Abstract

In this paper, we present two optical system design methods for beam circularization, collimation, and expansion of semiconductor laser output beam for possible application in LIDAR systems. Two different optical mirror systems are investigated: an off-axis hyperbolic∕parabolic mirror system and an off-axis parabolic mirror system. Equations specific to these mirror systems are derived and computer package programs such as ZEMAX and MATLAB are used to simulate the optical designs. The beam reshaping results are presented.

© 2007 Optical Society of America

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  1. A. V. Jelalian, Laser Radar Systems (Artech House, 1992), pp. 121-206.
  2. J. A. Reagan, H. Liu, and J. F. McCalmont, "Laser diode based new generation lidars," Geoscience and Remote Sensing Symposium (IEEE, 1996), (IGARSS'96) pp. 1535-1537.
  3. J. Alda, "Laser and Gaussian beam propagation and transformation," in Encyclopedia of Optical Engineering (Marcel Dekker, 2003), pp. 999-1013.
  4. K. Tatsuno and A. Arimoto, "Optical system for semiconductor laser," U.S. patent 4,564,268 (January 14, 1986).
  5. H. M. Presby and C. R. Giles, "Asymetric fiber microlenses for efficient coupling to elliptical laser beams," IEEE Photon. Tech. Lett. 5, 184-186 (1993).
    [CrossRef]
  6. S.-Y. Huang and C. Gaebe, "Astigmatic compensation for an anamorphic optical system," U.S. patent 6,301,059 (October 9, 2001).
  7. Z. Xiao-qun, B. N. K. Ann, and K. S. Seong, "Single aspherical lens for deastigmatism, collimation, and circularization of a laser beam," Appl. Opt. 39, 1148-1151 (2000).
    [CrossRef]
  8. C. E. Gaebe, S. Huang, K. A. Miller, T. Stanley, and G. T. Wiand, "Cruciform cylindrical lens for elliptical beam transformation," U.S. patent 5,973,853 (October 26, 1999).
  9. H. Hanada, "Beam shaping optical system," U.S. patent 4,318,594 (March 9, 1982).
  10. X. Zeng, C. Cao, and Y. An, "Asymmetrical prism for beam shaping of laser diode stacks," Appl. Opt. 44, 5408-5414 (2005).
    [CrossRef] [PubMed]
  11. P. Hello and C. N. Man, "Design of a low-loss off-axis beam expander," Appl. Opt. 35, 2534-2536 (1996).
    [CrossRef] [PubMed]
  12. D. L. Shealy and S.-H. Chao, "Geometric optics-based design of laser beam shapers," Opt. Eng. 42, 3123-3138 (2003).
    [CrossRef]
  13. H. Kogelnik, "Propagation of laser beams," in Applied Optics and Optical Engineering (Academic, 1979), Vol. VII, pp. 155-190.
  14. D. C. O'Shea, Elements of Modern Optical Design (Wiley, 1985), pp. 230-234.
  15. S. A. Self, "Focusing of Spherical Gaussian Beams," Appl. Opt. 22, 658-661 (1983).
    [CrossRef] [PubMed]
  16. W. A. E. Goethals, "Laser beam analysis by geometrical optics," in The Physics and Technology of Laser Resonators (IOP Publishing, 1989), pp. 143-153.
  17. L. A. Romero and F. M. Dickey, "Lossless laser beam shaping," J. Opt. Soc. Am. A 13, 751-760 (1996).
    [CrossRef]
  18. F. M. Dickey and S. C. Holswade, "Gaussian laser beam profile shaping," Opt. Eng. 35, 3285-3295 (1996).
    [CrossRef]
  19. F. M. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Techniques (Marcel Dekker, 2000), pp. 12-13.
  20. J. A. Hoffnagle and C. M. Jefferson, "Beam shaping with a plano-aspheric lens pair," Opt. Eng. 42, 3090-3099 (2003).
    [CrossRef]
  21. R. R. Shannon, "Aspheric surfaces," Applied Optics and Optical Engineering (Academic, 1980), Vol. VIII, pp. 55-85.
  22. C. H. Edwards and D. E. Penney, Calculus and Analytic Geometry (Prentice Hall, Inc., 1988), pp. 504-548.
  23. A. E. Siegman, Lasers (University Science Books, 1986), pp. 663-674.
  24. ZEMAX Optical Design program, User's Guide (ZEMAX Development Corporation, 2004).
  25. ZEMAX Development Corporation Web site, www.zemax.com.

