Abstract

A full cycle was realized of the photolithographic development and detailed testing of a diffractive optical element that transforms the diverging Gaussian beams of CO2 lasers into a uniformly filled-in rectangle. The zone feature size of the beam shaper, the diffractive efficiency and accuracy, the focus depth, and the stability with respect to the size and the divergence of incident Gaussian beams are studied by computer modeling. Calculated flattop intensity distributions are presented in the same form of gray-level pictures and three-dimensional plots as the corresponding results measured by an IR camera.

© 1995 Optical Society of America

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References

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  1. Y. S. Liu, “Sources, optics, and laser microfabrication system for direct writing and projection lithography,” in Laser Microfabrication, D. J. Ehrlich, J. Y. Tsao, eds. (Academic, London, 1989), pp. 3–84.
  2. W. B. Veldkamp, C. J. Kastner, “Beam profile shaping for laser radars that use detector arrays,” Appl. Opt. 21, 345–356 (1982).
    [Crossref] [PubMed]
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  4. J. Cordingley, “Application of a binary diffractive optic for beam shaping in semiconductor processing by lasers,” Appl. Opt. 32, 2538–2542 (1994).
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  5. O. Bryngdahl, “Geometrical transformation in optics,” J. Opt. Soc. Am. 64, 1092–1099 (1974).
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  7. C.-Y. Han, Y. Ishii, K. Murata, “Reshaping collimated laser beams with Gaussian profile to uniform profiles,” Appl. Opt. 22, 3644–3647 (1983).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  9. N. C. Roberts, “Multilevel computer-generated holograms with separable phase functions for beam shaping,” Appl. Opt. 31, 3198–3199 (1992).
    [Crossref] [PubMed]
  10. M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, I. N. Sisakyan, V. A. Soifer, S. I. Kharitonov, “Computational experiment with focusator of Gaussian beam into the rectangle with uniform intensity,” Comput. Opt. 7, 42–49 (1990).
  11. M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 297–309 (1991).
    [Crossref]
  12. C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
    [Crossref]
  13. V. A. Soifer, M. A. Golub, “Diffractive micro-optical element with nonpoint response,” in Miniature and Micro-Optics: Fabrication and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 140–151 (1993).
  14. L. L. Doskolovich, M. A. Golub, N. L. Kazanskiy, S. I. Kharitonov, V. A. Soifer, “Diffraction investigation of focusators into plane area,” in Sixteenth Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 656–657 (1993).
  15. R. M. Stevenson, M. J. Norman, T. H. Bett, D. A. Pepler, C. N. Danson, I. N. Ross, “Binary-phase zone plate arrays for the generation of uniform focal profiles,” Opt. Lett. 19, 363–365 (1994).
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  16. M. T. Eismann, A. M. Tai, J. N. Cederquist, “Iterative design of holographic beam former,” Appl. Opt. 28, 2641–2650 (1989).
    [Crossref] [PubMed]
  17. M. A. Golub, L. L. Doskolovich, V. V. Kotlyar, V. A. Soifer, “Iterative-phase method for diffractive flattening of the Gaussian beam intensity,” Comput. Opt. 13, 30–33 (1993).
  18. A. Sommerfeld, Vorlesungen über Theoretische Physik, Band IV (Optik) (Verlag Harri Deutsch, Thun Frankfurt, 1989), Chaps. 34 and 35.

1994 (2)

1993 (1)

M. A. Golub, L. L. Doskolovich, V. V. Kotlyar, V. A. Soifer, “Iterative-phase method for diffractive flattening of the Gaussian beam intensity,” Comput. Opt. 13, 30–33 (1993).

1992 (1)

1991 (2)

M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 297–309 (1991).
[Crossref]

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[Crossref]

1990 (1)

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, I. N. Sisakyan, V. A. Soifer, S. I. Kharitonov, “Computational experiment with focusator of Gaussian beam into the rectangle with uniform intensity,” Comput. Opt. 7, 42–49 (1990).

1989 (2)

1983 (1)

1982 (2)

1981 (1)

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized holograms,” Sov. Tech. Phys. Lett. 7, 264–266 (1981).

1974 (1)

Aleksoff, C. C.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[Crossref]

Bett, T. H.

Bryngdahl, O.

Cederquist, J. N.

Cordingley, J.

Danson, C. N.

Doskolovich, L. L.

M. A. Golub, L. L. Doskolovich, V. V. Kotlyar, V. A. Soifer, “Iterative-phase method for diffractive flattening of the Gaussian beam intensity,” Comput. Opt. 13, 30–33 (1993).

