Abstract

A matrix method is outlined for dealing with quasi-monochromatic, partially polarized light when spatial coherence is not necessarily complete and propagation occurs along beams. Both spatial coherence and polarization properties are described by a single 2×2 matrix whose elements have the structure of mutual intensity functions. Through a simple example it is shown that this matrix can account for differences that would not be revealed by a scalar treatment or by a locally defined polarization matrix.

© 1998 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  3. P. L. Greene and D. G. Hall, J. Opt. Soc. Am. A 13, 962 (1996), and references therein.
    [CrossRef]
  4. E. Wolf, Nuovo Cimento 12, 884 (1954).
    [CrossRef]
  5. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  6. G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
    [CrossRef]
  7. F. Gori, in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 363.

1996

1993

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

1954

E. Wolf, Nuovo Cimento 12, 884 (1954).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Gori, F.

F. Gori, in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 363.

Greene, P. L.

Hall, D. G.

Indebetouw, G.

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

Mandel, L.

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

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Wolf, E.

E. Wolf, Nuovo Cimento 12, 884 (1954).
[CrossRef]

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

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

J. Mod. Opt.

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Nuovo Cimento

E. Wolf, Nuovo Cimento 12, 884 (1954).
[CrossRef]

Other

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

F. Gori, in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 363.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

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

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Equations (13)

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J^r1, r2, z=Jxxr1, r2, z Jxyr1, r2, zJyxr1, r2, zJyyr1, r2, z,
Jαβr1, r2, z=Eα*r1, z; tEβr2, z; t.
Jyxr1, r2, z=Jxy*r2, r1, z.
Ir, z=Jxxr, r, z+Jyyr, r, z,
Jeqr1, r2, z=Jxxr1, r2, z+Jyyr1, r2, z.
Pr, z=1-4detJ^r, r, ztrJ^r, r, z21/2,
Ex1r, 0; t=athrexpiϑ, Ey1r, 0; t=bthrexp-iϑ;
Ex2r, 0; t=hr2atexpiϑ+btexp-iϑ, Ey2r, 0; t=ihr2atexpiϑ-btexp-iϑ,
hr=r/vexp-r/v2.
at2=bt2=I0, a*tbt=0,
Jxx1r1, r2, 0=I0hr1hr2exp-iϑ1-ϑ2, Jyy1r1, r2, 0=Jxx1r1, r2, 0*, Jxy1r1, r2, 0=0;
Jxx2r1, r2, 0=I0hr1hr2cosϑ1-ϑ2, Jyy2r1, r2, 0=Jxx2r1, r2, 0, Jxy2r1, r2, 0=I0hr1hr2sinϑ1-ϑ2.
Jeqjr1, r2, 0=2I0hr1hr2×cosϑ1-ϑ2  j=1,2.

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