Abstract

A family of special solutions of the paraxially pulsed wave equation is presented in closed form by use of the Fourier-transform method. These special solutions have the negative-power-function forms of a simple complex temporal–spatial beam parameter P. The imaginary part and the real part of the parameter P explicitly reveal the time delay and the pulse broadening, respectively. These pulsed negative-power-function light beams are used analytically to expand those isodiffracting pulsed beams.

© 1999 Optical Society of America

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References

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    [CrossRef]
  2. Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
    [CrossRef]
  3. M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
    [CrossRef] [PubMed]
  4. Z. L. Horváth and Z. Bor, “Focusing of femtosecond pulses having gaussian spatial distribution,” Opt. Commun. 100, 6–12 (1993).
    [CrossRef]
  5. R. W. Ziolkowski and D. B. Davidson, “Designer pulsed beams for enhanced space–time focusing,” Opt. Lett. 19, 284–286 (1994).
    [CrossRef] [PubMed]
  6. A. S. Marathay, “Propagation of optical pulses with spatial and temporal dependence,” Appl. Opt. 33, 3139–3145 (1994).
    [CrossRef] [PubMed]
  7. E. Ibragimov, “Focusing of ultrashort laser pulses by the combination of diffractive and refractive elements,” Appl. Opt. 34, 7280–7285 (1995).
    [CrossRef] [PubMed]
  8. J. Paye and A. Migus, “Space–time Wigner functions and their application to the analysis of a pulse shaper,” J. Opt. Soc. Am. B 12, 1480–1490 (1995).
    [CrossRef]
  9. M. Gu and X. S. Gan, “Fresnel diffraction by circular and serrated apertures illuminated with an ultrashort pulsed-laser beam,” J. Opt. Soc. Am. A 13, 771–778 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53, 364–366 (1985).
    [CrossRef]
  13. R. W. Ziolkowski and J. B. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021–2030 (1992).
    [CrossRef]
  14. Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
    [CrossRef]
  15. M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
    [CrossRef]
  16. E. Heyman and L. B. Felsen, “Complex-source pulsed-beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989).
    [CrossRef]
  17. T. Melamed and L. B. Felsen, “Pulsed-beam propagation in lossless dispersive media. I. Theory,” J. Opt. Soc. Am. A 15, 1268–1276 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
  19. R. W. Hellwarth and P. Nouchi, “Focused one-cycle electromagnetic pulses,” Phys. Rev. E 54, 889–895 (1996).
    [CrossRef]
  20. S. Feng, H. G. Winful, and R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998).
    [CrossRef]
  21. See, for example, M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997).
    [CrossRef] [PubMed]
  22. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 494–499.
  23. Q. Cao and X. Deng, “Spatial parametric characterization of general polychromatic light beams,” Opt. Commun. 142, 135–145 (1997).
    [CrossRef]

1998

1997

Z. Wang, Z. Xu, and Z. Zhang, “Diffraction integral formulas of the pulsed wave field in the temporal domain,” Opt. Lett. 22, 354–356 (1997).
[CrossRef] [PubMed]

See, for example, M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997).
[CrossRef] [PubMed]

Q. Cao and X. Deng, “Spatial parametric characterization of general polychromatic light beams,” Opt. Commun. 142, 135–145 (1997).
[CrossRef]

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
[CrossRef]

1996

1995

1994

1993

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[CrossRef] [PubMed]

Z. L. Horváth and Z. Bor, “Focusing of femtosecond pulses having gaussian spatial distribution,” Opt. Commun. 100, 6–12 (1993).
[CrossRef]

1992

1989

E. Heyman and L. B. Felsen, “Complex-source pulsed-beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989).
[CrossRef]

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
[CrossRef] [PubMed]

1985

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53, 364–366 (1985).
[CrossRef]

Anderson, J. M.

Bor, Z.

Z. L. Horváth and Z. Bor, “Focusing of femtosecond pulses having gaussian spatial distribution,” Opt. Commun. 100, 6–12 (1993).
[CrossRef]

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

Cao, Q.

Q. Cao and X. Deng, “Spatial parametric characterization of general polychromatic light beams,” Opt. Commun. 142, 135–145 (1997).
[CrossRef]

Christov, I. P.

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53, 364–366 (1985).
[CrossRef]

Davidson, D. B.

De Silvestri, S.

Deng, X.

Q. Cao and X. Deng, “Spatial parametric characterization of general polychromatic light beams,” Opt. Commun. 142, 135–145 (1997).
[CrossRef]

Felsen, L. B.