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, I. N. Sisakyan, V. A. Soifer, S. I. Kharitonov, “Computational experiment with focusator of Gaussian beam into the rectangle with uniform intensity,” Comput. Opt. 7, 42–49 (1990).

L. L. Doskolovich, M. A. Golub, N. L. Kazanskiy, S. I. Kharitonov, V. A. Soifer, “Diffraction investigation of focusators into plane area,” in Sixteenth Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 656–657 (1993).

Eismann, M. T.

Ellis, K. K.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[Crossref]

Golub, M. A.

M. A. Golub, L. L. Doskolovich, V. V. Kotlyar, V. A. Soifer, “Iterative-phase method for diffractive flattening of the Gaussian beam intensity,” Comput. Opt. 13, 30–33 (1993).

M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 297–309 (1991).
[Crossref]

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, I. N. Sisakyan, V. A. Soifer, S. I. Kharitonov, “Computational experiment with focusator of Gaussian beam into the rectangle with uniform intensity,” Comput. Opt. 7, 42–49 (1990).

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized holograms,” Sov. Tech. Phys. Lett. 7, 264–266 (1981).

V. A. Soifer, M. A. Golub, “Diffractive micro-optical element with nonpoint response,” in Miniature and Micro-Optics: Fabrication and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 140–151 (1993).

L. L. Doskolovich, M. A. Golub, N. L. Kazanskiy, S. I. Kharitonov, V. A. Soifer, “Diffraction investigation of focusators into plane area,” in Sixteenth Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 656–657 (1993).

Han, C.-Y.

Ishii, Y.

Karpeev, S. V.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized holograms,” Sov. Tech. Phys. Lett. 7, 264–266 (1981).

Kastner, C. J.

Kazanskiy, N. L.

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, I. N. Sisakyan, V. A. Soifer, S. I. Kharitonov, “Computational experiment with focusator of Gaussian beam into the rectangle with uniform intensity,” Comput. Opt. 7, 42–49 (1990).

L. L. Doskolovich, M. A. Golub, N. L. Kazanskiy, S. I. Kharitonov, V. A. Soifer, “Diffraction investigation of focusators into plane area,” in Sixteenth Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 656–657 (1993).

Kharitonov, S. I.

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, I. N. Sisakyan, V. A. Soifer, S. I. Kharitonov, “Computational experiment with focusator of Gaussian beam into the rectangle with uniform intensity,” Comput. Opt. 7, 42–49 (1990).

L. L. Doskolovich, M. A. Golub, N. L. Kazanskiy, S. I. Kharitonov, V. A. Soifer, “Diffraction investigation of focusators into plane area,” in Sixteenth Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 656–657 (1993).

Kotlyar, V. V.

M. A. Golub, L. L. Doskolovich, V. V. Kotlyar, V. A. Soifer, “Iterative-phase method for diffractive flattening of the Gaussian beam intensity,” Comput. Opt. 13, 30–33 (1993).

Liu, Y. S.

Y. S. Liu, “Sources, optics, and laser microfabrication system for direct writing and projection lithography,” in Laser Microfabrication, D. J. Ehrlich, J. Y. Tsao, eds. (Academic, London, 1989), pp. 3–84.

Murata, K.

Neagle, B. D.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[Crossref]

Norman, M. J.

Pepler, D. A.

Prokhorov, A. M.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized holograms,” Sov. Tech. Phys. Lett. 7, 264–266 (1981).

Roberts, N. C.

Ross, I. N.

Sisakyan, I. N.

M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 297–309 (1991).
[Crossref]

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, I. N. Sisakyan, V. A. Soifer, S. I. Kharitonov, “Computational experiment with focusator of Gaussian beam into the rectangle with uniform intensity,” Comput. Opt. 7, 42–49 (1990).

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized holograms,” Sov. Tech. Phys. Lett. 7, 264–266 (1981).

Soifer, V. A.

M. A. Golub, L. L. Doskolovich, V. V. Kotlyar, V. A. Soifer, “Iterative-phase method for diffractive flattening of the Gaussian beam intensity,” Comput. Opt. 13, 30–33 (1993).

M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 297–309 (1991).
[Crossref]

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, I. N. Sisakyan, V. A. Soifer, S. I. Kharitonov, “Computational experiment with focusator of Gaussian beam into the rectangle with uniform intensity,” Comput. Opt. 7, 42–49 (1990).

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized holograms,” Sov. Tech. Phys. Lett. 7, 264–266 (1981).

