Abstract

A 4×4 complex curvature tensor M-1 is introduced to describe partially coherent anisotropic Gaussian–Schell model (GSM) beams. An analytical propagation formula for the cross-spectral density of partially coherent anisotropic GSM beams is derived. The propagation law of M-1 that is also derived may be called partially coherent tensor ABCD law. The analytical formulas presented here are useful in treating the propagation and transformation of partially coherent anisotropic GSM beams, which include previous results for completely coherent Gaussian beams as special cases.

© 2002 Optical Society of America

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2001 (1)

2000 (3)

1998 (2)

1995 (2)

D. Subbarao, Opt. Lett. 20, 2162 (1995).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Quantum Electron. 27, 679 (1995).
[CrossRef]

1994 (2)

1993 (1)

1992 (1)

M. J. Bastiaans, Opt. Quantum Electron. 24, S1011 (1992).
[CrossRef]

1988 (2)

A. T. Friberg and J. Turunen, J. Opt. Soc. Am. A 5, 713 (1988).
[CrossRef]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

1985 (1)

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

1978 (1)

1970 (2)

J. A. Arnaud, Bell Syst. Tech. J. 49, 2311 (1970).
[CrossRef]

S. A. Collins, J. Opt. Soc. Am. 60, 1168 (1970).
[CrossRef]

1965 (1)

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).
[CrossRef]

Alda, J.

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Quantum Electron. 27, 679 (1995).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Lett. 18, 669 (1993).
[CrossRef] [PubMed]

Arnaud, J. A.

J. A. Arnaud, Bell Syst. Tech. J. 49, 2311 (1970).
[CrossRef]

J. A. Arnaud, in Progress in Optics XI, E. Wolf, ed. (North-Holland, Amsterdam, 1973), pp. 247–304.
[CrossRef]

Bastiaans, M. J.

M. J. Bastiaans, Opt. Quantum Electron. 24, S1011 (1992).
[CrossRef]

Bernabeu, E.

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Quantum Electron. 27, 679 (1995).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Lett. 18, 669 (1993).
[CrossRef] [PubMed]

Collett, E.

Collins, S. A.

Friberg, A. T.

Guillemin, V.

V. Guillemin and S. Sternberg, Symplectic Techniques in Physics (Cambridge U. Press, Cambridge, 1984), Chap. 1.

Kauderer, M.

M. Kauderer, Symplectic Matrices: First Order Systems and Special Relativity (World Scientific, Singapore, 1994), p. 29.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).
[CrossRef]

Lin, Q.

Q. Lin and L. Wang, Opt. Commun. 185, 263 (2000).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Quantum Electron. 27, 679 (1995).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Lett. 18, 669 (1993).
[CrossRef] [PubMed]

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, Calif., 1964), Chap. 4.

Mukunda, N.

Nemes, G.

G. Nemes and A. E. Siegman, J. Opt. Soc. Am. A 11, 2257 (1994).
[CrossRef]

G. Nemes and J. Serna, in Laser Beam and Optics Characterization 4, A. Giesen and M. Morin, eds. (Institut für Strahlwerkzeuge, Stuttgart, Germany, 1998), pp. 92–105.

Ponomarenko, S. A.

Serna, J.

G. Nemes and J. Serna, in Laser Beam and Optics Characterization 4, A. Giesen and M. Morin, eds. (Institut für Strahlwerkzeuge, Stuttgart, Germany, 1998), pp. 92–105.

Siegel, C. L.

C. L. Siegel, Symplectic Geometry (Academic, New York, 1964), pp. 1–8.

Siegman, A. E.

Simon, R.

Sternberg, S.

V. Guillemin and S. Sternberg, Symplectic Techniques in Physics (Cambridge U. Press, Cambridge, 1984), Chap. 1.

Subbarao, D.

Sudarshan, E. C. G.

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

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

Tervonen, E.

Turunen, J.

Wang, L.

