Abstract

Free-space propagation of ultrashort pulses is investigated. Space–time couplings are reduced for a particular form of beams that is termed a pulse beam, or a type 3 pulsed beam. General conditions for the formation of pulse beams in the paraxial approximation are presented. The free-space propagation of spatially localized ultrashort laser pulses is investigated. This treatment is based on a particular pulsed form of the well-known Bessel beam, which is termed a Bessel pulse beam. The connections with focus wave modes and X waves are discussed.

© 2001 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  5. M. M. Wefers, K. A. Nelson, “Space–time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
    [CrossRef]
  6. A. E. Kaplan, “Diffraction-induced transformation of near-cycle and sub-cycle pulses,” J. Opt. Soc. Am. B 15, 951–956 (1998).
    [CrossRef]
  7. G. P. Agrawal, “Spectrum-induced changes in diffraction of pulsed optical beams,” Opt. Commun. 157, 52–56 (1998).
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  9. C. J. R. Sheppard, X. Gan, “Free-space propagation of femto-second light pulses,” Opt. Commun. 133, 1–6 (1997).
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    [CrossRef]
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    [CrossRef]
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  33. J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, M. M. Salomaa, “Angular spectrum representation of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).
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  36. R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys. 26, 861–863 (1985).
    [CrossRef]
  37. E. Heyman, L. B. Felsen, “Propagating pulsed beam solutions by complex source parameter substitution,” IEEE Trans. Antennas Propag. AP-34, 1062–1065 (1986).
    [CrossRef]
  38. E. Heyman, B. Z. Steinberg, L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A 4, 2081–2091 (1987).
    [CrossRef]
  39. E. Heyman, B. Z. Steinberg, “Spectral analysis of complex-source pulsed beams,” J. Opt. Soc. Am. A 4, 3–10 (1987).
    [CrossRef]
  40. E. Heyman, L. B. Felson, “Complex-source pulsed-beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989).
    [CrossRef]
  41. E. Heyman, “Focus wave modes: a dilemma with causality,” IEEE Trans. Antennas Propag. 37, 1604–1608 (1989).
    [CrossRef]
  42. R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
    [CrossRef] [PubMed]
  43. I. Besieris, A. M. Shaarawi, “A bidirectional traveling wave representation of exact solutions of the scalar wave equation,” J. Math. Phys. 30, 1254–1269 (1989).
    [CrossRef]
  44. R. W. Ziolkowski, I. M. Besieris, A. M. Shaarawi, “Aperture realizations of exact solutions to homogeneous-wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993).
    [CrossRef]
  45. A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, “The propagating and evanescent field components of localized wave solutions,” Opt. Commun. 116, 183–192 (1995).
    [CrossRef]
  46. A. M. Shaarawi, R. W. Ziolkowski, I. M. Besieris, “On the evanescent fields and the causality of the focus wave modes,” J. Math. Phys. 36, 5565–5587 (1995).
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    [CrossRef]
  49. E. H. Linfoot, E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. London Sect. B 66, 145–149 (1953).
    [CrossRef]
  50. A. Yoshida, T. Asakura, “Electromagnetic field in the focal plane of a coherent beam from a wide-angular annular-aperture system,” Optik (Stuttgart) 40, 322–331 (1974).
  51. P. K. Overfelt, “Bessel–Gauss pulses,” Phys. Rev. A 44, 3941–3947 (1991).
    [CrossRef] [PubMed]
  52. A. Yoshida, T. Asakura, “Electromagnetic field near the focus of Gaussian beams,” Optik (Stuttgart) 41, 281–291 (1974).
  53. M. Couture, P.-A. Belanger, “From Gaussian beam to complex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981).
    [CrossRef]
  54. G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
    [CrossRef]
  55. C. J. R. Sheppard, S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
    [CrossRef]
  56. K. Reivelt, P. Saari, “Optical generation of focus wave modes,” J. Opt. Soc. Am. A 17, 1785–1790 (2000).
    [CrossRef]
  57. C. J. R. Sheppard, S. Saghafi, “Electromagnetic Gausssian beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 16, 1381–1386 (1999).
    [CrossRef]

2000

1999

C. J. R. Sheppard, S. Saghafi, “Electromagnetic Gausssian beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 16, 1381–1386 (1999).
[CrossRef]

