Abstract

We studied the spatial intensity profile of an ultrashort laser pulse passing through a laser beam shaping system, which uses diffractive optical elements to reshape a Gaussian beam profile into a flat-topped distribution. Both dispersion and nonlinear self-phase modulation are included in the theoretical model. Our calculation shows that this system works well for ultrashort pulses (~100 fs) when the pulse peak intensity is less than 5 × 1011 W/cm2. Experimental results are presented for 136 fs pulses at 800 nm wavelength from a Ti:sapphire laser with a 6 nJ pulse energy. We also studied the effects of lateral misalignment, beam-size deviation, and defocusing on the energy fluence profile.

© 2005 Optical Society of America

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  1. D. Karnakis, J. Fieret, P. T. Rumsby, M. C. Gower, “Microhole drilling using reshaped pulsed Gaussian laser beams,” in Laser Beam Shaping II, F. M. Dickey, S. C. Holswade, D. L. Shealy, eds., Proc. SPIE4443, 150–158 (2001).
    [CrossRef]
  2. L. Unnebrink, T. Henning, E. W. Kreutz, R. Poprawe, “Excimer beam homogenization for materials processing,” in OPTIKA 98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 126–129 (1998).
  3. E. B. Kley, M. Cunne, L. Witting, M. Thieme, “Beam shaping elements for holographic applications, micromachining and microfabrication,” in Micromachining Technology for Micro-Optics, S. H. Lee, E. G. Johnson, eds., Proc. SPIE4179, 58–65 (2000).
    [CrossRef]
  4. W. Zhao, P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
    [CrossRef]
  5. K. Ebata, K. Fuse, T. Hirai, K. Kurisu, “Advanced laser optics for laser material processing,” in Fourth International Symposium on Laser Precision Microfabrication, I. Miyamoto, A. Ostendorf, K. Sugioka, H. Helvajian, eds., Proc. SPIE5063, 411–417 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. P. Hariharan, Optical holography principles, techniques and applications, Vol. 1 of Cambridge Studies in Modern Optics (Cambridge U. Press, 1996).
    [CrossRef]
  14. W. Lee, “Method for converting a Gaussian laser beam into a uniform beam,” Opt. Commun. 36, 469–471 (1981).
    [CrossRef]
  15. W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
    [CrossRef]
  16. L. A. Romero, F. M. Dickey, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751–760 (1996).
    [CrossRef]
  17. J. Zhou, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, “Amplification of 26-fs, 2-TW pulses near the gain-narrowing limit in Ti:sapphire,” Opt. Lett. 20, 64–66 (1995).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  21. Y. R. Shen, Principles of Nonlinear Optics (Wiley, 1984), Chap. 17.7.
  22. 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]

2004

2003

1999

1996

1995

1993

W. Zhao, P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

1992

1988

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

1981

W. Lee, “Method for converting a Gaussian laser beam into a uniform beam,” Opt. Commun. 36, 469–471 (1981).
[CrossRef]

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

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Cunne, M.

E. B. Kley, M. Cunne, L. Witting, M. Thieme, “Beam shaping elements for holographic applications, micromachining and microfabrication,” in Micromachining Technology for Micro-Optics, S. H. Lee, E. G. Johnson, eds., Proc. SPIE4179, 58–65 (2000).
[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, 2000), Chap. 6.
[CrossRef]

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]

F. M. Dickey, L. S. Weichman, R. N. Shagam, “Laser beam shaping techniques,” in High Power Laser Ablation III, C. R. Phipps, ed., Proc. SPIE4065, 338–348 (2000).

Ebata, K.

K. Ebata, K. Fuse, T. Hirai, K. Kurisu, “Advanced laser optics for laser material processing,” in Fourth International Symposium on Laser Precision Microfabrication, I. Miyamoto, A. Ostendorf, K. Sugioka, H. Helvajian, eds., Proc. SPIE5063, 411–417 (2003).
[CrossRef]

Fieret, J.

