Abstract

The problem of maximizing the intensity that is transferred from a transmitter aperture to a receiver aperture is considered in which the propagation medium is random. Two optimization criteria are considered: maximal expected intensity transfer and minimal scintillation index. The beam that maximizes the expected intensity is shown to be fully coherent. Its coherent mode is determined as the principal eigenfunction for a kernel that is determined through the second-order moments of the propagation Green’s function. The beam that minimizes the scintillation index is shown to be partially coherent in general, with its coherent modes determined by minimizing a quadratic form that has nonlinear dependence on the coherent-mode fields, and on the second- and fourth-order moments of the propagation Green’s function.

© 2005 Optical Society of America

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References

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  1. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, Bellingham, Wash., 1998).
  2. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, Bellingham, Wash., 2001).
    [CrossRef]
  3. G. Gbur and E. Wolf, J. Opt. Soc. Am. A 19, 1592 (2002).
    [CrossRef]
  4. T. Shirai, A. Dogariu, and E. Wolf, J. Opt. Soc. Am. A 20, 1094 (2003).
    [CrossRef]
  5. J. C. Ricklin and F. M. Davidson, J. Opt. Soc. Am. A 20, 856 (2003).
    [CrossRef]
  6. J. C. Ricklin and F. M. Davidson, J. Opt. Soc. Am. A 19, 1794 (2002).
    [CrossRef]
  7. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, U.K., 1995).
    [CrossRef]
  8. C. W. Therrien, Discrete Random Signals and Statistical Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1992), pp. 242–243.

2003 (2)

2002 (2)

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, Bellingham, Wash., 1998).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, Bellingham, Wash., 2001).
[CrossRef]

Davidson, F. M.

Dogariu, A.

Gbur, G.

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, Bellingham, Wash., 2001).
[CrossRef]

Mandel, L.

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

Phillips, R. L.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, Bellingham, Wash., 2001).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, Bellingham, Wash., 1998).

Ricklin, J. C.

Shirai, T.

Therrien, C. W.

C. W. Therrien, Discrete Random Signals and Statistical Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1992), pp. 242–243.

Wolf, E.

T. Shirai, A. Dogariu, and E. Wolf, J. Opt. Soc. Am. A 20, 1094 (2003).
[CrossRef]

G. Gbur and E. Wolf, J. Opt. Soc. Am. A 19, 1592 (2002).
[CrossRef]

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

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

Other (4)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, Bellingham, Wash., 1998).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, Bellingham, Wash., 2001).
[CrossRef]

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

C. W. Therrien, Discrete Random Signals and Statistical Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1992), pp. 242–243.

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Equations (17)

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I ( r ) = U ( r , t ) 2 = J ( r , r ) = A 2 h ( r , r 1 ) J ( r 1 , r 2 ) h * ( r , r 2 ) d r 1 d r 2 ,
J ( r 1 , r 2 ) = k α k ψ k ( r 1 ) ψ k * ( r 2 ) , ( r 1 , r 2 ) A 2 ,
I A = def A I ( r ) d r = A J ( r , r ) d r = k α k ,
I R = def R I ( r ) d r = R A 2 h ( r 1 , r 2 ) J ( r 1 , r 2 ) h * ( r , r 2 ) d r 1 d r 2 d r = k α k R A h ( r , r ) ψ k ( r ) d r 2 d r .
E [ I R ] I A = k α k R E [ A h ( r , r ) ψ k ( r ) d r 2 ] d r l α l = k α k l α l μ k ( Ψ ) ,
μ k ( Ψ ) = R E [ A h ( r , r ) ψ k ( r ) d r 2 ] d r .
α k = { I A k = 1 0 k = 2 , 3 , 4 , } ,
μ 1 ( Ψ ) = R E [ A h ( r , r ) ψ 1 ( r ) d r 2 ] d r = A 2 ψ 1 * ( r 1 ) R E [ h * ( r , r 1 ) h ( r , r 2 ) ] d r × ψ 1 ( r 2 ) d r 1 d r 2 .
H ( r 1 , r 2 ) = R E [ h * ( r , r 1 ) h ( r , r 2 ) ] d r ,
H ( r 1 , r 2 ) = R h * ( r , r 1 ) h ( r , r 2 ) d r .
S = E [ I R 2 ] ( E [ I R ] ) 2 1 = var [ I R ] ( E [ I R ] ) 2 ,
( E [ I R ] ) 2 var [ I R ] = [ k α k μ k ( Ψ ) ] 2 k l α k R k l ( Ψ ) α l ,
R k l ( Ψ ) = E [ ξ k ( Ψ ) ξ l ( Ψ ) ] μ k ( Ψ ) μ l ( Ψ ) ,
ξ k ( Ψ ) = R A h ( r , r 1 ) ψ k ( r 1 ) d r 1 2 d r .
Ψ ̂ = arg max orthonormal Ψ k l μ k ( Ψ ) R k l 1 ( Ψ ) μ l ( Ψ ) ,
α ̂ k = l R k l 1 ( Ψ ̂ ) μ l ( Ψ ̂ ) ,
l R k l 1 ( Ψ ) R l m ( Ψ ) = { 1 k = m 0 k m } .

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