C. F. R. Caron, R. M. Potvliege, “Free-space propagation of ultrashort pulses: space–time couplings in Gaussian pulse beams,” J. Mod. Opt. 45, 1881–1892 (1999).
[CrossRef]

1998

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

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

Z. Y. Liu, D. Y. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, L17–L21 (1998).
[CrossRef]

S. Saghafi, C. J. R. Sheppard, “Near field and far field of elegant Hermite–Gaussian and Laguerre–Gaussian modes,” J. Mod. Opt. 45, 1999–2009 (1998).
[CrossRef]

A. E. Kaplan, “Diffraction-induced transformation of near-cycle and sub-cycle pulses,” J. Opt. Soc. Am. B 15, 951–956 (1998).
[CrossRef]

S. Feng, H. G. Winful, R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998).
[CrossRef]

C. J. R. Sheppard, S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
[CrossRef]

1997

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

D. You, P. H. Bucksbaum, “Propagation of half-cycle far infrared pulses,” J. Opt. Soc. Am. B 14, 1651–1655 (1997).
[CrossRef]

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, M. M. Salomaa, “Angular spectrum representation of nondiffracting pulses,” Opt. Commun. 136, 207–212 (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]

C. J. R. Sheppard, X. Gan, “Free-space propagation of femto-second light pulses,” Opt. Commun. 133, 1–6 (1997).
[CrossRef]

1996

Z. Wang, Z. Zhang, Z. Xu, Q. Lin, “Spectral and temporal properties of ultrashort light pulses in the far zone,” Opt. Commun. 123, 5–10 (1996).
[CrossRef]

M. M. Wefers, K. A. Nelson, “Space–time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

1995

M. Gu, C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short laser pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

D. E. Edmundson, R. H. Enns, “Particle-like nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995).
[CrossRef] [PubMed]

R. McLeod, K. Wagner, S. Blair, “(3+1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, “The propagating and evanescent field components of localized wave solutions,” Opt. Commun. 116, 183–192 (1995).
[CrossRef]

A. M. Shaarawi, R. W. Ziolkowski, I. M. Besieris, “On the evanescent fields and the causality of the focus wave modes,” J. Math. Phys. 36, 5565–5587 (1995).
[CrossRef]

1993

R. W. Ziolkowski, I. M. Besieris, A. M. Shaarawi, “Aperture realizations of exact solutions to homogeneous-wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993).
[CrossRef]

R. H. Enns, S. S. Rangnekar, “Variational approach to bistable solitary waves of the first kind in d dimensions,” Phys. Rev. E 48, 3998–4007 (1993).
[CrossRef]

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

1992

A. Federico, O. Martinez, “Distortion of femtosecond pulses due to chromatic aberration in lenses,” Opt. Commun. 91, 104–110 (1992).
[CrossRef]

J. Lu, J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free-space scalar wave equations and their finite aperture realizations,” 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]

1991

P. K. Overfelt, “Bessel–Gauss pulses,” Phys. Rev. A 44, 3941–3947 (1991).
[CrossRef] [PubMed]

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

1990

J. A. Campbell, S. Soloway, “Generation of a nondiffracting beam with a frequency independent beam width,” J. Acoust. Soc. Am. 88, 2467–2477 (1990).
[CrossRef]

1989

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

E. Heyman, “Focus wave modes: a dilemma with causality,” IEEE Trans. Antennas Propag. 37, 1604–1608 (1989).
[CrossRef]

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

I. Besieris, A. M. Shaarawi, “A bidirectional traveling wave representation of exact solutions of the scalar wave equation,” J. Math. Phys. 30, 1254–1269 (1989).
[CrossRef]

1987

E. Heyman, B. Z. Steinberg, “Spectral analysis of complex-source pulsed beams,” J. Opt. Soc. Am. A 4, 3–10 (1987).
[CrossRef]

E. Heyman, B. Z. Steinberg, L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A 4, 2081–2091 (1987).
[CrossRef]

F. Gori, G. Guatteri, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

1986

E. Heyman, L. B. Felsen, “Propagating pulsed beam solutions by complex source parameter substitution,” IEEE Trans. Antennas Propag. AP-34, 1062–1065 (1986).
[CrossRef]

1985

A. Sezginer, “A general formulation of focus wave modes,” J. Appl. Phys. 57, 678–683 (1985).
[CrossRef]

R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys. 26, 861–863 (1985).
[CrossRef]

