Abstract

This paper presents analysis of important issues associated with the design of refractive laser beam shaping systems. The concept of “singular radius” is introduced along with solutions to minimize its adverse effect on shaper performance. In addition, the surface boundary constraint is discussed in detail. This study provides useful guidelines to circumvent possible design errors that would degrade the shaper quality or add undesired complication to the system.

© 2008 Optical Society of America

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References

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  1. F. M. Dickey, S. C. Holswade, and D. L. Shealy, eds., Laser Beam Shaping Applications (CRC Press, 2005).
    [CrossRef]
  2. S. Zhang, G. Neil, and M. Shinn, "Single-element laser beam shaper for uniform flat-top profiles," Opt. Express 11, 1942-1948 (2003).
    [CrossRef] [PubMed]
  3. S. Zhang, "A simple bi-convex refractive laser beam shaper," J. Opt. A: Pure Appl. Opt. 9, 945-950 (2007)
    [CrossRef]
  4. W. Jiang, D. L. Shealy, and J. C. Martin, "Design and testing of a refractive reshaping system," in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer and W. J. Smith, eds., Proc. SPIE 2000, 64-75 (1993).
    [CrossRef]
  5. W. Jiang and D. L. Shealy, "Development and testing of a laser beam shaping system," Proc. SPIE 4095, 165-175 (2000).
    [CrossRef]
  6. J. A. Hoffnagle and C. M. Jefferson, "Beam shaping with a plano-aspheric lens pair," Opt. Eng. 42, 3090-3099 (2003).
    [CrossRef]
  7. J. A. Hoffnagle and C. M. Jefferson, "Design and performance of a refractive optical system that converts a Gaussian to a flattop beam," Appl. Opt. 39, 5488-5499 (2000).
    [CrossRef]
  8. J. A. Hoffnagle and C. M. Jefferson, "Refractive optical system that converts a laser beam to a collimated flat-top beam," U.S. patent 6,295,168 (25 September 2001).
  9. D. L. Shealy and J. A. Hoffnagle, "Laser beam shaping profiles and propagation," Appl. Opt. 45, 5118-5131 (2006)
    [CrossRef] [PubMed]
  10. B. R. Frieden, "Lossless conversion of a plane laser wave to a plane wave of uniform irradiance," Appl. Opt. 4, 1400-1403 (1965).
    [CrossRef]
  11. J. L. Kreuzer, "Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface," U.S. patent 3,476,463 (4 November 1969).
  12. P. Rhodes and D. Shealy, "Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis," Appl. Opt. 19, 3545-3553 (1980).
    [CrossRef] [PubMed]
  13. C. Wang and D. L. Shealy, "Design of gradient-index lens systems for laser beam reshaping," Appl. Opt. 32, 4763-4769 (1993).
    [CrossRef] [PubMed]

2007 (1)

S. Zhang, "A simple bi-convex refractive laser beam shaper," J. Opt. A: Pure Appl. Opt. 9, 945-950 (2007)
[CrossRef]

2006 (1)

2003 (2)

J. A. Hoffnagle and C. M. Jefferson, "Beam shaping with a plano-aspheric lens pair," Opt. Eng. 42, 3090-3099 (2003).
[CrossRef]

S. Zhang, G. Neil, and M. Shinn, "Single-element laser beam shaper for uniform flat-top profiles," Opt. Express 11, 1942-1948 (2003).
[CrossRef] [PubMed]

2000 (2)

1993 (1)

1980 (1)

1965 (1)

Frieden, B. R.

Hoffnagle, J. A.

Jefferson, C. M.

Jiang, W.

W. Jiang and D. L. Shealy, "Development and testing of a laser beam shaping system," Proc. SPIE 4095, 165-175 (2000).
[CrossRef]

Neil, G.

Rhodes, P.

Shealy, D.

Shealy, D. L.

Shinn, M.

Wang, C.

Zhang, S.

