Abstract

We found that, at the focus of a chromatic lens, a laser pulse with a self-modulated phase can be shortened due to the radial dependence of the group delay imposed by the lens. Normally, this group delay stretches a short pulse into a long pulse by spreading the arrival time of the pulse at the focus. However, for a pulse with a self-modulated phase, it causes the fields with different phases to overlap, thus resulting in destructive interference that shortens the pulse.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Z. Bor, Opt. Lett. 14, 119 (1989).
    [CrossRef] [PubMed]
  2. Z. Bor and Z. L. Horvath, Opt. Commun. 94, 249 (1992).
    [CrossRef]
  3. M. Kempe, U. Stamm, B. Wilhelmi, and W. Rudolph, J. Opt. Soc. Am. B 9, 1158 (1992).
    [CrossRef]
  4. Z. Bor, Z. Gogolak, and G. Szabo, Opt. Lett. 14, 862 (1989).
    [CrossRef] [PubMed]
  5. R. Netz, T. Feurer, R. Wolleschensky, and R. Sauerbrey, Appl. Phys. B 70, 833 (2000).
  6. J. Jasapara and W. Rudolph, Opt. Lett. 24, 777 (1999).
    [CrossRef]
  7. Y. Li and X. Chang, paper THPPH053 presented at the 2006 Free Electron Laser Conference, Berlin, August 27-September 1, 2006.
  8. J. D. Lindl, Nucl. Fusion 39, 825 (1999).
    [CrossRef]
  9. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  10. A. J. Taylor, G. Rodriguez, and T. S. Clement, Opt. Lett. 21, 1812 (1996).
    [CrossRef] [PubMed]
  11. J. W. Goodman, Statistical Optics (Wiley, 1985).
  12. A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, Phys. Rev. Lett. 82, 3883 (1999).
    [CrossRef]
  13. B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
    [CrossRef] [PubMed]
  14. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, Opt. Lett. 30, 2657 (2005).
    [CrossRef] [PubMed]
  15. K. D. Moll, A. L. Gaeta, and G. Fibich, Phys. Rev. Lett. 90, 203902 (2003).
    [CrossRef] [PubMed]

2005

2003

K. D. Moll, A. L. Gaeta, and G. Fibich, Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

2000

R. Netz, T. Feurer, R. Wolleschensky, and R. Sauerbrey, Appl. Phys. B 70, 833 (2000).

1999

J. D. Lindl, Nucl. Fusion 39, 825 (1999).
[CrossRef]

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, Phys. Rev. Lett. 82, 3883 (1999).
[CrossRef]

J. Jasapara and W. Rudolph, Opt. Lett. 24, 777 (1999).
[CrossRef]

1996

1995

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

1992

1989

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

Backus, S.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, Phys. Rev. Lett. 82, 3883 (1999).
[CrossRef]

Biegert, J.

Bor, Z.

Chang, X.

Y. Li and X. Chang, paper THPPH053 presented at the 2006 Free Electron Laser Conference, Berlin, August 27-September 1, 2006.

Clement, T. S.

Couairon, A.

Feit, M. D.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

Feurer, T.

R. Netz, T. Feurer, R. Wolleschensky, and R. Sauerbrey, Appl. Phys. B 70, 833 (2000).

Fibich, G.

K. D. Moll, A. L. Gaeta, and G. Fibich, Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

Franco, M.

Gaeta, A. L.

K. D. Moll, A. L. Gaeta, and G. Fibich, Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

Gogolak, Z.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985).

Horvath, Z. L.

Z. Bor and Z. L. Horvath, Opt. Commun. 94, 249 (1992).
[CrossRef]

Jasapara, J.

Kapteyn, H.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, Phys. Rev. Lett. 82, 3883 (1999).
[CrossRef]

Keller, U.

Kempe, M.

Li, Y.

Y. Li and X. Chang, paper THPPH053 presented at the 2006 Free Electron Laser Conference, Berlin, August 27-September 1, 2006.

Lindl, J. D.

J. D. Lindl, Nucl. Fusion 39, 825 (1999).
[CrossRef]

Moll, K. D.

K. D. Moll, A. L. Gaeta, and G. Fibich, Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

Mourou, G.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, Phys. Rev. Lett. 82, 3883 (1999).
[CrossRef]

Murnane, M.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, Phys. Rev. Lett. 82, 3883 (1999).
[CrossRef]

Mysyrowicz, A.

Netz, R.