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

1984

1983

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

J. N. Brittingham, “Focus wave modes in homogeneous Maxwell’s equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

1981

M. Couture, P.-A. Belanger, “From Gaussian beam to complex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

1978

C. J. R. Sheppard, “Electromagnetic field in the focal region of wide-angular annular lens and mirror systems,” IEE J. Microwaves Opt. Acoust. 2, 163–166 (1978).
[CrossRef]

C. J. R. Sheppard, T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves Opt. Acoust. 2, 105–112 (1978).
[CrossRef]

1974

J. F. Nye, M. Berry, “Dislocations of wave-fronts,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

A. Yoshida, T. Asakura, “Electromagnetic field near the focus of Gaussian beams,” Optik (Stuttgart) 41, 281–291 (1974).

A. Yoshida, T. Asakura, “Electromagnetic field in the focal plane of a coherent beam from a wide-angular annular-aperture system,” Optik (Stuttgart) 40, 322–331 (1974).

1973

1954

1953

E. H. Linfoot, E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. London Sect. B 66, 145–149 (1953).
[CrossRef]

1872

Lord Rayleigh, “On the diffraction of object glasses,” Mon. Not. R. Astron. Soc. 33, 59–63 (1872).

1841

G. B. Airy, “The diffraction of an annular aperture,” Phil. Mag. Ser. 3 18, 1–10 (1841).

Agrawal, G. P.

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

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

Airy, G. B.

G. B. Airy, “The diffraction of an annular aperture,” Phil. Mag. Ser. 3 18, 1–10 (1841).

Asakura, T.

A. Yoshida, T. Asakura, “Electromagnetic field near the focus of Gaussian beams,” Optik (Stuttgart) 41, 281–291 (1974).

A. Yoshida, T. Asakura, “Electromagnetic field in the focal plane of a coherent beam from a wide-angular annular-aperture system,” Optik (Stuttgart) 40, 322–331 (1974).

Belanger, P.-A.

M. Couture, P.-A. Belanger, “From Gaussian beam to complex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

Bélanger, P. A.

Berry, M.

J. F. Nye, M. Berry, “Dislocations of wave-fronts,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Besieris, I.

I. Besieris, A. M. Shaarawi, “A bidirectional traveling wave representation of exact solutions of the scalar wave equation,” J. Math. Phys. 30, 1254–1269 (1989).
[CrossRef]

Besieris, I. M.

A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, “The propagating and evanescent field components of localized wave solutions,” Opt. Commun. 116, 183–192 (1995).
[CrossRef]

A. M. Shaarawi, R. W. Ziolkowski, I. M. Besieris, “On the evanescent fields and the causality of the focus wave modes,” J. Math. Phys. 36, 5565–5587 (1995).
[CrossRef]

R. W. Ziolkowski, I. M. Besieris, A. M. Shaarawi, “Aperture realizations of exact solutions to homogeneous-wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993).
[CrossRef]

Blagoeva, A. B.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

Blair, S.

R. McLeod, K. Wagner, S. Blair, “(3+1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

Bor, Z. S.

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

Brittingham, J. N.

J. N. Brittingham, “Focus wave modes in homogeneous Maxwell’s equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

Bucksbaum, P. H.

Campbell, J. A.

J. A. Campbell, S. Soloway, “Generation of a nondiffracting beam with a frequency independent beam width,” J. Acoust. Soc. Am. 88, 2467–2477 (1990).
[CrossRef]

Caron, C. F. R.

C. F. R. Caron, R. M. Potvliege, “Free-space propagation of ultrashort pulses: space–time couplings in Gaussian pulse beams,” J. Mod. Opt. 45, 1881–1892 (1999).
[CrossRef]

Christov, I. P.

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

Couture, M.

M. Couture, P.-A. Belanger, “From Gaussian beam to complex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

Dinev, S. G.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

Dreischuh, A. A.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Edmundson, D. E.

D. E. Edmundson, R. H. Enns, “Particle-like nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995).
[CrossRef] [PubMed]

Enns, R. H.

D. E. Edmundson, R. H. Enns, “Particle-like nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995).
[CrossRef] [PubMed]

R. H. Enns, S. S. Rangnekar, “Variational approach to bistable solitary waves of the first kind in d dimensions,” Phys. Rev. E 48, 3998–4007 (1993).
[CrossRef]

Fagerholm, J.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, M. M. Salomaa, “Angular spectrum representation of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).

Fan, D. Y.

