Experimental implementation of the gyrator transform

Thumbnail Image
Full text at PDC
Publication Date
Rodrigo Martín-Romo, José Augusto
Alieva, Tatiana Krasheninnikova
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Optical Society of America
Google Scholar
Research Projects
Organizational Units
Journal Issue
The gyrator transform (GT) promises to be a useful tool in image processing, holography, beam characterization, mode transformation, and quantum information. We introduce what we believe to be the first flexible optical experimental setup that performs the GT for a wide range of transformation parameters. The feasibility of the proposed scheme is demonstrated on the gyrator transformation of Hermite-Gaussian modes. For certain parameters the output mode corresponds to the Laguerre-Gaussian one.
© 2007 Optical Society of America The Spanish Ministry of Education and Science is acknowledged for financial support, project TEC 2005-02180/MIC.
1. R. Simon and K. B. Wolf, "Structure of the set of paraxial optical systems”, J. Opt. Soc. Am. A 17, 342-355 (2000). 2. K. B. Wolf, Geometric Optics on Phase Space (Springer-Verlag, 2004). 3. J. A. Rodrigo, T. Alieva, and M. L. Calvo, "Gyrator transform: properties and applications”, Opt. Express 15, 2190-2203 (2007). 4. H. M. Ozaktas, Z. Zalevsky, and M. Alper Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001). 5. J. A. Rodrigo, T. Alieva, and M. L. Calvo, "Gyrator transform for image processing”, Opt. Commun. , in press, doi: 10.1016/j.optcom.2007.06.023. 6. G. F. Calvo, "Wigner representation and geometric transformations of optical orbital angular momentum spatial modes”, Opt. Lett. 30, 1207-1209 (2005). 7. T. Alieva and M. Bastiaans, "Orthonormal mode sets for the two-dimensional fractional Fourier transformation”, Opt. Lett. 32, 1226-1228 (2007). 8. E. G. Abramochkin and V. G. Volostnikov, "Generalized Gaussian beams”, J. Opt. A, Pure Appl. Opt. 6, S157-S161 (2004). 9. J. A. Rodrigo, T. Alieva, and M. L. Calvo, "Optical system design for ortho-symplectic transformations in phase space”, J. Opt. Soc. Am. A 23, 2494-2500 (2006). 10. J. Shamir, "Cylindrical lens described by operator algebra”, Appl. Opt. 18, 4195-4202 (1979). 11. 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). 12. V.A.Soifer, ed., Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).