Abstract

A circular Dammann grating that can produce circular equal intensities at various orders in the far field is described. A set of parameters such as order, circular number, uniformity, and diffraction efficiency has been defined to describe the novel diffractive phase elements. Numerical solutions of binary-phase 0,π circular Dammann gratings are given. The results of experiments with a four-order circular Dammann grating made by a lithographic technique are presented. This novel diffractive optical element should be highly interesting in a wide variety of practical applications.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademia-Verlag, Berlin, 1997), Chap. 6.
  2. H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
    [CrossRef]
  3. C. Zhou and L. Liu, Appl. Opt. 34, 5961 (1995).
    [CrossRef] [PubMed]
  4. C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, Opt. Lett. 26, 93 (2001).
    [CrossRef]
  5. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  6. T. R. M. Sales and G. M. Morris, J. Opt. Soc. Am. A 14, 1637 (1997).
    [CrossRef]
  7. S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).
    [CrossRef] [PubMed]
  8. P. Xi, C. Zhou, E. Dai, and L. Liu, Opt. Lett. 27, 228 (2002).
    [CrossRef]
  9. C. Zhou, P. Xi, E. Dai, L. Liu, and H. Ru, Proc. SPIE 4470, 138 (2001).
    [CrossRef]

2002

2001

C. Zhou, P. Xi, E. Dai, L. Liu, and H. Ru, Proc. SPIE 4470, 138 (2001).
[CrossRef]

C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, Opt. Lett. 26, 93 (2001).
[CrossRef]

1997

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademia-Verlag, Berlin, 1997), Chap. 6.

T. R. M. Sales and G. M. Morris, J. Opt. Soc. Am. A 14, 1637 (1997).
[CrossRef]

1995

1983

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

1977

H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

1975

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Brodeur, A.

Dai, E.

P. Xi, C. Zhou, E. Dai, and L. Liu, Opt. Lett. 27, 228 (2002).
[CrossRef]

C. Zhou, P. Xi, E. Dai, L. Liu, and H. Ru, Proc. SPIE 4470, 138 (2001).
[CrossRef]

Dammann, H.

H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

Garcia, J. F.

Gelatt, Jr., C. D.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Klotz, E.

H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

Liu, L.

Mazur, E.

Morris, G. M.

Ru, H.

C. Zhou, P. Xi, E. Dai, L. Liu, and H. Ru, Proc. SPIE 4470, 138 (2001).
[CrossRef]

Sales, T. R. M.

Schaffer, C. B.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Xi, P.

P. Xi, C. Zhou, E. Dai, and L. Liu, Opt. Lett. 27, 228 (2002).
[CrossRef]

C. Zhou, P. Xi, E. Dai, L. Liu, and H. Ru, Proc. SPIE 4470, 138 (2001).
[CrossRef]

Zhou, C.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Acta

H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

Opt. Lett.

Proc. SPIE

C. Zhou, P. Xi, E. Dai, L. Liu, and H. Ru, Proc. SPIE 4470, 138 (2001).
[CrossRef]

Science

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Other

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademia-Verlag, Berlin, 1997), Chap. 6.

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

Experimental system for optical demonstration of a CDG. The He–Ne laser beam is expanded and collimated as a uniform laser beam to illuminate the CDG that generates the circular equal-intensity pattern that is captured by a CCD camera in the focal plane (f) of the lens.

Fig. 2
Fig. 2

Illustration of a binary phase 0,ϕ0 CDG, where rj are the radii of the phase transition points of a CDG.

Fig. 3
Fig. 3

Theoretical normalized intensity in the far field of the four-order five-circle CDG in Table 1.

Fig. 4
Fig. 4

Surface profile of the fabricated four-order five-circle CDG measured with Taylor–Hobson Talysurf (S3F) equipment. The calculated radii are listed at the top of the figure.

Fig. 5
Fig. 5

(a) Experimental image of the fabricated four-order five-circle CDG and (b) plot of intensities from the center to the outside, which is in good agreement with the theoretical result in Fig. 3.

Tables (1)

Tables Icon

Table 1 Numerical Solutions of Binary-Phase 0,π CDGs

Equations (1)

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

Up=2pJ1p-1-expiϕ0-1N+1j=1N-1-1j×rjJ1prj,

Metrics