Z. Y. Liu, D. Y. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, L17–L21 (1998).
[CrossRef]

Federico, A.

A. Federico, O. Martinez, “Distortion of femtosecond pulses due to chromatic aberration in lenses,” Opt. Commun. 91, 104–110 (1992).
[CrossRef]

Felsen, L. B.

E. Heyman, B. Z. Steinberg, L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A 4, 2081–2091 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Propagating pulsed beam solutions by complex source parameter substitution,” IEEE Trans. Antennas Propag. AP-34, 1062–1065 (1986).
[CrossRef]

Felson, L. B.

Feng, S.

Friberg, A. T.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, M. M. Salomaa, “Angular spectrum representation of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).

Gan, X.

C. J. R. Sheppard, X. Gan, “Free-space propagation of femto-second light pulses,” Opt. Commun. 133, 1–6 (1997).
[CrossRef]

Gori, F.

F. Gori, G. Guatteri, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Greenleaf, J. F.

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

Gu, M.

M. Gu, C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short laser pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

Guatteri, G.

F. Gori, G. Guatteri, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Hellwarth, R. W.

Heyman, E.

E. Heyman, “Focus wave modes: a dilemma with causality,” IEEE Trans. Antennas Propag. 37, 1604–1608 (1989).
[CrossRef]

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

E. Heyman, B. Z. Steinberg, L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A 4, 2081–2091 (1987).
[CrossRef]

E. Heyman, B. Z. Steinberg, “Spectral analysis of complex-source pulsed beams,” J. Opt. Soc. Am. A 4, 3–10 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Propagating pulsed beam solutions by complex source parameter substitution,” IEEE Trans. Antennas Propag. AP-34, 1062–1065 (1986).
[CrossRef]

Horváth, Z. L.

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

Huttunen, J.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, M. M. Salomaa, “Angular spectrum representation of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).

Judkins, J. B.

Kaplan, A. E.

Lax, M.

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

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]

Z. Wang, Z. Zhang, Z. Xu, Q. Lin, “Spectral and temporal properties of ultrashort light pulses in the far zone,” Opt. Commun. 123, 5–10 (1996).
[CrossRef]

Linfoot, E. H.

E. H. Linfoot, E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. London Sect. B 66, 145–149 (1953).
[CrossRef]

Liu, Z. Y.

Z. Y. Liu, D. Y. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, L17–L21 (1998).
[CrossRef]

Lu, J.

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

Martinez, O.

A. Federico, O. Martinez, “Distortion of femtosecond pulses due to chromatic aberration in lenses,” Opt. Commun. 91, 104–110 (1992).
[CrossRef]

McLeod, J. H.

McLeod, R.

R. McLeod, K. Wagner, S. Blair, “(3+1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Morgan, D. P.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, M. M. Salomaa, “Angular spectrum representation of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).

Naidenov, A.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

Nelson, K. A.

M. M. Wefers, K. A. Nelson, “Space–time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

Nye, J. F.

J. F. Nye, M. Berry, “Dislocations of wave-fronts,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Overfelt, P. K.

P. K. Overfelt, “Bessel–Gauss pulses,” Phys. Rev. A 44, 3941–3947 (1991).
[CrossRef] [PubMed]

Padovani, C.

F. Gori, G. Guatteri, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Porras, M. A.

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

Potvliege, R. M.

C. F. R. Caron, R. M. Potvliege, “Free-space propagation of ultrashort pulses: space–time couplings in Gaussian pulse beams,” J. Mod. Opt. 45, 1881–1892 (1999).
[CrossRef]

Rangnekar, S. S.

R. H. Enns, S. S. Rangnekar, “Variational approach to bistable solitary waves of the first kind in d dimensions,” Phys. Rev. E 48, 3998–4007 (1993).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “On the diffraction of object glasses,” Mon. Not. R. Astron. Soc. 33, 59–63 (1872).

Reivelt, K.

Saari, P.

Saghafi, S.

C. J. R. Sheppard, S. Saghafi, “Electromagnetic Gausssian beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 16, 1381–1386 (1999).
[CrossRef]

S. Saghafi, C. J. R. Sheppard, “Near field and far field of elegant Hermite–Gaussian and Laguerre–Gaussian modes,” J. Mod. Opt. 45, 1999–2009 (1998).
[CrossRef]

C. J. R. Sheppard, S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
[CrossRef]

Salomaa, M. M.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, M. M. Salomaa, “Angular spectrum representation of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).

