Abstract

Ordinary gratings act on the amplitude and (or) the phase of a wave front. Polarization gratings produce instead a periodic modulation of the state of polarization. A simple grating of the latter type is constituted by a linear polarizer whose orientation varies periodically along a line. It is shown that, for a generic polarization state of the incident field, such a grating gives rise to first-order diffracted beams with counterrotating circular polarizations. It is also shown that such a grating can be used for measuring the Stokes parameters of a light beam in an achromatic manner. Several extensions are briefly discussed.

© 1999 Optical Society of America

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References

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  1. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  2. J. Turunen and F. Wyrowski, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), p. 111.
    [CrossRef]
  3. S. Martellucci and A. N. Chester, eds., Diffractive Optics and Optical Microsystems (Plenum, New York, 1997).? See in particular the contributions by F. Gori, p. 3; H. P. Herzig, p. 23; and C. Arnone, C. Giaconia, and G. Lullo, p. 119.
    [CrossRef]
  4. D. H. Raguin, S. Norton, and G. M. Norris, in Diffractive and Miniaturized Optics, S. H. Lee, ed. (SPIE Press, Bellingham, Wash., 1994), p. 234.
  5. Devices of this type are built by, for example, American Polarizers, Inc., 141 South 7th Street, Reading, Pa. 19602.
  6. L. Nikolova, T. Todorov, N. Tomova, and V. Dragostinova, Appl. Opt. 27, 1598 (1988).
    [CrossRef] [PubMed]
  7. E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987).
  8. C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).
  9. R. Simon, H. J. Kimble, and C. G. Sudarshan, Phys. Rev. Lett. 61, 19 (1988).
    [CrossRef] [PubMed]
  10. V. Bagini, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, Eur. J. Phys. 15, 71 (1994).
    [CrossRef]
  11. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, England, 1995).
    [CrossRef]
  12. R. Barakat, Eur. J. Phys. 19, 209 (1998).
    [CrossRef]
  13. J. A. Ferrari, E. M. Frins, and W. Dultz, Opt. Commun. 152, 252 (1998).
    [CrossRef]
  14. P. Hariharan and B. C. Sanders, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), Vol. XXXVI, p. 51.

1998 (2)

R. Barakat, Eur. J. Phys. 19, 209 (1998).
[CrossRef]

J. A. Ferrari, E. M. Frins, and W. Dultz, Opt. Commun. 152, 252 (1998).
[CrossRef]

1994 (1)

V. Bagini, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, Eur. J. Phys. 15, 71 (1994).
[CrossRef]

1988 (2)

Bagini, V.

V. Bagini, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, Eur. J. Phys. 15, 71 (1994).
[CrossRef]

Barakat, R.

R. Barakat, Eur. J. Phys. 19, 209 (1998).
[CrossRef]

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).

Dragostinova, V.

Dultz, W.

J. A. Ferrari, E. M. Frins, and W. Dultz, Opt. Commun. 152, 252 (1998).
[CrossRef]

Ferrari, J. A.

J. A. Ferrari, E. M. Frins, and W. Dultz, Opt. Commun. 152, 252 (1998).
[CrossRef]

Frezza, F.

V. Bagini, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, Eur. J. Phys. 15, 71 (1994).
[CrossRef]

Frins, E. M.

J. A. Ferrari, E. M. Frins, and W. Dultz, Opt. Commun. 152, 252 (1998).
[CrossRef]

Gori, F.

V. Bagini, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, Eur. J. Phys. 15, 71 (1994).
[CrossRef]

Hariharan, P.

P. Hariharan and B. C. Sanders, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), Vol. XXXVI, p. 51.

Hecht, E.

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987).

Kimble, H. J.

R. Simon, H. J. Kimble, and C. G. Sudarshan, Phys. Rev. Lett. 61, 19 (1988).
[CrossRef] [PubMed]

Mandel, L.

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

Nikolova, L.

Norris, G. M.

D. H. Raguin, S. Norton, and G. M. Norris, in Diffractive and Miniaturized Optics, S. H. Lee, ed. (SPIE Press, Bellingham, Wash., 1994), p. 234.

Norton, S.

D. H. Raguin, S. Norton, and G. M. Norris, in Diffractive and Miniaturized Optics, S. H. Lee, ed. (SPIE Press, Bellingham, Wash., 1994), p. 234.

