Abstract

The closed-form propagation equation of flattened Gaussian beams passing through a paraxial optical ABCD system, in which the linear gain and absorption media are included, is derived, and its general applicable advantage is illustrated with numerical examples.

© 2000 Optical Society of America

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References

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  1. F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
    [CrossRef]
  2. V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, “Propagation of axially symmetric flattened Gaussian beams,” J. Opt. Soc. Am. A 13, 1385–1394 (1996).
    [CrossRef]
  3. S.-A. Amarande, “Beam propagation factor and kurtosis parameter of flattened Gaussian beams,” Opt. Commun. 129, 311–317 (1996).
    [CrossRef]
  4. M. Santarsiero, D. Aiello, R. Borghi, S. Vicalvi, “Focus-ing of axially symmetric flattened Gaussian beams,” J. Mod. Opt. 44, 633–650 (1997).
    [CrossRef]
  5. R. Borghi, M. Santarsiero, S. Vicalvi, “Focal shift of focused flat-topped beams,” Opt. Commun. 154, 243–248 (1998).
    [CrossRef]
  6. B. Lü, S. Luo, B. Zhang, “A comparison between the flattened Gaussian beam and super-Gaussian beam,” Optik 110, 285–287 (1999).
  7. B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
    [CrossRef]
  8. B. Lü, B. Zhang, S. Luo, “Far-field intensity distribution, M2 factor, and propagation of flattened Gaussian beams,” Appl. Opt. 20, 4581–4584 (1999).
  9. R. Borghi, M. Santarsiero, “Modal decomposition of partially coherent flat-topped beams produced by multimode lasers,” Opt. Lett. 23, 313–315 (1998).
    [CrossRef]
  10. B. Lü, S. Luo, B. Zhang, “Propagation of three-dimensional flattened Gaussian beams,” J. Mod. Opt. 46, 1753–1762 (1999).
    [CrossRef]
  11. C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation of partially coherent beams in absorbing media,” J. Mod. Opt. 42, 1123–1135 (1995).
    [CrossRef]
  12. C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation and coherence evolution of optical beams in gain media,” J. Mod. Opt. 43, 139–153 (1996).
    [CrossRef]
  13. S. A. Collins, “Lens-system diffraction integral written terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970).
    [CrossRef]
  14. A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1, pp. 146, 386.

1999 (4)

B. Lü, S. Luo, B. Zhang, “A comparison between the flattened Gaussian beam and super-Gaussian beam,” Optik 110, 285–287 (1999).

B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
[CrossRef]

B. Lü, B. Zhang, S. Luo, “Far-field intensity distribution, M2 factor, and propagation of flattened Gaussian beams,” Appl. Opt. 20, 4581–4584 (1999).

B. Lü, S. Luo, B. Zhang, “Propagation of three-dimensional flattened Gaussian beams,” J. Mod. Opt. 46, 1753–1762 (1999).
[CrossRef]

1998 (2)

R. Borghi, M. Santarsiero, “Modal decomposition of partially coherent flat-topped beams produced by multimode lasers,” Opt. Lett. 23, 313–315 (1998).
[CrossRef]

R. Borghi, M. Santarsiero, S. Vicalvi, “Focal shift of focused flat-topped beams,” Opt. Commun. 154, 243–248 (1998).
[CrossRef]

1997 (1)

M. Santarsiero, D. Aiello, R. Borghi, S. Vicalvi, “Focus-ing of axially symmetric flattened Gaussian beams,” J. Mod. Opt. 44, 633–650 (1997).
[CrossRef]

1996 (3)

S.-A. Amarande, “Beam propagation factor and kurtosis parameter of flattened Gaussian beams,” Opt. Commun. 129, 311–317 (1996).
[CrossRef]

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation and coherence evolution of optical beams in gain media,” J. Mod. Opt. 43, 139–153 (1996).
[CrossRef]

V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, “Propagation of axially symmetric flattened Gaussian beams,” J. Opt. Soc. Am. A 13, 1385–1394 (1996).
[CrossRef]

1995 (1)

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation of partially coherent beams in absorbing media,” J. Mod. Opt. 42, 1123–1135 (1995).
[CrossRef]

1994 (1)

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

1970 (1)

Aiello, D.

M. Santarsiero, D. Aiello, R. Borghi, S. Vicalvi, “Focus-ing of axially symmetric flattened Gaussian beams,” J. Mod. Opt. 44, 633–650 (1997).
[CrossRef]

Amarande, S.-A.

S.-A. Amarande, “Beam propagation factor and kurtosis parameter of flattened Gaussian beams,” Opt. Commun. 129, 311–317 (1996).
[CrossRef]

Bagini, V.

Borghi, R.

R. Borghi, M. Santarsiero, S. Vicalvi, “Focal shift of focused flat-topped beams,” Opt. Commun. 154, 243–248 (1998).
[CrossRef]

R. Borghi, M. Santarsiero, “Modal decomposition of partially coherent flat-topped beams produced by multimode lasers,” Opt. Lett. 23, 313–315 (1998).
[CrossRef]

M. Santarsiero, D. Aiello, R. Borghi, S. Vicalvi, “Focus-ing of axially symmetric flattened Gaussian beams,” J. Mod. Opt. 44, 633–650 (1997).
[CrossRef]

V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, “Propagation of axially symmetric flattened Gaussian beams,” J. Opt. Soc. Am. A 13, 1385–1394 (1996).
[CrossRef]

Cincotti, G.

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation and coherence evolution of optical beams in gain media,” J. Mod. Opt. 43, 139–153 (1996).
[CrossRef]

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation of partially coherent beams in absorbing media,” J. Mod. Opt. 42, 1123–1135 (1995).
[CrossRef]

Collins, S. A.

