Abstract

We calculated the temporal and spatial characteristics of an ultrashort laser pulse propagating through a diffractive beam-shaping system that converts a Gaussian beam into a beam with a uniform irradiance profile that was originally designed for continuous waves [Proc. SPIE 2863, 237 (1996)]. The pulse front is found to be considerably curved for a 10-fs pulse, resulting in a temporal broadening of the pulse that increases with increasing radius. The spatial intensity distribution deviates significantly from a top-hat profile, whereas the fluence shows a homogeneous radial distribution.

© 2003 Optical Society of America

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References

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  1. S. M. Metev, V. P. Veiko, Laser Assisted Micro-Technology (Springer-Verlag, Berlin, 1994), Chap. 6.
    [CrossRef]
  2. P. Scott, “Reflective optics for irradiance redistribution of laser beams: design,” Appl. Opt. 20, 1606–1610 (1981).
    [CrossRef] [PubMed]
  3. P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3453 (1980).
    [CrossRef]
  4. G. Borek, D. Brown, “High performance diffractive optics for beam shaping,” in Diffractive and Holographic Technologies, Systems, and Spatial Light Modulators VI, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3633, 51–60 (1995).
    [CrossRef]
  5. W. B. Veldkamp, “Laser beam profile shaping with binary diffraction gratings,” Opt. Commun. 36, 469–471 (1981).
  6. E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).
  7. F. M. Dickey, B. D. O’Neil, “Multifaceted laser beam integrators: general formulation and design concepts,” Opt. Eng. 27, 999–1007 (1988).
    [CrossRef]
  8. F. M. Dickey, S. C. Holswade, Laser Beam Shaping, Theory and Techniques (Marcel Dekker, New York, 2000), Chap. 3.
  9. S. C. Holswade, F. M. Dickey, “Gaussian laser beam shaping: test and evaluation,” in Current Developments in Optical Design and Engineering VI, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2863, 237–245 (1996).
    [CrossRef]
  10. A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, New York, 1995), Chap. 15.
    [CrossRef]
  11. L. A. Romero, F. M. Dickey, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751–760 (1996).
    [CrossRef]
  12. Z. Bor, “Distortion of femtosecond laser pulses in lenses and lens systems,” J. Mod. Opt. 35, 1907–1918 (1988).
    [CrossRef]
  13. Z. L. Horvath, Z. Bor, “Focusing of femtosecond pulses having gaussian spatial distribution,” Opt. Commun. 100, 6–12 (1993).
    [CrossRef]

1996 (1)

1993 (1)

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

1988 (2)

Z. Bor, “Distortion of femtosecond laser pulses in lenses and lens systems,” J. Mod. Opt. 35, 1907–1918 (1988).
[CrossRef]

F. M. Dickey, B. D. O’Neil, “Multifaceted laser beam integrators: general formulation and design concepts,” Opt. Eng. 27, 999–1007 (1988).
[CrossRef]

1981 (2)

W. B. Veldkamp, “Laser beam profile shaping with binary diffraction gratings,” Opt. Commun. 36, 469–471 (1981).

P. Scott, “Reflective optics for irradiance redistribution of laser beams: design,” Appl. Opt. 20, 1606–1610 (1981).
[CrossRef] [PubMed]

1980 (1)

Bor, Z.

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

Z. Bor, “Distortion of femtosecond laser pulses in lenses and lens systems,” J. Mod. Opt. 35, 1907–1918 (1988).
[CrossRef]

Borek, G.

G. Borek, D. Brown, “High performance diffractive optics for beam shaping,” in Diffractive and Holographic Technologies, Systems, and Spatial Light Modulators VI, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3633, 51–60 (1995).
[CrossRef]

Brown, D.

G. Borek, D. Brown, “High performance diffractive optics for beam shaping,” in Diffractive and Holographic Technologies, Systems, and Spatial Light Modulators VI, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3633, 51–60 (1995).
[CrossRef]

Dickey, F. M.

L. A. Romero, F. M. Dickey, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751–760 (1996).
[CrossRef]

F. M. Dickey, B. D. O’Neil, “Multifaceted laser beam integrators: general formulation and design concepts,” Opt. Eng. 27, 999–1007 (1988).
[CrossRef]

F. M. Dickey, S. C. Holswade, Laser Beam Shaping, Theory and Techniques (Marcel Dekker, New York, 2000), Chap. 3.

S. C. Holswade, F. M. Dickey, “Gaussian laser beam shaping: test and evaluation,” in Current Developments in Optical Design and Engineering VI, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2863, 237–245 (1996).
[CrossRef]

Holswade, S. C.

