Gyrator transform: properties and applications

doi:10.1364/OE.15.002190

Gyrator transform: properties and applications

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

Optics Express, Vol. 15, Issue 5, pp. 2190-2203 (2007)
http://dx.doi.org/10.1364/OE.15.002190

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Abstract
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References (14)
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Abstract

In this work we formulate the main properties of the gyrator operation which produces a rotation in the twisting (position - spatial frequency) phase planes. This transform can be easily performed in paraxial optics that underlines its possible application for image processing, holography, beam characterization, mode conversion and quantum information.As an example, it is demonstrated the application of gyrator transform for the generation of a variety of stable modes.

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(140.3300) Lasers and laser optics : Laser beam shaping
(200.4740) Optics in computing : Optical processing

ToC Category:
Fourier Optics and Optical Signal Processing

History
Original Manuscript: December 7, 2006
Revised Manuscript: January 16, 2007
Manuscript Accepted: January 22, 2007
Published: March 5, 2007

Citation
José A. Rodrigo, Tatiana Alieva, and María L. Calvo, "Gyrator transform: properties and applications," Opt. Express 15, 2190-2203 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2190

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References

H. M. Ozaktas, Z. Zalevsky, and M. Alper Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (John Wiley and Sons, NY, USA (2001).
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). [CrossRef]
E. G. Abramochkin and V. G. Volostnikov, "Beam transformations and nontransformed beams," Opt. Commun. 83, 123-135 (1991). [CrossRef]
E. G. Abramochkin and V. G. Volostnikov, "Generalized Gaussian beams," J. Opt. A.: Pure Appl. Opt. 6, S157- S161 (2004). [CrossRef]
G. F. Calvo, "Wigner representation and geometric transformations of optical orbital angular momentum spatial modes," Opt. Lett. 30, 1207-1209 (2005). [CrossRef] [PubMed]
R. Simon and K. B. Wolf, "Structure of the set of paraxial optical systems," J. Opt. Soc. Am. A 17, 342-355 (2000). [CrossRef]
K. B. Wolf, Geometric Optics on Phase Space (Springer-Verlag, Berlin, 2004).
J. A. Rodrigo, T. Alieva, M. L. Calvo, "Optical system design for ortho-symplectic transformations in phase space," J. Opt. Soc. Am. A 23, 2494-2500 (2006). [CrossRef]
T. Alieva, V. Lopez, F. Agullo Lopez, L. B. Almeida, "The fractional Fourier transform in optical propagation problems, " J. Mod. Opt. 41, 1037-1044 (1994). [CrossRef]
M. Bastiaans and T. Alieva, "First-order optical systems with unimodular eigenvalues," J. Opt. Soc. Am. A 23, 1875-1883 (2006). [CrossRef]
T. Alieva and M. Bastiaans, "Mode mapping in paraxial lossless optics," Opt. Lett. 30, 1461-1463 (2005). [CrossRef] [PubMed]
M. Abramowitz and I. A. Stegun, eds., Pocketbook of Mathematical Functions, Frankfurt am Main, Germany (1984).
I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products (Academic Press, NY, USA, 1996).
V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs and J. Turunen, "Elliptic Laguerre- Gaussian beams," J. Opt. Soc. Am. A 23, 43-56, (2006). [CrossRef]

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[1] H. M. Ozaktas, Z. Zalevsky, and M. Alper Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (John Wiley and Sons, NY, USA (2001).

[2] 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). [CrossRef]

[3] E. G. Abramochkin and V. G. Volostnikov, "Beam transformations and nontransformed beams," Opt. Commun. 83, 123-135 (1991). [CrossRef]

[4] E. G. Abramochkin and V. G. Volostnikov, "Generalized Gaussian beams," J. Opt. A.: Pure Appl. Opt. 6, S157- S161 (2004). [CrossRef]

[5] G. F. Calvo, "Wigner representation and geometric transformations of optical orbital angular momentum spatial modes," Opt. Lett. 30, 1207-1209 (2005). [CrossRef] [PubMed]

[6] R. Simon and K. B. Wolf, "Structure of the set of paraxial optical systems," J. Opt. Soc. Am. A 17, 342-355 (2000). [CrossRef]

[7] K. B. Wolf, Geometric Optics on Phase Space (Springer-Verlag, Berlin, 2004).

[8] J. A. Rodrigo, T. Alieva, M. L. Calvo, "Optical system design for ortho-symplectic transformations in phase space," J. Opt. Soc. Am. A 23, 2494-2500 (2006). [CrossRef]

[9] T. Alieva, V. Lopez, F. Agullo Lopez, L. B. Almeida, "The fractional Fourier transform in optical propagation problems, " J. Mod. Opt. 41, 1037-1044 (1994). [CrossRef]

[10] M. Bastiaans and T. Alieva, "First-order optical systems with unimodular eigenvalues," J. Opt. Soc. Am. A 23, 1875-1883 (2006). [CrossRef]

[11] T. Alieva and M. Bastiaans, "Mode mapping in paraxial lossless optics," Opt. Lett. 30, 1461-1463 (2005). [CrossRef] [PubMed]

[12] M. Abramowitz and I. A. Stegun, eds., Pocketbook of Mathematical Functions, Frankfurt am Main, Germany (1984).

[13] I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products (Academic Press, NY, USA, 1996).

[14] V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs and J. Turunen, "Elliptic Laguerre- Gaussian beams," J. Opt. Soc. Am. A 23, 43-56, (2006). [CrossRef]

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Gyrator transform: properties and applications