Abstract

A reciprocity inequality is derived, involving the effective size of a planar, secondary, Gaussian Schell-model source and the effective angular spread of the beam that the source generates. The analysis is shown to imply that a fully spatially coherent source of that class (which generates the lowest-order Hermite–Gaussian laser mode) has certain minimal properties.

© 2000 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
    [CrossRef]
  2. E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
    [CrossRef]
  3. P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
    [CrossRef]
  4. J. D. Farina, L. M. Narducci, and E. Collett, Opt. Commun. 32, 203 (1980).
    [CrossRef]
  5. J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1978).
    [CrossRef]

1980 (1)

J. D. Farina, L. M. Narducci, and E. Collett, Opt. Commun. 32, 203 (1980).
[CrossRef]

1979 (1)

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

1978 (2)

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1978).
[CrossRef]

Collett, E.

J. D. Farina, L. M. Narducci, and E. Collett, Opt. Commun. 32, 203 (1980).
[CrossRef]

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

De Santis, P.

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Farina, J. D.

J. D. Farina, L. M. Narducci, and E. Collett, Opt. Commun. 32, 203 (1980).
[CrossRef]

Foley, J. T.

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1978).
[CrossRef]

Gori, F.

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Guattari, G.

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Mandel, L.

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

Narducci, L. M.

J. D. Farina, L. M. Narducci, and E. Collett, Opt. Commun. 32, 203 (1980).
[CrossRef]

Palma, C.

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Wolf, E.

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

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

Zubairy, M. S.

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1978).
[CrossRef]

Opt. Commun. (4)

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

J. D. Farina, L. M. Narducci, and E. Collett, Opt. Commun. 32, 203 (1980).
[CrossRef]

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1978).
[CrossRef]

Other (1)

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

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Figures (3)

Fig. 1
Fig. 1

Illustrating the notation.

Fig. 2
Fig. 2

Contours of the factor 1+4σIσg21/2, which represents the ratios Δθ/Δθcoh and Δρ/Δρcoh. [Eqs. (14) and (17)].

Fig. 3
Fig. 3

The factor 1+4σIσg21/2 plotted as a function of the parameter σI/σg.

Equations (19)

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

I0ρ,ν=A2νexp-ρ2/2σI2ν,
g0ρ2-ρ1,ν=exp-ρ2-ρ12/2σg2ν.
Js,ν=β2 exp-aθ2/2,
β=kAσIδ,  a=k2δ2,
1δ2=12σI2+1σg2,
k=2πν/c.
Δθ2=0π/2θ2Jθ2dθ0π/2Jθ2dθ.
Δθ=121kδ.
Δρ2=ρ2I0ρ2 d2ρI0ρ2 d2ρ,
Δρ=σI.
ΔθΔρ=σIkδ2
ΔθΔρ=1k221+4σIσg21/2.
ΔθcohΔρ=1k22,
Δθ=Δθcoh1+4σIσg21/2.
Δθ>Δθcoh
ΔθΔρcoh1k22.
Δρ=Δρcoh1+4σIσg21/2
1+4σIσg21/2,
1+4σIσg21/2

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