Abstract

We present two optical system designs using aspherical lenses for beam circularization, collimation, and expansion of semiconductor lasers for possible application in lidar systems. Two different optical lens systems are investigated; namely, two aspherical lens and single aspherical lens systems. Software package programs of zemax and matlab to simulate the optical designs are used. The beam reshaping results are presented for one specific laser beam output.

© 2008 Optical Society of America

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References

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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," in the International Geoscience and Remote Sensing Symposium (IGARSS '96) (IEEE, 1996), Vol. 3, pp. 1535-1537.
    [CrossRef]
  3. J. Alda, "Laser and Gaussian beam propagation and transformation," in Encyclopedia of Optical Engineering (Dekker, 2003), pp. 999-1013.
  4. K. Tatsuno and A. Arimoto, "Optical system for semiconductor laser," U.S. patent 4,564,268 (14 January 1986).
  5. H. M. Presby and C. R. Giles, "Asymetric fiber microlenses for efficient coupling to elliptical laser beams," IEEE Photon. Technol. 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 (9 October 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 (26 October 1999).
  9. J. J. Snyder, P. Reichert, and T. M. Baer, "Fast diffraction-limited cylindrical microlenses," Appl. Opt. 30, 2743-2747 (1991).
    [CrossRef] [PubMed]
  10. H. Hanada, "Beam shaping optical system," U.S. patent 4,318,594 (9 March 1982).
  11. S. D. Fantone, "Anamorphic prism: a new type," Appl. Opt. 30, 5008-5009 (1991).
    [CrossRef] [PubMed]
  12. X. Zeng, C. Cao, and Y. An, "Asymmetrical prism for beam shaping of laser diode stacks," Appl. Opt. 44, 5408-5414 (2005).
    [CrossRef] [PubMed]
  13. M. Serkan, H. Kirkici, and H. Cetinkaya, "Off-axis mirror based optical system design for circularization, collimation, and expansion of elliptical laser beams," Appl. Opt. 46, 5489-5499 (2007).
    [CrossRef] [PubMed]
  14. D. L. Shealy and S.-H. Chao, "Geometric optics-based design of laser beam shapers," Opt. Eng. 42, 3123-3138 (2003).
    [CrossRef]
  15. H. Kogelnik, "Propagation of laser beams," Applied Optics and Optical Engineering (Academic, 1979), Vol. VII, pp. 155-190.
  16. D. C. O'Shea, Elements of Modern Optical Design (Wiley, 1985), pp. 230-234.
  17. S. A. Self, "Focusing of spherical Gaussian beams," Appl. Opt. 22, 658-661 (1983).
    [CrossRef] [PubMed]
  18. W. A. E. Goethals, "Laser beam analysis by geometrical optics," in The Physics and Technology of Laser Resonators (IOP, 1989), pp. 143-153.
  19. L. A. Romero and F. M. Dickey, "Lossless laser beam shaping," J. Opt. Soc. Am. A 13, 751-760 (1996).
    [CrossRef]
  20. F. M. Dickey and S. C. Holswade, "Gaussian laser beam profile shaping," Opt. Eng. 35, 3285-3295 (1996).
    [CrossRef]
  21. F. M. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Techniques (Dekker, 2000), pp. 12-13.
  22. J. A. Hoffnagle and C. M. Jefferson, "Beam shaping with a plano-aspheric lens pair," Opt. Eng. 42, 3090-3099 (2003).
    [CrossRef]
  23. R. R. Shannon, "Aspheric surfaces," Applied Optics and Optical Engineering (Academic, 1980), Vol. VIII, pp. 55-85.
  24. C. H. Edwards and D. E. Penney, Calculus and Analytic Geometry (Prentice Hall, 1988), pp. 504-548.
  25. A. E. Siegman, Lasers (University Science Books, 1986), pp. 663-674.
  26. E. Hecht, Optics (Addison-Wesley, 1988), pp. 128-149.
  27. C.-L. Chen, Elements of Optoelectronics & Fiber Optics (Times Mirror Higher Education Group, 1996), pp. 55-57.
  28. ZEMAX Optical Design program, User's Guide (ZEMAX Development Corporation, 2004).
  29. ZEMAX Development Corporation website, www.zemax.com.
  30. Private conversation with the ZEMAX Instructor, Advanced Optical Design Using ZEMAX Training, Orlando, Fla. (personal communication, 2007).

