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Applied Optics

Applied Optics


  • Vol. 36, Iss. 34 — Dec. 1, 1997
  • pp: 8952–8957

Model of structure of hollow searchlight laser beam: low-frequency approximation

O. I. Aldoshina, V. V. Bacherikov, and A. V. Fabrikov  »View Author Affiliations

Applied Optics, Vol. 36, Issue 34, pp. 8952-8957 (1997)

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We introduce a powerful but simple methodology for numerical modeling of the far field of a hollow searchlight laser beam that is produced by passing a laser beam through a reflaxicon. Such a beam can be used in remote sensing as a space beacon. The far field is described by a Fourier–Bessel transform over an aperture function that includes a conical phase term introduced by the reflaxicon. Computations of the far field of the reflaxicon are difficult. The conventional approach for calculating the far field of such ideal aperture distributions as a plane wave or a Gaussian beam is to find exact solutions in the form of hypergeometric series and determine their asymptotic approximations for large values of some parameter. This approach does not extend to more complicated aperture distributions. We modify the transform by using the asymptotic form for the Bessel function as well as by limiting this form to include only the low-frequency (difference frequency) term. This approach is easily related to a one-dimensional Fourier transform of the aperture distribution, and thus numerical evaluations that make use of this approach can use the fast Fourier transform.

© 1997 Optical Society of America

Original Manuscript: July 21, 1997
Published: December 1, 1997

O. I. Aldoshina, V. V. Bacherikov, and A. V. Fabrikov, "Model of structure of hollow searchlight laser beam: low-frequency approximation," Appl. Opt. 36, 8952-8957 (1997)

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  1. W. R. Edmonds, “The reflaxicon, a new reflective optical element, and some applications,” Appl. Opt. 12, 1940–1945 (1973). [CrossRef]
  2. J. H. Mcleod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954). [CrossRef]
  3. P. A. Belanger, M. Rioux, “Diffraction ring pattern at the focal plane of a spherical lens–axicon doublet,” Can. J. Phys. 54, 1774–1780 (1976). [CrossRef]
  4. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. 6, 150–152 (1989). [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Toronto, 1975).
  6. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1981).
  7. P. A. Belanger, M. Rioux, “Ring pattern of a lens–axicon doublet illuminated by a Gaussian beam,” Appl. Opt. 17, 1080–1086 (1978). [CrossRef]
  8. M. Abramowitz, I. Stigan, eds., Handbook of Mathematical Functions with Formulas (National Bureau of Standards, Washington, D.C., 1964).
  9. Y. L. Luke, Mathematical Functions and Their Approximations (Academic, New York, 1975).
  10. O. I. Smokty, A. V. Fabrikov, “Modeling the diffraction field in axicon–lens system,” Izv. Vyssh. Uchebn. Zaved. Fiz. 12, 36–41 (1987) (in Russian).
  11. M. V. Perez, C. Gomez-Rieno, J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicon,” Opt. Acta 33, 1161–1176 (1986). [CrossRef]
  12. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), No. 7.340.
  13. O. I. Smokty, A. V. Fabrikov, “Modelling the diffraction field in axicon–lens system illuminated by Gaussian beam,” in Problems of Data Processing and Integral Automation of the Production in Transactions of Leningrad Institute of Information Science, Academy of Sciences of the USSR (Nauka, Leningrad, 1990), pp. 186–191 (in Russian).

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