In free space, U (r, t) must satisfy tne wave equation, V³U – (1/c")®U/d€ = 0. Use the definition (12.1-21) to show that the mutual coherence function G(r, , r2, 7) satisfies a pair of partial differential equations known as the Wolf equations, 1 ºG vi - (12.1-24a) 1 PG = 0, (12.1-24b) where Vị and V3 are the Laplacian operators with respect to r; and rɔ, respectively. G(ri, r2, 7) = (U*(r,, t)U (r2, t + 7)). (12.1-21) Mutual Coherence Function

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Chapter1: Units, Trigonometry. And Vectors
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In free space, U (r, t)
must satisfy tne wave equation, VU - (1/)U/at = 0. Use the definition (12.1-21) to show
that the mutual coherence function G(r1,r2, 7) satisfies a pair of partial differential cquations known
as the Wolf equations,
1 PG
= 0
vG –
(12.1-24a)
vG -
1 G
= 0,
(12.1-24b)
where V and V are the Laplacian operators with respect to r, and r2, respectively.
G(rı, r2, 7) = (U*(r1,t) U(r2, t + T)).
(12.1-21)
Mutual Coherence Function
Transcribed Image Text:In free space, U (r, t) must satisfy tne wave equation, VU - (1/)U/at = 0. Use the definition (12.1-21) to show that the mutual coherence function G(r1,r2, 7) satisfies a pair of partial differential cquations known as the Wolf equations, 1 PG = 0 vG – (12.1-24a) vG - 1 G = 0, (12.1-24b) where V and V are the Laplacian operators with respect to r, and r2, respectively. G(rı, r2, 7) = (U*(r1,t) U(r2, t + T)). (12.1-21) Mutual Coherence Function
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