D. Karnakis, J. Fieret, P. T. Rumsby, M. C. Gower, “Microhole drilling using reshaped pulsed Gaussian laser beams,” in Laser Beam Shaping II, F. M. Dickey, S. C. Holswade, D. L. Shealy, eds., Proc. SPIE4443, 150–158 (2001).
[CrossRef]

Fuse, K.

K. Ebata, K. Fuse, T. Hirai, K. Kurisu, “Advanced laser optics for laser material processing,” in Fourth International Symposium on Laser Precision Microfabrication, I. Miyamoto, A. Ostendorf, K. Sugioka, H. Helvajian, eds., Proc. SPIE5063, 411–417 (2003).
[CrossRef]

Gower, M. C.

D. Karnakis, J. Fieret, P. T. Rumsby, M. C. Gower, “Microhole drilling using reshaped pulsed Gaussian laser beams,” in Laser Beam Shaping II, F. M. Dickey, S. C. Holswade, D. L. Shealy, eds., Proc. SPIE4443, 150–158 (2001).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical holography principles, techniques and applications, Vol. 1 of Cambridge Studies in Modern Optics (Cambridge U. Press, 1996).
[CrossRef]

Henning, T.

L. Unnebrink, T. Henning, E. W. Kreutz, R. Poprawe, “Excimer beam homogenization for materials processing,” in OPTIKA 98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 126–129 (1998).

Hirai, T.

K. Ebata, K. Fuse, T. Hirai, K. Kurisu, “Advanced laser optics for laser material processing,” in Fourth International Symposium on Laser Precision Microfabrication, I. Miyamoto, A. Ostendorf, K. Sugioka, H. Helvajian, eds., Proc. SPIE5063, 411–417 (2003).
[CrossRef]

Holswade, S. C.

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]

F. M. Dickey, S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel-Dekker, 2000), Chap. 6.
[CrossRef]

Huang, C.-P.

Jiang, W.

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
[CrossRef]

Kapteyn, H. C.

Karnakis, D.

D. Karnakis, J. Fieret, P. T. Rumsby, M. C. Gower, “Microhole drilling using reshaped pulsed Gaussian laser beams,” in Laser Beam Shaping II, F. M. Dickey, S. C. Holswade, D. L. Shealy, eds., Proc. SPIE4443, 150–158 (2001).
[CrossRef]

Kley, E. B.

E. B. Kley, M. Cunne, L. Witting, M. Thieme, “Beam shaping elements for holographic applications, micromachining and microfabrication,” in Micromachining Technology for Micro-Optics, S. H. Lee, E. G. Johnson, eds., Proc. SPIE4179, 58–65 (2000).
[CrossRef]

Kreutz, E. W.

L. Unnebrink, T. Henning, E. W. Kreutz, R. Poprawe, “Excimer beam homogenization for materials processing,” in OPTIKA 98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 126–129 (1998).

Kurisu, K.

K. Ebata, K. Fuse, T. Hirai, K. Kurisu, “Advanced laser optics for laser material processing,” in Fourth International Symposium on Laser Precision Microfabrication, I. Miyamoto, A. Ostendorf, K. Sugioka, H. Helvajian, eds., Proc. SPIE5063, 411–417 (2003).
[CrossRef]

Lee, W.

W. Lee, “Method for converting a Gaussian laser beam into a uniform beam,” Opt. Commun. 36, 469–471 (1981).
[CrossRef]

Li, B.

Li, J.

Longtin, J. P.

Luepke, G.

Malyak, P. H.

Martin, J. C.

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
[CrossRef]

Metev, S. M.

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

Murnane, M. M.

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]

Palffy-Muhoray, P.

W. Zhao, P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

Poprawe, R.

L. Unnebrink, T. Henning, E. W. Kreutz, R. Poprawe, “Excimer beam homogenization for materials processing,” in OPTIKA 98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 126–129 (1998).

Ren, Y.

Romero, L. A.

Rumsby, P. T.

