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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 3 — Mar. 1, 2010
  • pp: 637–647

Propagation of a general-type beam through a truncated fractional Fourier transform optical system

Chengliang Zhao and Yangjian Cai  »View Author Affiliations


JOSA A, Vol. 27, Issue 3, pp. 637-647 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000637


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Abstract

Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams—such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams—through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.

© 2010 Optical Society of America

OCIS Codes
(350.5500) Other areas of optics : Propagation
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms
(140.3295) Lasers and laser optics : Laser beam characterization

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: November 24, 2009
Revised Manuscript: January 6, 2010
Manuscript Accepted: January 6, 2010
Published: February 26, 2010

Citation
Chengliang Zhao and Yangjian Cai, "Propagation of a general-type beam through a truncated fractional Fourier transform optical system," J. Opt. Soc. Am. A 27, 637-647 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-3-637


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References

  1. F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335-341 (1994). [CrossRef]
  2. Y. Li, “Light beam with flat-topped profiles,” Opt. Lett. 27, 1007-1009 (2002). [CrossRef]
  3. Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beam and its propagation properties,” Opt. Lett. 28, 1084-1086 (2003). [CrossRef] [PubMed]
  4. H. T. Eyyuboğlu and Y. Baykal, “Reciprocity of cos-Gaussian and cosh-Gaussian laser beams in turbulent atmosphere,” Opt. Express 12, 4659-4674 (2004). [CrossRef] [PubMed]
  5. H. T. Eyyuboğlu, “Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere,” J. Opt. Soc. Am. A 22, 1527-1535 (2005). [CrossRef]
  6. H. T. Eyyuboğlu and Y. Baykal, “Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere,” J. Opt. Soc. Am. A 22, 2709-2718 (2005). [CrossRef]
  7. D. Deng and Q. Guo, “Elegant Hermite-Laguerre-Gaussian beams,” Opt. Lett. 33, 1225-1227 (2008). [CrossRef] [PubMed]
  8. X. Chu, “Propagation of a cosh-Gaussian beam through an optical system in turbulent atmosphere,” Opt. Express 15, 17613-17618 (2007). [CrossRef] [PubMed]
  9. S. A. Arpali, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of higher order cos-Gaussian, cosh-Gaussian and annular beams,” J. Mod. Opt. 55, 227-239 (2008). [CrossRef]
  10. G. Zhou and X. Chu, “Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere,” Opt. Express 17, 10529-10534 (2009). [CrossRef] [PubMed]
  11. Y. Baykal, “Formulation of correlations for general-type beams in atmospheric turbulence,” J. Opt. Soc. Am. A 23, 889-893 (2006). [CrossRef]
  12. Ç. Arpali, C. Yazıcıoğlu, H. T. Eyyuboğlu, S. A. Arpali, and Y. Baykal, “Simulator for general-type beam propagation in turbulent atmosphere,” Opt. Express 14, 8918-8928 (2006). [CrossRef] [PubMed]
  13. H. T. Eyyuboğlu and Y. Baykal, “Angle-of-arrival fluctuations for general-type beams,” Opt. Eng. (Bellingham) 46, 096001 (2007). [CrossRef]
  14. Y. Baykal, “Structure functions in turbulence for incidence with arbitrary-field distribution,” J. Opt. Soc. Am. A 24, 1726-1730 (2007). [CrossRef]
  15. Y. Baykal and H. T. Eyyuboğlu, “Intensity fluctuations of focused general-type beams in atmospheric optics links,” Proc. SPIE 6603, 60320-1-60320-8 (2007).
  16. H. T. Eyyuboğlu and Y. Baykal, “Generalized beams in ABCD GH systems,” Opt. Commun. 272, 22-31 (2007). [CrossRef]
  17. X. Ji, X. Li, and G. Ji, “Directionality of general beams,” Opt. Express 16, 18850-18856 (2008). [CrossRef]