2007 (1)

2005 (1)

2003 (2)

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]

2000 (1)

1996 (2)

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]

1993 (1)

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

1991 (2)

1983 (1)

Appl. Opt. (6)

IEEE Photon. Technol. Lett. (1)

H. M. Presby and C. R. Giles, "Asymetric fiber microlenses for efficient coupling to elliptical laser beams," IEEE Photon. Technol. 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 (19)

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, 1988), pp. 504-548.

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

E. Hecht, Optics (Addison-Wesley, 1988), pp. 128-149.

C.-L. Chen, Elements of Optoelectronics & Fiber Optics (Times Mirror Higher Education Group, 1996), pp. 55-57.

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

ZEMAX Development Corporation website, www.zemax.com.

Private conversation with the ZEMAX Instructor, Advanced Optical Design Using ZEMAX Training, Orlando, Fla. (personal communication, 2007).

H. Kogelnik, "Propagation of laser beams," 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.

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 (26 October 1999).

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

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," in the International Geoscience and Remote Sensing Symposium (IGARSS '96) (IEEE, 1996), Vol. 3, pp. 1535-1537.
[CrossRef]

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

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

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

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

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

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Figures (20)

Fig. 1
Fig. 1

Free-space radiation pattern of a semiconductor laser with an elliptical beam profile.

Fig. 2
Fig. 2

Semiconductor laser beam in two transverse directions (x, perpendicular; y, parallel) as a function of propagation distance (z, optical axis).

Fig. 3
Fig. 3

Sketch of a general spherical surface and refraction parameters.

Fig. 4
Fig. 4

Schematic of the two-lens system. Here, S i j represents each refractive surface of the lenses used in this design. S 11 is rotationally symmetric, S 12 is cylindrical (flat in perpendicular direction), S 21 is cylindrical (flat in perpendicular direction), and S 22 is flat (in both directions).

Fig. 5
Fig. 5

Schematic of the two-lens system surfaces in the perpendicular direction (xz plane).

Fig. 6
Fig. 6

Schematic representation of the two-lens system surfaces in the parallel direction (yz plane).

Fig. 7
Fig. 7

Schematic of the single-lens system. Here, S 1 is a hyperbolic surface in the perpendicular direction and is elliptical in the parallel direction. The surface S 2 is a cylindrical symmetric surface (flat in perpendicular direction).

Fig. 8
Fig. 8

Schematic of the single-lens system surfaces in the perpendicular direction (xz plane).

Fig. 9
Fig. 9

Schematic of the single-lens system surfaces in the parallel direction (yz plane).

Fig. 10
Fig. 10

Ray tracing results obtained with matlab for the two-lens system: (a) in the xz plane, (b) in the yz plane.

Fig. 11
Fig. 11

Ray tracing results obtained with matlab for the single-lens system: (a) in the xz plane, (b) in the yz plane.

Fig. 12
Fig. 12

(Color online) Three-dimensional zemax illustration of the two-lens system.

Fig. 13
Fig. 13

(Color online) Ray tracing results obtained with zemax for the two-lens system: (a) in the xz plane, (b) in the yz plane.

Fig. 14
Fig. 14

(Color online) Ray tracing results obtained with zemax for the single-lens system: (a) in the xz plane, (b) in the yz plane.

Fig. 15
Fig. 15

Two-lens system: (a) input beam (window size: 4 μ m × 10 μ m ), (b) output beam at the system exit plane (window size: 8   cm × 8   cm ), and (c) output beam at 1   km distance (window size: 8   cm × 8   cm ).

Fig. 16
Fig. 16

Single-lens system: (a) input beam (window size: 4 μ m × 10 μ m ), (b) output beam at the system exit plane (window size: 8   cm × 8   cm ), and (c) output beam at 1   km distance (window size: 8   cm × 8   cm ).

Fig. 17
Fig. 17

(Color online) (a) Illumination X Scan (perpendicular direction) analysis result of the output beam. (b) Illumination Y Scan (parallel direction) analysis result of the output beam.

Fig. 18
Fig. 18

Two-lens system: (a) output beam at 1   km distance without considering astigmatism (window size: 8   cm × 8   cm ), (b) output beam at 1   km distance with considering astigmatism (window size: 8   cm × 8   cm ), (c) output beam at 10   km distance without considering astigmatism (window size: 40   cm × 40   cm ), and (d) output beam at 10   km distance with considering astigmatism (window size: 40   cm × 40   cm ).

Fig. 19
Fig. 19

Normalized beam spot sizes of the output beam at near- and far-field regions. (Normalization is accomplished by dividing the beam spot size of the output beam calculated with considering astigmatism to with neglecting astigmatism.)

