Abstract

In conventional conoscopic interference patterns of optically anisotropic materials the isochromatic interference fringes are inherently masked by the dark isogyres. We prove that the isochromatic fringes can be directly visualized by spinning the crossed linear polarizer and analyzer, regardless of the polarization state of the incident light. This simple method completely eliminates the isogyres and reveals the whole isochromatic fringes without the need of any additional optical elements or calculations. The system works at any wavelength that the linear polarizer permits. The validity of this method is demonstrated by observing the interference patterns of an LiNbO3 electro-optic crystal under different external electric fields.

© 2012 Optical Society of America

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References

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2010 (1)

M. D. Higgins, Can. Mineral. 48, 231 (2010).
[CrossRef]

2009 (2)

D. Rinaldi, P. Pietroni, and F. Davi, Nucl. Instrum. Methods Phys. Res. A 603, 294 (2009).
[CrossRef]

L. Dumitrascu, I. Dumitrascu, and D. O. Dorohoi, J. Appl. Crystallogr. 42, 878 (2009).
[CrossRef]

2007 (3)

A. Ciriaco, F. Davi, M. Lebeau, G. Majni, N. Paone, P. Pietroni, and D. Rinaldi, Nucl. Instrum. Methods Phys. Res. A 570, 55 (2007).
[CrossRef]

R. A. Bone and G. Draper, Appl. Opt. 46, 8351 (2007).
[CrossRef]

S. Chatterjee and Y. R. Kumar, Appl. Opt. 46, 1435 (2007).
[CrossRef]

2006 (2)

Z. Song, L. Liu, Y. Zhou, D. Liu, and H. Ren, Optik 117, 418 (2006).
[CrossRef]

V. P. Kompaneitsev, Crystallogr. Rep. 51, 680 (2006).
[CrossRef]

2002 (1)

M. A. Geday and A. M. Glazer, J. Appl. Crystallogr. 35, 185 (2002).
[CrossRef]

2001 (1)

2000 (1)

M. A. Geday, W. Kaminsky, J. G. Lewis, and A. M. Glazer, J. Microsc. 198, 1 (2000).
[CrossRef]

1999 (1)

1998 (1)

A. Bajor, L. Salbut, A. Szwedowski, and T. Piatkowski, Rev. Sci. Instrum. 69, 1476 (1998).
[CrossRef]

1996 (1)

A. M. Glazer, J. G. Lewis, and W. Kaminsky, Proc. R. Soc. Lond. Ser. A 452, 2751 (1996).
[CrossRef]

1991 (1)

E. Dijkstra, H. Meekes, and M. Kremers, J. Phys. D 24, 1861 (1991).
[CrossRef]

1983 (1)

J. Kobayashi and Y. Uesu, J. Appl. Crystallogr. 16, 204 (1983).
[CrossRef]

Ayras, P. H.

Bajor, A.

A. Bajor, L. Salbut, A. Szwedowski, and T. Piatkowski, Rev. Sci. Instrum. 69, 1476 (1998).
[CrossRef]

Bone, R. A.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).

Chatterjee, S.

Ciriaco, A.

A. Ciriaco, F. Davi, M. Lebeau, G. Majni, N. Paone, P. Pietroni, and D. Rinaldi, Nucl. Instrum. Methods Phys. Res. A 570, 55 (2007).
[CrossRef]

Davi, F.

D. Rinaldi, P. Pietroni, and F. Davi, Nucl. Instrum. Methods Phys. Res. A 603, 294 (2009).
[CrossRef]

A. Ciriaco, F. Davi, M. Lebeau, G. Majni, N. Paone, P. Pietroni, and D. Rinaldi, Nucl. Instrum. Methods Phys. Res. A 570, 55 (2007).
[CrossRef]

Dijkstra, E.

E. Dijkstra, H. Meekes, and M. Kremers, J. Phys. D 24, 1861 (1991).
[CrossRef]

Dorohoi, D. O.

L. Dumitrascu, I. Dumitrascu, and D. O. Dorohoi, J. Appl. Crystallogr. 42, 878 (2009).
[CrossRef]

Draper, G.

Dumitrascu, I.

L. Dumitrascu, I. Dumitrascu, and D. O. Dorohoi, J. Appl. Crystallogr. 42, 878 (2009).
[CrossRef]

Dumitrascu, L.