2005 (1)

2004 (1)

ZEMAX Optical Design program, User's Guide (ZEMAX Development Corporation, 2004).

2003 (3)

D. L. Shealy and S.-H. Chao, "Geometric optics-based design of laser beam shapers," Opt. Eng. 42, 3123-3138 (2003).
[CrossRef]

J. Alda, "Laser and Gaussian beam propagation and transformation," in Encyclopedia of Optical Engineering (Marcel Dekker, 2003), pp. 999-1013.

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

2000 (2)

1996 (4)

L. A. Romero and F. M. Dickey, "Lossless laser beam shaping," J. Opt. Soc. Am. A 13, 751-760 (1996).
[CrossRef]

F. M. Dickey and S. C. Holswade, "Gaussian laser beam profile shaping," Opt. Eng. 35, 3285-3295 (1996).
[CrossRef]

J. A. Reagan, H. Liu, and J. F. McCalmont, "Laser diode based new generation lidars," Geoscience and Remote Sensing Symposium (IEEE, 1996), (IGARSS'96) pp. 1535-1537.

P. Hello and C. N. Man, "Design of a low-loss off-axis beam expander," Appl. Opt. 35, 2534-2536 (1996).
[CrossRef] [PubMed]

1993 (1)

H. M. Presby and C. R. Giles, "Asymetric fiber microlenses for efficient coupling to elliptical laser beams," IEEE Photon. Tech. Lett. 5, 184-186 (1993).
[CrossRef]

1992 (1)

A. V. Jelalian, Laser Radar Systems (Artech House, 1992), pp. 121-206.

1989 (1)

W. A. E. Goethals, "Laser beam analysis by geometrical optics," in The Physics and Technology of Laser Resonators (IOP Publishing, 1989), pp. 143-153.

1988 (1)

C. H. Edwards and D. E. Penney, Calculus and Analytic Geometry (Prentice Hall, Inc., 1988), pp. 504-548.

1986 (1)

A. E. Siegman, Lasers (University Science Books, 1986), pp. 663-674.

1985 (1)

D. C. O'Shea, Elements of Modern Optical Design (Wiley, 1985), pp. 230-234.

1983 (1)

1980 (1)

R. R. Shannon, "Aspheric surfaces," Applied Optics and Optical Engineering (Academic, 1980), Vol. VIII, pp. 55-85.

1979 (1)

H. Kogelnik, "Propagation of laser beams," in Applied Optics and Optical Engineering (Academic, 1979), Vol. VII, pp. 155-190.

Alda, J.

J. Alda, "Laser and Gaussian beam propagation and transformation," in Encyclopedia of Optical Engineering (Marcel Dekker, 2003), pp. 999-1013.

An, Y.

Ann, B. N. K.

Arimoto, A.

K. Tatsuno and A. Arimoto, "Optical system for semiconductor laser," U.S. patent 4,564,268 (January 14, 1986).

Cao, C.

Chao, S.-H.

D. L. Shealy and S.-H. Chao, "Geometric optics-based design of laser beam shapers," Opt. Eng. 42, 3123-3138 (2003).
[CrossRef]

Dickey, F. M.

F. M. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Techniques (Marcel Dekker, 2000), pp. 12-13.

L. A. Romero and F. M. Dickey, "Lossless laser beam shaping," J. Opt. Soc. Am. A 13, 751-760 (1996).
[CrossRef]

F. M. Dickey and S. C. Holswade, "Gaussian laser beam profile shaping," Opt. Eng. 35, 3285-3295 (1996).
[CrossRef]

Edwards, C. H.

