Abstract

In this paper, interaction of an ultrashort single-cycle pulse (USCP) with a bound electron without ionization is reported for the first time. For a more realistic mathematical description of USCPs, Hermitian polynomials and combination of Laguerre functions are used for two different single cycle excitation cases. These single cycle pulse models are used as driving functions for the classical approach to model the interaction of a bound electron with an applied electric field. A new novel time-domain technique was developed for modifying the classical Lorentz damped oscillator model in order to make it compatible with USCP excitation. This modification turned the Lorentz oscillator model equation into a Hill-like function with non-periodic time varying damping and spring coefficients. Numerical results are presented for two different excitation models and for varying spring and damping constants. Our two driving model excitations provide quite different time response of the bound electron. Different polarization response will subsequently result in relative differences in the time dependent index of refraction.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53(1–2), (2006).
  2. M. A. Porras, “Nonsinusoidal few-cycle pulsed light beams in free space,” J. Opt. Soc. Am. B 16(9), 1468 (1999).
    [CrossRef]
  3. P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
    [CrossRef]
  4. A. Zewail, “Femtochemistry: atomic-scale dynamics of the chemical bond,” J. Phys. Chem. A 104(24), 5660–5694 (2000).
    [CrossRef]
  5. H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
    [CrossRef] [PubMed]
  6. J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
    [CrossRef] [PubMed]
  7. G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
    [CrossRef]
  8. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
    [CrossRef] [PubMed]
  9. Y. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83(11), 5391 (1985).
    [CrossRef]
  10. G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in Ultrashort Pulse Generation: Pushing the Limits in Linear and Nonlinear Optics,” Science 286(5444), 1507–1512 (1999).
    [CrossRef] [PubMed]
  11. K. Akimoto, Properties and Applications of ultrashort electromagnetic mono- and sub- cycle waves. Journal ofthe Physical Society of Japan, Vol. 65, No. 7, 2020–2032, 1996.
  12. R. M. Joseph, S. C. Hagness, and A. Taflove, “Direct time integration of Maxwell’s equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses,” Opt. Lett. 16(18), 1412–1414 (1991).
    [CrossRef] [PubMed]
  13. S. L. Dvorak, D. G. Dudley. Propagation of ultrawideband electromagnetic pulses through dispersive media. IEEE Transaction of Electromagnetic Compatibility, Vol. 37. No. 2, May 1995.
  14. S. A. Kozlov and S. V. Sazanov, “Nonlinear propagation of optical pulses of a few oscillations duration in dielectric media,” Sov. Phys. JETP 84(2), 221–228 (1997).
    [CrossRef]
  15. H. Wilkelmsson, J. H. Trombert, and J. F. Eloy, “Dispersive and dissipative medium response to an ultrashort pulse: A green’s function approach,” Phys. Scr. 52(1), 102–107 (1995).
    [CrossRef]
  16. P. Kinsler and G. H. C. New, “Few-cycle pulse propagation,” Phys. Rev. A 67(2), 023813 (2003).
    [CrossRef]
  17. J. F. Eloy, and F. Moriamez, Spectral analysis of EM ultrashort pulses at coherence limit. Modelling. SPIE Intense Microwave and Particle Beams III, Vol. 1629, 1992.
  18. J. F. Eloy and H. Wilhelmsson, “Response of a bounded plasma to ultrashort pulse excitation,” Phys. Scr. 55(4), 475–477 (1997).
    [CrossRef]
