Abstract

A mathematical model of a laser diode beam propagating through a collimating lens is presented. Wave propagation beyond the paraxial approximation is studied. The phase delay of the laser diode wave in passing through the lens is analyzed in detail. The propagation optical field after the lens is obtained from the diffraction integral by the stationary phase method. The model is employed to predict the light intensity at various beam cross sections, and the computed intensity distributions are in a good agreement with the corresponding measurements.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Katayama and Y. Komatsu, “Blue/DVD/CD compatible optical head,” Appl. Opt. 47, 4045-4054 (2008).
    [CrossRef] [PubMed]
  2. W. Sun, K. Liu, and J. Tien, “Laser expander design of highly efficient Blu-ray disc pickup head,” Opt. Express. 17, 2235-2246 (2009).
    [CrossRef] [PubMed]
  3. K. Otsuka and S. Chu, “Generation of vortex array beams from a thin-slice solid-state laser with shaped wide-aperture laser-diode pumping,” Opt. Lett. 34, 10-12 (2009).
    [CrossRef]
  4. Q. Zheng, Y. Yao, and B. Li, “13.2 W laser-diode-pumped Nd:YVO4 /LBO blue laser at 457 nm,” J. Opt. Soc. Am. B 26, 1238-1242 (2009).
    [CrossRef]
  5. N. Coluccelli, G. Galzerano, and D. Parisi, “Diode-pumped single-frequency Tm:LiLuF4 ring laser,” Opt. Lett. 33, 1951-1953 (2008).
    [CrossRef] [PubMed]
  6. X. Chen, X. Zhang, and Q. Wang, “Highly efficient diode-pumped actively Q-switched Nd:YAG-SrWO4 intracavity Raman laser,” Opt. Lett. 33, 705-707 (2008).
    [CrossRef] [PubMed]
  7. M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
    [CrossRef]
  8. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 101-104.
  9. M. Born and E. Wolf, Principle of Optics (Cambridge Univ. Press, 1999), pp. 171-174.
  10. X. Zeng and A. Naqwi, “Far-field distribution of double heterostructure laser diode beams,” Appl. Opt. 32, 4491-4494 (1993).
    [CrossRef] [PubMed]
  11. S. Nemoto, “Experimental evaluation of a new expression for the far field of a laser diode beam,” Appl. Opt. 33, 6387-6392(1994).
    [CrossRef] [PubMed]
  12. J. Stamnes, “Waves, rays, and the method of stationary phase,” Opt. Express 10, 740-751 (2002).
    [PubMed]

2009 (3)

2008 (3)

2002 (2)

M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
[CrossRef]

J. Stamnes, “Waves, rays, and the method of stationary phase,” Opt. Express 10, 740-751 (2002).
[PubMed]

1994 (1)

1993 (1)

Born, M.

M. Born and E. Wolf, Principle of Optics (Cambridge Univ. Press, 1999), pp. 171-174.

Chaen, S.

M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
[CrossRef]

Chen, X.

Chu, S.

Coluccelli, N.

Galzerano, G.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 101-104.

Ito, F.

M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
[CrossRef]

Itonaga, M.

M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
[CrossRef]

Katayama, R.

Komatsu, Y.

Li, B.

Liu, K.

W. Sun, K. Liu, and J. Tien, “Laser expander design of highly efficient Blu-ray disc pickup head,” Opt. Express. 17, 2235-2246 (2009).
[CrossRef] [PubMed]

Matsuzaki, K.

M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
[CrossRef]

M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
[CrossRef]

Naqwi, A.

Nemoto, S.

Nishizawa, A.

M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
[CrossRef]

Oishi, K.

M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
[CrossRef]

Otsuka, K.

Parisi, D.

Stamnes, J.

Sun, W.

W. Sun, K. Liu, and J. Tien, “Laser expander design of highly efficient Blu-ray disc pickup head,” Opt. Express. 17, 2235-2246 (2009).
[CrossRef] [PubMed]

Tien, J.

W. Sun, K. Liu, and J. Tien, “Laser expander design of highly efficient Blu-ray disc pickup head,” Opt. Express. 17, 2235-2246 (2009).
[CrossRef] [PubMed]

Ueno, T.

M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
[CrossRef]

Wang, Q.

Wolf, E.

M. Born and E. Wolf, Principle of Optics (Cambridge Univ. Press, 1999), pp. 171-174.

Yao, Y.

Zeng, X.

Zhang, X.

Zheng, Q.