C. H. Edwards and D. E. Penney, Calculus and Analytic Geometry (Prentice Hall, Inc., 1988), pp. 504-548.

Gaebe, C.

S.-Y. Huang and C. Gaebe, "Astigmatic compensation for an anamorphic optical system," U.S. patent 6,301,059 (October 9, 2001).

Gaebe, C. E.

C. E. Gaebe, S. Huang, K. A. Miller, T. Stanley, and G. T. Wiand, "Cruciform cylindrical lens for elliptical beam transformation," U.S. patent 5,973,853 (October 26, 1999).

Giles, C. R.

H. M. Presby and C. R. Giles, "Asymetric fiber microlenses for efficient coupling to elliptical laser beams," IEEE Photon. Tech. Lett. 5, 184-186 (1993).
[CrossRef]

Goethals, W. A. E.

W. A. E. Goethals, "Laser beam analysis by geometrical optics," in The Physics and Technology of Laser Resonators (IOP Publishing, 1989), pp. 143-153.

Hanada, H.

H. Hanada, "Beam shaping optical system," U.S. patent 4,318,594 (March 9, 1982).

Hello, P.

Hoffnagle, J. A.

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

Holswade, S. C.

F. M. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Techniques (Marcel Dekker, 2000), pp. 12-13.

F. M. Dickey and S. C. Holswade, "Gaussian laser beam profile shaping," Opt. Eng. 35, 3285-3295 (1996).
[CrossRef]

Huang, S.

C. E. Gaebe, S. Huang, K. A. Miller, T. Stanley, and G. T. Wiand, "Cruciform cylindrical lens for elliptical beam transformation," U.S. patent 5,973,853 (October 26, 1999).

Huang, S.-Y.

S.-Y. Huang and C. Gaebe, "Astigmatic compensation for an anamorphic optical system," U.S. patent 6,301,059 (October 9, 2001).

Jefferson, C. M.

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

Jelalian, A. V.

A. V. Jelalian, Laser Radar Systems (Artech House, 1992), pp. 121-206.

Kogelnik, H.

H. Kogelnik, "Propagation of laser beams," in Applied Optics and Optical Engineering (Academic, 1979), Vol. VII, pp. 155-190.

Liu, H.

J. A. Reagan, H. Liu, and J. F. McCalmont, "Laser diode based new generation lidars," Geoscience and Remote Sensing Symposium (IEEE, 1996), (IGARSS'96) pp. 1535-1537.

Man, C. N.

McCalmont, J. F.

J. A. Reagan, H. Liu, and J. F. McCalmont, "Laser diode based new generation lidars," Geoscience and Remote Sensing Symposium (IEEE, 1996), (IGARSS'96) pp. 1535-1537.

Miller, K. A.

C. E. Gaebe, S. Huang, K. A. Miller, T. Stanley, and G. T. Wiand, "Cruciform cylindrical lens for elliptical beam transformation," U.S. patent 5,973,853 (October 26, 1999).

O'Shea, D. C.

D. C. O'Shea, Elements of Modern Optical Design (Wiley, 1985), pp. 230-234.

Penney, D. E.

C. H. Edwards and D. E. Penney, Calculus and Analytic Geometry (Prentice Hall, Inc., 1988), pp. 504-548.

Presby, H. M.

H. M. Presby and C. R. Giles, "Asymetric fiber microlenses for efficient coupling to elliptical laser beams," IEEE Photon. Tech. Lett. 5, 184-186 (1993).
[CrossRef]

Reagan, J. A.

J. A. Reagan, H. Liu, and J. F. McCalmont, "Laser diode based new generation lidars," Geoscience and Remote Sensing Symposium (IEEE, 1996), (IGARSS'96) pp. 1535-1537.