Sezginer, A.

A. Sezginer, “A general formulation of focus wave modes,” J. Appl. Phys. 57, 678–683 (1985).
[CrossRef]

Shaarawi, A. M.

A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, “The propagating and evanescent field components of localized wave solutions,” Opt. Commun. 116, 183–192 (1995).
[CrossRef]

A. M. Shaarawi, R. W. Ziolkowski, I. M. Besieris, “On the evanescent fields and the causality of the focus wave modes,” J. Math. Phys. 36, 5565–5587 (1995).
[CrossRef]

R. W. Ziolkowski, I. M. Besieris, A. M. Shaarawi, “Aperture realizations of exact solutions to homogeneous-wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993).
[CrossRef]

I. Besieris, A. M. Shaarawi, “A bidirectional traveling wave representation of exact solutions of the scalar wave equation,” J. Math. Phys. 30, 1254–1269 (1989).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, S. Saghafi, “Electromagnetic Gausssian beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 16, 1381–1386 (1999).
[CrossRef]

S. Saghafi, C. J. R. Sheppard, “Near field and far field of elegant Hermite–Gaussian and Laguerre–Gaussian modes,” J. Mod. Opt. 45, 1999–2009 (1998).
[CrossRef]

C. J. R. Sheppard, S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
[CrossRef]

C. J. R. Sheppard, X. Gan, “Free-space propagation of femto-second light pulses,” Opt. Commun. 133, 1–6 (1997).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short laser pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

C. J. R. Sheppard, “Electromagnetic field in the focal region of wide-angular annular lens and mirror systems,” IEE J. Microwaves Opt. Acoust. 2, 163–166 (1978).
[CrossRef]

C. J. R. Sheppard, T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves Opt. Acoust. 2, 105–112 (1978).
[CrossRef]

Siegman, A. E.

Soloway, S.

J. A. Campbell, S. Soloway, “Generation of a nondiffracting beam with a frequency independent beam width,” J. Acoust. Soc. Am. 88, 2467–2477 (1990).
[CrossRef]

Steinberg, B. Z.

Wagner, K.

R. McLeod, K. Wagner, S. Blair, “(3+1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

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]

Z. Wang, Z. Xu, 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, Q. Lin, “Spectral and temporal properties of ultrashort light pulses in the far zone,” Opt. Commun. 123, 5–10 (1996).
[CrossRef]

Wefers, M. M.

M. M. Wefers, K. A. Nelson, “Space–time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

Wilson, T.

C. J. R. Sheppard, T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves Opt. Acoust. 2, 105–112 (1978).
[CrossRef]

Winful, H. G.

Wolf, E.

E. H. Linfoot, E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. London Sect. B 66, 145–149 (1953).
[CrossRef]

Xu, Z.

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

Z. Wang, Z. Zhang, Z. Xu, Q. Lin, “Spectral and temporal properties of ultrashort light pulses in the far zone,” Opt. Commun. 123, 5–10 (1996).
[CrossRef]

Yoshida, A.

A. Yoshida, T. Asakura, “Electromagnetic field near the focus of Gaussian beams,” Optik (Stuttgart) 41, 281–291 (1974).

A. Yoshida, T. Asakura, “Electromagnetic field in the focal plane of a coherent beam from a wide-angular annular-aperture system,” Optik (Stuttgart) 40, 322–331 (1974).

You, D.

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]

Z. Wang, Z. Xu, 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, Q. Lin, “Spectral and temporal properties of ultrashort light pulses in the far zone,” Opt. Commun. 123, 5–10 (1996).
[CrossRef]

Ziolkowski, R. W.

A. M. Shaarawi, R. W. Ziolkowski, I. M. Besieris, “On the evanescent fields and the causality of the focus wave modes,” J. Math. Phys. 36, 5565–5587 (1995).
[CrossRef]

A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, “The propagating and evanescent field components of localized wave solutions,” Opt. Commun. 116, 183–192 (1995).
[CrossRef]

R. W. Ziolkowski, I. M. Besieris, A. M. Shaarawi, “Aperture realizations of exact solutions to homogeneous-wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993).
[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]

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

R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys. 26, 861–863 (1985).
[CrossRef]

IEE J. Microwaves Opt. Acoust.

