RT Journal Article T1 Optical system design for orthosymplectic transformations in phase space A1 Rodrigo Martín-Romo, José Augusto A1 Alieva, Tatiana Krasheninnikova A1 Calvo Padilla, María Luisa AB 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. PB Optical Society of America SN 1084-7529 YR 2006 FD 2006-10 LK https://hdl.handle.net/20.500.14352/51044 UL https://hdl.handle.net/20.500.14352/51044 LA eng NO 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). NO © 2006 Optical Society of America.The Spanish Ministry of Education and Science is acknowledged for financial support (Ramon y Cajal grant, T. Alieva) and projects TIC 2002-01846 and TEC 2005-02180/MIC. The authors thank Martin Bastiaans for careful reading of the manuscript and helpful discussions. NO Ministerio de Educación y Ciencia (MEC), España DS Docta Complutense RD 9 dic 2023