Abstract

To resolve the diffraction problems of the pulsed wave field directly in the temporal domain, we extend the Rayleigh diffraction integrals to the temporal domain and then discuss the approximation condition of this diffraction formula.

© 1997 Optical Society of America

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References

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  1. R. W. Ziolkowski and D. B. Davidson, Opt. Lett. 4, 284 (1994).
    [CrossRef]
  2. M. Kempe and W. Rudolph, Phys. Rev. A 48, 4721 (1993).
    [CrossRef] [PubMed]
  3. Z. L. Horváth, Z. Benkó, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
    [CrossRef]
  4. Y. H. Chuang, L. Zheng, and D. D. Meyerhofer, IEEE J. Quantum Electron. 29, 270 (1993).
    [CrossRef]
  5. B. H. Kolner, Opt. Lett. 14, 630 (1989).
    [CrossRef] [PubMed]
  6. S. P. Dijaili, A. Dienes, and J. S. Smith, IEEE J. Quantum. Electron. 26, 1158 (1990).
    [CrossRef]
  7. O. E. Martinez, IEEE J. Quantum. Electron. 24, 2530 (1988); IEEE J. Quantum. Electron. 25, 296 (1989).
    [CrossRef]
  8. Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Lett. 18, 669 (1993).
    [CrossRef] [PubMed]
  9. Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, IEEE J. Quantum Electron. (to be published).
  10. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 8, pp. 377 and 389.
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3, p. 46.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. J. Zhou, C. Huang, C. Shi, M. M. Murnane, and H. C. Kapteyn, Opt. Lett. 19, 126 (1994).
    [CrossRef]
  17. D. Fan, Acta Opt. Sinica 3, 319 (1983).

1994 (3)

1993 (4)

M. Kempe and W. Rudolph, Phys. Rev. A 48, 4721 (1993).
[CrossRef] [PubMed]

Z. L. Horváth, Z. Benkó, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Y. H. Chuang, L. Zheng, and D. D. Meyerhofer, IEEE J. Quantum Electron. 29, 270 (1993).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Lett. 18, 669 (1993).
[CrossRef] [PubMed]

1990 (1)

S. P. Dijaili, A. Dienes, and J. S. Smith, IEEE J. Quantum. Electron. 26, 1158 (1990).
[CrossRef]

1989 (1)

1988 (1)

O. E. Martinez, IEEE J. Quantum. Electron. 24, 2530 (1988); IEEE J. Quantum. Electron. 25, 296 (1989).
[CrossRef]

1987 (1)

1983 (1)

D. Fan, Acta Opt. Sinica 3, 319 (1983).

1962 (2)

Alda, J.

Becker, P. C.

Benkó, Z.

Z. L. Horváth, Z. Benkó, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Bernabeu, E.

Bor, Z.

Z. L. Horváth, Z. Benkó, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 8, pp. 377 and 389.

Brito Cruz, C. H.

Chuang, Y. H.

Y. H. Chuang, L. Zheng, and D. D. Meyerhofer, IEEE J. Quantum Electron. 29, 270 (1993).
[CrossRef]

Davidson, D. B.

R. W. Ziolkowski and D. B. Davidson, Opt. Lett. 4, 284 (1994).
[CrossRef]

Dienes, A.

S. P. Dijaili, A. Dienes, and J. S. Smith, IEEE J. Quantum. Electron. 26, 1158 (1990).
[CrossRef]

Dijaili, S. P.

S. P. Dijaili, A. Dienes, and J. S. Smith, IEEE J. Quantum. Electron. 26, 1158 (1990).
[CrossRef]

Fan, D.

D. Fan, Acta Opt. Sinica 3, 319 (1983).

Fork, R. L.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3, p. 46.

Hazim, H. A.

Z. L. Horváth, Z. Benkó, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Horváth, Z. L.

Z. L. Horváth, Z. Benkó, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Huang, C.

Kapteyn, H. C.

Kempe, M.

M. Kempe and W. Rudolph, Phys. Rev. A 48, 4721 (1993).
[CrossRef] [PubMed]

Kolner, B. H.

Kovács, A. P.

Z. L. Horváth, Z. Benkó, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Krausz, F.

Lin, Q.

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Lett. 18, 669 (1993).
[CrossRef] [PubMed]

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, IEEE J. Quantum Electron. (to be published).

Marchand, E. W.

Martinez, O. E.

O. E. Martinez, IEEE J. Quantum. Electron. 24, 2530 (1988); IEEE J. Quantum. Electron. 25, 296 (1989).
[CrossRef]

Meyerhofer, D. D.

