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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 10 — Oct. 1, 2006
  • pp: 2494–2500

Optical system design for orthosymplectic transformations in phase space

José A. Rodrigo, Tatiana Alieva, and María Luisa Calvo  »View Author Affiliations

JOSA A, Vol. 23, Issue 10, pp. 2494-2500 (2006)

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On the basis of a matrix formalism, we analyze the paraxial optical systems composed by generalized lenses and fixed free-space intervals, suitable for orthosymplectic transformations in phase space. Flexible configurations to perform the attractive operations for optical information processing such as image rotation, separable fractional Fourier transformation, and twisting for different parameters are proposed.

© 2006 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.4560) Fourier optics and signal processing : Data processing by optical means
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(200.4740) Optics in computing : Optical processing
(220.4830) Optical design and fabrication : Systems design

ToC Category:
Fourier Optics and Optical Signal Processing

Original Manuscript: January 4, 2006
Revised Manuscript: April 18, 2006
Manuscript Accepted: May 11, 2006

José A. Rodrigo, Tatiana Alieva, and María Luisa Calvo, "Optical system design for orthosymplectic transformations in phase space," J. Opt. Soc. Am. A 23, 2494-2500 (2006)

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  1. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1966).
  2. J. Shamir, "Cylindrical lens described by operator algebra," Appl. Opt. 18, 4195-4202 (1979).
  3. B. Macukow and H. H. Arsenault, "Matrix decomposition for nonsymmetrical optical systems," J. Opt. Soc. Am. 73, 1360-1366 (1983).
  4. H. Braunecker, O. Bryngdahl, and B. Schnell, "Optical system for image rotation and magnification," J. Opt. Soc. Am. 70, 137-141 (1980).
  5. D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transform and their optical implementation," J. Opt. Soc. Am. A 10, 1875-1881 (1993).
  6. A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional order Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993).
  7. G. Nemes and A. G. Kostenbauder, "Optical systems for rotating a beam," in Proceedings of the Workshop on Laser Beam Characterization, P.M.Mejias, H.Weber, R.Martinez-Herrero, and A.Gonzales-Urena, eds. (Sociedad Española de Optica, 1993), pp. 99-109.
  8. G. Nemes and A. E. Seigman, "Measurement of all ten second-order moments of an astigmatic beam by use of rotating simple astigmatic (anamorphic) optics," J. Opt. Soc. Am. A 11, 2257-2264 (1994).
  9. D. Mendlovic, Y. Bitran, R. G. Dorsch, C. Ferreira, J. Garcia, and H. M. Ozaktas, "Anamorphic fractional Fourier transform: optical implementation and applications?" Appl. Opt. 34, 7451-7456 (1995).
  10. M. F. Erden, H. M. Ozaktas, A. Sahin, and D. Mendlovic, "Design of dynamically adjustable anamorphic fractional transformer Fourier," Opt. Commun. 136, 52-60 (1997).
  11. A. Sahin, H. M. Ozaktas, and D. Mendlovic, "Optical implementations of two-dimensional fractional Fourier transforms and linear canonical transforms with arbitrary parameters," Appl. Opt. 37, 2130-2141 (1998).
  12. I. Moreno, J. A. Davis, and K. Crabtree, "Fractional Fourier transform optical system with programmable diffractive lenses," Appl. Opt. 42, 6544-6548 (2003).
  13. A. A. Malyutin, "Tunable Fourier transformer of the fractional order," Quantum Electron. 36, 79-83 (2006).
  14. R. Simon and K. B. Wolf, "Fractional Fourier transforms in two dimensions," J. Opt. Soc. Am. A 17, 2368-2381 (2000).
  15. R. Simon and K. B. Wolf, "Structure of the set of paraxial optical systems," J. Opt. Soc. Am. A 17, 342-355 (2000).
  16. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123-132 (1993).
  17. E. G. Abramochkin and V. G. Volostnikov, "Generalized Gaussian beams," J. Opt. A, Pure Appl. Opt. 6, S157-S161 (2004).
  18. K. B. Wolf, Geometric Optics on Phase Space (Springer-Verlag, 2004).
  19. T. Alieva and M. Bastiaans, "Alternative representation of the linear canonical integral transform," Opt. Lett. 30, 3302-3304 (2005).

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