Abstract

A Collins transformation maps an orthonormal set of Hermite-Gaussian modes into an orthonormal set of beams with a Gaussian envelope. Among these beams are Laguerre-Gaussian beams and the recently introduced Hermite-Laguerre-Gaussian beams. Compact expressions for the complex field amplitudes of these modes are derived. The results obtained are useful for description of the propagation of light through first-order optical systems, for the solution of the phase-retrieval problem by noninterferometric techniques, and for the design of mode converters and information processing systems.

© 2005 Optical Society of America

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    [CrossRef]
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2005

M. J. Bastiaans and T. Alieva, J. Phys. A 38, L73 (2005).

2004

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

A. A. Malyutin, Quantum Electron. 34, 165 (2004).

2000

1970

Abramochkin, E. G.

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

Agarwal, G. S.

Alieva, T.

M. J. Bastiaans and T. Alieva, J. Phys. A 38, L73 (2005).

Bastiaans, M. J.

M. J. Bastiaans and T. Alieva, J. Phys. A 38, L73 (2005).

Collins, S. A.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, 1966).

Malyutin, A. A.

A. A. Malyutin, Quantum Electron. 34, 165 (2004).

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.

Wünsche, A.

A. Wünsche, J. Phys. A 33, 1603 (2000).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. A

M. J. Bastiaans and T. Alieva, J. Phys. A 38, L73 (2005).

A. Wünsche, J. Phys. A 33, 1603 (2000).
[CrossRef]

Opt. Lett.

Quantum Electron.

A. A. Malyutin, Quantum Electron. 34, 165 (2004).

Other

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, 1966).

M.Abramowitz and I.A.Stegun eds., Pocketbook of Mathematical Functions (Harri Deutsch, 1984).

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