Appl. Opt. (5)

J. Opt. A: Pure Appl. Opt. (1)

S. Zhang, "A simple bi-convex refractive laser beam shaper," J. Opt. A: Pure Appl. Opt. 9, 945-950 (2007)
[CrossRef]

Opt. Eng. (1)

J. A. Hoffnagle and C. M. Jefferson, "Beam shaping with a plano-aspheric lens pair," Opt. Eng. 42, 3090-3099 (2003).
[CrossRef]

Opt. Express (1)

Proc. SPIE (1)

W. Jiang and D. L. Shealy, "Development and testing of a laser beam shaping system," Proc. SPIE 4095, 165-175 (2000).
[CrossRef]

Other (4)

W. Jiang, D. L. Shealy, and J. C. Martin, "Design and testing of a refractive reshaping system," in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer and W. J. Smith, eds., Proc. SPIE 2000, 64-75 (1993).
[CrossRef]

F. M. Dickey, S. C. Holswade, and D. L. Shealy, eds., Laser Beam Shaping Applications (CRC Press, 2005).
[CrossRef]

J. A. Hoffnagle and C. M. Jefferson, "Refractive optical system that converts a laser beam to a collimated flat-top beam," U.S. patent 6,295,168 (25 September 2001).

J. L. Kreuzer, "Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface," U.S. patent 3,476,463 (4 November 1969).

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Figures (11)

Fig. 1.
Fig. 1.

Optical configurations of refractive laser beam shaper: (a) Galilean type, (b) Keplerian shaper, (c) Single-lens Galilean shaper, (d) Single-lens Keplerian shaper

Fig. 2.
Fig. 2.

Sag curves for the two single-lens beam shapers, (a) R=4mm, and (b) R=5mm.

Fig. 3.
Fig. 3.

Input and output beam radiance distributions for R=4mm in Fig. 2(a), (a) Input profile, (b) Output profile

Fig. 4.
Fig. 4.

Curve showing the relation between r 1 and r 2.

Fig. 5.
Fig. 5.

Singular radius changes with initial beam size W

Fig. 6,
Fig. 6,

Sag curves of rear surface for different lens thickness

Fig. 7,
Fig. 7,

Sag curves of rear surface for different index of refraction. S=30mm.

Fig. 8.
Fig. 8.

Singular radius changes with output beam parameter R

Fig. 9.
Fig. 9.

Surface profile showing the boundary constraint for Type-4 shaper

Fig. 10.
Fig. 10.

Dependency of Type-3 beam shaper surface boundary on different lens thickness

Fig. 11.
Fig. 11.

Shaper surface boundary changes with lens thickness for Type-4 shaper

Equations (13)

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Z 1 ( r ) = 0 r [ ( n 2 1 ) + ( ( n 1 ) s r 2 r 1 ) 2 ] 1 2 d r 1
Z 2 ( r ) = 0 r [ ( n 2 1 ) + ( ( n 1 ) s r 2 r 1 ) 2 ] 1 2 d r 2
Z 1 ( r ) = 0 r [ ( n 2 1 ) + ( ( n 1 ) s r 2 + r 1 ) 2 ] 1 2 d r 1
Z 2 ( r ) = 0 r [ ( n 2 1 ) + ( ( n 1 ) s r 2 + r 1 ) 2 ] 1 2 d r 2
Z 1 ( r ) = 0 r n [ ( n 2 1 ) + ( ( n 1 ) s r 2 r 1 ) 2 ] 1 2 d r 1
Z 2 ( r ) = 0 r n [ ( n 2 1 ) + ( ( n 1 ) s r 2 r 1 ) 2 ] 1 2 d r 2
Z 1 ( r ) = 0 r n [ ( n 2 1 ) + ( ( n 1 ) s r 2 r 1 ) 2 ] 1 2 d r 1
Z 2 ( r ) = 0 r n [ ( n 2 1 ) + ( ( n 1 ) s r 2 r 1 ) 2 ] 1 2 d r 2
g ( r ) = g 0 exp ( 2 ( r R ) P )
g 0 = 2 2 P P 2 π R 2 Γ ( 2 P )
r 1 = h ( r 2 ) = 9 2 ln ( 1 2 π 0 r 2 g ( r ) rdr )
r 1 r 2 = n 1 n + 1 s
r 1 + r 2 = n 1 n + 1 s

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