Abstract

A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincaré sphere are studied.

© 2007 Optical Society of America

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2006 (1)

2005 (3)

2004 (1)

E. G. Abramochkin and V. G. Volostnikov, J. Opt. A, Pure Appl. Opt. 6, S157 (2004).
[CrossRef]

2000 (2)

1999 (1)

T. Alieva and A. M. Barbé, J. Mod. Opt. 46, 83 (1999).
[CrossRef]

1998 (1)

L. Yu, W. D. Huang, M. C. Huang, Z. Z. Zhu, X. M. Zeng, and W. Ji, J. Phys. A 31, 9353 (1998).
[CrossRef]

1994 (1)

T. Alieva, V. Lopez, F. Agullo-Lopez, and L. B. Almeida, J. Mod. Opt. 41, 1037 (1994).

1970 (1)

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, J. Opt. A, Pure Appl. Opt. 6, S157 (2004).
[CrossRef]

Agarwal, G. S.

Agullo-Lopez, F.

T. Alieva, V. Lopez, F. Agullo-Lopez, and L. B. Almeida, J. Mod. Opt. 41, 1037 (1994).

Alieva, T.

Almeida, L. B.

T. Alieva, V. Lopez, F. Agullo-Lopez, and L. B. Almeida, J. Mod. Opt. 41, 1037 (1994).

Barbé, A. M.

T. Alieva and A. M. Barbé, J. Mod. Opt. 46, 83 (1999).
[CrossRef]

Bastiaans, M. J.

Calvo, G. F.

Collins, S. A.

Huang, M. C.

L. Yu, W. D. Huang, M. C. Huang, Z. Z. Zhu, X. M. Zeng, and W. Ji, J. Phys. A 31, 9353 (1998).
[CrossRef]

Huang, W. D.

L. Yu, W. D. Huang, M. C. Huang, Z. Z. Zhu, X. M. Zeng, and W. Ji, J. Phys. A 31, 9353 (1998).
[CrossRef]

Ji, W.

L. Yu, W. D. Huang, M. C. Huang, Z. Z. Zhu, X. M. Zeng, and W. Ji, J. Phys. A 31, 9353 (1998).
[CrossRef]

Kutay, M. A.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Lopez, V.

T. Alieva, V. Lopez, F. Agullo-Lopez, and L. B. Almeida, J. Mod. Opt. 41, 1037 (1994).

Ozaktas, H. M.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Simon, R.

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, J. Opt. A, Pure Appl. Opt. 6, S157 (2004).
[CrossRef]

Wolf, K. B.

Yu, L.

L. Yu, W. D. Huang, M. C. Huang, Z. Z. Zhu, X. M. Zeng, and W. Ji, J. Phys. A 31, 9353 (1998).
[CrossRef]

Zalevsky, Z.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Zeng, X. M.

L. Yu, W. D. Huang, M. C. Huang, Z. Z. Zhu, X. M. Zeng, and W. Ji, J. Phys. A 31, 9353 (1998).
[CrossRef]

Zhu, Z. Z.

L. Yu, W. D. Huang, M. C. Huang, Z. Z. Zhu, X. M. Zeng, and W. Ji, J. Phys. A 31, 9353 (1998).
[CrossRef]

J. Mod. Opt. (2)

T. Alieva, V. Lopez, F. Agullo-Lopez, and L. B. Almeida, J. Mod. Opt. 41, 1037 (1994).

T. Alieva and A. M. Barbé, J. Mod. Opt. 46, 83 (1999).
[CrossRef]

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

E. G. Abramochkin and V. G. Volostnikov, J. Opt. A, Pure Appl. Opt. 6, S157 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Phys. A (1)

L. Yu, W. D. Huang, M. C. Huang, Z. Z. Zhu, X. M. Zeng, and W. Ji, J. Phys. A 31, 9353 (1998).
[CrossRef]

Opt. Lett. (4)

Other (1)

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

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