L. Dumitrascu, I. Dumitrascu, and D. O. Dorohoi, J. Appl. Crystallogr. 42, 878 (2009).
[CrossRef]

Friberg, A. T.

Geday, M. A.

M. A. Geday and A. M. Glazer, J. Appl. Crystallogr. 35, 185 (2002).
[CrossRef]

M. A. Geday, W. Kaminsky, J. G. Lewis, and A. M. Glazer, J. Microsc. 198, 1 (2000).
[CrossRef]

Glazer, A. M.

M. A. Geday and A. M. Glazer, J. Appl. Crystallogr. 35, 185 (2002).
[CrossRef]

M. A. Geday, W. Kaminsky, J. G. Lewis, and A. M. Glazer, J. Microsc. 198, 1 (2000).
[CrossRef]

A. M. Glazer, J. G. Lewis, and W. Kaminsky, Proc. R. Soc. Lond. Ser. A 452, 2751 (1996).
[CrossRef]

Higgins, M. D.

M. D. Higgins, Can. Mineral. 48, 231 (2010).
[CrossRef]

Kaivola, M. A. J.

Kaminsky, W.

M. A. Geday, W. Kaminsky, J. G. Lewis, and A. M. Glazer, J. Microsc. 198, 1 (2000).
[CrossRef]

A. M. Glazer, J. G. Lewis, and W. Kaminsky, Proc. R. Soc. Lond. Ser. A 452, 2751 (1996).
[CrossRef]

Kobayashi, J.

J. Kobayashi and Y. Uesu, J. Appl. Crystallogr. 16, 204 (1983).
[CrossRef]

Kompaneitsev, V. P.

V. P. Kompaneitsev, Crystallogr. Rep. 51, 680 (2006).
[CrossRef]

Kremers, M.

E. Dijkstra, H. Meekes, and M. Kremers, J. Phys. D 24, 1861 (1991).
[CrossRef]

Kumar, Y. R.

Lebeau, M.

A. Ciriaco, F. Davi, M. Lebeau, G. Majni, N. Paone, P. Pietroni, and D. Rinaldi, Nucl. Instrum. Methods Phys. Res. A 570, 55 (2007).
[CrossRef]

Lewis, J. G.

M. A. Geday, W. Kaminsky, J. G. Lewis, and A. M. Glazer, J. Microsc. 198, 1 (2000).
[CrossRef]

A. M. Glazer, J. G. Lewis, and W. Kaminsky, Proc. R. Soc. Lond. Ser. A 452, 2751 (1996).
[CrossRef]

Liu, D.

Z. Song, L. Liu, Y. Zhou, D. Liu, and H. Ren, Optik 117, 418 (2006).
[CrossRef]

Liu, L.

Z. Song, L. Liu, Y. Zhou, D. Liu, and H. Ren, Optik 117, 418 (2006).
[CrossRef]

Majni, G.

A. Ciriaco, F. Davi, M. Lebeau, G. Majni, N. Paone, P. Pietroni, and D. Rinaldi, Nucl. Instrum. Methods Phys. Res. A 570, 55 (2007).
[CrossRef]

Meekes, H.

E. Dijkstra, H. Meekes, and M. Kremers, J. Phys. D 24, 1861 (1991).
[CrossRef]

Nesse, W. D.

W. D. Nesse, Introduction to Optical Mineralogy (Oxford Univ., 2003).

Paone, N.

A. Ciriaco, F. Davi, M. Lebeau, G. Majni, N. Paone, P. Pietroni, and D. Rinaldi, Nucl. Instrum. Methods Phys. Res. A 570, 55 (2007).
[CrossRef]

Piatkowski, T.

A. Bajor, L. Salbut, A. Szwedowski, and T. Piatkowski, Rev. Sci. Instrum. 69, 1476 (1998).
[CrossRef]

Pietroni, P.

D. Rinaldi, P. Pietroni, and F. Davi, Nucl. Instrum. Methods Phys. Res. A 603, 294 (2009).
[CrossRef]

A. Ciriaco, F. Davi, M. Lebeau, G. Majni, N. Paone, P. Pietroni, and D. Rinaldi, Nucl. Instrum. Methods Phys. Res. A 570, 55 (2007).
[CrossRef]

Ren, H.

Z. Song, L. Liu, Y. Zhou, D. Liu, and H. Ren, Optik 117, 418 (2006).
[CrossRef]

Rinaldi, D.

