Abstract

We propose and realize a simple technique to measure the tiny spin Hall effect of light from the ratio of the minimum and the maximum intensities along two cross-polarization directions, without the requirement of a position-sensitive detector in the conventional weak measurement. Furthermore, the weak intensity ratio is dramatically amplified by purposely choosing the intensity along the direction close to that of the minimum instead of the maximum along the perpendicular polarization direction, which is verified by the experimental results. In principle, this method also can be modified for measurement of the high extinction ratio of a polarizer.

© 2014 Optical Society of America

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  1. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2003).
  2. F. Goos and H. Hanchen, Ann. Phys. 436, 333 (1947).
    [CrossRef]
  3. H. Gilles, S. Girard, and J. Hamel, Opt. Lett. 27, 1421 (2002).
    [CrossRef]
  4. M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, Opt. Express 15, 15928 (2007).
    [CrossRef]
  5. O. Costa de Beauregard and C. Imbert, Phys. Rev. Lett. 28, 1211 (1972).
    [CrossRef]
  6. M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
    [CrossRef]
  7. K. Bliokh and Y. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
    [CrossRef]
  8. A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
    [CrossRef]
  9. L. Kong, S. Qian, Z. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
    [CrossRef]
  10. J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
    [CrossRef]
  11. O. Hosten and P. Kwiat, Science 319, 787 (2008).
    [CrossRef]
  12. Y. Qin, Y. Li, H. He, and Q. Gong, Opt. Lett. 34, 2551 (2009).
    [CrossRef]
  13. H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, Phys. Rev. A 84, 043806 (2011).
    [CrossRef]
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    [CrossRef]
  15. Y. Qin, Y. Li, X. Feng, Z. Liu, H. He, Y.-F. Xiao, and Q. Gong, Opt. Express 18, 16832 (2010).
    [CrossRef]
  16. X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
    [CrossRef]
  17. J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
    [CrossRef]
  18. B. Wang, Y. Li, M. Pan, J. Ren, Y.-F. Xiao, H. Yang, and Q. Gong, Phys. Rev. A 88, 043842 (2013).
    [CrossRef]
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    [CrossRef]
  20. A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
    [CrossRef]
  21. M. Dennis and J. Götte, New J. Phys. 14, 073013 (2012).
    [CrossRef]
  22. F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
    [CrossRef]
  23. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, Science 339, 1405 (2013).
    [CrossRef]
  24. C. Prajapati, D. Ranganathan, and J. Joseph, Opt. Lett. 38, 2459 (2013).
    [CrossRef]
  25. X. Luo, X. Zhou, H. Luo, and S. Wen, Acta Phys. Sin. 61, 194202 (2012).
  26. A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
    [CrossRef]

2014

J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
[CrossRef]

2013

B. Wang, Y. Li, M. Pan, J. Ren, Y.-F. Xiao, H. Yang, and Q. Gong, Phys. Rev. A 88, 043842 (2013).
[CrossRef]

F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
[CrossRef]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, Science 339, 1405 (2013).
[CrossRef]

C. Prajapati, D. Ranganathan, and J. Joseph, Opt. Lett. 38, 2459 (2013).
[CrossRef]

2012

X. Luo, X. Zhou, H. Luo, and S. Wen, Acta Phys. Sin. 61, 194202 (2012).

M. Dennis and J. Götte, New J. Phys. 14, 073013 (2012).
[CrossRef]

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, Appl. Phys. Lett. 100, 071109 (2012).
[CrossRef]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
[CrossRef]

L. Kong, S. Qian, Z. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

2011

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, Phys. Rev. A 84, 043806 (2011).
[CrossRef]

2010

2009

2008

2007

2006

K. Bliokh and Y. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

2004

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

2002

1988

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

1972

O. Costa de Beauregard and C. Imbert, Phys. Rev. Lett. 28, 1211 (1972).
[CrossRef]

1947

F. Goos and H. Hanchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

’t Hooft, G. W.

Aharonov, Y.

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

Aiello, A.

J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
[CrossRef]

F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
[CrossRef]

A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, Opt. Express 15, 15928 (2007).
[CrossRef]

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

Banzer, P.

J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
[CrossRef]

Bliokh, K.

K. Bliokh and Y. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Bliokh, Y.

K. Bliokh and Y. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2003).

Chen, J.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, Appl. Phys. Lett. 100, 071109 (2012).
[CrossRef]

Chille, V.

J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
[CrossRef]

Costa de Beauregard, O.

O. Costa de Beauregard and C. Imbert, Phys. Rev. Lett. 28, 1211 (1972).
[CrossRef]

Dennis, M.

M. Dennis and J. Götte, New J. Phys. 14, 073013 (2012).
[CrossRef]

Eliel, E. R.

Fan, D.