Q. Lin and L. Wang, Opt. Commun. 185, 263 (2000).
[CrossRef]

Wang, S.

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Quantum Electron. 27, 679 (1995).
[CrossRef]

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Lett. 18, 669 (1993).
[CrossRef] [PubMed]

Wolf, E.

Bell Syst. Tech. J. (2)

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).
[CrossRef]

J. A. Arnaud, Bell Syst. Tech. J. 49, 2311 (1970).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

Opt. Commun. (2)

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

Q. Lin and L. Wang, Opt. Commun. 185, 263 (2000).
[CrossRef]

Opt. Lett. (5)

Opt. Quantum Electron. (2)

Q. Lin, S. Wang, J. Alda, and E. Bernabeu, Opt. Quantum Electron. 27, 679 (1995).
[CrossRef]

M. J. Bastiaans, Opt. Quantum Electron. 24, S1011 (1992).
[CrossRef]

Phys. Rev. A (1)

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

Other (6)

J. A. Arnaud, in Progress in Optics XI, E. Wolf, ed. (North-Holland, Amsterdam, 1973), pp. 247–304.
[CrossRef]

G. Nemes and J. Serna, in Laser Beam and Optics Characterization 4, A. Giesen and M. Morin, eds. (Institut für Strahlwerkzeuge, Stuttgart, Germany, 1998), pp. 92–105.

C. L. Siegel, Symplectic Geometry (Academic, New York, 1964), pp. 1–8.

M. Kauderer, Symplectic Matrices: First Order Systems and Special Relativity (World Scientific, Singapore, 1994), p. 29.

V. Guillemin and S. Sternberg, Symplectic Techniques in Physics (Cambridge U. Press, Cambridge, 1984), Chap. 1.

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, Calif., 1964), Chap. 4.

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Equations (18)

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Γr1,r2= G0 exp-14r1TσI2-1r1+r2TσI2-1r2-12r1-r2Tσg2-1r1-r2-ik2r1-r2TR-1+μJr1+r2,
σI2-1=σI11-2σI12-2σI12-2σI22-2,  σg2-1=σg11-2σg12-2σg12-2σg22-2,  R-1=R11-1R12-1R21-1R22-1.
J=01-10.
Γr=G0 exp-ik2rTM-1r,
M-1=R-1-i2kσI2-1-ikσg2-1ikσg2-1+μJikσg2-1+μJT-R-1-i2kσI2-1-ikσg2-1,
M-1=M11-1M12-1M12-1T-M11-1*,
Eρ1=-iλdetB-1/2Er1exp-ikldr1,
l=l0+12r1ρ1TVr1ρ1,  V=B-1A-B-1C-DB-1ADB-1.
Γr=Er1E*r2,  Γρ=Eρ1E*ρ2,
Γρ=1λ2 detBΓrexp-ikl1-l2dr,
lj=l0+12rjρjTVrjρj,  j=1,2.
l1-l2=12rρTB¯-1A¯-B¯-1C¯-D¯B¯-1A¯D¯B¯-1rρ,
A¯=A00A,  B¯=B00-B,  C¯=C00-C,  D¯=D00D.
B¯-1A¯T=B¯-1A¯,  D¯B¯-1T=D¯B¯-1,  C¯-D¯B¯-1A¯=-B¯-1T.
Γρ=G0λ2detB¯1/2 exp-iπλLdr,
L= rTB¯-1A¯+Mi-1r-2rTB¯-1ρ+ρTD¯B¯-1ρ= B¯-1A¯+Mi-11/2r-B¯-1A¯+Mi-1-1/2B¯-1ρ2+ρT[C¯+D¯Mi-1)A¯+B¯Mi-1-1ρ.
Γρ=G0detA¯+B¯Mi-1-1/2 exp-ik2ρTMo-1ρ,
Mo-1=C¯+D¯Mi-1A¯+B¯Mi-1-1.

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