  19. M. Pietrzyk, I. Kanattsikov, and U. Bandelow, “On the propagation of vector ultrashort pulses,” J. Nonlinear Math. Phys. 15(2), 162–170 (2008).
    [CrossRef]
  20. B. Macke and B. Segard, “Propagation of light pulses at a negative group velocity,” Eur. Phys. J. D 23, 125–141 (2003).
    [CrossRef]
  21. Q. Zou and B. Lu, “Propagation properties of ultrashort pulsed beams with constant waist width in free space,” Opt. Laser Technol. 39(3), 619–625 (2007).
    [CrossRef]
  22. H. Xiao and K. E. Oughstun, “Failure of the group velocity description for ultrawideband pulse propagation in a casually dispersive, absorptive dielectric,” J. Opt. Soc. Am. B 16(10), 1773 (1999).
    [CrossRef]
  23. A. L. Gutman, “Electrodynamics of short pulses for pulse durations comparable to relaxation times of a medium,” Dokl. Phys. 43(6), 343–345 (1998).
  24. D. Hovhannisyan, “Propagation of a femtosecond laser pulse of a few optical oscillations in a uniaxial crystal,” Microw. Opt. Technol. Lett. 36(4), 280–285 (2003).
    [CrossRef]
  25. A. B. Shvartsburg, Single-cycle waveforms and non-periodic waves in dispersive media (exactly solvable models). Physics – Uspekhi, Vol. 41, No. 1, 77–94, 1998.
  26. Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33(4), (1997).
  27. A. B. Shvartsburg, Time-Domain Optics of Ultrashort Waveforms. Clarendon Press, Oxford, 1996.
  28. A. B. Shvartsburg, Impulse Time-Domain Electromagnetic of Continuos Media. Birkhauser Verlag, Boston, 1999.
  29. J. E. Rothenberg, “Space-time focusing: Breakdown of the slowly varying envelope approximation in the self-focusing of femtosecond pulses,” Opt. Lett. 17(19), 1340 (1992).
    [CrossRef] [PubMed]
  30. H. Kumagai, S. H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya, “Observation of the comples propagation of a femtosecond laser pulse in a dispersive transparent bulk material,” J. Opt. Soc. Am. 20(3), (2003).
  31. M. D. Crisp, “Propagation of small-area pulses of coherent light through a resonant medium,” Phys. Rev. A 1(6), 1604–1611 (1970).
    [CrossRef]
  32. B. K. P. Scaife, Principles of Dielectrics, Oxford University Press, Oxford, 1989.
  33. A. L. Gutman, Passage of short pulse throughout oscillating circuit with dielectric in condenser. Ultra-Wideband, Short-Pulse Electromagnetics 4, Kluwer Academic / Plenum Publishers, New York, 1999.
  34. V. V. Daniel, Dielectric Relaxation. Academic Press, New York, 1967.
  35. A. B. Shvartsburg, Optics of nonstationary media, Physics – Uspekhi, Vol. 48, No. 8, 797–823, 2005.
  36. A. B. Shvartsburg, G. Petite. Progress in Optics, Vol. 44 (Ed. E Wolf), p. 143, Elsevier Sci, 2002.
  37. K. S. Cole and R. H. Cole, “Dispersion and absorption in dielectrics,” J. Chem. Phys. 9(4), 341–351 (1941).
    [CrossRef]
  38. A. B. Djurišic and E. H. Li, “Modeling the index of refraction of insulating solids with a modified Lorentz oscillator model,” Appl. Opt. 37(22), 5291 (1998).
    [CrossRef]
  39. S. P. Blanc, R. Sauerbrey, S. C. Rae, and K. Burnett, “Spectral blue shifting of a femtosecond laser pulse propagating through a high-pressure gas,” J. Opt. Soc. Am. 10(10), (1993).
  40. G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
    [CrossRef]
  41. C. B. Schaffer, Interaction of femtosecond laser pulses with transparent materials, Ph.D. Thesis. Harvard University, May 2001.
  42. K. E. Oughstun and G. C. Sherman, “Uniform asymptotic description of electromagnetic pulse propagation in a linear dispersive medium with absorption (the Lorentz medium),” J. Opt. Soc. Am. A 6(9), 1394–1420 (1989).
    [CrossRef]
  43. L. N. Hand, and J. D. Finch, Analytical Mechanics. Cambridge University Press, 7th edition, Cambridge, 2008.

