Abstract

A mechanical method of flattening the Gaussian intensity distribution of laser beams in time average is presented. Specially shaped rotating shutters are the key feature of this method, which has been applied to achieve homogeneous submicrometer patterning of macroscopically large samples by laser interference exposure. This method represents a simple yet useful alternative to applying beam broadening or degaussing plates (apodizing filters).

© 2000 Optical Society of America

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References

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  1. S. K. Dew, R. R. Parsons, “Absorbing filter to flatten Gaussian beams,” Appl. Opt. 31, 3416–3419 (1992).
    [CrossRef] [PubMed]
  2. V. G. Mityakov, V. B. Fedorov, “Problem of apodization of light beams with a Gaussian intensity distribution,” Opt. Spectrosc. (USSR) 58, 825–827 (1985).
  3. K. M. Baker, “Highly corrected submicrometer grid patterning on curved surfaces,” Appl. Opt. 38, 339–351 (1999).
    [CrossRef]
  4. C. Xie, R. Gupta, H. Metcalf, “Beam profile flattener for Gaussian beams,” Opt. Lett. 18, 173–175 (1993).
    [CrossRef] [PubMed]
  5. M. Duparré, M. A. Golub, B. Lüdge, V. S. Pavelyev, V. A. Soifer, G. V. Uspleniev, “Investigation of computer-generated diffractive beam shapers for flattening of single-modal CO2 laser beams,” Appl. Opt. 34, 2489–2497 (1995).
    [CrossRef]
  6. I. Koudela, M. Miler, M. Skalský, “Holographic optical element converting the Gaussian laser beam into a more uniform one,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 84–88 (1994).
    [CrossRef]
  7. M. Schildenberger, Y. Bonetti, M. Aeschlimann, L. Scandella, J. Gobrecht, R. Prins, “Preparation of model catalysts by laser interference nanolithography followed by metal cluster deposition,” Catal. Lett. 56, 1–6 (1998).
    [CrossRef]

1999

1998

M. Schildenberger, Y. Bonetti, M. Aeschlimann, L. Scandella, J. Gobrecht, R. Prins, “Preparation of model catalysts by laser interference nanolithography followed by metal cluster deposition,” Catal. Lett. 56, 1–6 (1998).
[CrossRef]

1995

1993

1992

1985

V. G. Mityakov, V. B. Fedorov, “Problem of apodization of light beams with a Gaussian intensity distribution,” Opt. Spectrosc. (USSR) 58, 825–827 (1985).

Aeschlimann, M.

M. Schildenberger, Y. Bonetti, M. Aeschlimann, L. Scandella, J. Gobrecht, R. Prins, “Preparation of model catalysts by laser interference nanolithography followed by metal cluster deposition,” Catal. Lett. 56, 1–6 (1998).
[CrossRef]

Baker, K. M.

Bonetti, Y.

M. Schildenberger, Y. Bonetti, M. Aeschlimann, L. Scandella, J. Gobrecht, R. Prins, “Preparation of model catalysts by laser interference nanolithography followed by metal cluster deposition,” Catal. Lett. 56, 1–6 (1998).
[CrossRef]

Dew, S. K.

Duparré, M.

Fedorov, V. B.

V. G. Mityakov, V. B. Fedorov, “Problem of apodization of light beams with a Gaussian intensity distribution,” Opt. Spectrosc. (USSR) 58, 825–827 (1985).

Gobrecht, J.

M. Schildenberger, Y. Bonetti, M. Aeschlimann, L. Scandella, J. Gobrecht, R. Prins, “Preparation of model catalysts by laser interference nanolithography followed by metal cluster deposition,” Catal. Lett. 56, 1–6 (1998).
[CrossRef]

Golub, M. A.

Gupta, R.

Koudela, I.

I. Koudela, M. Miler, M. Skalský, “Holographic optical element converting the Gaussian laser beam into a more uniform one,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 84–88 (1994).
[CrossRef]

Lüdge, B.

Metcalf, H.

Miler, M.

I. Koudela, M. Miler, M. Skalský, “Holographic optical element converting the Gaussian laser beam into a more uniform one,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 84–88 (1994).
[CrossRef]

Mityakov, V. G.