D. Rinaldi, P. Pietroni, and F. Davi, Nucl. Instrum. Methods Phys. Res. A 603, 294 (2009).
[CrossRef]

A. Ciriaco, F. Davi, M. Lebeau, G. Majni, N. Paone, P. Pietroni, and D. Rinaldi, Nucl. Instrum. Methods Phys. Res. A 570, 55 (2007).
[CrossRef]

Salbut, L.

A. Bajor, L. Salbut, A. Szwedowski, and T. Piatkowski, Rev. Sci. Instrum. 69, 1476 (1998).
[CrossRef]

Salomaa, M. M.

Song, Z.

Z. Song, L. Liu, Y. Zhou, D. Liu, and H. Ren, Optik 117, 418 (2006).
[CrossRef]

Szwedowski, A.

A. Bajor, L. Salbut, A. Szwedowski, and T. Piatkowski, Rev. Sci. Instrum. 69, 1476 (1998).
[CrossRef]

Uesu, Y.

J. Kobayashi and Y. Uesu, J. Appl. Crystallogr. 16, 204 (1983).
[CrossRef]

Van Horn, B. L.

Winter, H. H.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).

Zhou, Y.

Z. Song, L. Liu, Y. Zhou, D. Liu, and H. Ren, Optik 117, 418 (2006).
[CrossRef]

Appl. Opt. (4)

Can. Mineral. (1)

M. D. Higgins, Can. Mineral. 48, 231 (2010).
[CrossRef]

Crystallogr. Rep. (1)

V. P. Kompaneitsev, Crystallogr. Rep. 51, 680 (2006).
[CrossRef]

J. Appl. Crystallogr. (3)

J. Kobayashi and Y. Uesu, J. Appl. Crystallogr. 16, 204 (1983).
[CrossRef]

M. A. Geday and A. M. Glazer, J. Appl. Crystallogr. 35, 185 (2002).
[CrossRef]

L. Dumitrascu, I. Dumitrascu, and D. O. Dorohoi, J. Appl. Crystallogr. 42, 878 (2009).
[CrossRef]

J. Microsc. (1)

M. A. Geday, W. Kaminsky, J. G. Lewis, and A. M. Glazer, J. Microsc. 198, 1 (2000).
[CrossRef]

J. Phys. D (1)

E. Dijkstra, H. Meekes, and M. Kremers, J. Phys. D 24, 1861 (1991).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (2)

D. Rinaldi, P. Pietroni, and F. Davi, Nucl. Instrum. Methods Phys. Res. A 603, 294 (2009).
[CrossRef]

A. Ciriaco, F. Davi, M. Lebeau, G. Majni, N. Paone, P. Pietroni, and D. Rinaldi, Nucl. Instrum. Methods Phys. Res. A 570, 55 (2007).
[CrossRef]

Optik (1)

Z. Song, L. Liu, Y. Zhou, D. Liu, and H. Ren, Optik 117, 418 (2006).
[CrossRef]

Proc. R. Soc. Lond. Ser. A (1)

A. M. Glazer, J. G. Lewis, and W. Kaminsky, Proc. R. Soc. Lond. Ser. A 452, 2751 (1996).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Bajor, L. Salbut, A. Szwedowski, and T. Piatkowski, Rev. Sci. Instrum. 69, 1476 (1998).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Cambridge Univ., 1999).

W. D. Nesse, Introduction to Optical Mineralogy (Oxford Univ., 2003).

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Figures (2)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental setup.

Fig. 2.
Fig. 2.

Conoscopic interference images of LiNbO3 at different voltages. (a) and (e), V=0; (b) and (f), V=Vπ; (c) and (g), V=2Vπ; (d) and (h), V=3Vπ. In (e)–(h) the spinning polarizer and analyzer method is employed.

Equations (3)

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

E=(cos2ψ2sinψ2cosψ2sinψ2cosψ2sin2ψ2)(cosφsinφsinφcosφ)(100eiδ)(cosφsinφsinφcosφ)(cos2ψ1sinψ1cosψ1sinψ1cosψ1sin2ψ1)(cosαsinαeiε).
I=E+E=14sin2δ2(1+IAC),
IAC=cos2(ωtα)12cos2(ωt2φ+α)2sin2αsin2ε2sin2ωtsin2αsin2ε2sin2(ωt2φ)+cos4(ωtφ)+sin2αsin2ε2sin(6ωt4φ)12cos(6ωt4φ2α).

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