2010

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[CrossRef]

2008

M. Pietrzyk, I. Kanattsikov, and U. Bandelow, “On the propagation of vector ultrashort pulses,” J. Nonlinear Math. Phys. 15(2), 162–170 (2008).
[CrossRef]

2007

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[CrossRef]

Q. Zou and B. Lu, “Propagation properties of ultrashort pulsed beams with constant waist width in free space,” Opt. Laser Technol. 39(3), 619–625 (2007).
[CrossRef]

2006

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53(1–2), (2006).

2005

2004

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

2003

B. Macke and B. Segard, “Propagation of light pulses at a negative group velocity,” Eur. Phys. J. D 23, 125–141 (2003).
[CrossRef]

P. Kinsler and G. H. C. New, “Few-cycle pulse propagation,” Phys. Rev. A 67(2), 023813 (2003).
[CrossRef]

D. Hovhannisyan, “Propagation of a femtosecond laser pulse of a few optical oscillations in a uniaxial crystal,” Microw. Opt. Technol. Lett. 36(4), 280–285 (2003).
[CrossRef]

H. Kumagai, S. H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya, “Observation of the comples propagation of a femtosecond laser pulse in a dispersive transparent bulk material,” J. Opt. Soc. Am. 20(3), (2003).

2002

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[CrossRef] [PubMed]

2000

A. Zewail, “Femtochemistry: atomic-scale dynamics of the chemical bond,” J. Phys. Chem. A 104(24), 5660–5694 (2000).
[CrossRef]

1999

1998

A. L. Gutman, “Electrodynamics of short pulses for pulse durations comparable to relaxation times of a medium,” Dokl. Phys. 43(6), 343–345 (1998).

A. B. Djurišic and E. H. Li, “Modeling the index of refraction of insulating solids with a modified Lorentz oscillator model,” Appl. Opt. 37(22), 5291 (1998).
[CrossRef]

1997

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33(4), (1997).

S. A. Kozlov and S. V. Sazanov, “Nonlinear propagation of optical pulses of a few oscillations duration in dielectric media,” Sov. Phys. JETP 84(2), 221–228 (1997).
[CrossRef]

J. F. Eloy and H. Wilhelmsson, “Response of a bounded plasma to ultrashort pulse excitation,” Phys. Scr. 55(4), 475–477 (1997).
[CrossRef]

1995

H. Wilkelmsson, J. H. Trombert, and J. F. Eloy, “Dispersive and dissipative medium response to an ultrashort pulse: A green’s function approach,” Phys. Scr. 52(1), 102–107 (1995).
[CrossRef]

1993

S. P. Blanc, R. Sauerbrey, S. C. Rae, and K. Burnett, “Spectral blue shifting of a femtosecond laser pulse propagating through a high-pressure gas,” J. Opt. Soc. Am. 10(10), (1993).

1992

1991

1989

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[CrossRef]

K. E. Oughstun and G. C. Sherman, “Uniform asymptotic description of electromagnetic pulse propagation in a linear dispersive medium with absorption (the Lorentz medium),” J. Opt. Soc. Am. A 6(9), 1394–1420 (1989).
[CrossRef]

1985

Y. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83(11), 5391 (1985).
[CrossRef]

1970

M. D. Crisp, “Propagation of small-area pulses of coherent light through a resonant medium,” Phys. Rev. A 1(6), 1604–1611 (1970).
[CrossRef]

1941

K. S. Cole and R. H. Cole, “Dispersion and absorption in dielectrics,” J. Chem. Phys. 9(4), 341–351 (1941).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[CrossRef]

Aoshima, S.

H. Kumagai, S. H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya, “Observation of the comples propagation of a femtosecond laser pulse in a dispersive transparent bulk material,” J. Opt. Soc. Am. 20(3), (2003).

Bandelow, U.

M. Pietrzyk, I. Kanattsikov, and U. Bandelow, “On the propagation of vector ultrashort pulses,” J. Nonlinear Math. Phys. 15(2), 162–170 (2008).
[CrossRef]

Bandrauk, A. D.

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[CrossRef] [PubMed]

Biegert, J.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53(1–2), (2006).

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

Blanc, S. P.

