Abstract

A useful relationship among the parameter called paraxial estimator [Opt. Lett. 32, 927 (2007) ] and two parameters concerning the beam quality, the M2 factor, and the beam spot size was derived. This relationship allows one to quantify the paraxiality for a monochromatic laser beam from standard measurements extending the applicability of such an estimator for real beams even if the beam profile shape does not have a closed-form representation. Hence, the paraxial estimator might be a suitable tool for deepening the analysis on the quality of a laser beam.

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References

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  1. A. E. Siegman, Proc. SPIE 1224, 2 (1990).
    [CrossRef]
  2. T. F. Johnston, Jr., M. W. Sasnett, J.-L. Doumont, and A. E. Siegman, Opt. Lett. 17, 198 (1992).
    [CrossRef] [PubMed]
  3. ISO Standard 11146, “Lasers and laser-related equipment--Test methods for laser beam widths, divergence angles and beam propagation ratios” (International Organization for Standardization, 2005).
  4. A. E. Siegman, G. Nemes, and J. Serna, in Proceedings of DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.
  5. P. Vaveliuk and M. Lopes da Silva, Opt. Lett. 33, 2035 (2008).
    [CrossRef] [PubMed]
  6. M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
    [CrossRef]
  7. P. Vaveliuk, G. F. Zebende, M. A. Moret, and B. Ruiz, J. Opt. Soc. Am. A 24, 3297 (2007).
    [CrossRef]
  8. A. E. Siegman, Lasers (University Science Books, 1986).
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    [CrossRef] [PubMed]
  10. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  12. M. W. Sasnett, in The Physics and Technology of Laser Resonators, D.R.Hall and P.E.Jackson, eds. (Adam Hilger, 1989).
  13. C.E.Webb and J.D. C.Jones, eds. Handbook of Laser Technology and Applications: Vol. II: Laser Design and Laser Systems (IOP, 2004).
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    [CrossRef]
  16. R. Borghi and M. Santarsiero, Opt. Lett. 22, 262 (1997).
    [CrossRef] [PubMed]

2008 (1)

2007 (2)

2005 (1)

ISO Standard 11146, “Lasers and laser-related equipment--Test methods for laser beam widths, divergence angles and beam propagation ratios” (International Organization for Standardization, 2005).

2004 (1)

C.E.Webb and J.D. C.Jones, eds. Handbook of Laser Technology and Applications: Vol. II: Laser Design and Laser Systems (IOP, 2004).

1998 (1)

A. E. Siegman, G. Nemes, and J. Serna, in Proceedings of DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.

1997 (1)

1992 (1)

1990 (1)

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

1989 (1)

M. W. Sasnett, in The Physics and Technology of Laser Resonators, D.R.Hall and P.E.Jackson, eds. (Adam Hilger, 1989).

1987 (2)

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

1986 (1)

A. E. Siegman, Lasers (University Science Books, 1986).

1978 (1)

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves, Opt. Acoust. 2, 105 (1978).
[CrossRef]

1975 (1)

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

1968 (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Borghi, R.

Doumont, J.-L.

Durnin, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Gori, F.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Johnston, T. F.

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Lencina, A.

Lopes da Silva, M.

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Moret, M. A.

Nemes, G.

A. E. Siegman, G. Nemes, and J. Serna, in Proceedings of DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Ruiz, B.

Santarsiero, M.

Sasnett, M. W.

T. F. Johnston, Jr., M. W. Sasnett, J.-L. Doumont, and A. E. Siegman, Opt. Lett. 17, 198 (1992).
[CrossRef] [PubMed]

M. W. Sasnett, in The Physics and Technology of Laser Resonators, D.R.Hall and P.E.Jackson, eds. (Adam Hilger, 1989).

Serna, J.

A. E. Siegman, G. Nemes, and J. Serna, in Proceedings of DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.

Sheppard, C. J. R.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves, Opt. Acoust. 2, 105 (1978).
[CrossRef]

Siegman, A. E.

A. E. Siegman, G. Nemes, and J. Serna, in Proceedings of DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.

T. F. Johnston, Jr., M. W. Sasnett, J.-L. Doumont, and A. E. Siegman, Opt. Lett. 17, 198 (1992).
[CrossRef] [PubMed]

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

A. E. Siegman, Lasers (University Science Books, 1986).

Vaveliuk, P.

Wilson, T.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves, Opt. Acoust. 2, 105 (1978).
[CrossRef]

Zebende, G. F.

IEE J. Microwaves, Opt. Acoust. (1)

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves, Opt. Acoust. 2, 105 (1978).
[CrossRef]

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

Opt. Commun. (1)

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Proc. SPIE (1)

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

Other (6)

ISO Standard 11146, “Lasers and laser-related equipment--Test methods for laser beam widths, divergence angles and beam propagation ratios” (International Organization for Standardization, 2005).

A. E. Siegman, G. Nemes, and J. Serna, in Proceedings of DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.

A. E. Siegman, Lasers (University Science Books, 1986).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

M. W. Sasnett, in The Physics and Technology of Laser Resonators, D.R.Hall and P.E.Jackson, eds. (Adam Hilger, 1989).

C.E.Webb and J.D. C.Jones, eds. Handbook of Laser Technology and Applications: Vol. II: Laser Design and Laser Systems (IOP, 2004).

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Figures (1)

Fig. 1
Fig. 1

(a) Paraxial–nonparaxial regions in terms of M i 2 ( W 0 i λ ) with i = x , y . This is a useful map for determining the PA validity for nonrotationally symmetric beams. (b) Paraxial–nonparaxial regions in terms of M 2 and the ratio W 0 λ . This map is useful for rotationally symmetric beams.

Equations (10)

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P = + Im { E p * z E p } d x d y + E p E p * k d x d y ,
ε p ( u , v , z ) = E p ( x , y , z ) e 2 π i ( u x + v y ) d x d y ,
P = + Im { ε p * z ε p } d u d v + ε p ε p * k d u d v .
ε p ( u , v ; z ) = ε 0 ( u , v ) e i k z i ( 2 π 2 k ) z ( u 2 + v 2 ) .
P = 1 λ 2 2 + ( u 2 + v 2 ) ε 0 2 d u d v + ε 0 2 d u d v .
σ 0 x 2 = x 2 E 0 ( x , y ) 2 d x d y E 0 ( x , y ) 2 d x d y ,
σ x 2 = + u 2 ε 0 ( u , v ) 2 d u d v + ε 0 ( u , v ) 2 d u d v ,
P = 1 λ 2 2 [ σ x 2 + σ y 2 ] .
P = 1 1 8 π 2 [ ( M x 2 W 0 x λ ) 2 + ( M y 2 W 0 y λ ) 2 ] .
P = 1 1 4 π 2 ( M 2 W 0 λ ) 2 .

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