Abstract

A representation of the mutual coherence function (MCF) of a light pulse as an incoherent sum of partially-coherent elementary pulses is introduced. It is shown that this MCF can be decomposed into fully and partially-coherent constituents and three different pulse models of partially-coherent constituents are constructed: single elementary-pulse fluctuations, emission of elementary fields driven by white noise, and elementary pulses triggered by Poisson impulses. The fourth-order correlation function of this last model includes as limit cases those of the fluctuating-pulse and noise-driven-emission models. These results provide a means of extending elementary-field models to higher-order coherence theory.

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  10. The support of p(z) is the set of values of z s.t. p(z) ≠ 0.The hypothesis of connectedness is necessary since the range of variation of a fluctuating pulse parameter is always assumed connected.
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    [CrossRef]
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    [CrossRef]
  14. C. R. Fernández-Pousa, “Nonstationary elementary-field light randomly triggered by Poisson impulses,” J. Opt. Soc. Am. A (to be published).
  15. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1965), Chap. 12.
  16. B. Picinbono, Random Signals and Systems (Prentice-Hall, 1993), Chap. 8.
  17. E. Parzen, Stochastic Processes (Society for Industrial and Applied Mathematics, 1999), Chap. 4.

2013

2011

2007

2006

1983

B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by Poisson random emissions,” Phys. Rev. A27(1), 360–374 (1983).
[CrossRef]

1978

F. Gori and C. Palma, “Partially coherent sources which give rise to highly directional beams,” Opt. Commun.27(2), 185–188 (1978).
[CrossRef]

Alonso, M. A.

Fernández-Pousa, C. R.

C. R. Fernández-Pousa, “Nonstationary elementary-field light randomly triggered by Poisson impulses,” J. Opt. Soc. Am. A (to be published).

Friberg, A. T.

Genty, G.

Gori, F.

F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett.32(24), 3531–3533 (2007).
[CrossRef] [PubMed]

F. Gori and C. Palma, “Partially coherent sources which give rise to highly directional beams,” Opt. Commun.27(2), 185–188 (1978).
[CrossRef]

Korhonen, M.

Lajunen, H.

Palma, C.

F. Gori and C. Palma, “Partially coherent sources which give rise to highly directional beams,” Opt. Commun.27(2), 185–188 (1978).
[CrossRef]

Ponomarenko, S. A.

Saastamoinen, T.

Saleh, B. E. A.

B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by Poisson random emissions,” Phys. Rev. A27(1), 360–374 (1983).
[CrossRef]

Santarsiero, M.

Stoler, D.

B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by Poisson random emissions,” Phys. Rev. A27(1), 360–374 (1983).
[CrossRef]

Teich, M. C.

B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by Poisson random emissions,” Phys. Rev. A27(1), 360–374 (1983).
[CrossRef]

Torres-Company, V.

Turunen, J.

Vahimaa, P.

Adv. Opt. Photon.

J. Opt. Soc. Am. A

C. R. Fernández-Pousa, “Nonstationary elementary-field light randomly triggered by Poisson impulses,” J. Opt. Soc. Am. A (to be published).

J. Opt. Soc. Am. B

Opt. Commun.

F. Gori and C. Palma, “Partially coherent sources which give rise to highly directional beams,” Opt. Commun.27(2), 185–188 (1978).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

B. E. A. Saleh, D. Stoler, and M. C. Teich, “Coherence and photon statistics for optical fields generated by Poisson random emissions,” Phys. Rev. A27(1), 360–374 (1983).
[CrossRef]

Other

The support of p(z) is the set of values of z s.t. p(z) ≠ 0.The hypothesis of connectedness is necessary since the range of variation of a fluctuating pulse parameter is always assumed connected.

J. W. Goodman, Statistical Optics (Wiley, 1985).

J. Perina, Coherence of Light (Kluwer, 1985).

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

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1965), Chap. 12.

B. Picinbono, Random Signals and Systems (Prentice-Hall, 1993), Chap. 8.

E. Parzen, Stochastic Processes (Society for Industrial and Applied Mathematics, 1999), Chap. 4.

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Equations (22)

