Abstract

The focal distribution produced by a zone plate under ultrashort pulsed laser illumination is investigated under the Fresnel approximation. A comparison of the diffraction patterns in the focal region between pulsed and continuous-wave illumination shows that the focal shape produced by a zone plate can be significantly altered when an ultrashort pulse is shorter than 100 fs. In particular, the focal width in the axial and the transverse directions is increased by approximately 5% and 85%, respectively, from continuous-wave illumination to 10-fs pulsed illumination.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. Z. Horvath, Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63, 026601-1–026601-11 (2001).
    [CrossRef]
  4. M. Gu, X. 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]
  5. H. Ichikawa, “Analysis of femtosecond-order optical pulses diffracted by periodic structure,” J. Opt. Soc. Am. A 16, 299–304 (1999).
    [CrossRef]
  6. M. Gu, X. Gan, “Effect of an ultrashort pulse on Fresnel diffraction by a circular opaque disk,” Opt. Commun. 125, 1–4 (1996).
    [CrossRef]
  7. M. Gu, X. S. Gan, “Fresnel diffraction by circular and serrated opaque disks under ultrashort pulse illumination,” in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. Chang, J. Lee, C. Nam, eds., Proc. SPIE2778, 592–594 (1996).
  8. M. Kempe, U. Stamm, B. Wilhelmi, W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 9, 1158–1165 (1992).
    [CrossRef]
  9. M. Kempe, W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. M. Sussman, “Elementary diffraction theory of zone plates,” Am. J. Phys. 28, 394–398 (1960).
    [CrossRef]
  13. O. Myers, “Studies of transmission zone plates,” Am. J. Phys. 19, 359–365 (1951).
    [CrossRef]
  14. M. Gu, Advanced Optical Imaging Theory (Springer Verlag, Heidelberg, 2000).
    [CrossRef]
  15. C. J. R. Sheppard, M. Hrynevych, “Diffraction by a circular aperture: a generalization of Fresnel diffraction theory,” J. Opt. Soc. Am. A 9, 274–281 (1992).
    [CrossRef]

2001 (1)

Z. Horvath, Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63, 026601-1–026601-11 (2001).
[CrossRef]

1999 (3)

1996 (2)

M. Gu, X. Gan, “Effect of an ultrashort pulse on Fresnel diffraction by a circular opaque disk,” Opt. Commun. 125, 1–4 (1996).
[CrossRef]

M. Gu, X. 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]

1993 (2)

1992 (2)

1989 (1)

1960 (1)

M. Sussman, “Elementary diffraction theory of zone plates,” Am. J. Phys. 28, 394–398 (1960).
[CrossRef]

1951 (1)

O. Myers, “Studies of transmission zone plates,” Am. J. Phys. 19, 359–365 (1951).
[CrossRef]

Angelow, G.

Bor, Z.

Z. Horvath, Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63, 026601-1–026601-11 (2001).
[CrossRef]

Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119–121 (1989).
[CrossRef] [PubMed]

Chen, Y.

Cho, S. H.

Fujimoto, J. G.

Gan, X.

M. Gu, X. 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]

M. Gu, X. Gan, “Effect of an ultrashort pulse on Fresnel diffraction by a circular opaque disk,” Opt. Commun. 125, 1–4 (1996).
[CrossRef]

Gan, X. S.

M. Gu, X. S. Gan, “Fresnel diffraction by circular and serrated opaque disks under ultrashort pulse illumination,” in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. Chang, J. Lee, C. Nam, eds., Proc. SPIE2778, 592–594 (1996).

Gu, M.

M. Gu, X. Gan, “Effect of an ultrashort pulse on Fresnel diffraction by a circular opaque disk,” Opt. Commun. 125, 1–4 (1996).
[CrossRef]

M. Gu, X. 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]

M. Gu, Advanced Optical Imaging Theory (Springer Verlag, Heidelberg, 2000).
[CrossRef]

M. Gu, X. S. Gan, “Fresnel diffraction by circular and serrated opaque disks under ultrashort pulse illumination,” in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. Chang, J. Lee, C. Nam, eds., Proc. SPIE2778, 592–594 (1996).

Haus, H.

Horvath, Z.

Z. Horvath, Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63, 026601-1–026601-11 (2001).
[CrossRef]

Hrynevych, M.

Ichikawa, H.

Ippen, E. P.

Kartner, F. X.

Kempe, M.

Morgner, U.

Myers, O.

O. Myers, “Studies of transmission zone plates,” Am. J. Phys. 19, 359–365 (1951).
[CrossRef]

Rudolph, W.

Scheuer, V.

Sheppard, C. J. R.

Stamm, U.

Sussman, M.

M. Sussman, “Elementary diffraction theory of zone plates,” Am. J. Phys. 28, 394–398 (1960).
[CrossRef]

Torizuka, K.

Tschudi, T.

Uemura, S.

Wilhelmi, B.

Am. J. Phys. (2)

M. Sussman, “Elementary diffraction theory of zone plates,” Am. J. Phys. 28, 394–398 (1960).
[CrossRef]

O. Myers, “Studies of transmission zone plates,” Am. J. Phys. 19, 359–365 (1951).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

M. Gu, X. Gan, “Effect of an ultrashort pulse on Fresnel diffraction by a circular opaque disk,” Opt. Commun. 125, 1–4 (1996).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

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

Phys. Rev. E (1)

Z. Horvath, Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E 63, 026601-1–026601-11 (2001).
[CrossRef]

Other (2)

M. Gu, X. S. Gan, “Fresnel diffraction by circular and serrated opaque disks under ultrashort pulse illumination,” in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. Chang, J. Lee, C. Nam, eds., Proc. SPIE2778, 592–594 (1996).

M. Gu, Advanced Optical Imaging Theory (Springer Verlag, Heidelberg, 2000).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Normalized intensity distributions in the region of the principal focus along the axial plane. The plot range corresponds to the variation of the Fresnel number N 0 from 200 to 25 and m 0 = 6. Part (a), cw illumination; (b), 100-fs pulsed illumination; (c), 10-fs pulsed illumination.

Fig. 2
Fig. 2

Axial [(a), (b), (c)] and transverse [(d), (e), (f)] normalized intensity profiles. The transverse intensity profiles are given at N 0 = 34 and m 0 = 6. Parts (a) and (d) are under cw illumination; (b) and (e) are under 100-fs pulsed illumination; (c) and (f) are under 10-fs pulsed illumination.

Fig. 3
Fig. 3

Dependence of the axial and the lateral focal widths, ΔZ and Δ(y/ a) on the pulse width. The values of ΔZ and ΔN have been multiplied by a factor of 10 and 0.1, respectively.

Equations (7)

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

Rm2=mfλ,
Uρ, z, ω= i2N exp-i2πz/λλzm=0M0ρmρm+1× U0ρ1, ωJ02Nρρ1exp-iNρ12ρ1dρ1,
ρm2= Rm2a2= mfλa2
N=πa2λz.
Iρ, N0=C 0+1N0exp- T2ω024NN0-12×m=0M0ρmρm+1 J02Nρρ1×exp-iNρ12ρ1dρ12dN,
IN0= sin2m0πN0Nfcos2πN02Nf
IN0=C 0+1N0exp- T2ω024NN0-12×sinm0πNNfcosπN2Nf2dN

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