De Santis, P.

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation and coherence evolution of optical beams in gain media,” J. Mod. Opt. 43, 139–153 (1996).
[CrossRef]

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation of partially coherent beams in absorbing media,” J. Mod. Opt. 42, 1123–1135 (1995).
[CrossRef]

Erdelyi, A.

A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1, pp. 146, 386.

Gori, F.

Guattari, G.

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation and coherence evolution of optical beams in gain media,” J. Mod. Opt. 43, 139–153 (1996).
[CrossRef]

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation of partially coherent beams in absorbing media,” J. Mod. Opt. 42, 1123–1135 (1995).
[CrossRef]

Lü, B.

B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
[CrossRef]

B. Lü, B. Zhang, S. Luo, “Far-field intensity distribution, M2 factor, and propagation of flattened Gaussian beams,” Appl. Opt. 20, 4581–4584 (1999).

B. Lü, S. Luo, B. Zhang, “A comparison between the flattened Gaussian beam and super-Gaussian beam,” Optik 110, 285–287 (1999).

B. Lü, S. Luo, B. Zhang, “Propagation of three-dimensional flattened Gaussian beams,” J. Mod. Opt. 46, 1753–1762 (1999).
[CrossRef]

Luo, S.

B. Lü, S. Luo, B. Zhang, “Propagation of three-dimensional flattened Gaussian beams,” J. Mod. Opt. 46, 1753–1762 (1999).
[CrossRef]

B. Lü, S. Luo, B. Zhang, “A comparison between the flattened Gaussian beam and super-Gaussian beam,” Optik 110, 285–287 (1999).

B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
[CrossRef]

B. Lü, B. Zhang, S. Luo, “Far-field intensity distribution, M2 factor, and propagation of flattened Gaussian beams,” Appl. Opt. 20, 4581–4584 (1999).

Magnus, W.

A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1, pp. 146, 386.

Oberhettinger, F.

A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1, pp. 146, 386.

Pacileo, A. M.

Palma, C.

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation and coherence evolution of optical beams in gain media,” J. Mod. Opt. 43, 139–153 (1996).
[CrossRef]

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation of partially coherent beams in absorbing media,” J. Mod. Opt. 42, 1123–1135 (1995).
[CrossRef]

Santarsiero, M.

R. Borghi, M. Santarsiero, S. Vicalvi, “Focal shift of focused flat-topped beams,” Opt. Commun. 154, 243–248 (1998).
[CrossRef]

R. Borghi, M. Santarsiero, “Modal decomposition of partially coherent flat-topped beams produced by multimode lasers,” Opt. Lett. 23, 313–315 (1998).
[CrossRef]

M. Santarsiero, D. Aiello, R. Borghi, S. Vicalvi, “Focus-ing of axially symmetric flattened Gaussian beams,” J. Mod. Opt. 44, 633–650 (1997).
[CrossRef]

V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, “Propagation of axially symmetric flattened Gaussian beams,” J. Opt. Soc. Am. A 13, 1385–1394 (1996).
[CrossRef]

Tricomi, F. G.

A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1, pp. 146, 386.

Vicalvi, S.

R. Borghi, M. Santarsiero, S. Vicalvi, “Focal shift of focused flat-topped beams,” Opt. Commun. 154, 243–248 (1998).
[CrossRef]

M. Santarsiero, D. Aiello, R. Borghi, S. Vicalvi, “Focus-ing of axially symmetric flattened Gaussian beams,” J. Mod. Opt. 44, 633–650 (1997).
[CrossRef]

Zhang, B.

B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
[CrossRef]

B. Lü, B. Zhang, S. Luo, “Far-field intensity distribution, M2 factor, and propagation of flattened Gaussian beams,” Appl. Opt. 20, 4581–4584 (1999).

B. Lü, S. Luo, B. Zhang, “Propagation of three-dimensional flattened Gaussian beams,” J. Mod. Opt. 46, 1753–1762 (1999).
[CrossRef]

B. Lü, S. Luo, B. Zhang, “A comparison between the flattened Gaussian beam and super-Gaussian beam,” Optik 110, 285–287 (1999).

Appl. Opt. (1)

B. Lü, B. Zhang, S. Luo, “Far-field intensity distribution, M2 factor, and propagation of flattened Gaussian beams,” Appl. Opt. 20, 4581–4584 (1999).

J. Mod. Opt. (4)

B. Lü, S. Luo, B. Zhang, “Propagation of three-dimensional flattened Gaussian beams,” J. Mod. Opt. 46, 1753–1762 (1999).
[CrossRef]

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation of partially coherent beams in absorbing media,” J. Mod. Opt. 42, 1123–1135 (1995).
[CrossRef]

C. Palma, P. De Santis, G. Cincotti, G. Guattari, “Propagation and coherence evolution of optical beams in gain media,” J. Mod. Opt. 43, 139–153 (1996).
[CrossRef]

M. Santarsiero, D. Aiello, R. Borghi, S. Vicalvi, “Focus-ing of axially symmetric flattened Gaussian beams,” J. Mod. Opt. 44, 633–650 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Commun. (4)

R. Borghi, M. Santarsiero, S. Vicalvi, “Focal shift of focused flat-topped beams,” Opt. Commun. 154, 243–248 (1998).
[CrossRef]

S.-A. Amarande, “Beam propagation factor and kurtosis parameter of flattened Gaussian beams,” Opt. Commun. 129, 311–317 (1996).
[CrossRef]

B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
[CrossRef]

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

Opt. Lett. (1)

Optik (1)

B. Lü, S. Luo, B. Zhang, “A comparison between the flattened Gaussian beam and super-Gaussian beam,” Optik 110, 285–287 (1999).

Other (1)

A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1, pp. 146, 386.

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