S. P. Blanc, R. Sauerbrey, S. C. Rae, and K. Burnett, “Spectral blue shifting of a femtosecond laser pulse propagating through a high-pressure gas,” J. Opt. Soc. Am. 10(10), (1993).

Burnett, K.

S. P. Blanc, R. Sauerbrey, S. C. Rae, and K. Burnett, “Spectral blue shifting of a femtosecond laser pulse propagating through a high-pressure gas,” J. Opt. Soc. Am. 10(10), (1993).

Cho, S. H.

H. Kumagai, S. H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya, “Observation of the comples propagation of a femtosecond laser pulse in a dispersive transparent bulk material,” J. Opt. Soc. Am. 20(3), (2003).

Cole, K. S.

K. S. Cole and R. H. Cole, “Dispersion and absorption in dielectrics,” J. Chem. Phys. 9(4), 341–351 (1941).
[CrossRef]

Cole, R. H.

K. S. Cole and R. H. Cole, “Dispersion and absorption in dielectrics,” J. Chem. Phys. 9(4), 341–351 (1941).
[CrossRef]

Corkum, P. B.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[CrossRef]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[CrossRef] [PubMed]

Couairon, A.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53(1–2), (2006).

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

Crisp, M. D.

M. D. Crisp, “Propagation of small-area pulses of coherent light through a resonant medium,” Phys. Rev. A 1(6), 1604–1611 (1970).
[CrossRef]

Djurišic, A. B.

Eggert, S.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[CrossRef]

Eloy, J. F.

J. F. Eloy and H. Wilhelmsson, “Response of a bounded plasma to ultrashort pulse excitation,” Phys. Scr. 55(4), 475–477 (1997).
[CrossRef]

H. Wilkelmsson, J. H. Trombert, and J. F. Eloy, “Dispersive and dissipative medium response to an ultrashort pulse: A green’s function approach,” Phys. Scr. 52(1), 102–107 (1995).
[CrossRef]

Franco, M.

Fujimoto, M.

H. Kumagai, S. H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya, “Observation of the comples propagation of a femtosecond laser pulse in a dispersive transparent bulk material,” J. Opt. Soc. Am. 20(3), (2003).

Gallmann, L.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in Ultrashort Pulse Generation: Pushing the Limits in Linear and Nonlinear Optics,” Science 286(5444), 1507–1512 (1999).
[CrossRef] [PubMed]

Gamble, E. B.

Y. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83(11), 5391 (1985).
[CrossRef]

Gutman, A. L.

A. L. Gutman, “Electrodynamics of short pulses for pulse durations comparable to relaxation times of a medium,” Dokl. Phys. 43(6), 343–345 (1998).

Hagness, S. C.

Hanke, T.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[CrossRef]

Hasbani, R.

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[CrossRef] [PubMed]

Hauri, C. P.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53(1–2), (2006).

Helbing, F. W.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53(1–2), (2006).

Hovhannisyan, D.

D. Hovhannisyan, “Propagation of a femtosecond laser pulse of a few optical oscillations in a uniaxial crystal,” Microw. Opt. Technol. Lett. 36(4), 280–285 (2003).
[CrossRef]

Huber, R.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[CrossRef]

Ishikawa, K.

H. Kumagai, S. H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya, “Observation of the comples propagation of a femtosecond laser pulse in a dispersive transparent bulk material,” J. Opt. Soc. Am. 20(3), (2003).

Itatani, J.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

Ivanov, M. Y.

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[CrossRef] [PubMed]

Joseph, R. M.

Kanattsikov, I.

M. Pietrzyk, I. Kanattsikov, and U. Bandelow, “On the propagation of vector ultrashort pulses,” J. Nonlinear Math. Phys. 15(2), 162–170 (2008).
[CrossRef]

Keller, U.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53(1–2), (2006).

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in Ultrashort Pulse Generation: Pushing the Limits in Linear and Nonlinear Optics,” Science 286(5444), 1507–1512 (1999).
[CrossRef] [PubMed]

Kieffer, J. C.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

Kinsler, P.

