Abstract

We derive a reciprocity inequality involving the product of the effective size of a statistically stationary, planar, secondary source of any state of coherence and of the angular spread of the far-zone intensity generated by the source. We show that of all possible such sources, the fully spatially coherent lowest-order Hermite–Gaussian laser mode has the smallest possible reciprocity product.

© 2000 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), Chap. 4.
  2. E. Colett and E. Wolf, Opt. Lett. 2, 26 (1978).
  3. A. T. Friberg and E. Wolf, Opt. Acta 30, 1417 (1983).
    [CrossRef]
  4. E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).
  5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
    [CrossRef]
  6. A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961), Vol. 1, pp. 133–134.
  7. This is because for the field distribution (20) the modulus of the spectral degree of coherence μ0ρ,ρ′,ω, defined as μ0ρ,ρ′,ω≡W0ρ,ρ′,ωW0ρ,ρ,ωW0ρ′,ρ′,ω, is equal to unity.

1983

A. T. Friberg and E. Wolf, Opt. Acta 30, 1417 (1983).
[CrossRef]

1982

1978

E. Colett and E. Wolf, Opt. Lett. 2, 26 (1978).

Colett, E.

E. Colett and E. Wolf, Opt. Lett. 2, 26 (1978).

Friberg, A. T.

A. T. Friberg and E. Wolf, Opt. Acta 30, 1417 (1983).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), Chap. 4.

Mandel, L.

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

Messiah, A.

A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961), Vol. 1, pp. 133–134.

Wolf, E.

A. T. Friberg and E. Wolf, Opt. Acta 30, 1417 (1983).
[CrossRef]

E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).

E. Colett and E. Wolf, Opt. Lett. 2, 26 (1978).

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

J. Opt. Soc. Am.

Opt. Acta

A. T. Friberg and E. Wolf, Opt. Acta 30, 1417 (1983).
[CrossRef]

Opt. Lett.

E. Colett and E. Wolf, Opt. Lett. 2, 26 (1978).

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), Chap. 4.

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

A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961), Vol. 1, pp. 133–134.

This is because for the field distribution (20) the modulus of the spectral degree of coherence μ0ρ,ρ′,ω, defined as μ0ρ,ρ′,ω≡W0ρ,ρ′,ωW0ρ,ρ,ωW0ρ′,ρ′,ω, is equal to unity.

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Figures (1)

Fig. 1
Fig. 1

Geometry of a partially coherent, statistically stationary, planar, secondary source. P is a point in the far zone of the source occupying a portion of the plane z=0. OP¯=rsˆ, sˆ2=1. θ denotes the angle which the line OP¯ makes with the z axis.

Equations (22)

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ΩAλ2.
Wρ,ρ,ω=fλfϕf*ρ,ωϕfρ,ω.
d2ρWρ,ρ,ωϕfρ=λfϕfρ,
λf0.
ρ2=d2ρρ2Iρd2ρIρ,
ρ2=fλfd2ρρ2ϕfρ2fλf.
s2=d2ss2Jks,ωd2sJks,ω.
Jks,ω=d2ρ2πd2ρ2πWρ,ρ,ω×exp-iks·ρ-ρ.
s2=fλfd2kss2ϕ˜fks2fλf,
ϕ˜fks=d2ρ2πϕfρexp-iksρ.
Λα=fλfd2ρgf*,gffλf0,
gf=ρϕfρ+αϕfρ,
Λα=fλfd2ρ[ρ2ϕf2+αρ·ϕf2fλf+fλfd2ρα2ϕfϕf*]fλf0.
d2ρϕfϕf*=d2ksk2s2ϕ˜fks2,
Λα=ρ2-2α+α2k2s20,
ρ2s2λ2π2,
ρ2θ2λ2π2.
ρϕfρ+αϕfρ=0
ϕfρ=12πσ2 exp-ρ2/2σ2,
W0ρ,ρ,ω=A exp-ρ2/2σ2exp-ρ2/2σ2,
Πρ2s2,
μ0ρ,ρ,ωW0ρ,ρ,ωW0ρ,ρ,ωW0ρ,ρ,ω,

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