Abstract

The beam shaper we developed shapes the transmit beam of a CO2 laser radar that uses a linear detector array. It consists of a diffraction grating and an anamorphic prism beam compressor and produces a stretched profile that efficiently and uniformly illuminates the far-field footprint of the detector array. The diffraction grating phase modulates the near field or the laser beam to generate a far-field flattop intensity profile, whereas the compressor produces the necessary profile eccentricity. We have achieved conversion efficiencies in the 70–90% range.

© 1982 Optical Society of America

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References

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  1. R. J. Hull, S. Marcus, in Proceedings, IEEE National Aerospace and Electronics Conference, Dayton, (IEEE, New York, 1978) p. 662.
  2. C. Bachman, Laser Radar Systems and Techniques (Artech, Dedham, Mass., 1979).
  3. W. B. Veldkamp, Proc. Soc. Photo-Opt. Instrum. Eng. 255, 1361980).
  4. P. Jacquinot, B. Roizendossier, Prog. Opt. 3, 31 (1964).
  5. Y. Belvaux, S. Virdi, Opt. Commun. 15, 193 (1975).
    [CrossRef]
  6. M. Quintanilla, A. M. de Frutos, Appl. Opt. 20, 879 (1981).
    [CrossRef] [PubMed]
  7. W. W. Simmons, G. W. Leppelmeir, B. C. Johnson, Appl. Opt. 13, 1629 (1974).
    [CrossRef] [PubMed]
  8. J. W. Ogland, Appl. Opt. 17, 2917 (1978).
    [CrossRef] [PubMed]
  9. D. Fink, Appl. Opt., 18, 581 (1979).
    [CrossRef] [PubMed]
  10. S. Ream, Laser Focus 68, (Nov.1979).
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 381.
  12. W. Veldkamp, Opt. Commun. 38, 381 (1981).
    [CrossRef]
  13. W. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 239.
  14. D. Hanna, P. Karkkainen, R. Wyatt, Opt. Quantum Electron. 7, 115 (1975).
    [CrossRef]
  15. H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
    [CrossRef]
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3.
  17. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1964, Eq. 7.4.32).
  18. B. R. Brown, A. W. Lohmann, Appl. Opt. 5, 967 (1966).
    [CrossRef] [PubMed]
  19. Y. Belvaux, S. Virdi, Opt. Commun. 15, 193 (1975).
    [CrossRef]
  20. K. Al-Marzouk, Opt. Commun. 35, 161 (1980).
    [CrossRef]
  21. B. Brown, A. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
    [CrossRef]
  22. R. Kingston, Detection of Optical and Infrared Radiation (Springer, New York, 1978), p. 28.
  23. A. Siegman, Proc. IEEE 54, 1350 (1966).
    [CrossRef]
  24. S. Ferris, H. Leamy, J. Posate, Eds., Laser-Solid Interactions and Laser Processing (American Institute of Physics, New York, 1978).

1981

1980

W. B. Veldkamp, Proc. Soc. Photo-Opt. Instrum. Eng. 255, 1361980).

K. Al-Marzouk, Opt. Commun. 35, 161 (1980).
[CrossRef]

1979

S. Ream, Laser Focus 68, (Nov.1979).

D. Fink, Appl. Opt., 18, 581 (1979).
[CrossRef] [PubMed]

1978

1975

D. Hanna, P. Karkkainen, R. Wyatt, Opt. Quantum Electron. 7, 115 (1975).
[CrossRef]

Y. Belvaux, S. Virdi, Opt. Commun. 15, 193 (1975).
[CrossRef]

Y. Belvaux, S. Virdi, Opt. Commun. 15, 193 (1975).
[CrossRef]

1974

1969

B. Brown, A. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

1966

A. Siegman, Proc. IEEE 54, 1350 (1966).
[CrossRef]

B. R. Brown, A. W. Lohmann, Appl. Opt. 5, 967 (1966).
[CrossRef] [PubMed]

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

1964

P. Jacquinot, B. Roizendossier, Prog. Opt. 3, 31 (1964).

Al-Marzouk, K.

K. Al-Marzouk, Opt. Commun. 35, 161 (1980).
[CrossRef]

Bachman, C.

C. Bachman, Laser Radar Systems and Techniques (Artech, Dedham, Mass., 1979).

Belvaux, Y.

Y. Belvaux, S. Virdi, Opt. Commun. 15, 193 (1975).
[CrossRef]

Y. Belvaux, S. Virdi, Opt. Commun. 15, 193 (1975).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 381.

Brown, B.

B. Brown, A. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

Brown, B. R.

de Frutos, A. M.

Fink, D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3.

Hanna, D.

D. Hanna, P. Karkkainen, R. Wyatt, Opt. Quantum Electron. 7, 115 (1975).
[CrossRef]

Hull, R. J.

R. J. Hull, S. Marcus, in Proceedings, IEEE National Aerospace and Electronics Conference, Dayton, (IEEE, New York, 1978) p. 662.