Raguin, D. H.

D. H. Raguin, S. Norton, and G. M. Norris, in Diffractive and Miniaturized Optics, S. H. Lee, ed. (SPIE Press, Bellingham, Wash., 1994), p. 234.

Sanders, B. C.

P. Hariharan and B. C. Sanders, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), Vol. XXXVI, p. 51.

Santarsiero, M.

V. Bagini, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, Eur. J. Phys. 15, 71 (1994).
[CrossRef]

Schettini, G.

V. Bagini, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, Eur. J. Phys. 15, 71 (1994).
[CrossRef]

Schirripa Spagnolo, G.

V. Bagini, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, Eur. J. Phys. 15, 71 (1994).
[CrossRef]

Simon, R.

R. Simon, H. J. Kimble, and C. G. Sudarshan, Phys. Rev. Lett. 61, 19 (1988).
[CrossRef] [PubMed]

Sudarshan, C. G.

R. Simon, H. J. Kimble, and C. G. Sudarshan, Phys. Rev. Lett. 61, 19 (1988).
[CrossRef] [PubMed]

Todorov, T.

Tomova, N.

Turunen, J.

J. Turunen and F. Wyrowski, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), p. 111.
[CrossRef]

Wolf, E.

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

Wyrowski, F.

J. Turunen and F. Wyrowski, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), p. 111.
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Appl. Opt. (1)

Eur. J. Phys. (2)

V. Bagini, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. Schirripa Spagnolo, Eur. J. Phys. 15, 71 (1994).
[CrossRef]

R. Barakat, Eur. J. Phys. 19, 209 (1998).
[CrossRef]

Opt. Commun. (1)

J. A. Ferrari, E. M. Frins, and W. Dultz, Opt. Commun. 152, 252 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

R. Simon, H. J. Kimble, and C. G. Sudarshan, Phys. Rev. Lett. 61, 19 (1988).
[CrossRef] [PubMed]

Other (9)

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

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1987).

C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).

P. Hariharan and B. C. Sanders, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1996), Vol. XXXVI, p. 51.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

J. Turunen and F. Wyrowski, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), p. 111.
[CrossRef]

S. Martellucci and A. N. Chester, eds., Diffractive Optics and Optical Microsystems (Plenum, New York, 1997).? See in particular the contributions by F. Gori, p. 3; H. P. Herzig, p. 23; and C. Arnone, C. Giaconia, and G. Lullo, p. 119.
[CrossRef]

D. H. Raguin, S. Norton, and G. M. Norris, in Diffractive and Miniaturized Optics, S. H. Lee, ed. (SPIE Press, Bellingham, Wash., 1994), p. 234.

Devices of this type are built by, for example, American Polarizers, Inc., 141 South 7th Street, Reading, Pa. 19602.

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Equations (11)

Equations on this page are rendered with MathJax. Learn more.

Ei=[AxAyexpiδ],
P=[cos2φsinφcosφsinφcosφsin2φ].
Ee=[Ax cos2φ+AyexpiδsinφcosφAxsinφcosφ+Ayexpiδ sin2φ].
Ee=[Ax2+Ax-iAyexpiδ4exp2iφ+Ax+iAyexpiδ4exp-2iφAyexpiδ2-iAx-iAyexpiδ4exp2iφ+iAx+iAyexpiδ4exp-2iφ].
E0=12[AxAyexpiδ],E1=Ax-iAyexpiδ41-i,E-1=Ax+iAyexpiδ41i.
Ei=Ax+iAyexpiδ21-i+Ax-iAyexpiδ21i,
s0=Ax2+Ay2,s1=Ax2-Ay2,s2=2AxAycosδ,s3=2AxAysinδ.
Ejβ=Ejxcosβ+Ejysinβ,j=0,±1.
E0β=Ax2cosβ+Ayexpiδ2sinβ,E1β=Ax-iAyexpiδ4exp-iβ,E-1β=Ax+iAyexpiδ4expiβ.
I0β=14Ax2 cos2β+Ay2 sin2β+AxAysin2βcosδ,I1=116Ax2+Ay2+2AxAysinδ,I-1=116Ax2+Ay2-2AxAysinδ.
s0=8I1+I-1,s1=8I00-I1-I-1,s2=8I0π/4-I1-I-1,s3=8I1-I-1.

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