D. Karnakis, J. Fieret, P. T. Rumsby, M. C. Gower, “Microhole drilling using reshaped pulsed Gaussian laser beams,” in Laser Beam Shaping II, F. M. Dickey, S. C. Holswade, D. L. Shealy, eds., Proc. SPIE4443, 150–158 (2001).
[CrossRef]

Scott, P.

Shagam, R. N.

F. M. Dickey, L. S. Weichman, R. N. Shagam, “Laser beam shaping techniques,” in High Power Laser Ablation III, C. R. Phipps, ed., Proc. SPIE4065, 338–348 (2000).

Shealy, D. L.

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
[CrossRef]

Shen, Y. R.

Y. R. Shen, Principles of Nonlinear Optics (Wiley, 1984), Chap. 17.7.

Thieme, M.

E. B. Kley, M. Cunne, L. Witting, M. Thieme, “Beam shaping elements for holographic applications, micromachining and microfabrication,” in Micromachining Technology for Micro-Optics, S. H. Lee, E. G. Johnson, eds., Proc. SPIE4179, 58–65 (2000).
[CrossRef]

Tong, T.

Unnebrink, L.

L. Unnebrink, T. Henning, E. W. Kreutz, R. Poprawe, “Excimer beam homogenization for materials processing,” in OPTIKA 98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 126–129 (1998).

Veiko, V. P.

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

Weichman, L. S.

F. M. Dickey, L. S. Weichman, R. N. Shagam, “Laser beam shaping techniques,” in High Power Laser Ablation III, C. R. Phipps, ed., Proc. SPIE4065, 338–348 (2000).

Welsch, E.

Witting, L.

E. B. Kley, M. Cunne, L. Witting, M. Thieme, “Beam shaping elements for holographic applications, micromachining and microfabrication,” in Micromachining Technology for Micro-Optics, S. H. Lee, E. G. Johnson, eds., Proc. SPIE4179, 58–65 (2000).
[CrossRef]

Zhang, S.

Zhao, W.

W. Zhao, P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

Zhou, J.

Appl. Opt.

Appl. Phys. Lett.

W. Zhao, P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

W. Lee, “Method for converting a Gaussian laser beam into a uniform beam,” Opt. Commun. 36, 469–471 (1981).
[CrossRef]

Opt. Eng.

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

Opt. Lett.

Other

P. Hariharan, Optical holography principles, techniques and applications, Vol. 1 of Cambridge Studies in Modern Optics (Cambridge U. Press, 1996).
[CrossRef]

D. Karnakis, J. Fieret, P. T. Rumsby, M. C. Gower, “Microhole drilling using reshaped pulsed Gaussian laser beams,” in Laser Beam Shaping II, F. M. Dickey, S. C. Holswade, D. L. Shealy, eds., Proc. SPIE4443, 150–158 (2001).
[CrossRef]

L. Unnebrink, T. Henning, E. W. Kreutz, R. Poprawe, “Excimer beam homogenization for materials processing,” in OPTIKA 98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 126–129 (1998).

E. B. Kley, M. Cunne, L. Witting, M. Thieme, “Beam shaping elements for holographic applications, micromachining and microfabrication,” in Micromachining Technology for Micro-Optics, S. H. Lee, E. G. Johnson, eds., Proc. SPIE4179, 58–65 (2000).
[CrossRef]

K. Ebata, K. Fuse, T. Hirai, K. Kurisu, “Advanced laser optics for laser material processing,” in Fourth International Symposium on Laser Precision Microfabrication, I. Miyamoto, A. Ostendorf, K. Sugioka, H. Helvajian, eds., Proc. SPIE5063, 411–417 (2003).
[CrossRef]

F. M. Dickey, L. S. Weichman, R. N. Shagam, “Laser beam shaping techniques,” in High Power Laser Ablation III, C. R. Phipps, ed., Proc. SPIE4065, 338–348 (2000).

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

F. M. Dickey, S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel-Dekker, 2000), Chap. 6.
[CrossRef]

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Y. R. Shen, Principles of Nonlinear Optics (Wiley, 1984), Chap. 17.7.

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]

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Figures (6)

Fig. 1
Fig. 1

Experimental layout of the beam shaping system.

