Abstract

Focusing of ultrashort light pulses with single lenses is analyzed by taking into account the unavoidable interplay between chromatic and spherical aberration simultaneously for the first time to our knowledge. The spatial intensity distribution is mainly affected by spherical aberration, whereas the temporal distribution is determined by both aberrations. The impact on second-harmonic generation for femtosecond pulse measurements is discussed. For example, the presence of spherical aberration allows one to record the correct autocorrelation of a 10-fs pulse even if chromatic aberration alone would cause a half-width of the autocorrelation function of 40 fs.

© 1993 Optical Society of America

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References

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  1. C. P. Huang, M. Asaki, J. W. McIntosh, M. M. Murnane, H. C. Kapteyn, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 218.
  2. R. L. Fork, C. H. Brito-Cruz, P. C. Becker, C. V. Shank, Opt. Lett. 12, 483 (1987).
    [CrossRef] [PubMed]
  3. F. Salin, J. Squier, G. Mourou, G. Vaillancourt, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 240.
  4. Z. Bor, J. Mod. Opt. 35, 1907 (1988).
    [CrossRef]
  5. M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, J. Opt. Soc. Am. B 9, 1158 (1992).
    [CrossRef]
  6. Z. Bor, Z. L. Horvath, in Dye Laser: 25 Years, Vol. 70 of Topics in Applied Physics, M. Stuke, ed. (Springer-Verlag, Berlin, 1992), pp. 87–94.
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989).

1992 (1)

1988 (1)

Z. Bor, J. Mod. Opt. 35, 1907 (1988).
[CrossRef]

1987 (1)

Asaki, M.

C. P. Huang, M. Asaki, J. W. McIntosh, M. M. Murnane, H. C. Kapteyn, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 218.

Becker, P. C.

Bor, Z.

Z. Bor, J. Mod. Opt. 35, 1907 (1988).
[CrossRef]

Z. Bor, Z. L. Horvath, in Dye Laser: 25 Years, Vol. 70 of Topics in Applied Physics, M. Stuke, ed. (Springer-Verlag, Berlin, 1992), pp. 87–94.
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989).

Brito-Cruz, C. H.

Fork, R. L.

Horvath, Z. L.

Z. Bor, Z. L. Horvath, in Dye Laser: 25 Years, Vol. 70 of Topics in Applied Physics, M. Stuke, ed. (Springer-Verlag, Berlin, 1992), pp. 87–94.
[CrossRef]

Huang, C. P.

C. P. Huang, M. Asaki, J. W. McIntosh, M. M. Murnane, H. C. Kapteyn, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 218.

Kapteyn, H. C.

C. P. Huang, M. Asaki, J. W. McIntosh, M. M. Murnane, H. C. Kapteyn, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 218.

Kempe, M.

McIntosh, J. W.

C. P. Huang, M. Asaki, J. W. McIntosh, M. M. Murnane, H. C. Kapteyn, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 218.

Mourou, G.

F. Salin, J. Squier, G. Mourou, G. Vaillancourt, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 240.

Murnane, M. M.

C. P. Huang, M. Asaki, J. W. McIntosh, M. M. Murnane, H. C. Kapteyn, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 218.

Rudolph, W.

Salin, F.

F. Salin, J. Squier, G. Mourou, G. Vaillancourt, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 240.

Shank, C. V.

Squier, J.

F. Salin, J. Squier, G. Mourou, G. Vaillancourt, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 240.

Stamm, U.

Vaillancourt, G.

F. Salin, J. Squier, G. Mourou, G. Vaillancourt, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 240.

Wilhelmi, B.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989).

J. Mod. Opt. (1)

Z. Bor, J. Mod. Opt. 35, 1907 (1988).
[CrossRef]

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

Opt. Lett. (1)

Other (4)

F. Salin, J. Squier, G. Mourou, G. Vaillancourt, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 240.

C. P. Huang, M. Asaki, J. W. McIntosh, M. M. Murnane, H. C. Kapteyn, in Conference on Lasers and Electro-Optics, Vol. 12 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 218.

Z. Bor, Z. L. Horvath, in Dye Laser: 25 Years, Vol. 70 of Topics in Applied Physics, M. Stuke, ed. (Springer-Verlag, Berlin, 1992), pp. 87–94.
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989).

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Figures (4)

Fig. 1
Fig. 1

Lens geometry.

Fig. 2
Fig. 2

Delay parameter τ (solid curves) and wave aberration A (dashed curves) versus numerical aperture for a plano-convex BK7 lens at a wavelength of 620 nm. The curves are calculated for a lens diameter of 5, 10, 15, and 20 mm (from the lower to the upper curves, respectively).

Fig. 3
Fig. 3

Space–time distribution of a Gaussian-shaped input pulse focused by a lens (parameters are given in the text), (a) A = 0, (b) A = 100 and paraxial focal plane, (c) A = 100 and marginal focal plane.

Fig. 4
Fig. 4

Second-harmonic signal and FWHM of the actual autocorrelation function normalized to the true FWHM versus the crystal position measured from the paraxial focal plane (lens and pulse parameters are given in the text; the dashed lines are only a guide for the eye). The marginal focal plane is located at approximately −1.3 mm.

Tables (1)

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Table 1 Conversion Factors for Fig. 2

Equations (4)

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τ = a 2 k 0 2 f 0 ( n 0 1 ) d n d ω | ω = ω 0 ,
ϕ ( 4 ) ( r ) = n 0 2 ( n 0 2 4 ) + 2 n 0 + 4 8 n 0 ( n 0 1 ) 2 ( n 0 + 2 ) r a ( r a f 0 ) 3 ,
U ( υ , u ; t ) d ( Δ ω ) A ( Δ ω ) 0 1 d r r J 0 [ r υ ( 1 + Δ ω ω 0 ) ] × exp ( r 2 / w 2 ) exp ( j u r 2 / 2 ) exp ( j A r 4 ) × exp [ j ( Δ ω ) 2 ( δ δ r 2 ) ] × exp { j ( Δ ω ) [ t + τ r 2 + r 2 u / ( 2 ω 0 ) ] } ,
E SHG ( Δ t , u ) = B 0 d υ υ d t I ( υ , u ; t ) I ( υ , u ; t + Δ t ) ,

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