Abstract

The M 2 factor of Bessel–Gauss beams derived by Borghi and Santarsiero [ Opt. Lett. 22, 262–264 (1997)] is shown to predict the e -2 axial position rather than the half-intensity position of the on-axis intensity as the Rayleigh range divided by M 2 for large values of k t w 0. For small values of k t w 0, the half-intensity axial position of the J 0 Bessel–Gauss beam is the Rayleigh range divided by M 2. Also, the ratio of the half-intensity lengths of J 0 Bessel–Gauss and comparable Gaussian beams having the same radial size of their central regions is shown to be M 2/1.3. For equal input powers and large k t w 0, the values of peak intensity times effective range for J 0 Bessel–Gauss beams is a constant and is a factor of 1.3 larger than the corresponding product for the comparable simple Gaussian beam.

© 1998 Optical Society of America

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References

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  1. A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).
  2. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

1997 (1)

1996 (3)

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

A. Giesen, M. Morin, eds., Third International Workshop on Laser Beam and Optics Characterization, Proc. SPIE 2870 (1996).

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

1994 (1)

1992 (2)

R. M. Herman, T. A. Wiggins, “Apodization of diffractionless beams,” Appl. Opt. 31, 5913–5915 (1992).
[Crossref] [PubMed]

A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quant. Electron. 24, S1071–S1079 (1992).
[Crossref]

1990 (1)

T. F. Johnston, “M2 concept characterizes beam quality,” Laser Focus World173–184 (May1990).

1987 (1)

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

1954 (1)

Ambrosini, D.

Bagini, V.

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

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

Borghi, R.

Frezza, F.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

Gori, F.

Guattari, G.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

Herman, R. M.

Johnston, T. F.

T. F. Johnston, “M2 concept characterizes beam quality,” Laser Focus World173–184 (May1990).

Lavigne, P.

A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quant. Electron. 24, S1071–S1079 (1992).
[Crossref]

McLeod, J. H.

Morin, M.

A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quant. Electron. 24, S1071–S1079 (1992).
[Crossref]

Pacileo, A.

Padovani, C.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

Parent, A.

A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quant. Electron. 24, S1071–S1079 (1992).
[Crossref]

Santarsiero, M.

Sasnett, M. W.

M. W. Sasnett, “Propagation of multimode laser beams—the M2 factor,” in Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, New York, 1989) pp. 132–142.

Schettini, G.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

Siegman, A. E.

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[Crossref]

Spagnolo, G.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

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

Wiggins, T. A.

Appl. Opt. (2)

J. Mod. Opt. (1)

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

J. Opt. Soc. Am. (1)

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

Laser Focus World (1)

T. F. Johnston, “M2 concept characterizes beam quality,” Laser Focus World173–184 (May1990).

Opt. Commun. (1)

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

Opt. Lett. (1)

Opt. Quant. Electron. (1)

A. Parent, M. Morin, P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quant. Electron. 24, S1071–S1079 (1992).
[Crossref]

Third International Workshop on Laser Beam and Optics Characterization (1)

A. Giesen, M. Morin, eds., Third International Workshop on Laser Beam and Optics Characterization, Proc. SPIE 2870 (1996).

Other (3)

M. W. Sasnett, “Propagation of multimode laser beams—the M2 factor,” in Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, New York, 1989) pp. 132–142.

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

Values of, a, Z R /Z R ′, b, M 2, and, c, Z R /Z e ′ as a function of k t w 0 for a J 0 BG beam.

Fig. 2
Fig. 2

Same as Fig. 1 but for a J 1 BG beam.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

I Z = I 0 1 + Z / Z R 2 - 1 ,
Z R = π w 0 2 / λ = kw 0 2 / 2 ,
Z R = Z R / M 2 ,
M 2 = 2 π σ 0 σ f
I Z / I 0 = 1 + Z / Z R 2 - n + 1 × exp - 2 k t w 0 / 2 2 Z / Z R 2 / 1 + Z / Z R 2 .

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