P. Kinsler and G. H. C. New, “Few-cycle pulse propagation,” Phys. Rev. A 67(2), 023813 (2003).
[CrossRef]

Kornelis, W.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53(1–2), (2006).

Kozlov, S. A.

S. A. Kozlov and S. V. Sazanov, “Nonlinear propagation of optical pulses of a few oscillations duration in dielectric media,” Sov. Phys. JETP 84(2), 221–228 (1997).
[CrossRef]

Krauss, G.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[CrossRef]

Krausz, F.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[CrossRef]

Kumagai, H.

H. Kumagai, S. H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya, “Observation of the comples propagation of a femtosecond laser pulse in a dispersive transparent bulk material,” J. Opt. Soc. Am. 20(3), (2003).

Légaré, F.

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[CrossRef] [PubMed]

Leitenstorfer, A.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[CrossRef]

Levesque, J.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

Li, E. H.

Lin, Q.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33(4), (1997).

Lohss, S.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[CrossRef]

Lu, B.

Q. Zou and B. Lu, “Propagation properties of ultrashort pulsed beams with constant waist width in free space,” Opt. Laser Technol. 39(3), 619–625 (2007).
[CrossRef]

Macke, B.

B. Macke and B. Segard, “Propagation of light pulses at a negative group velocity,” Eur. Phys. J. D 23, 125–141 (2003).
[CrossRef]

Matuschek, N.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in Ultrashort Pulse Generation: Pushing the Limits in Linear and Nonlinear Optics,” Science 286(5444), 1507–1512 (1999).
[CrossRef] [PubMed]

Midorikawa, K.

H. Kumagai, S. H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya, “Observation of the comples propagation of a femtosecond laser pulse in a dispersive transparent bulk material,” J. Opt. Soc. Am. 20(3), (2003).

Mysyrowicz, A.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53(1–2), (2006).

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005).
[CrossRef] [PubMed]

Nelson, K. A.

Y. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83(11), 5391 (1985).
[CrossRef]

New, G. H. C.

P. Kinsler and G. H. C. New, “Few-cycle pulse propagation,” Phys. Rev. A 67(2), 023813 (2003).
[CrossRef]

Niikura, H.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[CrossRef] [PubMed]

Olsson, N. A.

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[CrossRef]

Oughstun, K. E.

Pépin, H.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

Pietrzyk, M.

M. Pietrzyk, I. Kanattsikov, and U. Bandelow, “On the propagation of vector ultrashort pulses,” J. Nonlinear Math. Phys. 15(2), 162–170 (2008).
[CrossRef]

Porras, M. A.

Rae, S. C.

S. P. Blanc, R. Sauerbrey, S. C. Rae, and K. Burnett, “Spectral blue shifting of a femtosecond laser pulse propagating through a high-pressure gas,” J. Opt. Soc. Am. 10(10), (1993).

Rothenberg, J. E.

Sauerbrey, R.

S. P. Blanc, R. Sauerbrey, S. C. Rae, and K. Burnett, “Spectral blue shifting of a femtosecond laser pulse propagating through a high-pressure gas,” J. Opt. Soc. Am. 10(10), (1993).

Sazanov, S. V.

S. A. Kozlov and S. V. Sazanov, “Nonlinear propagation of optical pulses of a few oscillations duration in dielectric media,” Sov. Phys. JETP 84(2), 221–228 (1997).
[CrossRef]

Segard, B.

B. Macke and B. Segard, “Propagation of light pulses at a negative group velocity,” Eur. Phys. J. D 23, 125–141 (2003).
[CrossRef]

Sell, A.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[CrossRef]

Sherman, G. C.

Steinmeyer, G.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in Ultrashort Pulse Generation: Pushing the Limits in Linear and Nonlinear Optics,” Science 286(5444), 1507–1512 (1999).
[CrossRef] [PubMed]

Sutter, D. H.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in Ultrashort Pulse Generation: Pushing the Limits in Linear and Nonlinear Optics,” Science 286(5444), 1507–1512 (1999).
[CrossRef] [PubMed]

Taflove, A.

