Abstract

By expanding the hard-aperture function into a finite sum of complex Gaussian functions, we derived an approximate analytical formula for a partially coherent twisted anisotropic Gaussian Schell-model (AGSM) beam propagating through an apertured paraxial general astigmatic (GA) optical system by use of a tensor method. The results obtained by using the approximate analytical formula are in good agreement with those obtained by using the numerical integral calculation. Our formulas avoid time-consuming numerical integration and provide a convenient and effective way for studying the propagation and transformation of a partially coherent twisted AGSM beam through an apertured paraxial GA optical system.

© 2006 Optical Society of America

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References

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Y. Cai and Q. Lin, Opt. Commun. 211, 1 (2002).
[CrossRef]

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[CrossRef]

2000

1999

1994

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

A. T. Friberg, E. Tervonen, and J. Turunen, J. Opt. Soc. Am. A 11, 1818 (1994).
[CrossRef]

1993

1988

J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752 (1988).
[CrossRef]

1985

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef] [PubMed]

1970

Ambrosini, D.

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

Bagini, V.

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

Breazeale, M. A.

J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752 (1988).
[CrossRef]

Cai, Y.

Q. Lin and Y. Cai, Opt. Lett. 27, 216 (2002).
[CrossRef]

Y. Cai and Q. Lin, Opt. Commun. 211, 1 (2002).
[CrossRef]

Collins, S. A.

Ding, D.

Friberg, A. T.

Gori, F.

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

Lin, Q.

Y. Cai and Q. Lin, Opt. Commun. 211, 1 (2002).
[CrossRef]

Q. Lin and Y. Cai, Opt. Lett. 27, 216 (2002).
[CrossRef]

Liu, X.

Mandel, L.

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

Mukunda, N.

Santarsiero, M.

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

Simon, R.

Sudarshan, E. C. G.

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef] [PubMed]

Sundar, K.

Tervonen, E.

Turunen, J.

Wen, J. J.

J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752 (1988).
[CrossRef]

Wolf, E.

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

J. Acoust. Soc. Am.

J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752 (1988).
[CrossRef]

J. Mod. Opt.

D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, J. Mod. Opt. 41, 1391 (1994).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

Y. Cai and Q. Lin, Opt. Commun. 211, 1 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. A

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 31, 2419 (1985).
[CrossRef] [PubMed]

Other

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

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Figures (2)

Fig. 1
Fig. 1

Normalized cross irradiance ( y = 0 ) of a focused twisted AGSM beam at z = 60 mm versus different aperture widths.

Fig. 2
Fig. 2

Normalized cross irradiance ( y = 0 ) of a focused twisted AGSM beam at z = 60 mm versus different values of the initial transverse coherence width matrix with a 1 = b 1 = 0.1 mm .

Equations (16)

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Γ i ( r ̃ , 0 ) = G 0 exp ( i k 2 r ̃ T M i 1 r ̃ ) ,
M 1 = ( R 1 i 2 k ( σ I 2 ) 1 i k ( σ g 2 ) 1 i k ( σ g 2 ) 1 + μ J i k ( σ g 2 ) 1 + μ J T R 1 i 2 k ( σ I 2 ) 1 i k ( σ g 2 ) 1 )
J = ( 0 1 1 0 ) .
Γ o ( ρ ̃ , z ) = k 2 4 π 2 [ det ( B ¯ ) ] 1 2 Γ i ( r ̃ , 0 ) H ( r 1 ) H * ( r 2 ) exp [ i k 2 ( r ̃ T B ¯ 1 A ¯ r ̃ 2 r ̃ T B ¯ 1 ρ ̃ + ρ ̃ T D ¯ B ¯ 1 ρ ̃ ) ] d r ̃ ,
A ¯ = ( A 0 0 A ) , B ¯ = ( B 0 0 B ) ,
C ¯ = ( C 0 0 C ) , D ¯ = ( D 0 0 D ) .
H ( r 1 ) = m = 1 M A m exp ( B m a 1 2 r 1 2 ) ,
Γ i ( r ̃ , 0 ) H ( r 1 ) H * ( r 2 ) = m = 1 M n = 1 M A m A n * exp [ i k 2 r ̃ T ( B m n + M i 1 ) r ̃ ] ,
B m n = 2 i k a 1 2 ( B m I 0 0 B n * I )
Γ o ( ρ ̃ , z ) = m = 1 M n = 1 M A m A n * [ det ( A ¯ + B ¯ M i 1 + B ¯ B m n ) ] 1 2 exp [ i k 2 ρ ̃ T M o m n 1 ρ ̃ ] ,
M o m n 1 = [ C ¯ + D ¯ ( M i 1 + B m n ) ] [ A ¯ + B ¯ ( M i 1 + B m n ) ] 1 .
H ( x 1 , y 1 ) = m = 1 M A m exp ( B m a 1 2 x 1 2 ) n = 1 N A n exp ( B n b 1 2 y 1 2 ) .
Γ i ( r ̃ , 0 ) H ( r 1 ) H * ( r 2 ) = m = 1 M n = 1 N p = 1 M l = 1 N A m A n A p * A l * exp [ i k 2 r ̃ T ( B m n p l + M i 1 ) r ̃ ] ,
B m n p l = 2 i k ( B m a 1 2 0 0 0 0 B n b 1 2 0 0 0 0 B p * a 1 2 0 0 0 0 B l * b 1 2 ) .
Γ o ( ρ ̃ , z ) = m = 1 M n = 1 N p = 1 M l = 1 N A m A n A p * A l * [ det ( A ¯ + B ¯ M i 1 + B ¯ B m n p l ) ] 1 2 exp [ i k 2 ρ ̃ T M o m n p l 1 ρ ̃ ] ,
M o m n p l 1 = [ C ¯ + D ¯ ( M i 1 + B m n p l ) ] [ A ¯ + B ¯ ( M i 1 + B m n p l ) ] 1 .

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