V. A. Soifer, M. A. Golub, “Diffractive micro-optical element with nonpoint response,” in Miniature and Micro-Optics: Fabrication and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 140–151 (1993).

L. L. Doskolovich, M. A. Golub, N. L. Kazanskiy, S. I. Kharitonov, V. A. Soifer, “Diffraction investigation of focusators into plane area,” in Sixteenth Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 656–657 (1993).

Sommerfeld, A.

A. Sommerfeld, Vorlesungen über Theoretische Physik, Band IV (Optik) (Verlag Harri Deutsch, Thun Frankfurt, 1989), Chaps. 34 and 35.

Stevenson, R. M.

Tai, A. M.

Veldkamp, W. B.

Appl. Opt. (7)

Comput. Opt. (2)

M. A. Golub, L. L. Doskolovich, V. V. Kotlyar, V. A. Soifer, “Iterative-phase method for diffractive flattening of the Gaussian beam intensity,” Comput. Opt. 13, 30–33 (1993).

M. A. Golub, L. L. Doskolovich, N. L. Kazanskiy, I. N. Sisakyan, V. A. Soifer, S. I. Kharitonov, “Computational experiment with focusator of Gaussian beam into the rectangle with uniform intensity,” Comput. Opt. 7, 42–49 (1990).

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[Crossref]

Opt. Lasers Eng. (1)

M. A. Golub, I. N. Sisakyan, V. A. Soifer, “Infrared radiation focusators,” Opt. Lasers Eng. 15, 297–309 (1991).
[Crossref]

Opt. Lett. (1)

Sov. Tech. Phys. Lett. (1)

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized holograms,” Sov. Tech. Phys. Lett. 7, 264–266 (1981).

Other (4)

Y. S. Liu, “Sources, optics, and laser microfabrication system for direct writing and projection lithography,” in Laser Microfabrication, D. J. Ehrlich, J. Y. Tsao, eds. (Academic, London, 1989), pp. 3–84.

V. A. Soifer, M. A. Golub, “Diffractive micro-optical element with nonpoint response,” in Miniature and Micro-Optics: Fabrication and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1751, 140–151 (1993).

L. L. Doskolovich, M. A. Golub, N. L. Kazanskiy, S. I. Kharitonov, V. A. Soifer, “Diffraction investigation of focusators into plane area,” in Sixteenth Congress of the International Commission for Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1983, 656–657 (1993).

A. Sommerfeld, Vorlesungen über Theoretische Physik, Band IV (Optik) (Verlag Harri Deutsch, Thun Frankfurt, 1989), Chaps. 34 and 35.

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Figures (11)

Fig. 1
Fig. 1

Geometry of Gaussian-beam shaping: S, diffractive beam shaper.

Fig. 2
Fig. 2

Ray-tracing correspondence for shaping: S, diffractive beam shaper.

Fig. 3
Fig. 3

Computer-simulated intensity distribution for beam shaping for various clear apertures of the shaper (z 0 = 0, σ = 1.85 mm, λ = 10.6 μm, 2a = 1.75 mm, 2b = 3.5 mm, l = 100 mm): (a) 2A = 2B = 6.6 mm, Δx dif = 0.33 mm; (b) 2A = 2B = 4.4 mm, Δx dif = 0.5 mm.

Fig. 4
Fig. 4

Plots of minimum zone width Δmin divided by wavelength λ as a function of size a of the shaped rectangle divided by the focusing distance l for various values of f-number 2A/f (B = A) for the cases (b = 2a) and (σ/A = 0.56).

Fig. 5
Fig. 5

Computer-simulated intensity distribution for different cross sections of the shaped beam (collimated illuminating beam with z 0 = 0, σ = 1.85 mm, λ = 10.6 μm; 2A = 2B = 6.6 mm, 2a = 1.75 mm, 2b = 3.5 mm, l = 100 mm, 2A c = 5.33 mm, N c = 100, N FFT = 1024): (a) z = 90 mm, (b) z = 100 mm, (c) z = 110 mm.

Fig. 6
Fig. 6

Computer-simulated intensity distribution for the shaping of illuminating Gaussian beams with various angles of divergence (σ = 1.85 mm, λ = 10.6 μm, 2A = 2B = 6.6 mm, 2a = 1.75 mm, 2b = 3.5 mm, l = 100 mm): (a) θ = 3.84 × 10−3 rad, z 0 = 103 mm; (b) θ = 7.00 × 10−3 rad, z 0 = 119 mm.

