Abstract

We show that the apodized annular-aperture logarithmic axicon preserves excellent uniformity of the on-axis intensity, energy flow, and lateral resolution. Numerical evaluation of the Fresnel diffraction integral leads to results very close to geometrical-optics predictions. Once again the geometrical law of energy conservation turns out to be a useful tool in designing axicons.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Sochacki, A. Kołodziejczyk, Z. Jaroszewicz, S. Bará, Appl. Opt. 31, 5326 (1992).
    [CrossRef] [PubMed]
  2. J. Sochacki, S. Bará, Z. Jaroszewicz, A. Kołodziejczyk, Opt. Lett. 17, 7 (1992).
    [CrossRef] [PubMed]
  3. L. R. Staroński, J. Sochacki, Z. Jaroszewicz, A. Kołodziejczyk, J. Opt. Soc. Am. A 9, 2091 (1992).
    [CrossRef]
  4. J. Sochacki, Z. Jaroszewicz, L. R. Staroński, A. Kołodziejczyk, J. Opt. Soc. Am. A 10, 1765 (1993).
    [CrossRef]
  5. R. M. Herman, T. A. Wiggins, Appl. Opt. 31, 5913 (1992).
    [CrossRef] [PubMed]
  6. A. J. Cox, J. D’Anna, Opt. Lett. 17, 232 (1992).
    [CrossRef] [PubMed]

1993 (1)

1992 (5)

Bará, S.

Cox, A. J.

D’Anna, J.

Herman, R. M.

Jaroszewicz, Z.

Kolodziejczyk, A.

Sochacki, J.

Staronski, L. R.

Wiggins, T. A.

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 (3)

Fig. 1
Fig. 1

Geometry of the apodized annular-aperture logarithmic axicon.

Fig. 2
Fig. 2

On-axis intensity distribution for the apodized annular-aperture logarithmic axicon with d1 = 100 mm, d2 = 200 mm, and Δz = 20.5 mm (λ = 0.633 μm), calculated with the help of Eq. (10).

Fig. 3
Fig. 3

Lateral intensity distribution for the apodized annular-aperture logarithmic axicon along the focal region d1zd2. The axicon’s parameters are the same as in Fig. 2.

Equations (10)

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

φ ( r ) = R 2 ( d 1 + d 2 ) 2 d 2 2 ln [ d 1 d 2 d 1 + d 2 + d 2 2 R 2 ( d 1 + d 2 ) r 2 ] , d 1 d 2 R r R ,
z ( r ) = d 1 d 2 d 1 + d 2 + d 2 2 R 2 ( d 1 + d 2 ) r 2 , d 1 d 2 R r R ,
P z ( z ) = { P z sin 4 [ π ( z d 1 ) / 2 Δ z ] d 1 z d 1 + Δ z P z = const . d 1 + Δ z z d 2 Δ z P z sin 4 [ π ( d 2 z ) / 2 Δ z ] d 2 Δ z z d 2 ,
Δ z d 2 d 1 .
2 π P σ T ( r ) r d r = P z ( z ) d z ,
T ( r ) = d 2 2 π R 2 ( d 1 + d 2 ) P σ P z [ z ( r ) ] , d 1 d 2 R r R ,
π R 2 ( 1 d 1 2 / d 2 2 ) P σ = ( d 2 d 1 ) P z ,
T ( r ) = { sin 4 [ π d 2 2 ( r 2 R 2 d 1 2 / d 2 2 ) 2 R 2 ( d 1 + d 2 ) Δ z ] d 1 d 2 R r d 1 d 2 R ( 1 + d 1 + d 2 d 1 2 Δ z ) 1 / 2 1 d 1 d 2 R ( 1 + d 1 + d 2 d 1 2 Δ z ) 1 / 2 r R ( 1 d 1 + d 2 d 2 2 Δ z ) 1 / 2 sin 4 [ π d 2 2 ( R 2 r 2 ) 2 R 2 ( d 1 + d 2 ) Δ z ] R ( 1 d 1 + d 2 d 2 2 Δ z ) 1 / 2 r R .
A ( r ) = [ T ( r ) ] 1 / 2 .
I ( r , z ) = ( 2 π λ z ) 2 | d 1 R / d 2 R A ( r ) exp { 2 π i λ [ r 2 2 z + φ ( r ) ] } × J 0 ( 2 π r r / λ z ) r d r | 2 ,

Metrics