Abstract

A detailed study of ultrashort pulsed Bessel beams in linear dispersive media is performed. The spatial and temporal parts of pulsed Jn beams are separable in dispersive media, provided that the parameter α is independent of frequency ω. The spatial part keeps the Jn shape unchanged during propagation. The temporal evolution behavior of pulsed Jn beams depends on the material’s dispersion and diffraction. The pulses can be broadening and become negatively chirped while propagating in anomalous dispersive media. In normal dispersive media, the pulses can be broadening and positively or negatively chirped; even dispersion-free propagation can be achieved if the beam and material parameters are suitably chosen. The condition under which higher-order dispersive effects can be neglected is also discussed.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  6. R. W. Ziolkowski, J. B. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021–2030 (1992).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. M. A. Porras, “Nonsinusoidal few-cycle pulsed light beams in free space,” J. Opt. Soc. Am. B 16, 1468–1474 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2002

2001

2000

M. A. Porras, R. Borghi, M. Santarsiero, “Few-optical-cycle Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
[CrossRef]

1999

1998

I. P. Bilinsky, J. G. Fujimoto, J. N. Walpole, L. J. Missaggia, “Semiconductor-doped-silica saturable-absorber films for solid-state laser mode locking,” Opt. Lett. 23, 1766–1768 (1998).
[CrossRef]

G. P. Agrawal, “Spectrum-induced changes in diffraction of pulsed optical beams,” Opt. Commun. 157, 52–56 (1998).
[CrossRef]

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

Z. Y. Liu, D. Y. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, 17–21 (1998).
[CrossRef]

1997

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

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

T. Brabec, F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

1995

1992

J. Lu, J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free space scalar wave equation and their finite aperture realization,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
[CrossRef]

R. W. Ziolkowski, J. B. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021–2030 (1992).
[CrossRef]

1985

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

1965

Agrawal, G. P.

G. P. Agrawal, “Far-field diffraction of pulsed optical beams in dispersive media,” Opt. Commun. 167, 15–22 (1999).
[CrossRef]

G. P. Agrawal, “Spectrum-induced changes in diffraction of pulsed optical beams,” Opt. Commun. 157, 52–56 (1998).
[CrossRef]

See, e.g., G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997).

Angelow, G.

Bilinsky, I. P.

Borghi, R.

M. A. Porras, R. Borghi, M. Santarsiero, “Few-optical-cycle Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
[CrossRef]

Brabec, T.

T. Brabec, F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

Chen, Y.

Cho, S. H.

Christov, I. P.

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

De Silvestri, S.

Fan, D. Y.

Z. Y. Liu, D. Y. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, 17–21 (1998).
[CrossRef]

Feng, S.

S. Feng, H. G. Winful, “Spatiotemporal transformation of isodiffracting ultrashort pulses by nondispersive quadratic phase media,” J. Opt. Soc. Am. A 16, 2500–2509 (1999).
[CrossRef]

S. Feng, H. G. Winful, R. W. Hellwarth, “Spatiotemporal evolution of focused single-cycle electromagnetic pulses,” Phys. Rev. E 59, 4630–4649 (1999).
[CrossRef]

Ferencz, K.

Fujimoto, J. G.

Gallmann, L.

Genoud, F. M.

Greenleaf, J. F.

J. Lu, J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free space scalar wave equation and their finite aperture realization,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
[CrossRef]

Guo, H.

Haus, H. A.

Hellwarth, R. W.

S. Feng, H. G. Winful, R. W. Hellwarth, “Spatiotemporal evolution of focused single-cycle electromagnetic pulses,” Phys. Rev. E 59, 4630–4649 (1999).
[CrossRef]

Hu, W.

Ibragimov, E.

Ippen, E. P.

Judkins, J. B.

Kärtner, F. X.

Keller, U.

Krausz, F.

Lin, Q.

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

Liu, Z. Y.

Z. Y. Liu, D. Y. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, 17–21 (1998).
[CrossRef]

Lu, J.

J. Lu, J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free space scalar wave equation and their finite aperture realization,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
[CrossRef]

Malitson, I. H.

Mandel, L.

See, e.g., L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).

Matuschek, N.

Missaggia, L. J.

Morgner, U.

Nisoli, M.

Porras, M. A.

M. A. Porras, “Diffraction-free and dispersion-free pulsed beam propagation in dispersive media,” Opt. Lett. 26, 1364–1366 (2001).
[CrossRef]

M. A. Porras, R. Borghi, M. Santarsiero, “Few-optical-cycle Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
[CrossRef]

M. A. Porras, “Nonsinusoidal few-cycle pulsed light beams in free space,” J. Opt. Soc. Am. B 16, 1468–1474 (1999).
[CrossRef]

M. A. Porras, “Propagation of single-cycle pulse light beams in dispersive media,” Phys. Rev. A 60, 5069–5073 (1999).
[CrossRef]

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

Santarsiero, M.

M. A. Porras, R. Borghi, M. Santarsiero, “Few-optical-cycle Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
[CrossRef]

Sartania, S.

Scheuer, V.

Sheppard, C. J. R.

Spielmann, C.

Steinmeyer, G.

Sutter, D. H.

Svelto, O.

Szipöcs, R.

Tschudi, T.

Walpole, J. N.

Wang, Z.

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

Winful, H. G.