C. J. R. Sheppard, T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves Opt. Acoust. 2, 105–112 (1978).
[CrossRef]

C. J. R. Sheppard, “Electromagnetic field in the focal region of wide-angular annular lens and mirror systems,” IEE J. Microwaves Opt. Acoust. 2, 163–166 (1978).
[CrossRef]

IEEE J. Quantum Electron.

M. M. Wefers, K. A. Nelson, “Space–time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

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]

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, A. Naidenov, “Light bullets formation in a bulk media,” IEEE J. Quantum Electron. 27, 2060–2065 (1991).
[CrossRef]

IEEE Trans. Antennas Propag.

E. Heyman, L. B. Felsen, “Propagating pulsed beam solutions by complex source parameter substitution,” IEEE Trans. Antennas Propag. AP-34, 1062–1065 (1986).
[CrossRef]

E. Heyman, “Focus wave modes: a dilemma with causality,” IEEE Trans. Antennas Propag. 37, 1604–1608 (1989).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

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

J. Acoust. Soc. Am.

J. A. Campbell, S. Soloway, “Generation of a nondiffracting beam with a frequency independent beam width,” J. Acoust. Soc. Am. 88, 2467–2477 (1990).
[CrossRef]

J. Appl. Phys.

A. Sezginer, “A general formulation of focus wave modes,” J. Appl. Phys. 57, 678–683 (1985).
[CrossRef]

J. N. Brittingham, “Focus wave modes in homogeneous Maxwell’s equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

J. Math. Phys.

R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys. 26, 861–863 (1985).
[CrossRef]

I. Besieris, A. M. Shaarawi, “A bidirectional traveling wave representation of exact solutions of the scalar wave equation,” J. Math. Phys. 30, 1254–1269 (1989).
[CrossRef]

A. M. Shaarawi, R. W. Ziolkowski, I. M. Besieris, “On the evanescent fields and the causality of the focus wave modes,” J. Math. Phys. 36, 5565–5587 (1995).
[CrossRef]

J. Mod. Opt.

S. Saghafi, C. J. R. Sheppard, “Near field and far field of elegant Hermite–Gaussian and Laguerre–Gaussian modes,” J. Mod. Opt. 45, 1999–2009 (1998).
[CrossRef]

Z. Y. Liu, D. Y. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, L17–L21 (1998).
[CrossRef]

C. F. R. Caron, R. M. Potvliege, “Free-space propagation of ultrashort pulses: space–time couplings in Gaussian pulse beams,” J. Mod. Opt. 45, 1881–1892 (1999).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short laser pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Mon. Not. R. Astron. Soc.

Lord Rayleigh, “On the diffraction of object glasses,” Mon. Not. R. Astron. Soc. 33, 59–63 (1872).

Opt. Commun.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, M. M. Salomaa, “Angular spectrum representation of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).

F. Gori, G. Guatteri, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

C. J. R. Sheppard, X. Gan, “Free-space propagation of femto-second light pulses,” Opt. Commun. 133, 1–6 (1997).
[CrossRef]

Z. Wang, Z. Zhang, Z. Xu, Q. Lin, “Spectral and temporal properties of ultrashort light pulses in the far zone,” Opt. Commun. 123, 5–10 (1996).
[CrossRef]

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

A. Federico, O. Martinez, “Distortion of femtosecond pulses due to chromatic aberration in lenses,” Opt. Commun. 91, 104–110 (1992).
[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]

A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, “The propagating and evanescent field components of localized wave solutions,” Opt. Commun. 116, 183–192 (1995).
[CrossRef]

Opt. Lett.

Optik (Stuttgart)

A. Yoshida, T. Asakura, “Electromagnetic field near the focus of Gaussian beams,” Optik (Stuttgart) 41, 281–291 (1974).

A. Yoshida, T. Asakura, “Electromagnetic field in the focal plane of a coherent beam from a wide-angular annular-aperture system,” Optik (Stuttgart) 40, 322–331 (1974).

