Abstract

The generalized Huygens–Fresnel diffraction integral for misaligned asymmetric first-order optical systems is derived by using the canonical operator method, which enables us to study propagation properties of anisotropic Gaussian Schell-model (AGSM) beams through misaligned asymmetric first-order optical systems. It is shown that under the action of misaligned asymmetric first-order optical systems AGSM beams do not preserve the closed property. Therefore generalized partially coherent anisotropic Gaussian Schell-model beams called decentered anisotropic Gaussian Schell-model (DAGSM) beams are introduced, and AGSM beams can be regarded as a special case of DAGSM beams.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. G. Ding, X. Yuan, B. Lü, “Propagation characteristics of the ten-parameter family of partially coherent general anisotropic Gaussian Schell-model (AGSM) beams passing through first-order optical systems,” J. Mod. Opt. 47, 1483–1499 (1999).
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    [CrossRef]
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1999

B. Lü, H. Ma, B. Zhang, “Propagation properties of cosh-Gaussian beams,” Opt. Commun. 164, 165–170 (1999).
[CrossRef]

G. Ding, X. Yuan, B. Lü, “Propagation characteristics of the ten-parameter family of partially coherent general anisotropic Gaussian Schell-model (AGSM) beams passing through first-order optical systems,” J. Mod. Opt. 47, 1483–1499 (1999).

B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
[CrossRef]

R. Simon, N. Mukunda, “Gaussian Schell-model beams and general shape invariance,” J. Opt. Soc. Am. A 16, 2465–2475 (1999).
[CrossRef]

R. Simon, N. Mukunda, “Gaussian Schell-model beams and general shape invariance,” J. Opt. Soc. Am. A 16, 2465–2475 (1999).
[CrossRef]

1997

1996

M. Santarsiero, “Propagation of generalized Bessel–Gauss beams through ABCD optical systems,” Opt. Commun. 132, 1–7 (1996).
[CrossRef]

1994

1993

1992

1991

1988

1986

1985

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Anisotropic Gaussian Schell-model beams: passage through optical systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
[CrossRef] [PubMed]

1984

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized ray in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
[CrossRef]

1982

1981

H. Bacry, M. Cadilhac, “Metaplectic group and Fourier optics,” Phys. Rev. A 23, 2533–2536 (1981).
[CrossRef]

1970

Alda, J.

Bacry, H.

H. Bacry, M. Cadilhac, “Metaplectic group and Fourier optics,” Phys. Rev. A 23, 2533–2536 (1981).
[CrossRef]

Bastiaans, M. J.

Bernabeu, E.

Cadilhac, M.

H. Bacry, M. Cadilhac, “Metaplectic group and Fourier optics,” Phys. Rev. A 23, 2533–2536 (1981).
[CrossRef]

Collins, S. A.

Ding, G.

G. Ding, X. Yuan, B. Lü, “Propagation characteristics of the ten-parameter family of partially coherent general anisotropic Gaussian Schell-model (AGSM) beams passing through first-order optical systems,” J. Mod. Opt. 47, 1483–1499 (1999).

Dragt, A. J.

A. J. Dragt, E. Forest, K. B. Wolf, “Foundations of a Lie algebraic theory of geometrical optics,” in Lie Methods in Optics, J. Sanchez Mondragon, K. B. Wolf, eds. (Springer-Verlag, Berlin, 1986), p. 105.

Forest, E.

A. J. Dragt, E. Forest, K. B. Wolf, “Foundations of a Lie algebraic theory of geometrical optics,” in Lie Methods in Optics, J. Sanchez Mondragon, K. B. Wolf, eds. (Springer-Verlag, Berlin, 1986), p. 105.

Friberg, A. T.

A. T. Friberg, E. Tervonen, J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 11, 1818–1826 (1994).
[CrossRef]

A. T. Friberg, E. Tervonen, J. Turunen, “Focusing of twisted Gaussian Schell-model beams,” Opt. Commun. 106, 127–132 (1994).
[CrossRef]

Hardy, A.

Keren, E.

Lavi, S.

Lü, B.

B. Lü, H. Ma, B. Zhang, “Propagation properties of cosh-Gaussian beams,” Opt. Commun. 164, 165–170 (1999).
[CrossRef]

G. Ding, X. Yuan, B. Lü, “Propagation characteristics of the ten-parameter family of partially coherent general anisotropic Gaussian Schell-model (AGSM) beams passing through first-order optical systems,” J. Mod. Opt. 47, 1483–1499 (1999).

B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
[CrossRef]

Luo, S.

B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
[CrossRef]

Ma, H.

B. Lü, H. Ma, B. Zhang, “Propagation properties of cosh-Gaussian beams,” Opt. Commun. 164, 165–170 (1999).
[CrossRef]

Martinez-Herero, R.