Trombert, J. H.

H. Wilkelmsson, J. H. Trombert, and J. F. Eloy, “Dispersive and dissipative medium response to an ultrashort pulse: A green’s function approach,” Phys. Scr. 52(1), 102–107 (1995).
[CrossRef]

Tsuchiya, Y.

H. Kumagai, S. H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya, “Observation of the comples propagation of a femtosecond laser pulse in a dispersive transparent bulk material,” J. Opt. Soc. Am. 20(3), (2003).

Villeneuve, D. M.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[CrossRef] [PubMed]

Wang, Z.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33(4), (1997).

Wilhelmsson, H.

J. F. Eloy and H. Wilhelmsson, “Response of a bounded plasma to ultrashort pulse excitation,” Phys. Scr. 55(4), 475–477 (1997).
[CrossRef]

Wilkelmsson, H.

H. Wilkelmsson, J. H. Trombert, and J. F. Eloy, “Dispersive and dissipative medium response to an ultrashort pulse: A green’s function approach,” Phys. Scr. 52(1), 102–107 (1995).
[CrossRef]

Xiao, H.

Xu, Z.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33(4), (1997).

Yan, Y.

Y. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83(11), 5391 (1985).
[CrossRef]

Zeidler, D.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

Zewail, A.

A. Zewail, “Femtochemistry: atomic-scale dynamics of the chemical bond,” J. Phys. Chem. A 104(24), 5660–5694 (2000).
[CrossRef]

Zhang, Z.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33(4), (1997).

Zou, Q.

Q. Zou and B. Lu, “Propagation properties of ultrashort pulsed beams with constant waist width in free space,” Opt. Laser Technol. 39(3), 619–625 (2007).
[CrossRef]

Appl. Opt.

Dokl. Phys.

A. L. Gutman, “Electrodynamics of short pulses for pulse durations comparable to relaxation times of a medium,” Dokl. Phys. 43(6), 343–345 (1998).

Eur. Phys. J. D

B. Macke and B. Segard, “Propagation of light pulses at a negative group velocity,” Eur. Phys. J. D 23, 125–141 (2003).
[CrossRef]

IEEE J. Quantum Electron.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33(4), (1997).

G. P. Agrawal and N. A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[CrossRef]

J. Chem. Phys.

Y. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83(11), 5391 (1985).
[CrossRef]

K. S. Cole and R. H. Cole, “Dispersion and absorption in dielectrics,” J. Chem. Phys. 9(4), 341–351 (1941).
[CrossRef]

J. Mod. Opt.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53(1–2), (2006).

J. Nonlinear Math. Phys.

M. Pietrzyk, I. Kanattsikov, and U. Bandelow, “On the propagation of vector ultrashort pulses,” J. Nonlinear Math. Phys. 15(2), 162–170 (2008).
[CrossRef]

J. Opt. Soc. Am.

S. P. Blanc, R. Sauerbrey, S. C. Rae, and K. Burnett, “Spectral blue shifting of a femtosecond laser pulse propagating through a high-pressure gas,” J. Opt. Soc. Am. 10(10), (1993).

H. Kumagai, S. H. Cho, K. Ishikawa, K. Midorikawa, M. Fujimoto, S. Aoshima, and Y. Tsuchiya, “Observation of the comples propagation of a femtosecond laser pulse in a dispersive transparent bulk material,” J. Opt. Soc. Am. 20(3), (2003).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. Chem. A

A. Zewail, “Femtochemistry: atomic-scale dynamics of the chemical bond,” J. Phys. Chem. A 104(24), 5660–5694 (2000).
[CrossRef]

Microw. Opt. Technol. Lett.

D. Hovhannisyan, “Propagation of a femtosecond laser pulse of a few optical oscillations in a uniaxial crystal,” Microw. Opt. Technol. Lett. 36(4), 280–285 (2003).
[CrossRef]

Nat. Photonics

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4(1), 33–36 (2010).
[CrossRef]

Nat. Phys.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[CrossRef]

Nature

H. Niikura, F. Légaré, R. Hasbani, A. D. Bandrauk, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Sub-laser-cycle electron pulses for probing molecular dynamics,” Nature 417(6892), 917–922 (2002).
[CrossRef] [PubMed]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[CrossRef] [PubMed]

Opt. Laser Technol.

