Abstract

We present a simple mathematical model giving a possible description of a partially coherent light beam exhibiting a flat-topped transverse intensity profile. Such a model allows us to deduce the modal distribution inside a multimode stable optical cavity, assuming that the modes are of the Hermite–Gauss type. The analytical expression used to represent flat-topped profiles is of the flattened Gaussian type and leads to an exact, closed-form expression for the M2 factor of the output beam. An analogous procedure could be used to treat the general problem of deducing the modal distribution inside a laser cavity starting from intensity measurements of the output beam.

© 1998 Optical Society of America

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References

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  1. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  3. E. Wolf and G. S. Agarwal, J. Opt. Soc. Am. A 1, 541 (1984).
    [CrossRef]
  4. P. Spano, Opt. Commun. 33, 265 (1980).
    [CrossRef]
  5. E. G. Johnson, Appl. Opt. 25, 2967 (1986).
    [CrossRef]
  6. J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
    [CrossRef] [PubMed]
  7. A. T. Friberg, E. Tervonen, and J. Turunen, J. Opt. Soc. Am. A 11, 1818 (1994).
    [CrossRef]
  8. E. Collett and E. Wolf, Opt. Lett. 2, 27 (1978).
    [CrossRef]
  9. F. Gori, Opt. Commun. 34, 301 (1980).
    [CrossRef]
  10. A. Starikov and E. Wolf, J. Opt. Soc. Am. A 72, 923 (1982).
    [CrossRef]
  11. E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
    [CrossRef]
  12. A. E. Siegman and S. W. Townsend, IEEE J. Quantum Electron. 29, 1212 (1993).
    [CrossRef]
  13. F. Gori, Opt. Commun. 107, 335 (1994).
    [CrossRef]
  14. V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, D. Ambrosini, and G. Schirripa Spagnolo, J. Opt. Soc. Am. A 13, 1385 (1996).
    [CrossRef]
  15. S.-A. Amarande, Opt. Commun. 129, 311 (1996).
    [CrossRef]
  16. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
  17. A. E. Siegman, in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2 (1990).
    [CrossRef]
  18. F. Gori, in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 363.

1996 (2)

1994 (2)

1993 (1)

A. E. Siegman and S. W. Townsend, IEEE J. Quantum Electron. 29, 1212 (1993).
[CrossRef]

1989 (2)

J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
[CrossRef] [PubMed]

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

1986 (1)

1984 (1)

1982 (1)

A. Starikov and E. Wolf, J. Opt. Soc. Am. A 72, 923 (1982).
[CrossRef]

1980 (2)

P. Spano, Opt. Commun. 33, 265 (1980).
[CrossRef]

F. Gori, Opt. Commun. 34, 301 (1980).
[CrossRef]

1978 (1)

Abramowitz, M.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Agarwal, G. S.

Amarande, S.-A.

S.-A. Amarande, Opt. Commun. 129, 311 (1996).
[CrossRef]

Ambrosini, D.

Bagini, V.

Borghi, R.

Collett, E.

Friberg, A. T.

Gori, F.

V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, D. Ambrosini, and G. Schirripa Spagnolo, J. Opt. Soc. Am. A 13, 1385 (1996).
[CrossRef]

F. Gori, Opt. Commun. 107, 335 (1994).
[CrossRef]

F. Gori, Opt. Commun. 34, 301 (1980).
[CrossRef]

F. Gori, in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 363.

Johnson, E. G.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Pacileo, A. M.

Santarsiero, M.

Schirripa Spagnolo, G.

Siegman, A. E.

A. E. Siegman and S. W. Townsend, IEEE J. Quantum Electron. 29, 1212 (1993).
[CrossRef]

A. E. Siegman, in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2 (1990).
[CrossRef]

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

Spano, P.

P. Spano, Opt. Commun. 33, 265 (1980).
[CrossRef]

Starikov, A.

A. Starikov and E. Wolf, J. Opt. Soc. Am. A 72, 923 (1982).
[CrossRef]

Stegun, I.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Tervonen, E.

Townsend, S. W.

A. E. Siegman and S. W. Townsend, IEEE J. Quantum Electron. 29, 1212 (1993).
[CrossRef]

Turunen, J.

Wolf, E.

E. Wolf and G. S. Agarwal, J. Opt. Soc. Am. A 1, 541 (1984).
[CrossRef]

A. Starikov and E. Wolf, J. Opt. Soc. Am. A 72, 923 (1982).
[CrossRef]

E. Collett and E. Wolf, Opt. Lett. 2, 27 (1978).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. E. Siegman and S. W. Townsend, IEEE J. Quantum Electron. 29, 1212 (1993).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Commun. (4)

P. Spano, Opt. Commun. 33, 265 (1980).
[CrossRef]

S.-A. Amarande, Opt. Commun. 129, 311 (1996).
[CrossRef]

F. Gori, Opt. Commun. 34, 301 (1980).
[CrossRef]

F. Gori, Opt. Commun. 107, 335 (1994).
[CrossRef]

Opt. Lett. (2)

Other (5)

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

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

A. E. Siegman, in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2 (1990).
[CrossRef]

F. Gori, in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 363.

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Figures (2)

Fig. 1
Fig. 1

Flattened Gaussian intensity profiles for several values of N.

Fig. 2
Fig. 2

Normalized coefficients λnN for several values of N.

Equations (12)

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

INx=exp-N+1w02x2n=0N1n!N+1w02x2n,
INx=n=0NλnNΦnx2,
Φnx=2v01/212nn!πHnx2v0exp-x2v02,
v0=w02N+11/2.
N=2w0v02-1,
n=0NαnNHn2ξ=n=0N1n!ξ2n,
ξ=x2v0,
αnN=2π1/2λnN2nn!v0 n=0, 1, N.
Hn2ξ=k=0npn, kξ2k,
n=kNαnNpn, k=1k! k=0, 1, , N.
αNN=1pN,NN!, αkN=1pk, k1k!-n=k+1NαnNpn, k k=N-1, N-2, , 0.
M2=1+2N/3.

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