Abstract

The problem of diffraction of few-cycle light pulses is solved by means of a perturbative technique. The propagated field is expressed as a series of correction terms to the field obtained from diffraction laws for many-cycle pulses. The features previously reported for diffraction of ultrashort pulses are reproduced by first- and second-order corrections.

© 2001 Optical Society of America

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References

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  9. A. E. Kaplan, J. Opt. Soc. Am. B 15, 951 (1998). Equation  (2.10) gives the exact Eon for a Gaussian aperture and an arbitrary (subcycle and multicycle) temporal form as a simple integral, which however has to be evaluated for each specific pulse form.
    [CrossRef]
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2000

M. A. Porras, F. Salazar-Bloise, and L. Vázquez, Phys. Rev. Lett. 85, 2104 (2000).
[CrossRef] [PubMed]

1999

G. P. Agrawal, Opt. Commun. 167, 15 (1999).
[CrossRef]

1998

1997

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997)Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

C. J. R. Sheppard and X. Gan, Opt. Commun. 133, 1 (1997).
[CrossRef]

1994

1992

R. W. Ziolkowski and J. B. Judkins, J. Opt. Soc. Am. B 9, 2021 (1992).
[CrossRef]

1986

1985

I. P. Christov, Opt. Commun. 53, 364 (1985).
[CrossRef]

1975

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Opt. Commun. 167, 15 (1999).
[CrossRef]

G. P. Agrawal, Opt. Commun. 157, 52 (1998).
[CrossRef]

Belenov, E. M.

Brabec, T.

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997)Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Christov, I. P.

I. P. Christov, Opt. Commun. 53, 364 (1985).
[CrossRef]

Felsen, L. B.

Gan, X.

C. J. R. Sheppard and X. Gan, Opt. Commun. 133, 1 (1997).
[CrossRef]

Judkins, J. B.

R. W. Ziolkowski and J. B. Judkins, J. Opt. Soc. Am. B 9, 2021 (1992).
[CrossRef]

Kaplan, A. E.

Krausz, F.

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997)Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Melamed, T.

Nazarkin, A. V.

Porras, M. A.

M. A. Porras, F. Salazar-Bloise, and L. Vázquez, Phys. Rev. Lett. 85, 2104 (2000).
[CrossRef] [PubMed]

M. A. Porras, Phys. Rev. E 58, 1086 (1998).
[CrossRef]

Salazar-Bloise, F.

M. A. Porras, F. Salazar-Bloise, and L. Vázquez, Phys. Rev. Lett. 85, 2104 (2000).
[CrossRef] [PubMed]

Sheppard, C. J. R.

C. J. R. Sheppard and X. Gan, Opt. Commun. 133, 1 (1997).
[CrossRef]

Vázquez, L.

M. A. Porras, F. Salazar-Bloise, and L. Vázquez, Phys. Rev. Lett. 85, 2104 (2000).
[CrossRef] [PubMed]

Zauderer, E.

Ziolkowski, R. W.

R. W. Ziolkowski and J. B. Judkins, J. Opt. Soc. Am. B 9, 2021 (1992).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

C. J. R. Sheppard and X. Gan, Opt. Commun. 133, 1 (1997).
[CrossRef]

I. P. Christov, Opt. Commun. 53, 364 (1985).
[CrossRef]

G. P. Agrawal, Opt. Commun. 157, 52 (1998).
[CrossRef]

G. P. Agrawal, Opt. Commun. 167, 15 (1999).
[CrossRef]

Phys. Rev. A

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Phys. Rev. E

M. A. Porras, Phys. Rev. E 58, 1086 (1998).
[CrossRef]

Phys. Rev. Lett.

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997)Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

M. A. Porras, F. Salazar-Bloise, and L. Vázquez, Phys. Rev. Lett. 85, 2104 (2000).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

Instantaneous intensity diffraction patterns for the illumination Er,t=exp-t2/T2exp-r2/a2exp-iω0t, ω0=3.8 fs-1, T=1.40 fs, a=1 mm. The observation plane is z=zR=6.3×103 mm. Circles, exact paraxial solution; solid curves, zero-order or quasi-monochromatic solution; long-dashed curves, first-order solution; short-dashed curves, second-order solution. The selected times correspond to the maxima of Fig.  2(a).

Fig. 2
Fig. 2

On-axis field for the illumination Er,t=exp-t21+iC/T2exp-r2/a2exp-iω0t, ω0=3.8 fs-1, T=1.40 fs, a=1 mm. (a), (b) C=0; (c), (d) C=1.2. Circles, exact solution; solid curves, zero-order solution; dashed curves, first-order solution.

Equations (12)

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ΔE-2/cztE=0,
Δψ+2ik0z1+i/ω0tψ=0,
Δψ+2ik0z1+iητψ=0,
ψ=ϕ0+ηϕ1+η2ϕ2+
ψ0+ψ1+ψ2+
Δψ0+2ik0zψ0=0,Δψn+2ik0zψn=2/cztψn-1,n1.
ψ0x,0,t=ψx,t,ψnx,0,t=0,n1.
ψnx,z,t=-iω0nntnn-1zn-1znn!ψ0z.
ψ0=ftg0x,z=ft-izRqexpik0r22q,
ψn=-iω0ndnftdtnm=1nn-1m-1zmm!mg0zm,
ψn=-iω0ndnftdtnm=1nn-1m-1-zqm×Lm-ik0r22qg0.
Eon1ω0zRq-iω0ft+zqdftdtexp-iω0t.

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