F. M. Dickey, S. C. Holswade, Laser Beam Shaping, Theory and Techniques (Marcel Dekker, New York, 2000), Chap. 3.

S. C. Holswade, F. M. Dickey, “Gaussian laser beam shaping: test and evaluation,” in Current Developments in Optical Design and Engineering VI, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2863, 237–245 (1996).
[CrossRef]

Horvath, Z. L.

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

Loewen, E. G.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Metev, S. M.

S. M. Metev, V. P. Veiko, Laser Assisted Micro-Technology (Springer-Verlag, Berlin, 1994), Chap. 6.
[CrossRef]

O’Neil, B. D.

F. M. Dickey, B. D. O’Neil, “Multifaceted laser beam integrators: general formulation and design concepts,” Opt. Eng. 27, 999–1007 (1988).
[CrossRef]

Popov, E.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Rhodes, P. W.

Romero, L. A.

Scott, P.

Shealy, D. L.

Veiko, V. P.

S. M. Metev, V. P. Veiko, Laser Assisted Micro-Technology (Springer-Verlag, Berlin, 1994), Chap. 6.
[CrossRef]

Veldkamp, W. B.

W. B. Veldkamp, “Laser beam profile shaping with binary diffraction gratings,” Opt. Commun. 36, 469–471 (1981).

Walther, A.

A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, New York, 1995), Chap. 15.
[CrossRef]

Appl. Opt. (2)

J. Mod. Opt. (1)

Z. Bor, “Distortion of femtosecond laser pulses in lenses and lens systems,” J. Mod. Opt. 35, 1907–1918 (1988).
[CrossRef]

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

Opt. Commun. (2)

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

W. B. Veldkamp, “Laser beam profile shaping with binary diffraction gratings,” Opt. Commun. 36, 469–471 (1981).

Opt. Eng. (1)

F. M. Dickey, B. D. O’Neil, “Multifaceted laser beam integrators: general formulation and design concepts,” Opt. Eng. 27, 999–1007 (1988).
[CrossRef]

Other (6)

F. M. Dickey, S. C. Holswade, Laser Beam Shaping, Theory and Techniques (Marcel Dekker, New York, 2000), Chap. 3.

S. C. Holswade, F. M. Dickey, “Gaussian laser beam shaping: test and evaluation,” in Current Developments in Optical Design and Engineering VI, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2863, 237–245 (1996).
[CrossRef]

A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, New York, 1995), Chap. 15.
[CrossRef]

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

G. Borek, D. Brown, “High performance diffractive optics for beam shaping,” in Diffractive and Holographic Technologies, Systems, and Spatial Light Modulators VI, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3633, 51–60 (1995).
[CrossRef]

S. M. Metev, V. P. Veiko, Laser Assisted Micro-Technology (Springer-Verlag, Berlin, 1994), Chap. 6.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the laser beam-shaping system (after Ref. 9).

Fig. 2
Fig. 2

Spatiotemporal intensity distribution in (a) the target plane of the beam-shaping system and (b) the focal plane of a single focusing lens.

Fig. 3
Fig. 3

(a) Maximum intensity and fluence distribution as a function of radius, (b) pulse duration as a function of radius.

Equations (6)

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Er, t=E0 exp-r22ri2exp-t22τ2cosΩ0t,
Ěrf, zf, Ω= Ěr, ΩTLr, Ω1iλzf×exp-ikzfexp-ik rf-r22zfdr,
1iλzfexp-ikzfexp-ik rf-r22zf
TLξ, Ω=expiβξ π2erfξ+12exp-ξ2-12-kri2ξ22f,
TLξ, Ω=exp(-ikmΩtξ+kvΩt0-tξ),
Eξf, t= E0 exp-12 ξ2exp-Ω-Ω0δ2×exp-iTLξ, ΩΩ-Ω0nΩ0Ω0-Ω0nΩ0-ξfξ ΩΩ0exp-ikmΩ0tξΩ-Ω0exp-12 ikmΩ0tξΩ-Ω021iλzfexp-ikvrf-r22zf×expiΩtdΩdξ,

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