Romero, L. A.

Self, S. A.

Seong, K. S.

Shannon, R. R.

R. R. Shannon, "Aspheric surfaces," Applied Optics and Optical Engineering (Academic, 1980), Vol. VIII, pp. 55-85.

Shealy, D. L.

D. L. Shealy and S.-H. Chao, "Geometric optics-based design of laser beam shapers," Opt. Eng. 42, 3123-3138 (2003).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986), pp. 663-674.

Stanley, T.

C. E. Gaebe, S. Huang, K. A. Miller, T. Stanley, and G. T. Wiand, "Cruciform cylindrical lens for elliptical beam transformation," U.S. patent 5,973,853 (October 26, 1999).

Tatsuno, K.

K. Tatsuno and A. Arimoto, "Optical system for semiconductor laser," U.S. patent 4,564,268 (January 14, 1986).

Wiand, G. T.

C. E. Gaebe, S. Huang, K. A. Miller, T. Stanley, and G. T. Wiand, "Cruciform cylindrical lens for elliptical beam transformation," U.S. patent 5,973,853 (October 26, 1999).

Xiao-qun, Z.

Zeng, X.

Appl. Opt. (4)

IEEE Photon. Tech. Lett. (1)

H. M. Presby and C. R. Giles, "Asymetric fiber microlenses for efficient coupling to elliptical laser beams," IEEE Photon. Tech. Lett. 5, 184-186 (1993).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (3)

F. M. Dickey and S. C. Holswade, "Gaussian laser beam profile shaping," Opt. Eng. 35, 3285-3295 (1996).
[CrossRef]

D. L. Shealy and S.-H. Chao, "Geometric optics-based design of laser beam shapers," Opt. Eng. 42, 3123-3138 (2003).
[CrossRef]

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

Other (16)

R. R. Shannon, "Aspheric surfaces," Applied Optics and Optical Engineering (Academic, 1980), Vol. VIII, pp. 55-85.

C. H. Edwards and D. E. Penney, Calculus and Analytic Geometry (Prentice Hall, Inc., 1988), pp. 504-548.

A. E. Siegman, Lasers (University Science Books, 1986), pp. 663-674.

ZEMAX Optical Design program, User's Guide (ZEMAX Development Corporation, 2004).

ZEMAX Development Corporation Web site, www.zemax.com.

H. Kogelnik, "Propagation of laser beams," in Applied Optics and Optical Engineering (Academic, 1979), Vol. VII, pp. 155-190.

D. C. O'Shea, Elements of Modern Optical Design (Wiley, 1985), pp. 230-234.

F. M. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Techniques (Marcel Dekker, 2000), pp. 12-13.

W. A. E. Goethals, "Laser beam analysis by geometrical optics," in The Physics and Technology of Laser Resonators (IOP Publishing, 1989), pp. 143-153.

S.-Y. Huang and C. Gaebe, "Astigmatic compensation for an anamorphic optical system," U.S. patent 6,301,059 (October 9, 2001).

C. E. Gaebe, S. Huang, K. A. Miller, T. Stanley, and G. T. Wiand, "Cruciform cylindrical lens for elliptical beam transformation," U.S. patent 5,973,853 (October 26, 1999).

H. Hanada, "Beam shaping optical system," U.S. patent 4,318,594 (March 9, 1982).

A. V. Jelalian, Laser Radar Systems (Artech House, 1992), pp. 121-206.

J. A. Reagan, H. Liu, and J. F. McCalmont, "Laser diode based new generation lidars," Geoscience and Remote Sensing Symposium (IEEE, 1996), (IGARSS'96) pp. 1535-1537.

J. Alda, "Laser and Gaussian beam propagation and transformation," in Encyclopedia of Optical Engineering (Marcel Dekker, 2003), pp. 999-1013.