S. Feng, H. G. Winful, “Spatiotemporal transformation of isodiffracting ultrashort pulses by nondispersive quadratic phase media,” J. Opt. Soc. Am. A 16, 2500–2509 (1999).
[CrossRef]

S. Feng, H. G. Winful, R. W. Hellwarth, “Spatiotemporal evolution of focused single-cycle electromagnetic pulses,” Phys. Rev. E 59, 4630–4649 (1999).
[CrossRef]

Wolf, E.

See, e.g., L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).

Xu, Z.

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

Ziolkowski, R. W.

Appl. Opt.

IEEE J. Quantum Electron.

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

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

J. Lu, J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free space scalar wave equation and their finite aperture realization,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
[CrossRef]

J. Mod. Opt.

Z. Y. Liu, D. Y. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, 17–21 (1998).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

G. P. Agrawal, “Far-field diffraction of pulsed optical beams in dispersive media,” Opt. Commun. 167, 15–22 (1999).
[CrossRef]

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

G. P. Agrawal, “Spectrum-induced changes in diffraction of pulsed optical beams,” Opt. Commun. 157, 52–56 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. A. Porras, “Propagation of single-cycle pulse light beams in dispersive media,” Phys. Rev. A 60, 5069–5073 (1999).
[CrossRef]

Phys. Rev. E

S. Feng, H. G. Winful, R. W. Hellwarth, “Spatiotemporal evolution of focused single-cycle electromagnetic pulses,” Phys. Rev. E 59, 4630–4649 (1999).
[CrossRef]

M. A. Porras, R. Borghi, M. Santarsiero, “Few-optical-cycle Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
[CrossRef]

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

Phys. Rev. Lett.

T. Brabec, F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

Other

See, e.g., L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).

See, e.g., G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997).

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Figures (7)

Fig. 1
Fig. 1

β2 as a function of transverse spatial parameter γ. The calculation parameters are given in the text.

Fig. 2
Fig. 2

Broadening factor δ as a function of propagation distance z. (a) p=4, (b) p=6.

Fig. 3
Fig. 3

Variation of the carrier frequency ω0 with local time τ. (a) p=4, (b) p=6.

Fig. 4
Fig. 4

Pulse forms of a pulsed Jn beam for γ=1.5°. (a) z=0, (b) z=0.2 mm, (c) z=0.4 mm.

Fig. 5
Fig. 5

Pulse forms of a pulsed Jn beam for γ=10.4°. (a) z=0, (b) z=0.2 mm, (c) z=0.4 mm.

Fig. 6
Fig. 6

Normalized dispersion lengths L2/λ0, L3/λ0 versus transverse spatial parameter γ (a) in anomalous dispersive medium, (b) in normal dispersive medium.

Fig. 7
Fig. 7

Contour lines of L3/L2 (a) in anomalous dispersive medium, (b) in normal dispersive medium.

Equations (27)

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[2+k(ω)2]Eˆ(x, y, z, ω)=0,
k(ω)=n(ω)ω/c.
Eˆ(r, z, ω)=Jn(αr)exp[iβ(ω)z+inϕ]S(ω),
β(ω)=[k2(ω)-α2]1/2,
β(ω)=β0+m=1βmm!(ω-ω0)m,
Eˆ(r, z, ω)=Jn(αr)S(ω)exp(inϕ)×expizβ0+m=1βmm!(ω-ω0)m.
E(r, z, t)=12πJn(αr)exp(inϕ)×-+expizβ0+m=1βmm!(ω-ω0)m×S(ω)exp(-iωt)dω.
E(r, z, t)=A(r, z, t)exp[i(β0z-ω0t)].
A(r, z, t)=12πJn(αr)exp(inϕ)×-+expizm=1βmm!Δωm×S(Δω+ω0)exp(-iΔωt)dΔω,
A(r, z, t)=Jn(αr)ψ(z, t),
ψ(z, t)=12π-+expizm=1βmm!Δωm×exp(inϕ)S(Δω+ω0)exp(-iΔωt)dΔω.
S(ω)=T2agexp-T2(ω-ω0)24ag2,
ψ(z, t)=Tag(T2/ag2-2iβ2z)-1/2 exp(inϕ)×exp-(t-β1z)2T2/ag2+4β22z2/(T2/ag2)×exp-2iβ2z(t-β1z)2T4/ag4+4β22z2.
β1=k1/cosγ
β2=k2/cosγ+[1/(k0 cosγ)-1/(k0 cos3 γ)]k12,
n2(λ)=1+i=13Bi1-λi2/λ2,
tanγ<k0k2/k1,
δ=(1+4ag4β22z2/T4)1/2,
ω0=ω0+4β2z(t-β1z)T4/ag4+4β22z2,
tp=k1z/cosγ.
tanγ=k0k2/k1,
tanγ>k0k2/k1,
S(ω)=π2TassechπT2as(ω-ω0),
E(r, z, t)=T2asJn(αr)exp(inϕ)×-+expizβ0+β1(ω-ω0)+β22(ω-ω0)2sechπT2as(ω-ω0)×exp(-iωt)dω.
L2=T2/|β2|,
L3=T3/|β3|,
β3=k3/cosγ+3k1k2/k0(1/cosγ-1/cos3 γ)+3k13/k02(1/cos5 γ-1/cos3 γ).

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