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.

© 2007 Optical Society of America

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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).
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    [CrossRef]
  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]

2006 (3)

2005 (2)

2004 (1)

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

2000 (1)

1994 (1)

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).

1993 (1)

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]

1991 (1)

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

Abramochkin, E. G.

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

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

Agullo Lopez, F.

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).

Alieva, T.

Allen, L.

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]

Almazov, A. A.

Almeida, L. B.

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).

Bastiaans, M.

Beijersbergen, M. W.

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]

Calvo, G. F.

Calvo, M. L.

Jefimovs, K.

Khonina, S. N.

Kotlyar, V. V.

Lopez, V.

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).

Rodrigo, J. A.

Simon, R.

Soifer, V. A.

Turunen, J.

Van der Veen, H. E. L. O.

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]

Volostnikov, V. G.

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

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

Woerdman, J. P.

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]

Wolf, K. B.

J. Mod. Opt. (1)

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).

J. Opt. A.: Pure Appl. Opt. (1)

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

J. Opt. Soc. Am. A (4)

Opt. Commun. (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]

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

Opt. Lett. (2)

Other (4)

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).

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

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).

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