Jacquinot, P.

P. Jacquinot, B. Roizendossier, Prog. Opt. 3, 31 (1964).

Johnson, B. C.

Karkkainen, P.

D. Hanna, P. Karkkainen, R. Wyatt, Opt. Quantum Electron. 7, 115 (1975).
[CrossRef]

Kingston, R.

R. Kingston, Detection of Optical and Infrared Radiation (Springer, New York, 1978), p. 28.

Kogelnik, H.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Leppelmeir, G. W.

Li, T.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Lohmann, A.

B. Brown, A. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

Lohmann, A. W.

Marcus, S.

R. J. Hull, S. Marcus, in Proceedings, IEEE National Aerospace and Electronics Conference, Dayton, (IEEE, New York, 1978) p. 662.

Ogland, J. W.

Quintanilla, M.

Ream, S.

S. Ream, Laser Focus 68, (Nov.1979).

Roizendossier, B.

P. Jacquinot, B. Roizendossier, Prog. Opt. 3, 31 (1964).

Siegman, A.

A. Siegman, Proc. IEEE 54, 1350 (1966).
[CrossRef]

Simmons, W. W.

Smith, W.

W. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 239.

Veldkamp, W.

W. Veldkamp, Opt. Commun. 38, 381 (1981).
[CrossRef]

Veldkamp, W. B.

W. B. Veldkamp, Proc. Soc. Photo-Opt. Instrum. Eng. 255, 1361980).

Virdi, S.

Y. Belvaux, S. Virdi, Opt. Commun. 15, 193 (1975).
[CrossRef]

Y. Belvaux, S. Virdi, Opt. Commun. 15, 193 (1975).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 381.

Wyatt, R.

D. Hanna, P. Karkkainen, R. Wyatt, Opt. Quantum Electron. 7, 115 (1975).
[CrossRef]

Appl. Opt.

IBM J. Res. Dev.

B. Brown, A. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

Laser Focus 68

S. Ream, Laser Focus 68, (Nov.1979).

Opt. Commun.

W. Veldkamp, Opt. Commun. 38, 381 (1981).
[CrossRef]

Y. Belvaux, S. Virdi, Opt. Commun. 15, 193 (1975).
[CrossRef]

Y. Belvaux, S. Virdi, Opt. Commun. 15, 193 (1975).
[CrossRef]

K. Al-Marzouk, Opt. Commun. 35, 161 (1980).
[CrossRef]

Opt. Quantum Electron.

D. Hanna, P. Karkkainen, R. Wyatt, Opt. Quantum Electron. 7, 115 (1975).
[CrossRef]

Proc. IEEE

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

A. Siegman, Proc. IEEE 54, 1350 (1966).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

W. B. Veldkamp, Proc. Soc. Photo-Opt. Instrum. Eng. 255, 1361980).

Prog. Opt.

P. Jacquinot, B. Roizendossier, Prog. Opt. 3, 31 (1964).

Other

S. Ferris, H. Leamy, J. Posate, Eds., Laser-Solid Interactions and Laser Processing (American Institute of Physics, New York, 1978).

R. Kingston, Detection of Optical and Infrared Radiation (Springer, New York, 1978), p. 28.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3.

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1964, Eq. 7.4.32).

R. J. Hull, S. Marcus, in Proceedings, IEEE National Aerospace and Electronics Conference, Dayton, (IEEE, New York, 1978) p. 662.

C. Bachman, Laser Radar Systems and Techniques (Artech, Dedham, Mass., 1979).

W. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 239.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 381.

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Figures (18)

Fig. 1
Fig. 1

Elements of a CO2 imaging laser radar system (in heterodyne mode) showing the position of the beam shaper subsystem in the optical train. The image detector array footprint is illuminated efficiently by a shaped laser beam profile (shaded area).

Fig. 2
Fig. 2

Conceptual focal plane beam shape formation of a binary central phase reversed grating on an incident Gaussian beam profile, Gauss(x). Higher diffraction orders (third, fifth, etc.) contribute to the losses and the sidelobes of the focal plane beam shaper.

Fig. 3
Fig. 3

Elements and concept of the anamorphic focal plane beam shaper. Orientation of the prisms relative to the incident beam controls eccentricity.

Fig. 4
Fig. 4

Beam compressor ratio and Fresnel reflection losses away from normal incidence angle Δ for a one-stage and two-stage poly-GaAs prism compressor.

Fig. 5
Fig. 5

Two binary π-phase beam shaper configurations.

Fig. 6
Fig. 6

Focal plane amplitude distributions of binary phase gratings under uniform plane wave illumination. Grating size is truncated at 12A. Top and center graphs show the grating dispersion with and without central π-phase modulation depth. Bottom graph shows the quadrature components of the π-phase reversed grating with a π/2 modulation depth (note the π/2 phase shift in fields between zeroth and first diffraction orders).