Y. H. Chuang, L. Zheng, and D. D. Meyerhofer, IEEE J. Quantum Electron. 29, 270 (1993).
[CrossRef]

Mukunda, N.

Murnane, M. M.

Rudolph, W.

M. Kempe and W. Rudolph, Phys. Rev. A 48, 4721 (1993).
[CrossRef] [PubMed]

Shank, C. V.

Shi, C.

Smith, J. S.

S. P. Dijaili, A. Dienes, and J. S. Smith, IEEE J. Quantum. Electron. 26, 1158 (1990).
[CrossRef]

Spielmann, C.

Stingl, A.

Szipöcs, R.

Wang, S.

Wang, Z.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, IEEE J. Quantum Electron. (to be published).

Wolf, E.

E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 52, 761 (1962).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 8, pp. 377 and 389.

Xu, Z.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, IEEE J. Quantum Electron. (to be published).

Zhang, Z.

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, IEEE J. Quantum Electron. (to be published).

Zheng, L.

Y. H. Chuang, L. Zheng, and D. D. Meyerhofer, IEEE J. Quantum Electron. 29, 270 (1993).
[CrossRef]

Zhou, J.

Ziolkowski, R. W.

R. W. Ziolkowski and D. B. Davidson, Opt. Lett. 4, 284 (1994).
[CrossRef]

Acta Opt. Sinica (1)

D. Fan, Acta Opt. Sinica 3, 319 (1983).

IEEE J. Quantum Electron. (1)

Y. H. Chuang, L. Zheng, and D. D. Meyerhofer, IEEE J. Quantum Electron. 29, 270 (1993).
[CrossRef]

IEEE J. Quantum. Electron. (2)

S. P. Dijaili, A. Dienes, and J. S. Smith, IEEE J. Quantum. Electron. 26, 1158 (1990).
[CrossRef]

O. E. Martinez, IEEE J. Quantum. Electron. 24, 2530 (1988); IEEE J. Quantum. Electron. 25, 296 (1989).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Eng. (1)

Z. L. Horváth, Z. Benkó, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (1)

M. Kempe and W. Rudolph, Phys. Rev. A 48, 4721 (1993).
[CrossRef] [PubMed]

Other (3)

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, IEEE J. Quantum Electron. (to be published).

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 8, pp. 377 and 389.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3, p. 46.

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Equations (26)

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

U(r,ω)=-12πΣU(r,ω)zexp(iks)sdΩ,
U(r,ω)=-iω2πcΣU(r,ω)exp(iks)cos θsdΩ.
U(r,t)=12πcΣcos θsddtU(r,t-s/c)dΩ,
U(r,t-s/c)=12π-+U(r,ω)exp[iw(t-s/c)]dω.
U(r,τ)=AE(τ)exp(iω0τ),
U(r,t)=iAλ0ΣE(τ)exp(iω0τ)cos θsdΩ-iA2πcΣddtE(τ)exp(iω0τ)cos θsdΩ.
NTω0=δω01,
U(r,t)=iAλ0ΣE(τ)exp(iω0τ)cos θsdΩ.
U(r,t)=iAλ0RΣE(τ)exp(iω0τ)dΩ.
NNcTω01
NTω0λ02πa
E(τ)=A exp-τ22T2expiS2τ2+μ3τ3+,
ddtE(τ)=-τT2+i(Sτ+μτ2+)E(τ)=ω0-1Tω0τT+iΔωLω0τT+ΔωNLω0×τ2T2+E(τ),
ΔωNLω0ΔωLω0δω0=NTω0, 1Tω0NTω0,
sR+x2+y2-2(xx+yy)2R-18[x2+y2-2(xx+yy)]2R3+,
E(τ)=A0 expiω02p(t-s/c)2,
1p=Sω0+iω0T2.
E(τ)=A0 expiω02p(t-R/c)2-(t-R/c)x2+y2-2(xx+yy)cR+x2+y2-2(xx+yy)2cR2.
T·Sω0=Δωω0δω=NTω0, 1Tω0NTω0,
π|x2+y2|maxλ0R=πa2λ0Rπa2λ0z=Nc,
(t-R/c)TNTω0π|x2+y2|maxλ0RNNcTω0,
N(Tω0)2π|x2+y2|maxλ0R2NNc2(Tω0)2,
NNcTω01,
(t-R/c)TNTω0πλ0xx+yyRmax<NTω0πλ0|x+y|max=NTω02πaλ0,
N(Tω0)22π(xx+yy)λ0Rmax2<N(Tω0)2×2πλ02|x2+y2|max=N(Tω0)22πaλ02.
NTω0λ02πa,

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