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, Phys. Rev. A 84, 043806 (2011).
[CrossRef]

Feng, X.

Gilles, H.

Girard, S.

Gong, Q.

B. Wang, Y. Li, M. Pan, J. Ren, Y.-F. Xiao, H. Yang, and Q. Gong, Phys. Rev. A 88, 043842 (2013).
[CrossRef]

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
[CrossRef]

Y. Qin, Y. Li, X. Feng, Z. Liu, H. He, Y.-F. Xiao, and Q. Gong, Opt. Express 18, 16832 (2010).
[CrossRef]

Y. Qin, Y. Li, H. He, and Q. Gong, Opt. Lett. 34, 2551 (2009).
[CrossRef]

Goos, F.

F. Goos and H. Hanchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Götte, J.

M. Dennis and J. Götte, New J. Phys. 14, 073013 (2012).
[CrossRef]

Gu, B.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, Appl. Phys. Lett. 100, 071109 (2012).
[CrossRef]

Hamel, J.

Hanchen, H.

F. Goos and H. Hanchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

He, H.

Hosten, O.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef]

Imbert, C.

O. Costa de Beauregard and C. Imbert, Phys. Rev. Lett. 28, 1211 (1972).
[CrossRef]

Joseph, J.

Kong, L.

L. Kong, S. Qian, Z. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, Appl. Phys. Lett. 100, 071109 (2012).
[CrossRef]

Korger, J.

J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
[CrossRef]

Kwiat, P.

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef]

Leuchs, G.

J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

Li, S.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, Appl. Phys. Lett. 100, 071109 (2012).
[CrossRef]

Li, Y.

B. Wang, Y. Li, M. Pan, J. Ren, Y.-F. Xiao, H. Yang, and Q. Gong, Phys. Rev. A 88, 043842 (2013).
[CrossRef]

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, Appl. Phys. Lett. 100, 071109 (2012).
[CrossRef]

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
[CrossRef]

Y. Qin, Y. Li, X. Feng, Z. Liu, H. He, Y.-F. Xiao, and Q. Gong, Opt. Express 18, 16832 (2010).
[CrossRef]

Y. Qin, Y. Li, H. He, and Q. Gong, Opt. Lett. 34, 2551 (2009).
[CrossRef]

Lin, Y.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
[CrossRef]

Lindlein, N.

J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

Liu, Z.

Luo, H.

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

X. Luo, X. Zhou, H. Luo, and S. Wen, Acta Phys. Sin. 61, 194202 (2012).

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, Phys. Rev. A 84, 043806 (2011).
[CrossRef]

Luo, X.

X. Luo, X. Zhou, H. Luo, and S. Wen, Acta Phys. Sin. 61, 194202 (2012).

Marquardt, C.

J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

Merano, M.

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Ornigotti, M.

F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
[CrossRef]

Pan, M.

B. Wang, Y. Li, M. Pan, J. Ren, Y.-F. Xiao, H. Yang, and Q. Gong, Phys. Rev. A 88, 043842 (2013).
[CrossRef]

Prajapati, C.

Qian, S.

L. Kong, S. Qian, Z. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

Qin, Y.

Ranganathan, D.

Ren, J.

B. Wang, Y. Li, M. Pan, J. Ren, Y.-F. Xiao, H. Yang, and Q. Gong, Phys. Rev. A 88, 043842 (2013).
[CrossRef]

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
[CrossRef]

Ren, Z.

L. Kong, S. Qian, Z. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

Rho, J.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, Science 339, 1405 (2013).
[CrossRef]

Shu, W.

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, Phys. Rev. A 84, 043806 (2011).
[CrossRef]

Töppel, F.

F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
[CrossRef]

Vaidman, L.

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

van Exter, M. P.

Wang, B.

B. Wang, Y. Li, M. Pan, J. Ren, Y.-F. Xiao, H. Yang, and Q. Gong, Phys. Rev. A 88, 043842 (2013).
[CrossRef]

Wang, H.

L. Kong, S. Qian, Z. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, Appl. Phys. Lett. 100, 071109 (2012).
[CrossRef]

Wang, X.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, Appl. Phys. Lett. 100, 071109 (2012).
[CrossRef]

L. Kong, S. Qian, Z. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

Wang, Y.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, Science 339, 1405 (2013).
[CrossRef]

Wen, S.

X. Luo, X. Zhou, H. Luo, and S. Wen, Acta Phys. Sin. 61, 194202 (2012).

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, Phys. Rev. A 84, 043806 (2011).
[CrossRef]

Wittmann, C.

J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
[CrossRef]

Woerdman, J. P.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2003).

Wu, R.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
[CrossRef]

Xiao, Y.-F.

