Abstract

An efficient method is presented for propagating light emitted by a wide class of spatially partially coherent sources. This class includes all quasihomogeneous sources with slowly varying intensity distributions in comparison to their spatial coherence areas. The method is based on the construction of a set of individually coherent but mutually uncorrelated, identical, laterally shifted elementary sources of finite extent.

© 2006 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).
  2. E. Wolf, "New theory of coherence in the space-frequency domain. Part I: Spectra and cross-spectra of steadystate sources," J. Opt. Soc. Am. 72, 343-351 (1982).
    [CrossRef]
  3. F. Gori and C. Palma, "Partially coherent sources which give rise to highly directional light beams," Opt. Commun. 27, 185-187 (1978).
    [CrossRef]
  4. A. C. Schell, "A technique for the determination of the radiation pattern of a partially coherent source," IEEE Trans. Antennas Propag. 15, 187-188 (1967).
    [CrossRef]
  5. M. Peeters, G. Verschaffelt, H. Thienpont, S. K. Mandre, I. Fischer, and M. Grabbherr, "Spatial decoherence of pulsed broad-area vertical-cavity surface-emitting lasers," Opt. Express 13, 9337-9345 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-23-9337
    [CrossRef] [PubMed]
  6. M. Peeters, G. Verschaffelt, J. Speybrouck, J. Danckaert, H. Thienpont, P. Vahimaa, and J. Turunen, "Propagation of spatially partially coherent vertical-cavity surface emitting laser emission," in Diffractive Optics 2005 (Warsaw, Poland, September 3-7, 2005), ISBN 83-922174-0-3, p. 94.
  7. S. A. Collins, "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Am. 60, 1168-1177 (1970).
    [CrossRef]

2005 (1)

1982 (1)

1978 (1)

F. Gori and C. Palma, "Partially coherent sources which give rise to highly directional light beams," Opt. Commun. 27, 185-187 (1978).
[CrossRef]

1970 (1)

1967 (1)

A. C. Schell, "A technique for the determination of the radiation pattern of a partially coherent source," IEEE Trans. Antennas Propag. 15, 187-188 (1967).
[CrossRef]

Collins, S. A.

Fischer, I.

Gori, F.

F. Gori and C. Palma, "Partially coherent sources which give rise to highly directional light beams," Opt. Commun. 27, 185-187 (1978).
[CrossRef]

Grabbherr, M.

Mandre, S. K.

Palma, C.

F. Gori and C. Palma, "Partially coherent sources which give rise to highly directional light beams," Opt. Commun. 27, 185-187 (1978).
[CrossRef]

Peeters, M.

Schell, A. C.

A. C. Schell, "A technique for the determination of the radiation pattern of a partially coherent source," IEEE Trans. Antennas Propag. 15, 187-188 (1967).
[CrossRef]

Thienpont, H.

Verschaffelt, G.

Wolf, E.

IEEE Trans. Antennas Propag. (1)

A. C. Schell, "A technique for the determination of the radiation pattern of a partially coherent source," IEEE Trans. Antennas Propag. 15, 187-188 (1967).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

F. Gori and C. Palma, "Partially coherent sources which give rise to highly directional light beams," Opt. Commun. 27, 185-187 (1978).
[CrossRef]

Opt. Express (1)

Other (2)

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

M. Peeters, G. Verschaffelt, J. Speybrouck, J. Danckaert, H. Thienpont, P. Vahimaa, and J. Turunen, "Propagation of spatially partially coherent vertical-cavity surface emitting laser emission," in Diffractive Optics 2005 (Warsaw, Poland, September 3-7, 2005), ISBN 83-922174-0-3, p. 94.

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Figures (1)

Fig. 1.
Fig. 1.

Evolution of the intensity profile of a partially coherent beam radiated by a supergaussian source (N = 3) with a Gaussian degree of coherence. (a) w = 500λ, σ = 5λ. (b) w = 250λ, σ = 25λ (normalization to unity at origin and contours at intervals of 0.1).

Equations (23)

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W ( ρ 1 , ρ 2 , z 0 ) = [ S ρ 1 z 0 S ρ 2 z 0 ] 1 2 μ ρ 1 ρ 2 z 0 ,
W r 1 r 2 = 1 ( 2 π ) 4 A k 1 k 2 z 0 exp [ i ( k 1 r 1 k 2 r 2 ) ] d 2 k 1 d 2 k 2 ,
A ( k 1 , k 2 ) = W ( ρ 1 , ρ 2 , z 0 ) exp [ i ( k 1 ρ 1 k 2 ρ 2 ) ] d 2 ρ 1 d 2 ρ 2
W ( r 1 s 1 , r 2 s 2 ) = ( 2 πk ) 2 cos θ 1 cos θ 2 A ( s 1 , s 2 ) exp [ i k ( r 1 r 2 ) ] r 1 r 2 ,
A ( k 1 , k 2 ) = [ F ( k 1 ) F ( k 2 ) ] 1 / 2 γ ( Δ k ) ,
J ( s ) = r 2 W ( k s , k s ) = ( 2 π k ) 2 cos 2 θ F ( k s ) .
W ( ρ 1 , ρ 2 , z 0 ) = s ( ρ ) f * ( ρ 1 ρ ) f ( ρ 2 ρ ) d 2 ρ .
A ( k 1 , k 2 ) = f ͂ * ( k 1 ) f ͂ ( k 2 ) s ͂ ( Δ k ) .
f ͂ * ( k 1 ) f ͂ ( k 2 ) = [ F ( k 1 ) F ( k 2 ) ] 1 / 2 .
f ( ρ ) = 1 2 π [ F ( k ] 1 / 2 exp ( i ρ k ) d 2 k .
W e ( ρ 1 , ρ 2 , z 0 ) = f * ( ρ 1 ) f ( ρ 2 ) .
s ( ρ ) = 1 2 π γ ( Δ k ) exp ( i ρ Δ k ) d 2 Δ k
W ( ρ 1 , ρ 2 , z 0 ) = S ( ρ ¯ , z 0 ) μ ( Δ ρ , z 0 ) ,
A ( k 1 , k 2 ) = S ͂ ( Δ k ) μ ͂ ( k ¯ ) ,
f ͂ ( k ) 2 = μ ͂ k ,
W ( ρ 1 , ρ 2 , z 0 ) = S ( ρ ) f * ( ρ 1 ρ ) f ( ρ 2 ρ ) d 2 ρ .
W ( ρ 1 , ρ 2 , z 0 ) m = 1 M s ( ρ m ) f * ( ρ 1 ρ m ) f ( ρ 2 ρ m ) ,
W ( ρ 1 , ρ 2 , z 0 ) S ( ρ ¯ ) m = 1 M f * ( ρ 1 ρ m ) f ( ρ 2 ρ m ) .
W ( x 1 , x 2 , z 0 ) = exp ( x ¯ 2 N w 2 N ) exp ( Δ x 2 2 σ 2 ) ,
f ( x ) = exp ( x 2 σ 2 ) .
A ( k 1 , k 2 ) = F ( k ) G * ( k 1 k ) G ( k 2 k ) d 2 k ,
W ( ρ 1 , ρ 2 , z 0 ) = F ( k ) U * ( ρ 1 , k ) U ( ρ 2 , k ) d 2 k ,
U ( ρ , k ) = [ S ( ρ , z 0 ) ] 1 / 2 exp ( i ρ k ) .

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