christov, Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

Walraet, F.

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

Walther, H.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Wang, J. X.

H. Hora, M. Hoelss, W. Scheid, J. X. Wang, Y. K. Ho, F. Osman, and R. Castillo, Laser Part. Beams 18, 135 (2000).
[CrossRef]

Weber, S.

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

Wiersma, D. A.

Zeek, E.

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

Laser Part. Beams (2)

H. Hora, M. Hoelss, W. Scheid, J. X. Wang, Y. K. Ho, F. Osman, and R. Castillo, Laser Part. Beams 18, 135 (2000).
[CrossRef]

S. Weber, G. Riazuelo, P. Michel, R. Loubere, F. Walraet, V. T. Tikhonchuk, V. Malka, J. Ovadia, and G. Bonnaud, Laser Part. Beams 22, 189 (2004).
[CrossRef]

Nature (1)

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Opt. Lett. (6)

Phys. Rev. (1)

J. A. Stratton and L. J. Chu, Phys. Rev. 56, 99 (1939).
[CrossRef]

Phys. Rev. E (2)

B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998).
[CrossRef]

A. A. Balakin, G. M. Fraiman, N. J. Fisch, and S. Suckewer, Phys. Rev. E 72, 036401 (2005).
[CrossRef]

Phys. Rev. Lett. (6)

A. Maltsev and T. Ditmire, Phys. Rev. Lett. 90, 053002 (2003).
[CrossRef] [PubMed]

B. Rau, T. Tajima, and H. Hojo, Phys. Rev. Lett. 78, 3310 (1997).
[CrossRef]

J. Faure, Y. Glinec, J. J. Santos, F. Ewald, J.-P. Rousseau, S. Kiselev, A. Pukhov, T. Hosokai, and V. Malka, Phys. Rev. Lett. 95, 205003 (2005).
[CrossRef] [PubMed]

N. M. Naumova, J. A. Nees, I. V. Sokolov, B. Houl, and G. A. Mourou, Phys. Rev. Lett. 92, 063902 (2004).
[CrossRef] [PubMed]

N. L. Wagner, E. A. Gibson, T. Popmintchev, and I. P. Christov, Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

S. Banerjee, S. Sepke, R. Shah, A. Valenzuela, A. Maksimchuk, and D. Umstadter, Phys. Rev. Lett. 95, 035004 (2005).
[CrossRef] [PubMed]

Phys. Scr. (1)

A. Ludu and R. F. O'Connell, Phys. Scr. 65, 369 (2002).
[CrossRef]

Other (1)

H. Hora, Laser Plasma Physics (SPIE, 2000), and references therein.

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 (1)

Fig. 1
Fig. 1

E x evaluated for a single-cycle pulse ( Δ τ = λ c ) at the peak of the pulse along x = y in the focal plane by using the monochromatic model of Eqs. (2, 3, 4, 5) (red dashed curve) and the full polychromatic model (blue solid curve).

Equations (18)

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

E x = E ̃ 0 ϵ 2 ( I 1 + x 2 y 2 r 3 I 2 + y 2 r 2 I 3 ) ,
E y = E ̃ 0 ϵ 2 x y r 2 ( 2 r I 2 I 3 ) , E z = E ̃ 0 ϵ 2 x r I 4 ,
I 1 = 2 e i ω 0 t s = 0 ( a s 1 + a s 2 ) i s C s 1 2 ( z ρ ) j s ( ω ρ ¯ ) ,
I 2 = 2 e i ω 0 t c 2 ω 2 r s = 0 a s 0 i s C s 1 2 ( z ρ ) j s ( ω ρ ¯ ) ,
I 3 = 2 e i ω 0 t s = 0 ( a s 0 a s 2 ) i s C s 1 2 ( z ρ ) j s ( ω ρ ¯ ) ,
I 4 = 2 i e i ω 0 t c ω r s = 0 ( a s 0 + a s 1 ) i s C s 1 2 ( z ρ ) j s ( ω ρ ¯ ) ,
I 1 = s = 0 ( a s 1 + a s 2 ) C s 1 2 ( z ρ ) I s , 0 ,
I 2 = c r ρ s = 0 a s 0 { ( c z ρ 2 ) C s 1 3 2 ( z ρ ) I s , 2 i C s 1 2 ( z ρ ) [ s I s 1 , 1 + ( s + 1 ) I s + 1 , 1 2 s + 1 ] } ,
I 3 = s = 0 ( a s 0 a s 2 ) C s 1 2 ( z ρ ) I s , 0 ,
I 4 = r ρ s = 0 ( a s 0 + a s 1 ) { ( i c z ρ 2 ) C s 1 3 2 ( z ρ ) I s , 1 + C s 1 2 ( z ρ ) [ s I s 1 , 0 + ( s + 1 ) I s + 1 , 0 2 s + 1 ] } ,
I s , ν = 2 i s f ̃ ( ω ω 0 ) exp [ i ( ω ω 0 ) t ] ω ν j s ( ω ρ ¯ ) d ω .
F { j s ( ω ρ ¯ ) } = π i s rect ( T ρ ¯ ) k = 0 2 k s C k ( s ) ( 1 ) k ρ ¯ 2 k s 1 T s 2 k ,
I s , ν = i s π f ( t T ) G ν ( T ) e i ω 0 T d T ,
I s , 0 = k = 0 2 k s C k ( s ) ( 1 ) s + k ρ ¯ 2 k s 1 F s 2 k ( ρ ¯ , ρ ¯ ) ,
I s , 1 = i k = 0 2 k s C k ( s ) ( 1 ) s + k 2 s k + 1 ( F s 2 k + 1 ( ρ ¯ , ρ ¯ ) ρ ¯ s 2 k + 1 + ( 1 ) s 2 k { F 0 ( ρ ¯ , ρ ¯ ) + [ 1 + ( 1 ) s 2 k ] F 0 ( ρ ¯ , ) } ) ,
I s , 2 = k = 0 2 k s C k ( s ) ( 1 ) s + k ( F s 2 k + 2 ( ρ ¯ , ρ ¯ ) ρ ¯ 2 k 2 1 ( s 2 k + 1 ) ( s 2 k + 2 ) + ρ ¯ ( 1 ) s 2 k s 2 k + 2 { F 0 ( ρ ¯ , ρ ¯ ) + [ 1 ( 1 ) s 2 k ] F 0 ( ρ ¯ , ) } + ( 1 ) s 2 k s 2 k + 1 { F 1 ( ρ ¯ , ρ ¯ ) + [ 1 + ( 1 ) s 2 k ] F 1 ( ρ ¯ , ) } ) ,
F n ( α , β ) = 1 4 ( { 2 C n ( ω 0 ) + cos ( Ω 0 t ) [ C n ( Ω + ) + C n ( Ω ) ] + sin ( Ω 0 t ) [ S 0 ( Ω + ) + S n ( Ω ) ] } + i { 2 S n ( ω 0 ) + cos ( Ω 0 t ) [ S n ( Ω + ) S n ( Ω ) ] sin ( Ω 0 t ) [ C n ( Ω + ) C n ( Ω ) ] } ) α β ,
S p ( ω ) x p sin ( ω x ) d x = { ( 1 ) p 2 + 1 ( p ! ) [ cos ( ω x ) k = 0 p 2 ( 1 ) k x 2 k ( 2 k ) ! ω p 2 k + 1 + sin ( ω x ) k = 1 p 2 ( 1 ) k + 1 x 2 k 1 ( 2 k 1 ) ! ω p 2 k + 2 ] p even ( x p ω ) cos ( ω x ) + ( p ω ) C p 1 ( ω ) p odd } ,

Metrics