Fig. 20
Fig. 20

(a) FFT PSF X Cross Section (perpendicular direction) analysis result of the output beam at 0.1   km . (b) FFT PSF Y Cross Section (parallel direction) analysis result of the output beam at 0.1   km .

Tables (5)

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Table 1 Two-Lens System Parameters

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Table 2 Single-Lens System Parameters

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Table 3 β Parameter Calculations of the Two-Lens System Separately for the Perpendicular and Parallel Transverse Directions

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Table 4 β Parameter Calculations of the Single-Lens System Separately for the Perpendicular and Parallel Transverse Directions

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Table 5 Analytical Calculations of the Input and the Desired Output Beam

Equations (35)

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z 0 = π w 0 2 λ ,
β = 2 π w i w o d λ ,
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 ,
n 1 s 1 + n 2 s 2 = n 2 n 1 R ,
z 11 ( ) = w f tan ( θ ) ,
n 0 d 1 + n x S 11 = n 0 w f 2 + z 11 ( ) 2 ,
n 0 ( z 11 ( ) x S 11 ) + n x S 11 = n 0 w f 2 + z 11 ( ) 2 .
( z 11 ( ) ( d 1 a 1 ) c 1 ) 2 + w f 2 ( a 1 L 1 + x S 11 ) = e 1 .
R 1 = b 1 2 a 1 ,
c 1 = a 1 2 + b 1 2 = a 1 2 + a 1 R 1 ,
e 1 = c 1 a 1 = a 1 2 + a 1 R 1 a 1 ,
L 1 = a 1 2 c 1 = a 1 2 a 1 2 + a 1 R 1 ,
K 1 = 1 b 1 2 a 1 2 .
( x S 11 + a 1 a 1 2 + a 1 R 1 ) 2 + x 0 2 ( a 1 a 1 2 a 1 2 + a 1 R 1 + x S 11 ) = a 1 2 + a 1 R 1 a 1 ;
h w f = 0.5   ln ( 1 P a P T ) .
t 1 = z h a 1 = a 1 ( ( h b 1 ) 2 + 1 1 ) .
n 0 d 1 + n y S 11 = n 0 y 11 2 + ( d 1 + y S 11 ) 2 ;
tan ( θ ) = y 11 d 1 + y S 11 .
tan ( θ ) = w f y 11 d 2 y S 12 + y S 21 = y 11 q 1 + y S 12 ;
n ( t 1 y S 11 ) + n 0 d 2 + n y S 21 = n ( t 1 y S 11 + y S 12 ) + n 0 ( d 2 y S 12 + y S 21 ) 2 + ( w f y 11 ) 2 .
n 0 q 1 + n y S 12 = n 0 y 11 2 + ( q 1 + y S 12 ) 2 .
( y S 12 + a 2 a 2 2 + a 2 R 12 ( ) ) 2 + y 11 2 ( a 2 a 2 2 a 2 2 + a 2 R 12 ( ) + y S 12 ) = a 2 2 + a 2 R 12 ( ) a 2 ,
( y S 21 + a 3 a 3 2 + a 3 R 21 ( ) ) 2 + w f 2 ( a 3 a 3 2 a 3 2 + a 3 R 21 ( ) + y S 21 ) = a 3 2 + a 3 R 21 ( ) a 3 .
t 2 = z h a 3 = a 3 ( ( h b 3 ) 2 + 1 1 ) .
n ( q 1 + y S 1 + t ) = n ( q 1 + y S 1 + t y S 2 ) 2 + w f 2 + n 0 y S 2 ;
tan ( θ ) = y 1 d y S 1 .
tan ( θ ) = w f y 1 t y S 2 + y S 1 = y 1 q 1 .
n 0 d + n t = n 0 ( d y S 1 ) 2 + y 1 2 + n ( w f y 1 ) 2 + ( t y S 2 + y S 1 ) 2 + n 0 y S 2 .
R 1 y = 0.5095 ( q 1 + y S 1 ) d ( q 1 + y S 1 ) 1.5095 d ( R 1 y = R 1 ( ) ) ,
R 2 y = 0.5095 ( q 1 + y S 1 + t ) ( R 2 y = R 2 ( ) ) .
y s 1 = C 1 y y 1 2 1 + 1 C 1 y 2 y 1 2 ( 1 + K 1 y ) ( C 1 y = 1 / R 1 y ) ,
y s 2 = C 2 y w f 2 1 + 1 C 2 y 2 w f 2 ( 1 + K 2 y ) ( C 2 y = 1 / R 2 y ) .
A ( ρ ) = e G ρ 2 ,
EPD = 2 w s t 1 / G ,

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