Q. Zou and B. Lu, “Propagation properties of ultrashort pulsed beams with constant waist width in free space,” Opt. Laser Technol. 39(3), 619–625 (2007).
[CrossRef]

Opt. Lett.

Phys. Rev. A

P. Kinsler and G. H. C. New, “Few-cycle pulse propagation,” Phys. Rev. A 67(2), 023813 (2003).
[CrossRef]

M. D. Crisp, “Propagation of small-area pulses of coherent light through a resonant medium,” Phys. Rev. A 1(6), 1604–1611 (1970).
[CrossRef]

Phys. Scr.

J. F. Eloy and H. Wilhelmsson, “Response of a bounded plasma to ultrashort pulse excitation,” Phys. Scr. 55(4), 475–477 (1997).
[CrossRef]

H. Wilkelmsson, J. H. Trombert, and J. F. Eloy, “Dispersive and dissipative medium response to an ultrashort pulse: A green’s function approach,” Phys. Scr. 52(1), 102–107 (1995).
[CrossRef]

Science

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in Ultrashort Pulse Generation: Pushing the Limits in Linear and Nonlinear Optics,” Science 286(5444), 1507–1512 (1999).
[CrossRef] [PubMed]

Sov. Phys. JETP

S. A. Kozlov and S. V. Sazanov, “Nonlinear propagation of optical pulses of a few oscillations duration in dielectric media,” Sov. Phys. JETP 84(2), 221–228 (1997).
[CrossRef]

Other

S. L. Dvorak, D. G. Dudley. Propagation of ultrawideband electromagnetic pulses through dispersive media. IEEE Transaction of Electromagnetic Compatibility, Vol. 37. No. 2, May 1995.

J. F. Eloy, and F. Moriamez, Spectral analysis of EM ultrashort pulses at coherence limit. Modelling. SPIE Intense Microwave and Particle Beams III, Vol. 1629, 1992.

K. Akimoto, Properties and Applications of ultrashort electromagnetic mono- and sub- cycle waves. Journal ofthe Physical Society of Japan, Vol. 65, No. 7, 2020–2032, 1996.

B. K. P. Scaife, Principles of Dielectrics, Oxford University Press, Oxford, 1989.

A. L. Gutman, Passage of short pulse throughout oscillating circuit with dielectric in condenser. Ultra-Wideband, Short-Pulse Electromagnetics 4, Kluwer Academic / Plenum Publishers, New York, 1999.

V. V. Daniel, Dielectric Relaxation. Academic Press, New York, 1967.

A. B. Shvartsburg, Optics of nonstationary media, Physics – Uspekhi, Vol. 48, No. 8, 797–823, 2005.

A. B. Shvartsburg, G. Petite. Progress in Optics, Vol. 44 (Ed. E Wolf), p. 143, Elsevier Sci, 2002.

C. B. Schaffer, Interaction of femtosecond laser pulses with transparent materials, Ph.D. Thesis. Harvard University, May 2001.

A. B. Shvartsburg, Time-Domain Optics of Ultrashort Waveforms. Clarendon Press, Oxford, 1996.

A. B. Shvartsburg, Impulse Time-Domain Electromagnetic of Continuos Media. Birkhauser Verlag, Boston, 1999.

A. B. Shvartsburg, Single-cycle waveforms and non-periodic waves in dispersive media (exactly solvable models). Physics – Uspekhi, Vol. 41, No. 1, 77–94, 1998.

L. N. Hand, and J. D. Finch, Analytical Mechanics. Cambridge University Press, 7th edition, Cambridge, 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 (9)

Fig. 1
Fig. 1

(a) Applied Laguerre USCP with pulse duration τp = 8x10−16. (b) 1st derivative of the LaguerreUSCP.