  18. D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875-1881 (1993). [CrossRef]
  19. H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522-2531 (1993). [CrossRef]
  20. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181-2186 (1993). [CrossRef]
  21. A. W. Lohmann, D. Medlovic, and Z. Zalevsky, “Fractional transformations in optics,” in Progress in Optics, Vol. XXXVIII, E.Wolf, ed. (Elsevier, 1998). [CrossRef]
  22. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).
  23. Q. Lin and Y. Cai, “Fractional Fourier transform for partially coherent Gaussian Schell-model beams,” Opt. Lett. 27, 1672-1674 (2002). [CrossRef]
  24. Y. Cai and Q. Lin, “Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane,” J. Opt. Soc. Am. A 20, 1528-1536 (2003). [CrossRef]
  25. Y. Cai, D. Ge, and Q. Lin, “Fractional Fourier transform for partially coherent and partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 5, 453-459 (2003). [CrossRef]
  26. D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, and X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148-154 (2004). [CrossRef]
  27. Z. Mei and D. Zhao, “Propagation of Laguerre-Gaussian and elegant Laguerre-Gaussian beams in apertured fractional Hankel transform systems,” J. Opt. Soc. Am. A 21, 2375-2381 (2004). [CrossRef]
  28. Y. Cai and Q. Lin, “Fractional Fourier transform for elliptical Gaussian beam,” Opt. Commun. 217, 7-13 (2003). [CrossRef]
  29. Y. Cai and Q. Lin, “Properties of flattened Gaussian beam in the Fractional Fourier transform plane,” J. Opt. A, Pure Appl. Opt. 5, 272-275 (2003). [CrossRef]
  30. F. Wang and Y. Cai, “Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics,” J. Opt. Soc. Am. A 24, 1937-1944 (2007). [CrossRef]
  31. F. Wang, Y. Cai, and Q. Lin, “Experimental observation of truncated fractional Fourier transform for a partially coherent Gaussian Schell-model beam,” J. Opt. Soc. Am. A 25, 2001-2010 (2008). [CrossRef]
  32. G. Zhou, “Fractional Fourier transform of a higher-order cosh-Gaussian beam,” J. Mod. Opt. 56, 886-892 (2009). [CrossRef]
  33. B. Tang and M. Xu, “Fractional Fourier transform for beams generated by Gaussian mirror resonator,” J. Mod. Opt. 56, 1276-1282 (2009). [CrossRef]
  34. Y. Cai, Q. Lin, and S. Zhu, “Coincidence fractional Fourier transform with entangled photon pairs and incoherent light,” Appl. Phys. Lett. 86, 021112 (2005). [CrossRef]
  35. Y. Cai and S. Zhu, “Coincidence fractional Fourier transform with partially coherent light radiation,” J. Opt. Soc. Am. A 22, 1798-1804 (2005). [CrossRef]
  36. F. Wang, Y. Cai, and S. He, “Experimental observation of coincidence fractional Fourier transform with a partially coherent beam,” Opt. Express 14, 6999-7004 (2006). [CrossRef] [PubMed]
  37. Y. Cai and F. Wang, “Lensless optical implementation of the coincidence fractional Fourier transform,” Opt. Lett. 31, 2278-2280 (2007). [CrossRef]
  38. F. Wang, Y. Cai, and Y. Ma, “Sixth-order coincidence fractional Fourier transform implemented with partially coherent light,” Appl. Phys. B 98, 187-193 (2010). [CrossRef]
  39. S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168-1177 (1970). [CrossRef]
  40. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U. S. Department of Commerce, 1970).
  41. A. Erdelyi, W. Magnus, and F. Oberhettinger, Tables of Integral Transforms (McGraw-Hill, 1954).
  42. J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752-1756 (1988). [CrossRef]
  43. D. Ding and X. Liu, “Approximate description of Bessel, Bessel-Gauss, and Gaussian beams with finite aperture,” J. Opt. Soc. Am. A 16, 1296-1293 (1999). [CrossRef]
  44. W. H. Carter, “Spot size and divergence for Hermite-Gaussian beams of any order,” Appl. Opt. 19, 1027-1029 (1980). [CrossRef] [PubMed]

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