Fig. 7
Fig. 7

Focal plane intensity distributions under Gaussian plane wave illuminations for various σ’s (σ = grating periodicity/1/e beamwidth). Note assumed collimated incident beam. Dashed lines represent the unshaped reference profiles.

Fig. 8
Fig. 8

Focal plane intensity distributions as in Fig. 7 center for various phase modulation depth parameters. Dashed lines represent the focal plane intensity distributions under uniform illumination.

Fig. 9
Fig. 9

Enlarged transmission patterns of 1-D and 2-D beam shaping photoemulsion masks.

Fig. 10
Fig. 10

Elements of a poly-GaAs anamorphic flattop CO2 laser beam shaper.

Fig. 11
Fig. 11

Experimental setup of focal plane measurements. (In far-field measurements, the distance between beam shaper and detector was increased to more than 12 m.)

Fig. 12
Fig. 12

Scanned far-field intensity profiles of a TEM00 CO2 laser beam deflected from a reflection mode beam shaper with various grating and phase depth parameters σ and ϕ.

Fig. 13
Fig. 13

Scanned far-field intensity profiles of a CO2 laser beam (a) with no beam shaper, (b) with transmission mode beam shaper parameters σ = 1.00, ϕ = 0.7 π, and (c) with σ = 0.83, ϕ = 0.7π.

Fig. 14
Fig. 14

Far-field liquid crystal thermographic recording of the shaped far-field intensity distribution with σ = 0.83, ϕ = 0.7π.

Fig. 15
Fig. 15

Far-field CO2 transverse beam shaper profiles (no compressions) without (a) and with (b) an approximately A/2 axial misalignment between incident beam and diffraction grating. Focal plane characteristics of profile (b) are desirable in sweeping laser annealing systems.

Fig. 16
Fig. 16

Characteristics of a binary diffraction grating with both phase and amplitude shaping functions. When d1 = d2 the relief surfaces on both sides of the substrate can be combined to form a compound binary phase interlace grating.

Fig. 17
Fig. 17

Near-field amplitude weight w(xn) as a funtion of normalized local grating depth d2(xn) and as a function of normalized groove width γ(xn) in the grating depth and duty cycle modulation schemes.

Fig. 18
Fig. 18

Four weighting functions (weighting on center and first sidelobes) applied to an incident Gaussian beam profile and their effects on far-field profile shaping and sidelobe suppresion.

Tables (1)

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Table I One- and Two-Stage Compression Ratios at Normal Incidence Angle for Four Common 10.6-μm Transparent Substrate Materials and Their Brewster Angles

Equations (18)

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C = sin ( θ B + ξ ) cos { sin - 1 [ n cos ( θ B + ξ ) ] } ,
θ out = θ in · C m ,
ψ ( x , z ) = A 0 exp ( - x 2 ω 0 2 + j k x 2 2 R c ) exp ( - j k z )
ψ ( x , z ) = A 0 exp [ x 2 ( ω 0 / C ) 2 + j k x 2 2 ( R c / C 2 ) ] exp ( - j k z ) .
R p = tan 2 ( θ 1 - θ 2 ) tan 2 ( θ 1 + θ 2 ) ,
θ 2 = sin - 1 ( n sin θ 1 ) , θ 1 = ( 90 ° - θ B ) + sin - 1 ( 1 / n sin Δ ) ,
T ( u , v ) = T ( u , v ) H ( u , v ) ,
T ( u , v ) = [ T ( u , v ) G ( u , v ) ] · H ( u , v ) .
t ( x / A ) = 1 / 2 { [ exp ( j ϕ ) - 1 ] ( - 1 ) k + [ exp ( j ϕ ) + 1 ] } ,
T ( u A ) = - t ( x / A ) exp ( - j 2 π u x ) d x / A ,
T ( u A ) = 2 0 t ( x / A ) cos ( 2 π u x ) d x / A .
T ( u A ) = i = 0 N - 1 ( [ ( cos ϕ - 1 ) ( - 1 ) i + ( cos ϕ + 1 ) ] + j [ sin ϕ ( - 1 ) i + sin ϕ ] { sin [ 2 π u ( i + 1 ) A ] - sin ( 2 π u i A ) } 2 π u ) .
g ( x ) = exp [ - ( x 2 ω 2 + j π x 2 λ R ) ] .
I ( u ) ~ G ( u ) T ( u ) 2 .
T ( x ) = { 1 - n = - n 2 - n 1 rect [ x - 2 n A 2 γ ( x n ) ] - n = n 1 n 2 rect [ x - 2 n A 2 γ ( x n ) ] } ,
w ( x n ) = ( m = 1 m max ɛ 0 ɛ 0 + ɛ m ) 1 / 2 ,
ɛ m = [ ( - 1 ) m - 1 ] 2 ( m π ) 2 · sin 2 π m d 2 ( x n ) λ , ɛ 0 = 1 - sin 2 π m d 2 ( x n ) λ .
Λ ( x ) = 1 - x x 1 , 0 otherwise ,

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