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Γ( t 1 , t 2 )= duλ(u) e 0 * ( t 1 u) e 0 ( t 2 u)
Γ( t 1 , t 2 )= dxp(x) e 0 * ( t 1 |x) e 0 ( t 2 |x)
a * ( t 1 )a( t 2 ) = λ( t 1 )λ( t 2 ) n * ( t 1 )n( t 2 ) =λ( t 1 )δ( t 2 t 1 )
Γ( t 1 , t 2 )= duλ(u) dzp(z) e 0 * ( t 1 u|z) e 0 ( t 2 u|z) = duλ(u) e 0 * ( t 1 u|Z) e 0 ( t 2 u|Z) Z = duλ(u) Γ 0 ( t 1 u, t 2 u)
p(z)= n q n δ(z z n ) + m p m (z) λ(u)= r σ r δ(u u r ) + s λ s (u)
Γ( t 1 , t 2 )= n,r q n σ r e 0 * ( t 1 u r | z n ) e 0 ( t 2 u r | z n ) + n,s q n du λ s (u) e 0 * ( t 1 u| z n ) e 0 ( t 2 u| z n )+ m,r σ r dz p m (z) e 0 * ( t 1 u r |z) e 0 ( t 2 u r |z) + m,s du λ s (u) dz p m (z) e 0 * ( t 1 u|z) e 0 ( t 2 u|z)
e 1 (t)= N 0 e 0 (tU|Z) e jΘ
e 2 (t)= du λ(u) k e 0 (tu| Z k ) a k φ k (u)
e 2 * ( t 1 ) e 2 ( t 2 ) Z k a k = d u 1 d u 2 λ( u 1 )λ( u 2 ) k φ k * ( u 1 ) φ k ( u 2 ) e 0 * ( t 1 u 1 | Z k ) e 0 ( t 2 u 2 | Z k ) Z k
e 3 (t)= k e 0 (t τ k ) = e 0 (t) k δ(t τ k ) = e 0 (t)Δ(t)
Δ( t 1 )Δ( t 2 ) P = Δ( t 1 ) P Δ( t 2 ) P +λ( t 1 )δ( t 2 t 1 )
e 3 (t)= k e 0 (t τ k | Z k )
Φ( s 1 , s 2 )=expΨ( s 1 , s 2 )= exp( s 1 e 3 * ( t 1 )+ s 2 e 3 ( t 2 ) ) P Z k
Ψ( s 1 , s 2 )=logΦ( s 1 , s 2 )= duλ(u) [ e s 1 e 0 * ( t 1 u|Z)+ s 2 e 0 ( t 2 u|Z) Z 1 ]
e 3 ( t 2 ) P Z k = 2 Φ( s 1 , s 2 ) | s 1 = s 2 =0 =( 2 Ψ) e Ψ( s 1 , s 2 ) | s j =0 = 2 Ψ | s j =0 =λ( t 2 ) e 0 ( t 2 |Z) Z =0
e 3 * ( t 1 ) e 3 ( t 2 ) P Z k = 1 2 Φ( s 1 , s 2 ) | s j =0 =( 1 Ψ 2 Ψ+ 1 2 Ψ ) e Ψ( s 1 , s 2 ) | s j =0 = 1 2 Ψ | s j =0
Φ( s 1 , s 2 , s 3 , s 4 )=expΨ( s 1 , s 2 , s 3 , s 4 )=exp [ q=1,3 s q e 3 * ( t q ) + p=2,4 s p e 3 ( t p ) ] P Z k
Ψ( s 1 , s 2 , s 3 , s 4 )=logΦ( s 1 , s 2 , s 3 , s 4 )= duλ(u) [ e q=1,3 s q e 0 * ( t q u|Z) + p=2,4 s p e 0 ( t p u|Z) Z 1 ]
Γ 3 ( t 1 , t 2 , t 3 , t 4 )= e 3 * ( t 1 ) e 3 ( t 2 ) e 3 * ( t 3 ) e 3 ( t 4 ) P Z k =Γ( t 1 , t 2 )Γ( t 3 , t 4 )+Γ( t 1 , t 4 )Γ( t 3 , t 2 ) + duλ(u) e 0 * ( t 1 u|Z) e 0 ( t 2 u|Z) e 0 * ( t 3 u|Z) e 0 ( t 4 u|Z) Z
Γ 2 ( t 1 , t 2 , t 3 , t 4 )= e 2 * ( t 1 ) e 2 ( t 2 ) e 2 * ( t 3 ) e 2 ( t 4 ) Z k a k =Γ( t 1 , t 2 )Γ( t 3 , t 4 )+Γ( t 1 , t 4 )Γ( t 3 , t 2 )
Γ 1 ( t 1 , t 2 , t 3 , t 4 )= N 0 duλ(u)   e 0 * ( t 1 u|Z) e 0 ( t 2 u|Z) e 0 * ( t 3 u|Z) e 0 ( t 4 u|Z) Z
Γ 3 ( t 1 , t 2 , t 3 , t 4 )= Γ 2 ( t 1 , t 2 , t 3 , t 4 )+ 1 N 0 Γ 1 ( t 1 , t 2 , t 3 , t 4 )

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