B. Wang, Y. Li, M. Pan, J. Ren, Y.-F. Xiao, H. Yang, and Q. Gong, Phys. Rev. A 88, 043842 (2013).
[CrossRef]

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
[CrossRef]

Y. Qin, Y. Li, X. Feng, Z. Liu, H. He, Y.-F. Xiao, and Q. Gong, Opt. Express 18, 16832 (2010).
[CrossRef]

Xiao, Z.

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

Yang, H.

B. Wang, Y. Li, M. Pan, J. Ren, Y.-F. Xiao, H. Yang, and Q. Gong, Phys. Rev. A 88, 043842 (2013).
[CrossRef]

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
[CrossRef]

Yang, J.

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
[CrossRef]

Ye, Z.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, Science 339, 1405 (2013).
[CrossRef]

Yin, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, Science 339, 1405 (2013).
[CrossRef]

Zhang, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, Science 339, 1405 (2013).
[CrossRef]

Zhou, X.

X. Luo, X. Zhou, H. Luo, and S. Wen, Acta Phys. Sin. 61, 194202 (2012).

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, Phys. Rev. A 84, 043806 (2011).
[CrossRef]

Acta Phys. Sin.

X. Luo, X. Zhou, H. Luo, and S. Wen, Acta Phys. Sin. 61, 194202 (2012).

Ann. Phys.

F. Goos and H. Hanchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Appl. Phys. Lett.

L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, Appl. Phys. Lett. 100, 071109 (2012).
[CrossRef]

J. Ren, Y. Li, Y. Lin, Y. Qin, R. Wu, J. Yang, Y.-F. Xiao, H. Yang, and Q. Gong, Appl. Phys. Lett. 101, 171103 (2012).
[CrossRef]

New J. Phys.

M. Dennis and J. Götte, New J. Phys. 14, 073013 (2012).
[CrossRef]

F. Töppel, M. Ornigotti, and A. Aiello, New J. Phys. 15, 113059 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

B. Wang, Y. Li, M. Pan, J. Ren, Y.-F. Xiao, H. Yang, and Q. Gong, Phys. Rev. A 88, 043842 (2013).
[CrossRef]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, Phys. Rev. A 84, 043806 (2011).
[CrossRef]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

L. Kong, S. Qian, Z. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

Phys. Rev. Lett.

J. Korger, A. Aiello, V. Chille, P. Banzer, C. Wittmann, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 112, 113902 (2014).
[CrossRef]

O. Costa de Beauregard and C. Imbert, Phys. Rev. Lett. 28, 1211 (1972).
[CrossRef]

M. Onoda, S. Murakami, and N. Nagaosa, Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

K. Bliokh and Y. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

Science

O. Hosten and P. Kwiat, Science 319, 787 (2008).
[CrossRef]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, Science 339, 1405 (2013).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2003).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the SHEL at an air–glass interface.

Fig. 2.
Fig. 2.

Schematics of the intensity distribution after P2. (a) P1 perpendicular to P2, i.e., α=0. (b) P2 is rotated by a small angle α=1°; in case of δs<0, the lower part of the beam become brighter. (c) α=1°; in case of δs>0, the upper part of the beam become brighter.

Fig. 3.
Fig. 3.

Experimental setup: P1 and P2, Glan-polarizers; L1 and L2, lenses with 25 and 125 mm focal lengths, respectively; prism, a right-angle prism with an angle of 45 deg. He–Ne laser at 632.8 nm, 18 mW.

Fig. 4.
Fig. 4.

SHEL displacements of left-handed component, as a function of the incident angle θ, in the case of (a) s polarization and (b) p polarization. The dots are experimental results, and solid curves are theoretical prediction.

Equations (10)

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

P^irp(P^rkxrklnrpθP^r+kyδpS^r),S^irs(S^rkxrklnrsθS^rkyδsP^r).
E⃗r(kxr,ky)=rs(S^kxrklnrsθS^kyδsP^)×ew024(kxr2+ky2),
E⃗r(kxr,ky)·(cosαP^+sinαS^)=rs[(1kxrklnrsθ)sinαkyδscosα]×ew024(kxr2+ky2).
Is(α)=kxr,ky|E⃗r(kxr,ky)·(cosαP^+sinαS^)|2dkxrdky.
Is(P)Is(S)=11+(lnrsθ)2λ̵2w02|δs|2w02.
Is(P)Is(S)=|δs|2w02.
(rsS^kxrkrsθS^+kykcotθ(rp+rs)P^)+Δ1eiϕ1(rpP^kxrkrpθP^kykcotθ(rp+rs)S^).
Is(P)Is(S)=ρ2+ρ1rp2+λ̵2w02(rp/θ)2rs2+λ̵2w02(rs/θ)2+|δs|2w02.
Is(P)Is(S)cot2α=Is(α)Is(α)/cos2αIs(P).
Is(α)Is(α)/cos2αIs(P)(ρ2+|δs|2w02)cot2α.

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