Mejias, P. M.

Mukunda, N.

R. Simon, N. Mukunda, “Gaussian Schell-model beams and general shape invariance,” J. Opt. Soc. Am. A 16, 2465–2475 (1999).
[CrossRef]

R. Simon, N. Mukunda, “Gaussian Schell-model beams and general shape invariance,” J. Opt. Soc. Am. A 16, 2465–2475 (1999).
[CrossRef]

R. Simon, N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 10, 95–109 (1993).
[CrossRef]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Anisotropic Gaussian Schell-model beams: passage through optical systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
[CrossRef] [PubMed]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized ray in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
[CrossRef]

Nazarathy, M.

Nemes, G.

Paima, C.

Porras, M. A.

Prochaska, R.

Santarsiero, M.

M. Santarsiero, “Propagation of generalized Bessel–Gauss beams through ABCD optical systems,” Opt. Commun. 132, 1–7 (1996).
[CrossRef]

Serna, J.

Shamir, J.

Siegman, A. E.

Simon, R.

R. Simon, N. Mukunda, “Gaussian Schell-model beams and general shape invariance,” J. Opt. Soc. Am. A 16, 2465–2475 (1999).
[CrossRef]

R. Simon, N. Mukunda, “Gaussian Schell-model beams and general shape invariance,” J. Opt. Soc. Am. A 16, 2465–2475 (1999).
[CrossRef]

R. Simon, N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 10, 95–109 (1993).
[CrossRef]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Anisotropic Gaussian Schell-model beams: passage through optical systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
[CrossRef] [PubMed]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized ray in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
[CrossRef]

Sudarshan, E. C. G.

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Anisotropic Gaussian Schell-model beams: passage through optical systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
[CrossRef] [PubMed]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized ray in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
[CrossRef]

Tervonen, E.

A. T. Friberg, E. Tervonen, J. Turunen, “Focusing of twisted Gaussian Schell-model beams,” Opt. Commun. 106, 127–132 (1994).
[CrossRef]

A. T. Friberg, E. Tervonen, J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 11, 1818–1826 (1994).
[CrossRef]

Turunen, J.

A. T. Friberg, E. Tervonen, J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 11, 1818–1826 (1994).
[CrossRef]

A. T. Friberg, E. Tervonen, J. Turunen, “Focusing of twisted Gaussian Schell-model beams,” Opt. Commun. 106, 127–132 (1994).
[CrossRef]

Wolf, K. B.

A. J. Dragt, E. Forest, K. B. Wolf, “Foundations of a Lie algebraic theory of geometrical optics,” in Lie Methods in Optics, J. Sanchez Mondragon, K. B. Wolf, eds. (Springer-Verlag, Berlin, 1986), p. 105.

Yuan, X.

G. Ding, X. Yuan, B. Lü, “Propagation characteristics of the ten-parameter family of partially coherent general anisotropic Gaussian Schell-model (AGSM) beams passing through first-order optical systems,” J. Mod. Opt. 47, 1483–1499 (1999).

Zhang, B.

B. Lü, H. Ma, B. Zhang, “Propagation properties of cosh-Gaussian beams,” Opt. Commun. 164, 165–170 (1999).
[CrossRef]

B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

G. Ding, X. Yuan, B. Lü, “Propagation characteristics of the ten-parameter family of partially coherent general anisotropic Gaussian Schell-model (AGSM) beams passing through first-order optical systems,” J. Mod. Opt. 47, 1483–1499 (1999).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

A. T. Friberg, E. Tervonen, J. Turunen, “Focusing of twisted Gaussian Schell-model beams,” Opt. Commun. 106, 127–132 (1994).
[CrossRef]

M. Santarsiero, “Propagation of generalized Bessel–Gauss beams through ABCD optical systems,” Opt. Commun. 132, 1–7 (1996).
[CrossRef]

B. Lü, H. Ma, B. Zhang, “Propagation properties of cosh-Gaussian beams,” Opt. Commun. 164, 165–170 (1999).
[CrossRef]

B. Lü, S. Luo, B. Zhang, “Propagation of flattened Gaussian beams with rectangular symmetry passing through a paraxial optical ABCD system with and without aperture,” Opt. Commun. 164, 1–6 (1999).
[CrossRef]

Phys. Rev. A

H. Bacry, M. Cadilhac, “Metaplectic group and Fourier optics,” Phys. Rev. A 23, 2533–2536 (1981).
[CrossRef]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized ray in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).
[CrossRef]

R. Simon, E. C. G. Sudarshan, N. Mukunda, “Anisotropic Gaussian Schell-model beams: passage through optical systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985).
[CrossRef] [PubMed]

Other

A. J. Dragt, E. Forest, K. B. Wolf, “Foundations of a Lie algebraic theory of geometrical optics,” in Lie Methods in Optics, J. Sanchez Mondragon, K. B. Wolf, eds. (Springer-Verlag, Berlin, 1986), p. 105.

