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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 3 — Feb. 9, 2004
  • pp: 377–383

Communication modes applied to axicons

Anna Burvall, Per Martinsson, and Ari T. Friberg  »View Author Affiliations


Optics Express, Vol. 12, Issue 3, pp. 377-383 (2004)
http://dx.doi.org/10.1364/OPEX.12.000377


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Abstract

The communication modes, which constitute a convenient method for the propagation and information analysis of optical fields, are formulated in the generalized axicon geometry. The transmitting region is the axicon’s annular aperture, and the observation domain is the optical axis containing the focal line segment. We show that in rotational symmetry one may employ the prolate spheroidal wave functions to represent the communication modes. Further, in usual circumstances the modes can be approximated by quadratic waves in the aperture domain and by sinc functions in the image domain. Both the exact communication modes and the approximate technique are confirmed numerically, with linear axicons as examples.

© 2004 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(100.3190) Image processing : Inverse problems
(230.0230) Optical devices : Optical devices

ToC Category:
Research Papers

History
Original Manuscript: December 17, 2003
Revised Manuscript: January 15, 2004
Published: February 9, 2004

Citation
Anna Burvall, Per Martinsson, and Ari Friberg, "Communication modes applied to axicons," Opt. Express 12, 377-383 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-3-377


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References

  1. J.H. McLeod, �??The axicon: a new type of optical element,�?? J. Opt. Soc. Am. 44, 592�??597 (1954). [CrossRef]
  2. L.M. Soroko, Meso-Optics �?? Foundations and Applications (World Scientific, Singapore, 1996), Chap. 2 and references therein.
  3. Z. Jaroszewicz, Axicons: Design and Propagation Properties, Research & Development Treatises, Vol. 5 (SPIE Polish Chapter, Warsaw, 1997).
  4. J.A. Davis, E. Carcole, and D.M. Cottrell, �??Range-finding by triangulation with nondifracting beams,�?? Appl. Opt. 35, 2159�??2161 (1996). [CrossRef] [PubMed]
  5. G. Haüsler and W. Heckel, �??Light sectioning with large depth and high resolution,�?? Appl. Opt. 27, 5165�??5169 (1988). [CrossRef] [PubMed]
  6. V.E. Peet and R.V. Tusbin, �??Third-harmonic generation and multiphoton ionization in Bessel beams,�?? Phys. Rev. A 56, 1613�??1620 (1997). [CrossRef]
  7. J. Arlt, T. Hitomi, and K. Dholakia, �??Atom guiding along Laguerre-Gaussian and Bessel light beams,�?? Appl. Phys. B 71, 549�??554 (2000). [CrossRef]
  8. Z. Ding, H. Ren, Y. Zhao, J.S. Nelson, and Z. Chen, �??High resolution optical coherence tomography over a large depth range with an axicon lens,�?? Opt. Lett. 27, 243�??245 (2002). [CrossRef]
  9. F. Gori and R. Grella, �??The converging prolate spheroidal functions and their use in Fresnel optics,�?? Opt. Commun. 45, 5�??10 (1983). [CrossRef]
  10. R. Pierri and F. Soldovieri, �??On the information content of the radiated fields in the near zone over bounded domains,�?? Inverse Problems 14, 321-337 (1998). [CrossRef]
  11. D.A.B. Miller, �??Communicating with waves between volumes: evaluating orthogonal spatial channels and limits on coupling strengths,�?? Appl. Opt. 39, 1681�??1699 (2000). [CrossRef]
  12. B.R. Frieden, �??Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions,�?? in Progress in Optics, Vol. IX, E. Wolf, editor (North-Holland, Amsterdam, 1971), pp. 311�??407. [CrossRef]
  13. A. Thaning, P. Martinsson, M. Karelin, and A.T. Friberg, �??Limits of diffractive optics by communication modes,�?? J. Opt. A: Pure Appl. Opt. 5 153�??158 (2003). [CrossRef]
  14. R. Pierri, A. Liseno, F. Soldovieri, and R. Solimene, �??In-depth resolution for a strip source in the Fresnel zone,�?? J. Opt. Soc. Am. A 18, 352-359 (2001). [CrossRef]
  15. R. Pierri, A. Liseno, R. Solimene, and F. Tartaglione, �??In-depth resolution from multifrequency Born fields scattered by a dielectric strip in the Fresnel zone,�?? J. Opt. Soc. Am. A 19, 1234�??1238 (2002). [CrossRef]
  16. D. Slepian and H.O. Pollak, �??Prolate spheroidal wave functions, Fourier analysis and uncertainty �?? I,�?? Bell Syst. Techn. J. 40, 43�??63 (1961).
  17. H.J. Landau and H.O. Pollak, �??Prolate spheroidal wave functions, Fourier analysis and uncertainty �?? II,�?? Bell Syst. Techn. J. 40, 65�??84 (1961).
  18. B. Saleh, Photoelectron Statistics (Springer-Verlag, Heidelberg, 1978), chap. 2.4.4.

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