Fig. 7
Fig. 7

Computer-simulated intensity distribution for the shaping of illuminating Gaussian beams with various sizes σ (λ = 10.6 μm, 2A = 2B = 6.6 mm, 2a = 1.75 mm, 2b = 3.5 mm, l = 100 mm, z 0 = 0): (a) σ = (1.85 × 0.9) mm, (b) σ = (1.85 × 1.1) mm.

Fig. 8
Fig. 8

View of the fourth mask of the beam shaper with the parameters σ = 1.85 mm, λ = 10.6 μm, 45° angle of incidence, 2A = 2B = 4.4 mm, 2a = 1.75 mm, 2b = 3.5 mm, l = 100 mm, z 0 = 0.

Fig. 9
Fig. 9

Experimental setup for the investigation of the shaped intensity distribution I(x, y, z) and of the diffraction efficiency.

Fig. 10
Fig. 10

Experimentally measured intensity distribution I(x, y, z) of the beam shaped by the fabricated shaper as a function of the distance z between the shaper’s plane and the plane under investigation (λ = 10.6 μm, 2A = 2B = 4.4 mm, 2a = 1.75 mm, 2b = 3.5 mm, l = 100 mm, σ = 1.85 mm, θ = 3.84 × 10−3 rad, z 0 = 302 mm): (a) z = 90 mm, (b) z = 103 mm, (c) z = 115 mm.

Fig. 11
Fig. 11

Computer-simulated intensity distribution I(x, y, z) of the shaped beam for exactly the same set of parameters as that of the experimentally investigated shaper in Fig. 10: (a) z = 90 mm, (b) z = 103 mm, (c) z = 115 mm.

Tables (2)

Tables Icon

Table 1 Numerically Estimated Values of Diffraction Efficiency ∊ and Relative Root-Mean-Square Deviation δ A of Amplitude of the Shaped Beam with Respect to Deviation Δz from the Plane of Optimal Focusing a

Tables Icon

Table 2 Numerically Estimated Values of Diffraction Efficiency ∊ and Relative Root-Mean-Square Deviation δ A of the Amplitude of the Shaped Beam with Respect to Variations of the Parameter σ d of the Illuminating Beam Size a

Equations (14)

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ψ ( u ) = [ x ( u ) u ] / L R [ x ( u ) u ] / l , [ 1 | ψ ( u ) | 2 ] 1 / 2 = l / L R 1 ,
x ( u ) = a E A erf ( u 2 σ ) , E A = erf ( 2 A / σ ) , erf ( t ) = 2 π 0 t exp ( s 2 ) d s ,
0 u I 0 ( u ) d u = 0 x ( u ) I d x , | u | A , | x ( u ) | a , x ( A ) = a , I = const .
k ψ ( u ) = k u 2 / 2 l + φ a ( u ) , φ a ( u ) = φ x ( u ) + φ y ( ν ) , u = ( u , ν ) ,
φ x ( u ) = k a l E A { u erf ( u 2 σ ) σ 2 π [ 1 exp ( 2 u 2 σ 2 ) ] } .
φ ( u ) = k u 2 / 2 f + φ a ( u ) , 1 / f = 1 / l + 1 / l 0 ,
Δ min = 2 π / max | u | A , | ν | B | φ ( u , ν ) | .
Δ min = [ Δ min u 2 + Δ min ν 2 ] 1 / 2 ,
Δ min u = { λ | a / l A / f | 1 , if t m 1 λ min [ | x ( u m ) / l u m / f | 1 , | a / l A / f | 1 ] , u m = σ [ ln ( t m ) / 2 ] 1 / 2 , t m = 2 2 fa / π l σ E A otherwise .
w ( x , z ) = k 2 π iz exp [ i k ( z + x 2 2 z ) ] A A B B [ I 0 ( u ) ] 1 / 2 × exp [ i k φ a ( u ) ] exp ( i 2 π x λ z u i k u 2 2 f def ) d 2 u ,
= a ds a ds b ds b ds | w ( x , l ) | 2 d 2 x / A A B B I 0 ( u ) d 2 u ,
δ A = a ds a ds b ds b ds [ | w ( x , l ) A m | 2 d 2 x / a ds a ds b ds b ds | w ( x , l ) | 2 d 2 x , A m = 1 2 a ds 2 b ds a ds a ds b ds b ds | w ( x , l ) | 2 d 2 x .
z 0 d = { [ σ / tan ( θ d / 2 ) ] 2 ( L 0 d / 2 ) 2 } 1 / 2 , L 0 d = 4 / k tan 2 ( θ d / 2 ) .
a d / l d = a / l , b d / l d = b / l ,

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