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Equations (49)

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rp=Srp
STJS=J,J=0I-I0,
S=ABCD,
S-1=DT-BT-CTAT.
χψ(x, y)=xyψ(x, y),
τψ(x, y)=ik/x/yψ(x, y),
χτTJχτ=-2ik.
χτ=TχτT-1.
χτ=S-1χτ,
χτTJχτ=-2ik.
T=--dxidyig(x0, y0; xi, yi),
--dxidyi g(x0, y0; xi, yi)xiyii/kxii/kyi
=S-1x0y0i˙/kx0i/ky0--dxidyig(x0, y0; xi, yi).
xiyi-i/kxi-i/kyig(x0, y0; xi, yi)
=S-1x0y0i/kx0i/ky0g(x0, y0; x1, y1).
g(r0; ri)=ik2π(det B)1/2×exp-ik2rir0TB-1A-B-1-(B-1)TDB-1rir0,
T[S]=ik2π(det B)1/2--dxi dyi×exp-ik2rir0TB-1A-B-1-(B-1)TDB-1rir0.
E0(x0, y0)=T[S]Ei(xi, yi).
e=(ex, ey)T,
f=(fx, fy)T.
M=eSf001,
rp1=Mrp1.
Δef=expikefTJχτ.
Δefψ(x, y)=exp[ikeTf]×exp[-ik(fxx+fyy)]ψ(x-ex, y-ey),
T[S]ΔefT-1[S]=ΔSef.
T[M, l]=exp(-ikl)ΔefT[S],
E0(x0, y0)=T[M, l]Ei(xi, yi)=exp(-ikl)ΔefT[S]Ei(xi, yi).
Γ(r1, r2)=12π det σI×exp-14[r1T(σI2)-1r1+r2T(σI2)-1r2]-12(r1-r2)T(σg2)-1(r1-r2)-ik2(r1TR-1r1-r2TR-1r2)-ikμr1Tβr2,
W(r, p)=k2π2Γ(r-r/2, r+r/2)exp(-ikpTr)dr.
W(r, p)=k2(2π)2det γdet σIexp-12rT(σI2)-1r-12k2×[p-(R-1+μβ)r]Tγ2×[p-(R-1+μβ)r],
q=(x, y, px, py)T,
q¯=1IqW(q)dq,
V=(q-q¯)(q-q¯)T¯=1I(q-q¯)(q-q¯)TW(q)dq,
q¯=[0, 0, 0, 0]T,
V=σI2σI2(R-1-μβ)(R-1+μβ)σI21k214(σI2)-1+(σg2)-1+(R-1+μβ)σI2(R-1-μβ).
W(q)=14π2[det(V)]-1/2 exp(-qTV-1q).
Γ(r1, r2)=Δ1efΔ2ef*--Γ(r1, r2)G(r1, r1)G*(r2, r2)dr1dr2,
--dx1dx2 exp(a0+a1x1+a2x2+a3x12+a4x1x2
+a5x22)=2π expa0-a22a3-a1a2a4+a12a54a3a5-a42(4a3a5-a42)1/2,
Γ(r1, r2)
=12π det σ1exp-14[(r1-r¯)T(σI2)-1(r1-r¯)+(r2-r¯)T(σI2)-1(r2-r¯)]-12(r1-r2)T(σg2)-1×(r1-r2)-ik2[(r1-r¯)TR-1(r1-r¯)-(r2-r¯)TR-1(r2-r¯)]-ikμ(r1-r¯)T×β(r2-r¯)-ik[(r1-r¯)Tp¯-(r2-r¯)Tp¯],
σI2=[AB]V[AB]T,
(σg2)-1=k2[CD]V[CD]T-[CD]V[AB]T([AB]V[AB]T)-1×[AB]V[CD]T-([AB]V[AB]T)-14,
R-1={[CD]V[AB]T([AB]V[AB]T)-1+([AB]V[AB]T)-1[AB]V[CD]T}/2,
μJ={[CD]V[AB]T([AB]V[AB]T)-1-([AB]V[AB]T)-1[AB]V[CD]T}/2,
r¯p¯=ef,
W(r, p)=k24π2det γdet σIexp-12(r-r¯)T(σI2)-1(r-r¯)-12k2[(p-p¯)-(R-1+μβ)(r-r¯)]T×γ2[(p-p¯)-(R-1+μβ)(r-r¯)],
q¯=[x¯y¯p¯xp¯y]T=[exeyfxfy]T.
V=σI2σI2(R-1-μβ)(R-1+μβ)σI21k214(σI2)-1+(σg2)-1+(R-1+μβ)σI2(R-1-μβ)=SVST.

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