Appl. Opt. (3)

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

Jpn. J. Appl. Phys. (1)

M. Itonaga, F. Ito, K. Matsuzaki, K. Matsuzaki, S. Chaen, K. Oishi, T. Ueno, and A. Nishizawa, “Single objective lens having numerical aperture of 0.85 for a high density optical disk system,” Jpn. J. Appl. Phys. 41, 1798-1803 (2002).
[CrossRef]

Opt. Express (1)

Opt. Express. (1)

W. Sun, K. Liu, and J. Tien, “Laser expander design of highly efficient Blu-ray disc pickup head,” Opt. Express. 17, 2235-2246 (2009).
[CrossRef] [PubMed]

Opt. Lett. (3)

Other (2)

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 101-104.

M. Born and E. Wolf, Principle of Optics (Cambridge Univ. Press, 1999), pp. 171-174.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

LD beam propagation though a collimation lens.

Fig. 2
Fig. 2

Measured and theoretical intensity profiles in the x z plane without the collimating lens.

Fig. 3
Fig. 3

Measured and theoretical intensity profiles in the y z plane without the collimating lens.

Fig. 4
Fig. 4

Measured and theoretical intensity profiles in the x z plane after the collimating lens.

Fig. 5
Fig. 5

Measured and theoretical intensity profiles in the y z plane after the collimating lens.

Equations (22)

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

ϕ ( x , y ) = k n Δ ( x , y ) + k [ Δ 0 Δ ( x , y ) ] = k Δ 0 + k ( n 1 ) Δ ( x , y ) ,
E 2 ( x , y ) = exp [ i k Δ 0 + i k ( n 1 ) Δ ( x , y ) ] E 1 ( x , y ) .
Δ ( x , y ) = Δ 0 R 1 ( 1 1 x 2 + y 2 R 1 2 ) + R 2 ( 1 1 x 2 + y 2 R 2 2 ) .
l H = f L = r 1 Δ 0 n ( r 2 r 1 ) + ( n 1 ) Δ 0
E 1 ( x , y ) = A L r exp ( i k r ) r Γ 2 Γ 2 + x 2 exp ( y 2 Ω 2 ) ,
A = u 0 2 i λ p π q ,
Γ 2 = p 2 k 2 r 2 ,
Ω 2 = 4 q k 2 r 2 ,
r = x 2 + y 2 + L 2 .
E 2 ( x , y ) = A f l H r exp ( i k r ) r Γ 2 Γ 2 + x 2 exp ( y 2 Ω 2 ) exp [ i k Δ 0 + i k ( n 1 ) Δ ( x , y ) ] .
E 3 ( x , y , z ) = 1 2 π s E 2 ( x 0 , y 0 ) z [ exp ( i k R ) R ] d x 0 d y 0 , R = ( x x 0 ) 2 + ( y y 0 ) 2 + z 2 ,
R ρ + ( x 0 2 + y 0 2 2 x x 0 2 y y 0 ) / ( 2 ρ ) , ρ = x 2 + y 2 + z 2 , E 3 ( x , y , z ) = i z λ ρ exp ( i k ρ ) ρ s E 2 ( x 0 , y 0 ) × exp [ i k ( x 0 2 + y 0 2 2 x x 0 2 y y 0 ) / ( 2 ρ ) ] d x 0 d y 0
U ( x , y , z ) = D f ( x 0 , y 0 ) exp [ i k g ( x 0 , y 0 ) ] d x 0 d y 0 2 π σ k | H | f ( x s , y s ) exp [ i k g ( x s , y s ) ] ,
H = 2 g x 0 2 2 g y 0 2 ( 2 g x 0 y 0 ) 2
σ = { 1 ( if     H < 0 ) i ( if     H > 0 , 2 g x 0 2 | x s , y s > 0 ) i ( if     H > 0 , 2 g x 0 2 | x s , y s < 0 ) .
g ( x 0 , y 0 ) = ( x 0 2 + y 0 2 2 x x 0 2 y y 0 ) / ( 2 ρ ) .
g x 0 = x 0 x x 2 + y 2 + z 2 = 0 , g y 0 = y 0 y x 2 + y 2 + z 2 = 0 ,
x s = x , y s = y ,
H = 2 g x 0 2 2 g y 0 2 ( 2 g x 0 y 0 ) 2 = 1 x 2 + y 2 + z 2 = 1 ρ 2
σ = i .
E 3 ( x , y , z ) = A ( f l H ) z ρ r 2 Γ 2 Γ 2 + x 2 exp ( y 2 Ω 2 ) exp [ i k Δ 0 + i k ( n 1 ) Δ ( x , y ) ] exp [ i k ( r + ρ ) i k ( x 2 + y 2 ) / ( 2 ρ ) ] ,
I 3 ( x , y , z ) = [ A ( f l H ) z ρ r 2 Γ 2 Γ 2 + x 2 exp ( y 2 Ω 2 ) ] 2 .

Metrics