Fig. 2
Fig. 2

(a) Applied Hermitian USCP with pulse duration τp=8x10−15, (b) 1st derivative of the Hermitian USCP.

Fig. 3
Fig. 3

Schematic representation of self modulation (pulse chirping). Although we are interested in the low intensity applied fields for linear polarization in this study, temporal dependence of the intensity profile of the applied field can still cause a temporal dependence in the refractive index [41].

Fig. 4
Fig. 4

Bounded electron motion under Laguerre USCP excitation ((a), (c), (e), (g), (i)) and Hermitian USCP excitation ((b), (d), (f), (h), (j)) for various values of spring constant ( k o ) with a fixed damping constant ( δ o = 1 x 10 14 ).

Fig. 8
Fig. 8

Hermitian pulse excitation oscillations for damping constant: δ o = 1 x 10 17

Fig. 5
Fig. 5

Laguerre pulse excitation oscillations for damping constant: δ o = 1 x 10 16

Fig. 6
Fig. 6

Laguerre Pulse Excitation physical parameter solutions for spring constant k o = 525 N/m. (a), (b), (e), (f) and (i) are the solutions of Fig. 4(g) (damping constant δ o = 1 x 10 14 ). (b) and (f) are the magnified views of (a) and (e) respectively. (c), (d), (g), (h) and (j) are the solutions of Fig. 5(a) (damping constant δ o = 1 x 10 16 ). (d) and (h) are the magnified views of (c) and (g) respectively.

Fig. 7
Fig. 7

(a) – (b): Magnified views of left wings of Figs. 6(a)-6(c). (c) – (d): Magnified views of right wings of Figs. 6(a)-6(c).

Fig. 9
Fig. 9

Hermitian pulse excitation modifier functions for damping constant: δ o = 1 x 10 17

Equations (14)

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

E 2 ( α ) = exp ( ( 7.5 α ) 2 ) [ 1 24 α 4 + 15 24 α 3 5 2 α 2 + 2 α ] ,
0 E 2 ( α ) d α = 0.
E ( α ) = ( 1 α 2 ) exp ( α 2 / 2 ) .
n = ( 1 + P ( t ) ε o E ( t ) ) 1 2 ,
2 E ( z , t ) z 2 1 c 0 2 2 E ( z , t ) t 2 = μ o 2 P t 2 ,
m e d 2 x ( t ) d t 2 + m e γ o d x ( t ) d t + k o x ( t ) = e E ( t ) ,
x ( t ) = x o ( t ) E ( t ) ,
m e d 2 ( x o ( t ) E ( t ) ) d t 2 + m e γ o d ( x o ( t ) E ( t ) ) d t + k o ( x o ( t ) E ( t ) ) = e E ( t ) .
m e d 2 x o ( t ) d t 2 E ( t ) + 2 m e d x o ( t ) d t d E ( t ) d t + m e x o d 2 E ( t ) d t 2 + m e γ o d x o ( t ) d t E ( t ) + m e γ o x o ( t ) d E ( t ) d t + k o x o ( t ) E ( t ) = e E ( t ) ,
m e E ( t ) d 2 x o ( t ) d t 2 + m e ( 2 d E ( t ) d t + γ o E ( t ) ) d x o ( t ) d t + m e ( d 2 E ( t ) d t 2 + γ o d E ( t ) d t + k o m e E ( t ) ) x o ( t ) = e E ( t )
d 2 x o ( t ) d t 2 + ( 2 E ( t ) d E ( t ) d t + γ o ) d x o ( t ) d t + ( 1 E ( t ) d 2 E ( t ) d t 2 + γ o E ( t ) d E ( t ) d t + k o m e ) x o ( t ) = e m e .
d 2 x o ( t ) d t 2 + P ( t ) d x o ( t ) d t + Q ( t ) x o ( t ) = e m e ,
P ( t ) = 2 E ( t ) d E ( t ) d t + γ o ,
Q ( t ) = 1 E ( t ) d 2 E ( t ) d t 2 + γ o E ( t ) d E ( t ) d t + k o m e .

Metrics