Fig. 2
Fig. 2

Normalized energy-fluence profiles. (a) Profile along the central axis of the target plane with optimum alignment. (b)–(f) Effects of misalignment of the beam profile; (b) effect of lateral misalignment of 10% of the original laser beam diameter; (c), (d) effects of input beam size 10% larger and smaller than the designed value, respectively; (e), (f) defocusing effects before and after the focusing plane of the Fourier lens by 2.5% of the focusing length. The theoretical result is plotted as solid curves, and the two sets of experimental data are plotted as filled squares and triangles.

Fig. 3
Fig. 3

(a) Profile of the beam shaper designed for β = 32. The smooth curve is the theoretical surface profile, compared with the fabricated step structure. (b) Calculated energy fluence in the target plane when the step structure of the beam shaper is used in the simulation.

Fig. 4
Fig. 4

(a) Input laser beam with Gaussian profile, (b) output beam with top-hat beam profile.

Fig. 5
Fig. 5

Numerical simulation of the intensity distribution of a 100 fs laser pulse as a function of time and radius in the target plane. The propagation integral includes SPM. The wavelength is 800 nm. The peak intensity (pulse energy) is (a) 1.5 × 1011 W/cm2 (3 mJ), (b) 5 × 1011 W/cm2, (c) 2.5 × 1012 W/cm2 (50 mJ), and (d) 5 × 1012 W/cm2 (100 mJ).

Fig. 6
Fig. 6

Integrated normalized energy fluence as a function of the radius of the target plane. The pulse width is 100 fs, and the pulse energy is (a) 3, (b) 10, (c) 50, and (d) 100 mJ. The peak intensities [W/cm] are given.

Equations (7)

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E ( ξ f , t ) = E 0 exp ( - ½ ξ 2 ) exp [ - ( Ω - Ω 0 δ ) 2 ] × exp { - i β [ ϕ Ω - Ω n n ( Ω 0 ) Ω 0 - Ω 0 n ( Ω 0 ) - ξ ξ f Ω Ω 0 ] } × exp [ - i k m ( Ω 0 ) t ( ξ ) ( Ω - Ω 0 ) ] × exp [ - ½ i k m ( Ω 0 ) t ( ξ ) ( Ω - Ω 0 ) 2 ] 1 i λ z f × exp [ - i k v ( ξ f R 0 ) 2 2 z f ] exp ( i Ω t ) d Ω d ξ ,
ϕ ( ξ ) = β [ ξ π / 2 erf ( ξ ) + ½ exp ( - ξ 2 ) - 1 / 2 ] .
t ( ξ ) = d 0 + λ 2 π ( n 0 - 1 ) [ ϕ ( ξ ) + 2 π ξ 2 r i 2 λ f ]
[ ( 1 + i ω 0 τ ) - 1 2 + 2 i k 0 z + 2 k 0 D ^ ] A ( r , t ) = - 4 π ω 0 2 c 2 ( 1 + i ω 0 τ ) p ˜ ,
n 2 ( g ) = 48 π 2 n 2 c χ ( 3 ) ( ω 0 ) [ 1 + 1 2 ω 0 χ ( 3 ) ( ω 0 ) d χ ( 3 ) d ω ] ,
ψ NL = n 2 E 2 k 0 t ( ξ ) ,
E ( ξ f , t ) = E 0 exp ( - ½ ξ 2 ) exp [ - ( Ω - Ω 2 δ ) 2 ] × exp { - i β [ ϕ Ω - Ω 0 n ( Ω 0 ) Ω 0 - Ω 0 n ( Ω 0 ) - ξ ξ f Ω Ω 0 ] } × exp [ - i k m ( Ω 0 ) t ( ξ ) ( Ω - Ω 0 ) ] × exp [ - ½ i k m ( Ω 0 ) t ( ξ ) ( Ω - Ω 0 ) 2 ] 1 i λ z f × exp [ - i k v ( ξ f R 0 ) 2 2 z f ] exp ( i Ω t ) × exp ( i ψ NL ) d Ω d ξ .

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