R. Netz, T. Feurer, R. Wolleschensky, and R. Sauerbrey, Appl. Phys. B 70, 833 (2000).

Perry, M. D.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

Rodriguez, G.

Rubenchik, A. M.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

Rudolph, W.

Sauerbrey, R.

R. Netz, T. Feurer, R. Wolleschensky, and R. Sauerbrey, Appl. Phys. B 70, 833 (2000).

Shore, B. W.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

Stamm, U.

Stuart, B. C.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

Szabo, G.

Taylor, A. J.

Tien, A.-C.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, Phys. Rev. Lett. 82, 3883 (1999).
[CrossRef]

Wilhelmi, B.

Wolleschensky, R.

R. Netz, T. Feurer, R. Wolleschensky, and R. Sauerbrey, Appl. Phys. B 70, 833 (2000).

Appl. Phys. B

R. Netz, T. Feurer, R. Wolleschensky, and R. Sauerbrey, Appl. Phys. B 70, 833 (2000).

J. Opt. Soc. Am. B

Nucl. Fusion

J. D. Lindl, Nucl. Fusion 39, 825 (1999).
[CrossRef]

Opt. Commun.

Z. Bor and Z. L. Horvath, Opt. Commun. 94, 249 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, Phys. Rev. Lett. 82, 3883 (1999).
[CrossRef]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

K. D. Moll, A. L. Gaeta, and G. Fibich, Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

J. W. Goodman, Statistical Optics (Wiley, 1985).

Y. Li and X. Chang, paper THPPH053 presented at the 2006 Free Electron Laser Conference, Berlin, August 27-September 1, 2006.

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 (3)

Fig. 1
Fig. 1

Real part of the complex field arriving at the focus as a function of time and radius for (a) ζ = T d and (b) ζ = 1 , and the corresponding intensity of the integrated field (solid curve) and the input pulse (dashed curve) as a function of time for the same cases [(c) and (d)]. The FWHM of the pulse is shortened from 1 ps to (c) 210 fs and (d) 200 fs , a reduction by a factor of 5. The calculation assumes an f = 150 mm lens with R = 12 mm and d = 5 mm . The pulse wavelength is 0.249 nm with μ = 15 at a laser intensity of 5 × 10 11 W cm 2 .

Fig. 2
Fig. 2

Pulse duration ratio as a function of time-shift parameter ρ [defined in Eq. (11)] and the phase-shift parameter μ [defined in Eq. (8)] for a τ = 1 ps Gaussian pulse for ζ = 1 . The two dotted curves are ρ μ = 2 π (lower) and ρ μ = 3 π (upper). Calculations for pulse duration ranging from a few femtoseconds to a few nanoseconds gives identical distributions when GVDI is ignored. The wavy structure is due to the generation of multiple peaks.

Fig. 3
Fig. 3

On-axis laser pulse envelope as a function of the defocusing distance; the intensity as a function of time and radius for a pulse (b) without and (c) with the SPM effect. The calculation assumes the same conditions as for Fig. 1.

Equations (12)

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

U ( ω ) = 2 π r d r A ( ω ) Γ ( r , ω ) ,
Γ ( r , ω ) = exp ( j k l d + j k a 2 f r 2 ) exp [ j ( k l k a ) r 2 2 ( n 1 ) f ] .
u ( t ) = 2 π r d r a * γ ,
Γ ( r , ω ) = exp [ j k ( β T Δ ω + χ T Δ ω 2 ) ] ,
T ( r ) = d r 2 2 ( n 1 ) f , β = d n d ω , χ = β 1 ω + 1 2 d 2 n d ω 2 .
u ( t ) = 2 π a 0 r d r 1 ( 1 + Λ 2 ) 1 4 exp [ 2 ln 2 ( t k β T ) 2 τ 2 ( 1 + Λ 2 ) ( 1 j Λ ) ] exp [ j tan 1 ( Λ ) ] ,
γ ( r , t ) = δ ( t k β T ) .
a ( r , t ) = a 0 exp ( 2 ln 2 t 2 τ 2 ) exp [ j μ exp ( 4 ln 2 t 2 τ 2 ) ζ ] .
u ( t ) = a 0 r d r exp [ 2 ln 2 ( t k β T ) 2 τ 2 ] exp { j μ exp [ 4 ln 2 ( t k β T ) 2 τ 2 ] ζ } .
ρ μ constant ,
ρ = β R 2 2 ( n 1 ) f τ = 2 N A β R τ .
Δ z

Metrics