Phil. Mag. Ser. 3

G. B. Airy, “The diffraction of an annular aperture,” Phil. Mag. Ser. 3 18, 1–10 (1841).

Phys. Rev. A

D. E. Edmundson, R. H. Enns, “Particle-like nature of colliding three-dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995).
[CrossRef] [PubMed]

R. McLeod, K. Wagner, S. Blair, “(3+1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

P. K. Overfelt, “Bessel–Gauss pulses,” Phys. Rev. A 44, 3941–3947 (1991).
[CrossRef] [PubMed]

M. Couture, P.-A. Belanger, “From Gaussian beam to complex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

C. J. R. Sheppard, S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
[CrossRef]

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

Phys. Rev. E

R. H. Enns, S. S. Rangnekar, “Variational approach to bistable solitary waves of the first kind in d dimensions,” Phys. Rev. E 48, 3998–4007 (1993).
[CrossRef]

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

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Proc. Phys. Soc. London Sect. B

E. H. Linfoot, E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. London Sect. B 66, 145–149 (1953).
[CrossRef]

Proc. R. Soc. London Ser. A

J. F. Nye, M. Berry, “Dislocations of wave-fronts,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Variation in intensity in a transverse plane for a Bessel pulse beam for t=0 for three values of parameter s.

Fig. 2
Fig. 2

Variation in intensity, shown on a logarithmic plot, in a transverse plane for a Bessel pulse beam for t=0 for several values of parameter s.

Fig. 3
Fig. 3

Amplitude pulse shape on the axis for Bessel pulse beams for three values of s.

Fig. 4
Fig. 4

Amplitude pulse shape for Bessel pulse beams for various distances from the axis when s=1, showing that the pulse shape can become distorted.

Fig. 5
Fig. 5

Instantaneous intensity in an azimuthal cross section through a type 3 Bessel pulse for u=0, showing that the pulse is well behaved.

Fig. 6
Fig. 6

Angular spectrum of the focus wave mode for several values of the parameters k0z0 and s.

Equations (26)

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

f(ω)=[(s+1)ω/ω1]s+1ωΓ(s+1) exp-(s+1) ωω1,ω>0,
U(x, y, z; ω)=1λf -+P(x0, y0; ω)expikz2f2(x02+y02)×exp-ikf(xx0+yy0)exp(ikz)dx0dy0,
U˜(x, y, z; t)=12πfc -+ P(x0, y0; ω)expikz2f2(x02+y02)×exp-ikf(xx0+yy0)×exp[i(kz-ωt)]f(ω)ωdx0dy0dω,
t=t-z/c,
k(x02+y02)=k1(x012+y012),
P(x0, y0, ω)=Q(x01, y01)
x1=k/k1x,y1=k/k1y,
F(t)=-+f(ω)exp(-iωt)dω.
U˜(x1, y1, z1; t)=k12πfF(t)-+Q(x01, y01)expik1z2f2(x012+y012)×exp-ik1f(x1x01+y1y01)dx01dy01,
U(r, z)=J0(kr sin θ)exp(ikz cos θ)exp(-iωt)=J0(kr sin θ)exp-2ikz sin2 θ2exp(-iωt),
U(r, z, t)=-+J0(kr sin θ)×exp-2ikz sin2 θ2f(ω)exp(-iωt)dω.
Ω=ω/ω1=θ12/θ2
v=k1rθ1,
u=k1zθ12,
U(v, u, t)=(s+1)s+1Γ(s+1) exp-iu20J0(vΩ)×exp[-(s+1)Ω]exp(-iΩω1t)ΩsdΩ.
U(v, u, t)=s+1(s+1)+iω1(t-z/c)exp-iu2×Lsv24[(s+1)+iω1t]×exp-v24[(s+1)+iω1t],
U(ρ, z, t)=k02πz0 exp[k0(z0-2iz)]×exp[-k(z0-iz)]×J0{2ρ[k0(k-k0)]1/2}exp(-ikct)dk,
U(ρ, z)=k02πz0 exp[-(k-k0)z0]J0[kρ sin θ(k)]×exp[ikz cos θ(k)]exp(-ikct)dk,
k sin2θ(k)2=k0,
f(k)dk=z0 exp[-(k-k0)z0]dk,
a(θ)cos θ2 csc2 θ2 dθ=exp-k0z0 cot2 θ2cot θ2 csc2 θ2 dθ.
p2=cot2 θ2=k-k0k0,
U(ρ, z)=2πk0z0 exp[-ik0(z+ct)]k02g(p)×J0(2k0ρp)exp(-ik0ctp2)pdp,
g(p)pdp=exp(-k0z0p2)pdp.
f(k)=z0(s+1)Γ(s+1)[(k-k0)z0]s exp[-(k-k0)z0],
g(p)=(s+1)Γ(s+1)(k0z0p2)s exp(-k0z0p2)=(-1)s(s+1)Ls-s(k0z0p2)exp(-k0z0p2),

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