Abstract

Analytical expressions for the M2 factor and the mode-coherence coefficients of hyperbolic-cosine– (cosh-) Gaussian beams have been derived, and a simple method of producing cosh-Gaussian beams in an experiment, superposition of two decentered Gaussian beams, has been proposed. Our results will be useful for studying more-general Hermite–sinusoidal-Gaussian beams.

© 1999 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  9. K. M. Du, “Kohärenz, Polarisation und Fluktuation von Laserstrahlung,” Ph.D.??dissertation (Verlag der Augustinus-Buchhandlung, Aachen, Germany, 1992).

1998 (2)

1997 (1)

1992 (2)

H. Weber, Opt. Quatum Electron. 24, 1047 (1992).

K. M. Du, G. Herziger, P. Loosen, and F. Rühl, Opt. Quantum Electron. 24, 1081 (1992).
[CrossRef]

1990 (1)

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

1982 (1)

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

Casperson, L. W.

Du, K. M.

K. M. Du, G. Herziger, P. Loosen, and F. Rühl, Opt. Quantum Electron. 24, 1081 (1992).
[CrossRef]

K. M. Du, “Kohärenz, Polarisation und Fluktuation von Laserstrahlung,” Ph.D.??dissertation (Verlag der Augustinus-Buchhandlung, Aachen, Germany, 1992).

Hall, D. G.

Herziger, G.

K. M. Du, G. Herziger, P. Loosen, and F. Rühl, Opt. Quantum Electron. 24, 1081 (1992).
[CrossRef]

Loosen, P.

K. M. Du, G. Herziger, P. Loosen, and F. Rühl, Opt. Quantum Electron. 24, 1081 (1992).
[CrossRef]

Rühl, F.

K. M. Du, G. Herziger, P. Loosen, and F. Rühl, Opt. Quantum Electron. 24, 1081 (1992).
[CrossRef]

Siegman, A. E.

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

A. E. Siegman, in DPSS Lasers: Application and Issues, M. W. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), p. 184.

Starikov, A.

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

Tovar, A. A.

Weber, H.

H. Weber, Opt. Quatum Electron. 24, 1047 (1992).

Wolf, E.

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

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

Opt. Quantum Electron. (1)

K. M. Du, G. Herziger, P. Loosen, and F. Rühl, Opt. Quantum Electron. 24, 1081 (1992).
[CrossRef]

Opt. Quatum Electron. (1)

H. Weber, Opt. Quatum Electron. 24, 1047 (1992).

Proc. SPIE (1)

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

Other (2)

A. E. Siegman, in DPSS Lasers: Application and Issues, M. W. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), p. 184.

K. M. Du, “Kohärenz, Polarisation und Fluktuation von Laserstrahlung,” Ph.D.??dissertation (Verlag der Augustinus-Buchhandlung, Aachen, Germany, 1992).

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Figures (1)

Fig. 1
Fig. 1

M2 factor of a ChG beam as a function of δ.

Equations (18)

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Ex,0=exp-x2w02coshΩ0x,
coshΩ0x=expΩ0x+exp-Ω0x2.
Ex,0=12expw02Ω024exp-x-w02Ω022w02+exp-x+w02Ω022w02.
Ix,0=Ex,0E*x,0,
σx2=w0241+δ1+exp-δ/2,
σk2=14π2w021-δexp-δ/21+exp-δ/2,
δ=w02Ω02.
M2=4πσxσk=1-δexp-δ+2-δ2exp-δ/2+δ+11/21+exp-δ/2.
Ex,0=mcmφmx,
φmx=umexp-α22x2Hmαx,
α=2/w0h,
cm=-+φm*xexp-x2w02coshΩ0xdx.
cm=νπ1/2α2+ν1/2expδ21+ν2-ν4+2νm/2m!-1/2Hmνδ4-ν2,m=even numbers0,m=odd numbers,
ν=w02α2.
Wx1,x2=mmcmcm*φmx1φm*x2=mmλmmφmx1φm*x2,
λmm=cmcm*
μmm=νπα2+νexpδ1+ν2-ν4+2νmm!×Hmνδ4-ν22,
μm,m+2=νπα2+νexpδ1+ν2-ν4+2νm+1m!m+2!×Hmνδ4-ν2Hm+2νδ4-ν2,

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