V. G. Mityakov, V. B. Fedorov, “Problem of apodization of light beams with a Gaussian intensity distribution,” Opt. Spectrosc. (USSR) 58, 825–827 (1985).

Parsons, R. R.

Pavelyev, V. S.

Prins, R.

M. Schildenberger, Y. Bonetti, M. Aeschlimann, L. Scandella, J. Gobrecht, R. Prins, “Preparation of model catalysts by laser interference nanolithography followed by metal cluster deposition,” Catal. Lett. 56, 1–6 (1998).
[CrossRef]

Scandella, L.

M. Schildenberger, Y. Bonetti, M. Aeschlimann, L. Scandella, J. Gobrecht, R. Prins, “Preparation of model catalysts by laser interference nanolithography followed by metal cluster deposition,” Catal. Lett. 56, 1–6 (1998).
[CrossRef]

Schildenberger, M.

M. Schildenberger, Y. Bonetti, M. Aeschlimann, L. Scandella, J. Gobrecht, R. Prins, “Preparation of model catalysts by laser interference nanolithography followed by metal cluster deposition,” Catal. Lett. 56, 1–6 (1998).
[CrossRef]

Skalský, M.

I. Koudela, M. Miler, M. Skalský, “Holographic optical element converting the Gaussian laser beam into a more uniform one,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 84–88 (1994).
[CrossRef]

Soifer, V. A.

Uspleniev, G. V.

Xie, C.

Appl. Opt.

Catal. Lett.

M. Schildenberger, Y. Bonetti, M. Aeschlimann, L. Scandella, J. Gobrecht, R. Prins, “Preparation of model catalysts by laser interference nanolithography followed by metal cluster deposition,” Catal. Lett. 56, 1–6 (1998).
[CrossRef]

Opt. Lett.

Opt. Spectrosc. (USSR)

V. G. Mityakov, V. B. Fedorov, “Problem of apodization of light beams with a Gaussian intensity distribution,” Opt. Spectrosc. (USSR) 58, 825–827 (1985).

Other

I. Koudela, M. Miler, M. Skalský, “Holographic optical element converting the Gaussian laser beam into a more uniform one,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 84–88 (1994).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Normalized Gaussian beam profile (see Subsection 2.A).

Fig. 2
Fig. 2

Shape of rotating shutter with mounting stem, the center of rotation, and the beam axis at the left for ρ = 3 cm and w = 4.8 cm (see text).

Fig. 3
Fig. 3

Schematic top view of an interference lithography setup.

Fig. 4
Fig. 4

SEM images of exposed photoresist: (a) at the beam center and (b) 3 cm from the center on an unmodified half; (c) at center and (d) 4 cm from center on an modified half.

Equations (22)

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Jr, w=exp-2 r2w2,
Kr=0r02π Js, wsdθds=πw221-Jr, w,
K=π2 w2.
I0=2P0πw2.
ηv=v.
ρ=w×ln1-v-21/2.
gr, wIr, w=IR, w=minr=0...ρ Ir, w.
gr, w=Iρ, wIr, w=Jρ, wJr, w=exp-2 ρ2-r2w2,
Ir=0ρ=I0Jρ, w.
ηρ, w=πρ2I0Jρ, wI0π2 w2=2 ρ2w2 Jρ, w,
±θr=π1-gr, w=π1-exp-2 ρ2-r2w2,
rθ=ρ2+w22ln1-|θ|π1/2,
r=x2+y21/2x×1+y22x2,
ep+erexpikx1+1rexpik y22x
π=k y22x
y=xλ1/2.
Vr, Δr, w=gr, wIr-Δr, wgr, wIr, w=Ir-Δr, wIr, w=Jr-Δr, wJr, w=exp2w2r2-r-Δr2=exp2Δrw22r-Δr1+2Δrw22r-Δr,
Vr, Δr, w1+4rΔrw2.
v=V+ρ, Δr, w-V-ρ, Δr, wV+ρ, Δr, w8ρΔrw21+4ρΔrw2=8ρΔrw2+4rΔr,
Δrvmaxw24ρ×2-vmax.
300 s×0.1 mWcm2=30 mJcm2
720 s×0.1 mWcm2×0.46=33 mJcm2

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