K. Tatsuno and A. Arimoto, "Optical system for semiconductor laser," U.S. patent 4,564,268 (January 14, 1986).

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Figures (14)

Fig. 1
Fig. 1

(a) Free-space radiation pattern of a semiconductor laser, showing a non-cylindrical symmetric beam profile. (b) Illustration of propagation of a semiconductor laser beam. (c) Semiconductor laser beam in two transverse directions (x, perpendicular; y, parallel) as a function of propagation distance (z, optical axis).

Fig. 2
Fig. 2

Beam profile plot as a function of propagation direction. It is plotted with a MATLAB routine demonstrating a laser beam with 46° divergence angle in the perpendicular transverse direction and 12° divergence angle in the parallel transverse direction, assuming both the perpendicular and transverse angles originate at the same location at z = 0 .

Fig. 3
Fig. 3

Illustration of the general design approach.

Fig. 4
Fig. 4

x-z plane illustration of the first design method.

Fig. 5
Fig. 5

y-z plane illustration of the first design method.

Fig. 6
Fig. 6

Illustration of the hyperbola function.

Fig. 7
Fig. 7

Optical path of the “chief ray” of the beam.

Fig. 8
Fig. 8

Illustration of the parabola function.

Fig. 9
Fig. 9

MATLAB plot demonstrating the representative beam propagation in the y-z plane for the first design method first example.

Fig. 10
Fig. 10

x-z plane illustration of the second design method.

Fig. 11
Fig. 11

y-z plane illustration of the second design method.

Fig. 12
Fig. 12

First design method 10°–30° beam example for the stated image sizes: (a) input ( 4 μ m × 10 μ m ) , (b) output ( 40 c m × 40 c m ) , (c) output at 0.5 km distance ( 40 c m × 40 c m ) , (d) output at 1 km distance ( 40 c m × 40 c m ) .

Fig. 13
Fig. 13

First design method 12°–46° beam example for the stated image sizes: (a) input ( 4 μ m × 10 μ m ) , (b) output ( 40 c m × 40 c m ) , (c) output at 0.5 km distance ( 40 c m × 40 c m ) , (d) output at 1 km distance ( 40 c m × 40 c m ) .

Fig. 14
Fig. 14

Second design method 12°–46° beam example for the stated image sizes: (a) input ( 4 μ m × 10 μ m ) , (b) output ( 40 c m × 40 c m ) , (c) output at 0.5 km distance ( 40 c m × 40 c m ) , (d) output at 1 km distance ( 40 c m × 40 c m ) .

Tables (11)

Tables Icon

Table 1 General Mirror Equations

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Table 2 Global Coordinate Equations of the Mirrors

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Table 3 Equations of the Slopes of the Rays Reflected from Each Surface

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Table 4 Parameters of the First Example Designed with the First Method

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Table 5 Parameters of the Second Example Designed with the First Method

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Table 6 General Mirror and Ray Equations

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Table 7 Global Coordinate Equations of the Mirrors

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Table 8 Parameters of the Example Designed with the Second Method

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Table 9 β Parameter Calculations of Each Studied Example Separately for Perpendicular and Parallel Transverse Directions

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Table 10 Analytical Calculations of the Input and Output Beam for Both 10°–30° and 12°–46° Beam Examples

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Table 11 Output Beam Results of all Studied Design Examples

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

z 0 = π w 0 2 λ ,
β = 2 π w 0 w f d λ ,
| A , E | = | B , D | + | D , E | .
| B , D | = | C , D | + 2 a .
| A , E | = | C , E | + 2 d .
a = d .
c = a 2 + b 2 ,
f = d 2 + e 2 .
R = b 2 a , K = 1 b 2 a 2 , for   hyperbolas ,
R = 2 g , K = 1 , for   parabolas .
A ( ρ ) = e G ρ 2 ,
E P D = 2 w s t 1 / G ,
w ( z ) = w 0 1 + z 2 / z 0 2 ,
θ w ( z ) z w 0 z 0 = λ π w 0 , z z 0 ,

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