Feng, S.

Ferencz, K.

Gan, X. S.

Gu, M.

Hellwarth, R. W.

Heyman, E.

Horváth, Z. L.

Z. L. Horváth and Z. Bor, “Focusing of femtosecond pulses having gaussian spatial distribution,” Opt. Commun. 100, 6–12 (1993).
[CrossRef]

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

Ibragimov, E.

Judkins, J. B.

Kempe, M.

Krausz, F.

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, 566–573 (1997).
[CrossRef]

Marathay, A. S.

Melamed, T.

Migus, A.

Nisoli, M.

Nouchi, P.

R. W. Hellwarth and P. Nouchi, “Focused one-cycle electromagnetic pulses,” Phys. Rev. E 54, 889–895 (1996).
[CrossRef]

Paye, J.

Porras, M. A.

M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
[CrossRef]

Roychoudhuri, C.

Rudolph, W.

Sartania, S.

Spielmann, C.

Stamm, U.

Svelto, O.

Szipöcs, R.

Wang, Z.

Z. Wang, Z. Xu, and Z. Zhang, “Diffraction integral formulas of the pulsed wave field in the temporal domain,” Opt. Lett. 22, 354–356 (1997).
[CrossRef] [PubMed]

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
[CrossRef]

Wilhelmi, B.

Winful, H. G.

Xu, Z.

Z. Wang, Z. Xu, and Z. Zhang, “Diffraction integral formulas of the pulsed wave field in the temporal domain,” Opt. Lett. 22, 354–356 (1997).
[CrossRef] [PubMed]

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
[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, 566–573 (1997).
[CrossRef]

Z. Wang, Z. Xu, and Z. Zhang, “Diffraction integral formulas of the pulsed wave field in the temporal domain,” Opt. Lett. 22, 354–356 (1997).
[CrossRef] [PubMed]

Ziolkowski, R. W.

Appl. Opt.

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, 566–573 (1997).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
[CrossRef]

Z. L. Horváth and Z. Bor, “Focusing of femtosecond pulses having gaussian spatial distribution,” Opt. Commun. 100, 6–12 (1993).
[CrossRef]

I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53, 364–366 (1985).
[CrossRef]

Q. Cao and X. Deng, “Spatial parametric characterization of general polychromatic light beams,” Opt. Commun. 142, 135–145 (1997).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[CrossRef] [PubMed]

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
[CrossRef] [PubMed]

Phys. Rev. E

R. W. Hellwarth and P. Nouchi, “Focused one-cycle electromagnetic pulses,” Phys. Rev. E 54, 889–895 (1996).
[CrossRef]

M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 494–499.

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Equations (23)

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2x2+2y2V-1c22Vt2+2Vz2=0,
ψ(fx, fy, ν, z)=ψ(fx, fy, ν, 0)expi2πzνc-cf22ν
ψ(fx, fy, ν, z)=-V(x, y, t, z)×exp[-i2π(fxx+fyy-νt)]dxdydt.
ϕ(x, y, t, z)=20 φ(x, y, ν, z)exp(-i2πνt)dν,
φ(x, y, ν, z)=- V(x, y, t, z)exp(i2πνt)dt.
ϕ(x, y, ν, z)=- ψ(fx, fy, ν, z)×exp[i2π(fxx+fyy)]dfxdfy.
V(x, y, t, z)=Re[ϕ(x, y, t, z)].
2ϕzt+1c2ϕt2-c22x2+2y2ϕ=0.
i2kAz+2x2+2y2A=0,
ψn(fx, fy, ν, 0)=νn-1 exp(-aν)exp-bf2ν,
- exp[-(αu2+2βu)]du=πα expβ2α,
φn(x, y, ν, z)=πνnb+iπzcexp-a-i2πzcν×exp-π2r2νb+iπzc,
0 um exp(-αu)du=m!αm+1,
ϕn(x, y, t, z)=2πn!P-(n+1)b+iπzc,
P=a+i2πτ+π2r2b+iπzc,
1q=iπcb+iπzc;
ϕn(x, y, t, z)=-i2n!P-(n+1)qc,
P=a+πr2cIm1q+i2πτ-r22cR.
φ(x, y, ν, z)=g(ν)πb+iπzc×expi2πzcνexp-π2r2νb+iπzc,
g(ν)=n=0 gnνn(0ν<).
g(ν)=n=0 Cnνn exp(-aν),
Cn=m=0ngman-m(n-m)!.
ϕ(x, y, t, z)=n=0 Cnϕn(x, y, t, z),

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