Abstract

A refracting system is designed for transforming an annular Gaussian laser beam into a circular Bessel beam. The slope of the input and output surfaces fitted well with a sixth-order polynomial. The radii of curvature of the resulting aspheric surfaces are found to vary smoothly over the surface. The diffraction-free length for this system is found to be 59.4735 m at 633 nm.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. E. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  2. J. E. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 54, 1499–1501 (1987).
    [CrossRef]
  3. J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988).
    [CrossRef] [PubMed]
  4. A. J. Cox, D. C. Dibble, “Holographic reproduction of a diffraction-free beam,” Appl. Opt. 30, 1330–1332 (1991).
    [CrossRef] [PubMed]
  5. J. K. Jabczynski, “A diffraction-free resonator,” Opt. Commun. 77, 292–294 (1990).
    [CrossRef]
  6. M. A. Karim, A. K. Cherri, A. A. S. Awwal, A. Basit, “Refracting system for annular laser transformation,” Appl. Opt. 26, 2446–2449 (1987).
    [CrossRef] [PubMed]
  7. S. R. Jahan, M. A. Karim, “Refracting system for Gaussian-to-uniform beam transformations,” Opt. Laser Technol. 21, 27–30 (1989).
    [CrossRef]
  8. K. Thews, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
    [CrossRef]
  9. K. M. Iftekharuddin, A. A. S. Awwal, M. A. Karim, “Gaussian-to-Bessel beam transformation using a split refracting system,” Appl. Opt. 32, 2252–2256 (1993).
    [CrossRef]
  10. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  11. E. Kreyszig, Advanced Engineering Mathematics (Wiley, New York, 1983).

1993 (1)

1991 (2)

K. Thews, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

A. J. Cox, D. C. Dibble, “Holographic reproduction of a diffraction-free beam,” Appl. Opt. 30, 1330–1332 (1991).
[CrossRef] [PubMed]

1990 (1)

J. K. Jabczynski, “A diffraction-free resonator,” Opt. Commun. 77, 292–294 (1990).
[CrossRef]

1989 (1)

S. R. Jahan, M. A. Karim, “Refracting system for Gaussian-to-uniform beam transformations,” Opt. Laser Technol. 21, 27–30 (1989).
[CrossRef]

1988 (1)

1987 (3)

Awwal, A. A. S.

Basit, A.

Cherri, A. K.

Cox, A. J.

Dibble, D. C.

Durnin, J. E.

J. E. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. E. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 54, 1499–1501 (1987).
[CrossRef]

Eberly, J. H.

J. E. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 54, 1499–1501 (1987).
[CrossRef]

Friberg, A. T.

Iftekharuddin, K. M.

Jabczynski, J. K.

J. K. Jabczynski, “A diffraction-free resonator,” Opt. Commun. 77, 292–294 (1990).
[CrossRef]

Jahan, S. R.

S. R. Jahan, M. A. Karim, “Refracting system for Gaussian-to-uniform beam transformations,” Opt. Laser Technol. 21, 27–30 (1989).
[CrossRef]

Karim, M. A.

K. M. Iftekharuddin, A. A. S. Awwal, M. A. Karim, “Gaussian-to-Bessel beam transformation using a split refracting system,” Appl. Opt. 32, 2252–2256 (1993).
[CrossRef]

K. Thews, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

S. R. Jahan, M. A. Karim, “Refracting system for Gaussian-to-uniform beam transformations,” Opt. Laser Technol. 21, 27–30 (1989).
[CrossRef]

M. A. Karim, A. K. Cherri, A. A. S. Awwal, A. Basit, “Refracting system for annular laser transformation,” Appl. Opt. 26, 2446–2449 (1987).
[CrossRef] [PubMed]

Kreyszig, E.

E. Kreyszig, Advanced Engineering Mathematics (Wiley, New York, 1983).

Miceli, J. J.

J. E. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 54, 1499–1501 (1987).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Thews, K.

K. Thews, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

Turunen, J.

Vasara, A.

Appl. Opt. (4)

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

Opt. Commun. (1)

J. K. Jabczynski, “A diffraction-free resonator,” Opt. Commun. 77, 292–294 (1990).
[CrossRef]

Opt. Laser Technol. (2)

S. R. Jahan, M. A. Karim, “Refracting system for Gaussian-to-uniform beam transformations,” Opt. Laser Technol. 21, 27–30 (1989).
[CrossRef]

K. Thews, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

Phys. Rev. Lett. (1)

J. E. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 54, 1499–1501 (1987).
[CrossRef]

Other (2)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

E. Kreyszig, Advanced Engineering Mathematics (Wiley, New York, 1983).

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 (6)

Fig. 1
Fig. 1

Half of the axially symmetric single-element refracting system.

Fig. 2
Fig. 2

Intensity profile for (a) annular Gaussian, (b) Bessel beams.

Fig. 3
Fig. 3

Plots of (a) dy i /dr i versus r i , (b) dy o /dr o versus r o for the system.

Fig. 4
Fig. 4

Plots of (a) y i versus r i , (b) y o versus r o for the system.

Fig. 5
Fig. 5

Plots of R versus r for (a) input, (b) output surfaces.

Fig. 6
Fig. 6

Ray tracing through the refractive system.

Equations (14)

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

I r = 1 - R o exp - 2 r 2 / w o 2 exp - 2 r 2 / w 2 ,
0 r i   r 1 - R o exp - 2 r 2 / w o 2 exp - 2 r 2 / w 2 d r = 0 r o   2 π ρ J o 2 α ρ d ρ ,
tan θ ii - θ ri = tan θ io - θ ro = r i - r o / D - y i + y o ,
y i + n r i - r o 2 + D - y i + y o 2 1 / 2 + d - y o = f .
w 2 4 1 - exp - 2 r i 2 / w 2 - R o 4 w o 2 w 2 w o 2 + w 2 × 1 - exp - 2 r i 2 1 w o 2 + 1 w 2 = r o 2 2   J 0 2 α r o + r o 2 2   J 1 2 α r 0 .
f = f - D - d ,
r i - r o n - cos θ ii - θ ri / sin θ ii - θ ri = f .
d y i / d r i = tan   θ ii = tan   θ io = d y o / d r o .
d y i / d r i = d y o / d r o = n / f / r i - r o 2 - n 2 + 1 1 / 2 .
d y i d r i = - 0.0003 + 0.3761 r i - 0.5897 r i 2 - 0.4568 r i 3 + 3.0606 r i 4 - 1.5157 r i 5 - 1.5018 r i 6 ,
d y o d r o = - 0.0003 + 1.2170 r o - 13.4478 r o 2 + 98.3631 r o 3 - 413.2893 r o 4 + 929.6702 r o 5 - 845.9483 r o 6 .
y i = - 0.0003 r i + 0.1881 r i 2 - 0.1966 r i 3 - 0.1142 r i 4 + 0.6121 r i 5 - 0.2526 r i 6 - 0.2145 r i 7 ,
y o = - 0.0003 r o + 0.6085 r o 2 - 4.4826 r o 3 + 24.5908 r o 4 - 82.6579 r o 5 + 154.9450 r o 6 - 120.8498 r o 7 .
R = 1 + d y / d r 2 3 / 2 / | d 2 y / d r 2 | .

Metrics